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THE 


LONDON, EDINBURGH, an» DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


CONDUCTED BY 


SIR, DAVID BREWSTER, K.H. LL.D. F.B.S.L. & E. &. 
SIR ROBERT KANE, M.D., F.R.S., M.R.LA. 
WILLIAM FRANCIS, Pu.D. F.L.S. F.B.AS. F.C.S. 
JOHN TYNDALL, F.RS. &c. 


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


; ‘a 


A ce 
< 


¢ 


WR Me eee Ye 
a Ss i 


ee 
i 


VOL. XXL=FOURTH SERIES. 
JANUARY—JUNE, 1861. 


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.3 WHITTAKER AND CO.; AND PIPER AND CO., LONDON :—— 
BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, 
EDINBURGH; SMITH AND SON, GLASGOW ; HODGES 
AND SMITH, DUBLIN; AND PUTNAM, 
NEW YORK, 


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


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


CONTENTS OF VOL. XXI. 


(FOURTH SERIES.) 


NUMBER CXXXVII.—JANUARY 1861. 


Page 
Mr. T. A. Hirst on Ripples, and their relation to the Velocities 
pemmeeats. (With a Plate.) .. 2.44 saekoa wes Gives 
Sir David Brewster on certain Affections of the Retina...... 20 


M..W. Siemens’s Proposal for a new reproducible Standard 
Measure of Resistance to Galvanic Currents (With a Plate.) 25 

Mr. G. B. Jerrard’s Remarks on Mr. Harley’s paper on Quintics. 39 

Mr. J. 5. Stuart Glennie on the Principles of the Science of _ 


Motion (Mechanics, Physics, Chemics............se+005 41 
_ Mr. W. Crookes on the Opacity of the Yellow Soda- ‘Flame to 
Pee enewh Colour 664. Sor eda he  sereoaal. 55 
Mr. T. ‘Tate’s Experimental Researches on the Laws of Absorp- 
tion of Liquids by Porous Substances ...........++-00. ee 
Prof. Challis on a Theory of Magnetic Force .............. 65 


Mr. C. W. Siemens on a new Resistance Thermometer...... 73 
Proceedings of the Royal Society :— 

Mr. F. Jenkin on the Insulating Properties of Gutta Percha. 75 
On the Lithium Spectrum, by William Crookes, Esq. ...... 79 
On a constant Copper-carbon Battery, by Julius Thomsen.... 80 


NUMBER CXXXVIII.—FEBRUARY. 


Prof. J. D. Forbes’s Note respecting Ampére’s Experiment on 
the Repulsion of a Rectilinear Electrical Current on itself. 


(With a Plate.) .. : 81 
F, W. and A. Dupré o: on the existence of a Fourth Member of 
merc Carerum Group of Metals... yis6 oid Gece ee tails: - 86 
Prof. Schcenbein on the Insulation of Antozone ............ 88 
Mr. J, Cockle’s Note on the Remarks of Mr. Jerrard........ 90 
Prof, Challis on a Theory of Magnetic Force .............- 92 
Dr. Matthiessen on an Alloy which eS used as a Standard 

of Electrical Resistance. . 107 
Mr. T. Tate’s Experimental Researches on the Laws of Absorp- 

tion of Liquids by Porous Substances’...............-5 - 115 


Dr. Atkinson’s Chemical Notices from Foreign Journals .... 120 
Prof. Sylvester’s Note on the Numbers of Bernoulli and Euler, 


and a new Theorem concerning Prime Numbers.......... 127 
Mr. W. Dittmar on a new Method of arranging Numerical 
ebles (With 4 Plate ndirees iia cteipela thduay diascat «- 137 


_ Mr. W. Dittmar on Graphical Interpolation ............-- 139 


ly CONTENTS OF VOL. XXI.—FOURTH SERIES. 


Page 
Proceedings of the Royal Society :— 
Prof. Maxwell on the Theory of Compound Colours, and 
the Relations of the Colours of the Spectrum........ 141 
Prof. Faraday on, Regelatioi: oeuica.<004+ ssc oo eee os, 146 


Proceedings of the Geological Society :— 
Mr. D. Forbes on the ‘Geology of Bolivia and Southern Peru. 154 


Prof. Huxley on a New Species of Macrauchenia ...... 156 

Mr. J. W. Salter on the Paleozoic Fossils brought by 
Mr..D. Forbes from Bolivian, . 2: ..s%se-«cl = 5 eee a+ > oe 
On the Polarization of Light by Diffusion, by G. Govi...... 157 
On Electric Endosmose, by M..C. Matteucci vi: /7 ). eae 159 


NUMBER CXXXIX.—MARCH. 
Prof. Maxwell on Physical Lines of Force .............++« 161 


Mr. A.H. Church on the Benzole Series, . sia c'oe I ¥ Rare 
Mr. A. Cayley’s Note on the Theory of Determinants........ 180 
Prot. Kirchhoff on the Chemical Analy sis of the Solar Atmo- 
sphetez, &. tp. aw ol adblon nacins ot, Dale ee 185 
Mr. I’. A. Hirst on Ripples, and their relation to the Velocities 
of Currents. (With a Plate.) .. 188 


M. G. R. Dahlander on the Equilibrium of a Fluid Mass ‘revol- 
ving freely within a Hollow Spheroid about an Axis which is 


not its Axis of symmetry ... .198 
Dr. Woods's Remarks on Sainte-Claire Deville’s Theory ‘of Dis- 

BOCIALION WG QI 5 Mallets. Wel Hace ie be deuolle etn setae a 202 
Prof. Swan on the ian: Correction of ee Baro- 

meters | ..i5 206 
Mian A.. Cayley’ s Note on Mr. Jerrard’s Researches on 1 the Equa- 

tion of the. Fifth ‘Order .°..4.4 Edy dvd cpa i ee 210 
Prof. Davy on some further applications of the Ferrocyanide of 

Potassium in Chemical Analysis ........00.eeeeeeeee «. 214 


Proceedings of the Royal Society :-— 

MM. Matthiessen and Holzmann on the Effect of the 
Presence of Metals and Metalloids upon the Electric Con- 
duetivity:of Pure Copper... #42'7. 2 SPP 7. ae 224 

Dr. Chowne on the relations between the Elastic Force of 
Aqueous Vapour, at ordinary Temperatures, and its 
Motive Force in producing Currents of Air in Vertical 


Tubes. re DEFT RY Be 
M. Kopp « on the relation. between Boiling point and Com- 

position in Organic Compounds ........ 0.0.2 eee 227 
Messrs. W. Fairbairn and ‘IT’. Tate on the Density of Steam 

at all Teniperabares * 00.5. 2 ee Pee ee .. 230 


Proceedings of the Geological Society :— 
Prof. Nicol on the Structure of the North-west Highlands. 233 
Mr. T. F. Jamieson on the Geclogical Structure of the 
South-west Highlands of Scotland ..............-. 235 
The Rey. H. Mitchell on the position of the Beds of the 


CONTENTS OF VOL. XXI.-~-FOURTH SERIES. 


Old Red Sandstone in the Counties of Forfar and Kin- 
cardine, Scotland ..... 
The Rev. P. B. Brodie on the Distribution of the Corals in 
MORAY e 35 die ie Od ho Ab VISIR Baers 
The Rev. W. 8. Symonds on the Sections of the Malvern 
and Ledbury Tunnels, on the Worcester and Hereford 
Railway . : 
On the Fibrous Arrangement of Iron and Glass T ubes, by Dr. 
EE ehh if wn ed sod se ye na 00 «8 


On the Calcium Spectrum, by F. W. and A. Dupré ........ 
On the Lunar Tables and the Inequalities of Long Period due to 
the Action of Venus, by M. de Pontécoulant .......... i's 


NUMBER CXL.—APRIL. 


Prof. Kirchhoff on a New Proposition in the Theory of Heat. . 
Mr. J. Croll’s Remarks on Ampére’s Experiment on the Repul- 
sion of a Rectilinear Electrical Current on itself.......... 
Prof. Challis on ‘Theories of Magnetism and other Forces, in 
reply to Remarks by Professor Maxwell . a 
Mr. ‘I. Tate on certain peculiar Forms of Capillary Action fe 
Mr, A. Cayley on a Theorem of Abel’s relating to Equations of 
SM OFCEE OVP ne. ae UP ebb ck Chee dak 
Mr. D. Vaughan on ‘the Stability of Satellites in small Orbits, 
and the Theory of Saturn’s Rings .... 
Mr. J. S. Stuart Glennie on the ‘Principles of Energetics. — 
Part I. Ordinary Mechanics..... : 
Prof. Maxwell on Physical Lines of Force. (With ¢ a Plate. ie : 
Dr. Atkinson’s Chemical Notices from Foreign Journals...... 
Mr. W. Crookes on the existence of a new ‘Element, probably 
Mere SDM GROUP We )h fei. eds Mae eek 
Proceedings of the Geological Society :-— 


Mr. J. D.Smithe on the Gravel and Boulders of the Punjab. ¢ 3 


Prot lauxiey on Pieraspis Dunensis. 0... eee ee eck ss 

Mr. W. Whitaker on the ‘ Chalk-rock’ lying between the 

Lower and the Upper Chalk in Wilts, Berks, Oxon, 

Pee OMOGELCUUS es ee ee soe hss eed ele ielae « 

Sir R. I. Murchison and Mr. A. Geikie on the Altered 

Rocks of the Western and Central Highlands, and on 

the Coincidence between Stratification and Foliation in 

the Crystalline Rocks of the Highlands ............. 

Prof. Harkness on the Rocks of portions of the Highlands 

of Scotland. . 

Mr. F. Drew on ‘the Succession’ of Beds in the Hastings 
Sand in the Northern portion of the Wealden Area. . 

Mr. J. W. Kirkby on the Permian Rocks of the South of 

Yorkshire ...... esos 

On some Results in Electro-magnetism ‘obtained “with the 

Balance Galvanometer, by George Blan, WEA. GERK LED. GS 


306 


306 
308 
309 
310 


311 


vl CONTENTS OF VOL. XXI,——FOURTH SERIES. 


Page 

On the presence of Arsenic and Antimony in the Sources and 4 

Beds of Streams and Rivers, by Dugald Campbell, Esq..... 318 
Note on a Modification of the Apparatus employed for one of 
Ampeéere’s fundamental Experiments in Electrodynamics, by 

Profensar Wait: ei ess s 0 2, lae ge PU glee ae oni! nity pile 319 

Note respecting Ozone, by G. Gore, Esq. .....02..2222 0008 320 


NUMBER CXLI.—MAY. 


M. L. Lorenz on the Determination of the Direction of the Vi- 
brations of Polarized Light by means of Diffraction ...... 321 

Mr. T. Tate on certain Laws relating to the Boiling-points of 
different Liquids at the ordinary Pressure of the Atmosphere. 331 


Prof. Maxwell on Physical Lines of Force ................ 3838 
Mr. G. B. Jerrard’s Remarks on Mr. Cayley’s Note’... eee 348 
Mr. J. Stuart Glennie on the Principles of piper S tox 

Part II. Molecular Mechanics . sal el Ge 


Dr. Atkinson’s Chemical Notices from Foreign Journals .... 358 
Prof. Rijke on the Duration of the Spark which accompanies ~ 


the Discharge of an Electrical Conductor................ 365 
Prof. Sylvester’s Note on the Historical Origin of the unsym- 
metrical Six-valued Function of six Letters.............. 369 


Dr, Ph. Carl on the Galvanic Polarization of buried Metal Plates. 377 
Mr. J. Cockle on Transcendental and Algebraic Solution .... 379 
Proceedings of the Royal Society :— 
Mr. J. A. Broun on the Lunar-diurnal Variation of Mag- 
netic Declination at the Magnetic Equator.......... 384 
Mr. B. Stewart on the Nature of the Light emitted by 
heated Faumbaline), 7 isa). dean's Levin aale s Gee 391 
On the Motion of the Strings of a Violin, by Prof. H. Helmholtz. 393 
On Clairaut’s Theorem, by Prof. Hennessy, F.R.S. ........ 396 
On a Method of taking Vapour-densities at Low Temperatures, 
by Dr. Lyon Playfair, and J. A. Wanklyn................ 398 


NUMBER CXLII.—JUNE. 


Mr. J. J. Waterston on a Law of Liquid Expansion that con- 
nects the Volume of a Liquid with its Temperature and with 


the Density of its saturated Vapour. (With a Plate.)...... 401 
Prof. Kobell on a peculiar Acid (Dianic Acid) met with in the 

Group of Tantalum and Niobium compounds............ 415 
Mr. A. Cayley on the Partitions of a Close................ 424 


Prof. Chapman on the Drift Deposits of Western Canada, and 
on the Ancient Extension of the Lake Area of that Region . 428 
Mr. F. Field on the Neutralization of Colour in the mixtures of 
Miolutions of certain Salts <.),.... s; -ne. ees » 5 eee 435 
M. H. Fizeau on several Phenomena connected with the Polari- 
vation of. Light: id: d¢;. viele 4 raees ver seb eee’ } ase 438 


CONTENTS OF VOL. XXI.—FOURTH SERIES. 


M. G. Wertheim on the Cubical Compressibility of certain 
sold tromorenedus Bodies: oo... ris tici. bis eetewens ci 
Mr. T. Tate on a New Electrometer (the Siphon Electrometer) 
for measuring the Electrical Charge of the Prime Conductor 
of a Machine; and on the Dispersion of different Liquids by 
Migew@i@al Action [5 i.) ci cise fnew iid ae po eka 
“gece of the Royal Society :— 
Dr. Hofman on the Action of Nitrous Acid upon Nitro- 
Preuylenediamine:.), .... +. veal ei Ieidaa i dawyias 
Mr. W. Hopkins on the Construction of a new Calorimeter 
_ for determining the Radiating Powers of Surfaces .... 
Mr. C. G. Williams on Isoprene and Caoutchine ...... 
Dr. Joule and Prof. W. Thomson on the Thermal Effects 
me Pinas in Motion. . ...< . --.-.22 Rt Ue Pe EES ey eee 
Mr. E. J. Lowe on a new Ozone-box and Test-slips .. .. 
Proceedings of the Cambridge Philosophical Society :— 
The Rev. Dr. Donaldson on the Origin and proper value 
geene word. © Armument 1.5 deh wigs tse a.com eo chs ose 
Prof. Challis on the Planet within the orbit of Mercury.. 
Prof. De Morgan on the Syllogism, No. IV., and on the 
Bozic of Relations. .isavc as .aegedtt Weed oes 
The Public Orator on the Pronunciation of the Ancient 
and Modern Greek Languages .. 
Mr. H. D. Macleod on the present State of the Science ‘of 
2S LT ew bn 5061057 1h ee a a eT an lei See RD nEnT 
On the Optical Properties of the Picrate of Manganese, by M. 
ELE? LYSE 8 OIE Se ae ae ee er Pe 
Experiments on the possibility of a Capillary Infiltration through 
Porous Substances, notwithstanding a strong counterpres- 
sure of vapour, by M. Daubrée 


PS eS. OLW 6 Ss 608.6: e) 0) ie! 6: 0) 6 8 ee 0.8) 6)» 


NUMBER CXLIII.—SUPPLEMENT TO VOL. XXI. 


M. L. Lorenz on the Reflexion of Light at the Boundary of two 
eomec Uransparent Media: . 22.05. 2.4. ia ee ele 3 hig ore'e's 
Mr, A. Cayley on a Surface of the Fourth Order .......... 
Dr. Atkinson’s Chemical Notices from Foreign Journals 
rae @uallis on Theoretical Physics... 60.0605... 66 cece ws 
Mr. D. Vaughan on Phenomena which may be traced to the 
Presence of a Medium pervading all Space .............. 
Prof. Sylvester on a Problem in Tactic which serves to disclose 
the existence of a Four-valued Function of three sets of three 
PPeES CACO VY OE a ee RIGS SRW ES ERMA RET SPER EL 
Notices respecting New Books :—Mr. Todhunter’s History of 
the Progress of the Calculus of Variations during the Nine- 
Rene MCONUUEY: 53 8 ood oicisi oS vs Beda de wind os,i sipaits 
Proceedings of the Royal Society :— 
Messrs. J. B. Lawes, J. H. Gilbert, and Dr. Pugh on the 
Sources of the Nitrogen of Vegetation.............. 
Mr. F. J. Evans on the Deviations of the Compass observed 
on Board of all the Iron-built Ships and a selection of 
the Wood-built Steam-ships in Her Majesty’s Navy, &c. 


Vii 
Page 
447 


452 


457 


462 
463 


466 
466 


469 
470 


. 473 


474 


515 


520 


521 


531 


Vil CONTENTS OF VOL. XXI.—FOCRTH SERIES. 


Proceedings of the Geological Society :— 
Dr. Hector on the Geology of the Country between Lake 
Superior and the Pacific Ocean...............6.-.-- 987 
Dr. A. Gesner on Elevations and Depressions of the Earth 
in Worth Awmienca 2. {0 SFE ry. vs Oo. 5 SC 539 
On the Theory of Cylindrical Condensers, by M. J. M. Gaugain 539 
On the Production of Graphite by the Decomposition of Cy- 


anogen Compounds, by Dr. P. Pauli........ Ss Re > oh ee 
On Electrical Partial Discharges, by P. Riess.............- 542 
On the Freezing of Water and the Formation of Hail, by M. L. 
RN. SS Bas at oie 5, SS ORE, ee 543 
On an Apparatus for Experiments on Respiration and Perspira- 
tion) by Professor-Pettenkofer 2. 2... 25% «Sue ity RR oie ee 
DGC re pia o'er wiettin swiavs Gann ahpyniht tate ree ain ah & ptainiete Ree 547 
ERRATA. 


Page 322, line 20, for coordinates 2, y, z read the coordmates y, 2. 
— 323, lne 9, for > (wu, t, y, z) read (wt, y, Zz). 
— 324, line 2 from bottom, for behind, the opening in the screen must 
read behind the opening in the screen, 7 must. 

At page 373 the parentheses in lines 12, 13 left vacant should be filled 
in with the number 32. And at page 375 the following words 
explanatory of the Table at foot (which were accidentally omitted) 
should be supplied :— 

By means of the substitutions 


the preceding eight aggregates become developed into thirty-two, 
which together constitute the exhaustive Table in question. 
Page 376, line 2, for eight read thirty-two. 


PLATES, 


J. Illustrative of Mr. T. A. Hirst’s Paper on Ripples, and their relation 
to the Velocities of Currents. 


II. Illustrative of M. W. Siemens’s Paper ona Standard Measure of Re- 
sistance to Galvanic Currents, and Dr. Forbes‘s Paper on the Re- 
pulsion of a Rectilinear Electrical Current on itself. 

III. Illustrative of Mr. W. Dittmar’s Paper on a new Method of arranging 
Numerical Tables. 


IV. Illustrative of Mr. T. A. Hirst’s Paper on Ripples, and their rela- 
tion to the Velocities of Currents. 


V. Illustrative of Prof. Maxwell’s Paper on Physical Lines of Force. 


VI. Illustrative of Mr. J. J. Waterston’s Paper on a Law of Liquid Ex- 
pansion that connects the Volume of a Liquid with its Tempera- 
ture and with the Density of its saturated Vapour. 


THE 
LONDON, EDINBURGH ano DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FOURTH SERIES.} 


JANUARY 1861. 


I. On Ripples, and their relation to the Velocities of Currents. 
By T. Arcuer Hirst, Mathematical Master at University 
College School, London*. 

[With a Plate. | 

. eee oe we are all familiar with the ripples which 

solid bodies produce upon the surface of a stream in 

which they are partially immersed, their precise nature and their 
relation to the velocity of the current appear to have received 
but little investigation. The reason of this is no doubt to be 
sought in the well-known difficulties presented by the hydrody- 
namical problem whose solution is here, strictly speaking, in- 
volved. Upon this problem Newton, Laplace, Lagrange, Poisson, 
Cauchy, and others have expended the greatest analytical power 
and mathematical skill, and in every case the inherent difficulties 
of the subject have compelled them to introduce hypotheses and 
restrictions which more or less vitiate the results at which they 
at length arrived. The brothers Weber, again, by their elaborate 
researches, have shown that, in the experimental investigation 
of the problem in question, difficulties of equal magnitude are en- 
countered. 

But instead of considering the phenomena of ripples as a par- 
ticular case of this general and complicated hydrodynamical 
problem, the question arises, can we not in some more direct and 
simple manner arrive at the general relation which must exist 
between these beautifully symmetric ripples, and the velocities 
of the several parts of the current upon whose surface they are 
produced. Professor Tyndall, in his recent work ‘ On the Glaciers 
of the Alps’ (p. 398), has, in fact, prepared the way for us, in his 
chapter 29, “On the ripple theory of the veined structure of 


* Communicated by the Author. 
Phil. Mag. 8. 4. Vol. 21. No. 187. Jan. 1861. 5 


2 T. A. Hirst on Ripples, 


glaciers,’ by giving an exceedingly clear and simple explanation 
of the origin of ripples on the surfaces of streams. In the present 
paper I propose to pursue the subject somewhat further than 
he found it necessary to do, and to put his views into a mathe- 
matical form. 

2. When a spherical body—or a drop of water—falls upon 
the surface of still water, a system of concentric and circular 
waves are formed around the point of impact. The foremost of 
these waves generally exceeds the rest in magnitude, and being 
on that account most visible, will be referred to as the wave: its 
height and breadth, as well as the velocity > with which it 
recedes from the point of impact, all depend upon the magnitude 
of the body, and the height from which it fell. According to 
Weber*, this velocity > of propagation varies also with the time, 
or, more strictly, decreases as the radius of the circle formed by 
the wave increases: this variation, however, is admitted by Weber 
to be small+, and according to Poisson’s calculations, has no 
existence. In the present paper this possible variation of X is 
not overlooked, although, to obtain definite results capable of 
being compared with those of experiment, A is often treated as a 
constant; the error incurred by so doing being rendered less 
important by the circumstance that the waves with which we 
shall then be concerned cease, in reality, to be visible before 
their radu have reached any great magnitude. 

3. If we suppose the spherical body to fall into a current of 
water whose velocity v is everywhere the same, the particles 
forming the surface of the current will still be relatively at rest, 
and the wave will again be cireular in form, the centre of the 
circle being carried down the current whilst its radius increases 
with a velocity X, which we may assume to be the same as before. 
If the velocity and direction of the current vary from point to 
point, the circular form of the wave will be destroyed as it floats 
downwards, and the variations of form through which it will pass 
will, as Weber remarks, indicate in some measure the variations 
in the direction and velocity of the current at its several points. 

4. Let us next suppose a succession of drops to fall into the 
stream, the points of impact being fixed in space. Each drop 
will occasion a wave; and if there be no current, the several 
waves will form a system of concentric circles around the pomt 
of impact ; if there be acurrent, however, and its velocity be not 
too small, the successive waves will intersect one another, and at 
the points of intersection the water will be raised to a height ex- 
ceeding that of either of the intersecting waves. Lastly, if the 

* Wellenlehre, p. 182. Tt Ibid. p. 210. 


{ Mémoires de ? Acad. Roy. des Sciences de I’ Institut, 1816, vol. i. p. 165. 
See also Wellenlehre, p. 423. 


and their relation to the Velocities of Currents. 3 


drops succeed each other with sufficient rapidity, in short, if 
they constitute a jet of water falling into the current, the suc- 
cessive wayes will, by their intersection, give rise to a continuous 
series of points elevated above the general level of the liquid, and 
forming a ripple more visible than the waves which it envelopes. 
If we replace the jet by a solid cylinder, the effect will be essen- 
tially the same: the waves, it is true, may differ in form and 
even in the velocity with which they are propagated ; but, as 
before, the ripple will be their envelope. It is m this manner 
that the pebbles and other partially immersed bodies on the 
banks of a stream give rise to ripples whose forms, as we shall 
see, indicate in every case the velocities of the adjacent parts of 
the current. It is scarcely necessary to add that bodies moving 
on the surface of still water produce precisely similar effects ; the 
tipples caused by boats and water-fowl are examples familiar to all. 

5. The relation between the form of the ripple and the velo- 
city of the stream may be easily determined without even know- 
ing the forms of the waves of which the ripple is the envelope. 
Deferring this determination, however, to art. 10, let us first, 
for the sake of completeness, consider the following question :— 

The initial form of a wave being known, through what varia- 
tions will it pass as it floats down a stream where the velocity 
and direction of the current vary from point to point according 
to a given law? 

Let z and y be the coordinates of any point m on the sur- 
face of the stream, and let v and & be given functions of x and 
y, denoting respectively the velocity of the current at the point 
m, and the angle between its direction and the abscissa axis; 
the problem is to find the equation 

Gay Dil «vane fe si? (dh) 
of the wave at the ees of a time ¢, the sagen 
of the wave at the origin ‘of f that nee being known. 

At the time ¢ in question, the point m of the wave dbme will 
have two velocities ; one, A, in the direction of the normal mn to 
the wave, and another, v, in the direction ma determined by the 


angle amX=a. At the expiration = 
of the element of time dt, there- 
fore, the point m will arrive at the 
opposite angle m! of a small paral- 
lelogram, whose sides mn =)dt and 
ma=vdt have the directions above 
defined. If we call z' and y’ the 


coordinates of m!, and d= nmX the 
_ angle between the external normal 


B22: 


4, T. A. Hirst on Ripples, 
and the positive direction of the abscissa axis, 

z'=x+ (Xcosd+v cos ade, 

y'=y+ (Asin d +0 sin ajdt. 
But on changing ¢ into ¢+dt, the coordinates 2’, y' should 
satisfy the equation (1); hence 

y+(Asingd+vsina)dt=/[v7+(rAcosd+vecosa)dt, t+dt}. 

Developing the function on the right, neglecting powers of dé 
higher than the first, and recalling the equation (1), we have 


dy dy 
Asin d+ v sin a= yp C08 b+ cos a) + aH 
or, since dy 


1 


if fdyy® and cos 7 
a/ 1+ (Gs) Vola 


dy \? 5 di di 
ay / s = ay gy . e e 
1+ oe +vsin a v7, coset a (3) 


This is the partial differential equation whose general integral 
will include the equations of all possible waves which can be 
formed under the given conditions. The arbitrary function 
which this integral involves will in each case be determined by 
the known equation (2) of the wave which corresponds to t=O. 
With respect to this equation, however, it must be remembered 
that X varies with the nature of the displacement to which the 
waves owe their origin ; in our case it depends upon the magni- 
tude and velocity of the jet-—a fact which Weber’s experiments* 
establish beyond doubt. Apart from this variation, however, it 
follows from art. 2 that, even when the jet remains the same 
throughout, X may vary from point to point of a wave; in other 
words, it may be a function of # and y. In assuming J to be 
constant, therefore, approximate results can alone be expected. 

6. If we assume the direction of the current to be everywhere 
the same, and parallel to the abscissa axis, then a is always zero, 
and the equation (3) becomes 


dy\?__ dy , dy | 
WANT E! Se ee nC) 


The velocity v still remains a function of both zw and y; but 
without departing too much from the actual state of things in 
rectilinear streams, we may regard v as a function of y alone; 
that is to say, we may suppose the velocity of the current to 


sin o= 


* Wellenlehre, p. 183. 


and their relation to the Velocities of Currents. 5 


remain the same at the same distance from its banks, and to 
_ vary only on crossing the stream. Under these conditions the 
equation (4) is integrable; and if X be constant, one of its com- 
plete integrals will be found to be 


fdy/(c—vP?—N=AMw—ct)+ O(c); . « (5) 


where ¢ is an arbitrary constant, and ® an arbitrary function. 
The general integral will result from the elimination of c between 
this equation and its differential according to c, which is 


ae =35 t Meets Hage) se yee nie) 


7. The arbitrary function ® may be determined from the 
known equation 


Ie. = One re wae Fe ee ai ee anen) 
of the initial wave in the followmg manner. Putting ‘=O in 


the equations (5) and (6), we know that the result of eliminating 
c from the equations 


fdy/(e—v)? —N =a +(e), . . . « (5a) 


(c—v)dy ae 
rarer Diy ake ns cota poet (OO) 
must coincide with the equation (7). But eliminating c from 
these equations is equivalent to replacing c in the first by a func- 
tion of x and y determined from the second. Now on differen- 
tiating (5a) on the hypothesis that c is a function of 2 and y thus 
determined, we have, in virtue of (6a), 


dy V (ec—v)?—-VN=X aa, 


an equation which ought also to coincide with the result of dif- 
ferentiating (7), that is, with 


d¥ d¥ 
a tae ae —— dz=0, 
We conclude then that 
eee 
ap V (e—2)? SH eae ee a giv at Behe yay (SB) 


The result of eliminating x and y from the equations (7), (5a), 
and (8), therefore, will lead to the required relation between ®(c) 
and c. 

_ 8. As an example, let the velocity v of the current be constant, 
or the same at all points. The complete integral (5) of the 
equation (4) will then become 


V (e—v)?—AN=Aa—ct) +c, spe) ete 46 hia} 


6 T. A. Hirst on Ripples, 


where c, is a function of ¢ to be determined from the initial form 
of the wave. If we suppose this initial form to be that of a circle 
with radius a around the origin, the required relation between ¢ 
and c, will result from eliminating # and y from the following 
equations, to which (7), (5a), and (8) become respectively re- 
duced: 

+y=a, 

wie=iP—N—ra=ey | «abana 

aar/ (c—v)?—d? + rAy=0. J 
From these we easily deduce 

ale—v) = EK tyisok ox!) aay eee 
by means of which (9) becomes 

yr/ 62 — ar? =ar(x—vt) + ¢,(a+ rt). 
Differentiating this according to c,, we have, corresponding to 
(€), the equation 


ee NED ee V2 


The equation of the wave at the end of the time ¢ results from 
the elimination of c, from these two equations, or from the fol- 
lowing two, to which they are equivalent : 

cy? =anr(x—vt)(a+ At) +¢,(aF Ad)’, 
a+Xt 


¢, = —ar : 
I “L—vt 


The result is clearly 

oy? + (ool) t= (asa y. f re 
which, as might have been anticipated, is the equation of a circle 
whose centre is on the abscissa axis at a distance from the origin 
equal to vi—the space described in the time ¢ by each point of 
the current—and whose radius, from being a, has become a+Xé, 
in consequence of the propagation of the wave with the constant _ 
velocity X. The upper sign in (12) is, of course, foreign to the 
present inquiry ; it refers to the propagation of the wave inwards, 
a case which is included in the differential equation (4) *. 


* It is worthy of notice that when v=0, the differential equation (3) or 


(4) becomes 
dy dy \2 
(zi) ao) (a) 


where k=dé, a relation which all parallel curves must satisfy, and which 
may be at once obtained from the definition of these curves. If 2, y, and 
k be regarded as the coordinates of a point in space, the above partial dif- 
ferential equation represents a developable surface generated by a plane 


and their relation to the Velocities of Currents. 7 


9. Let us next consider the ripple which envelopes a system 
of waves having at their origin the same position and form. If, 


as in art. 5, 
y=fle,t) . - (1) 
represent the equation of any wave, ‘ 
y=flz, t+ dt)=flz, t)+ 2 dt + &c... 


will be that of the next preceding wave, and the values of # and 
y which satisfy both equations, or which satisfy (1) and the 
equation 

dy 

= 8 ty RRM CS Ore a) EO 

Yo, (13) 
will refer to a point on the required ripple. In short, the equa- 
tion of this ripple will be the result of the elimination of ¢ from 
the equations (1) and (13). If we differentiate (1), regarding ¢ 
as a function of 2 determined by (13), and use brackets to di- 
stinguish partial from Sone differential coefficients, we have 


oH _(@) 4 cee shi 

da 

1) ot, 

bag ae ete e 


an equation which merely expresses the well-known fact, that at 
their point of contact the wave and ripple have the same tangent. 
But it was shown in art. 5 that the equation (1) satisfies the 
partial differential equation (3); and the latter, by means of (13) 
and (14), becomes transformed into the ordinary differential 
equation 


hence by (13), 


— | 
ry 14 E+ vsinaxol cose, Say Ae cA 


which is clearly that of the ripple. If the coordinate axes be 
turned around the origin until the abscissa axis 1s parallel to the 
direction of the current at any point M(ay) of the ripple, then, 
since «=O at that point, (15) becomes 


which is constantly inclined at an angle of 45° to the plane (xy) or axis k, 
and the sections of this surface made by planes parallel to (wy) will consti- 
tute a system of parallel curves. If the base of this system be a curve 
traced on the coordinate plane of (xy), the generating planes of the deve- 
lopable will always touch the same. The developable, in fact, has for its 
edge of regression a curve which cuts at an angle of 45° all the generators 
of a right cylinder whose base is the evolute of the curve traced on the 
plane (zy). 


8 T. A, Hirst on Ripples, 


ae, ee 
dy? v 


where 6 is thé inclination of the ripple to the direction of the 
current at any point M of the former. We are thus led to the 
following simple and interesting result :— 

At any point of a ripple, the sine of the angle between its direc- 
tion and that of the current ts inversely proportional to the velocity 
of the latter, and directly proportional to the velocity of propa- 
gation of the wave which touches the ripple im that point. 

10. This result may be arrived at in 
a simpler manner. When the velocity 
and direction of the current remain the 
same at all points, the waves produced 
at a point A retain their circular form 
as they float down the current. If the 
radi of the several circular waves in- 
crease with the same velocity A, then 
the ripple, their envelope, will clearly 
consist of two right lines diverging 
from A and touching all the circles. 
if from the centre B of any wave the 
radius B M be drawn to its point of 
contact with the ripple, then, since the 
wave has been propagated over the 
space BM in the same time that a 
point of the current has described the 
space A B, we have clearly 


eseeay GRE hf Sie Ge 


If, as Weber asserts (see art. 2), the 
velocity with which the wave is pro- 
pagated diminishes as its magnitude 
or radius BM increases, the ripple will 
no longer be rectilineal, but at the 
point M of the ripple the law of art. 9 
will still hold. To prove this, it is 
only necessary to consider two im- 
mediately succeeding circular waves 
around B and B/, and from these 
points to let fall the perpendiculars & 
BM, B'M’ upon their common tan- sige 
gent MM!, which will also be the 
tangent to the ripple at the point M ; 


and their relation to the Velocities of Currents. < 


drawing BC parallel to M M’, we have, as before, 


! 

as = sin B/BC= sin 0= ~ 
where @ is the angle between the directions of the ripple and the 
current at the point M. The velocity v being constant, @ and » 
will decrease simultaneously ; so that, according to Weber, the 
ripple should consist of two curved lines, AM, AM,, turning 
their concavities towards each other. This property of the wave 
suggests a crucial experiment as to the variation of 1; to apply 
it, however, a perfectly uniform current would be required, or 
what is equally difficult to realize, a jet must be made to de- 
scribe a right line with perfectly uniform velocity over still water. 
In ordinary experiments, as will be hereafter seen, the ripple, as 
long as it remains visible, and as far as the eye can judge, is 
rectilinear. 

Again, it may easily be shown that when the velocity and 
direction of the current vary from point to point, so as to destroy 
the circular form of the waves, the law of art. 9 is still fulfilled. 
In fact, in the immediate vicinity of the pot M of the ripple 
we may regard this velocity and direction as constant; and in 
place of the non-circular wave, to whose intersection with the 
immediately preceding and succeeding waves the ripple at M is 
due, we may substitute a circular one osculating the real wave 
in M, increasing with the same velocity X, and moving parallel 
to the current at M with the velocity v which exists at that 
point. This fictitious circular wave will clearly produce a ripple 
coincident with the actual one in the neighbourhood of the point 
M, and thus the relation (16) between XA, v, and @ will still 
exist at that point. 

11. From the relation 


sin 0= Ms 
v 


7 
2 
when the velocity of the current is equal to the velocity with which 
the wave is propagated, the several waves all touch a line at 
right angles to the direction of the current; they will con- 
sequently touch each other, and the ripple will become reduced 
to their point of contact. When A exceeds v, 0 is imaginary; im 
fact, in this case the waves will clearly be propagated up the 
stream, and will no longer intersect. Strictly speaking, however, 
this is the case only when the waves are produced by a discon- 
tinuous series of drops ; experiment shows that when a solid cy- 
linder or jet is partially immersed in so slow a current, the water 
flows past it without its surface suffering any visible*disturbance. 
From this it follows that a ripple which has been produced in a 


it follows that when A and v are equal, O= =; that isto say, 


10 T. A. Hirst on Ripples, 


stream, where the velocity diminishes from the centre towards 
the sides, will end abruptly as soon as it has reached a point 
where that velocity is less than.X; the pebbles on the banks of 
such a stream will produce no ripples. Ina similar manner, too, 
® may be regarded asa limit beyond which the velocity of a body 
moving through still water cannot be increased without visibly 
rippling its surface. 

12. For the sake of further illustration, let us assume, as in 
art. 6, that the direction of the current is everywhere parallel to 
the abscissa axis, and that its velocity v varies only with the di- 
stance y from this axis. The differential equation (15) of the 
ripple then becomes 


dy VP ava ie. 
whose integral, > being considered as a constant, is 
{dy Ver—e=de+C, . .. o = (19) 


where the constant C will be determined as soon as any point in 
the ripple is known. By (18) we can determine v whenever the 
form of the ripple is known, and by (19) we may find the equa- 
tion of the ripple whenever the law in the variation of the cur- 
rent’s velocity is given. 

For instance, we may determine the nature of the current, the 
ripples upon whose surface are parabolas. For in this case the 
equation of any ripple being 


yy? =2Qpa, 
we have at once 
Ch dn Sa p 
da Joey 
whence we deduce 


np? 


and conclude that, to produce parabolic ripples, the velocity of 
the current at any distance y from the axis of the parabola will 
be represented by the abscissa of a hyperbola having that axis 
for transverse axis (2X), the vertex of the parabola for centre, and 
a conjugate axis equal to the parameter of the parabola. 

Conversely, if the velocity of the current at any distance y 
from the abscissa axis satisfy the relation 


that is to say, if this velocity can be represented by the abscissa, 
corresponding to the ordinate y, of an ellipse having its centre 
at the origin, then the equation of the ripple, as given by (19), 


and their relation to the Velocities of Currents. 1] 
would be 
J dyp/ @—2— Fy =a +C, 
where c= 53 on integrating, we find the equation of the ripple 


in this case to be 


ENE, 


cy V a? —n?— cy? + (a? —X2) are sin 

7 nile G22 
where the arbitrary constant has vanished on assuming that the 
ripple passes through the orig. The tangent of the inclination 
of the ripple to the current at any point 2, y has of course the value 


dy _ r 
dx J @— rn? — Py? 
which varies between the minimum limit a the origin, 


a — 
and the maximum o at the point A, whose coordinates are 


ah az—r2 a a Jer? 
Cc 


4 cr 


Further, since the equation is unchanged when 2 and y are 
replaced by —z and —y, it is evident that the ripple consists 
of two similar branches in opposite quadrants, and has a point of 
inflexion at the origin, where it is least inclined to the current. 
‘Proceeding from this point, its inclination to the current in- 
creases until, at the points A and A’, current and ripple are at 
right angles to each other. Here the latter ends abruptly, in 
consequence of the velocity of the current having become equal 
to that with which the wave is propagated (art. 11). 

In Plate I. fig. 1, let O X be the direction of the current, and 
let its velocity at any point of a line parallel to O X be repre- 
sented by half the chord which is intercepted upon that line by 
an ellipse, X Y X’ Y'. Let the semi-chords A B and A! B! repre- 
sent the velocity ) with which the wave is propagated. The 
curve A’O A will then represent the ripple produced by partially 
immersing a body at any one of its points, as A’. The tangent 
OC at the point of inflexion O is easily constructed, since it 
passes at the distance X= XC=AB from the vertex X*, 

13. In order to test by experiment the law enunciated in 
art. 9, two methods suggest themselves. First, to examine the 
ripples produced by a stationary jet falling into currents of dif- 
ferent but known velocities ; and secondly, to give to the jet or 
partially immersed body a definite motion, the water being mo- 
tionless. This second method has many advantages, arising 
from the fact that the motion of the jet is more under our con- 
trol than that of a current, which in general varies from point 

* Compare the fig. in chapter 29 of ‘ Glaciers of the Alps.’ 


12 T. A. Hirst on Ripples, 


to point according to imperfectly known laws. Now of all con- 
ceivable motions which might be imparted to the jet, a circular 
one is beyond doubt most feasible ; so that we are naturally led 
to inquire what will be the form of the ripple produced by a jet - 
which, as it falls into still water, describes a circle with a given 
constant velocity u. 

We shall throughout assume the velocity with which the 
waves are propagated to be independent of the magnitude of the 
latter, and, in accordance with art. 4, we shall seek the envelope 
of the several waves which the moving jet originates. There is 
one case where the nature of this envelope can be at once deter- 
mined: it is when the jet moves with the same velocity » as the 
waves. For at the moment when the jet arrives at a point A 
(fig. 2), the wave which it produced when at B will have acquired 
a radius equal to the arc AB; instead of intersecting, therefore, 
every two successive waves around B and B! will touch each 
other, the difference between their radi being equal to the 
distance B B! between their centres, and their point of contact 
A! will be in the tangent to the circle at the point B; in fact, 
the ripple in this case will be the involute of the circle A A! C, 
or the curve formed by unwrapping, under tension, a string ori- 
ginally wrapped round the circle as far as A. If the velocity of 
the jet were less than 2, the successive waves would precede the 
jet, and neither intersect nor touch each other; in other words, 
there would be no ripple. But if the velocity of the jet exceed 
r, the ripple will separate into two branches (fig. 7), one of which 
will be outside the circle, whilst the other will enter it; but 
since the waves continue to increase in radius, this latter branch 
will necessarily leave the circle again, and never re-enter it. In 
art. 20 we shall find, in fact, that this branch, after approaching 
to within a certain distance of the centre, suddenly turns and 
recedes, the turning-point or cusp C bemg due to the intersec- 
tion in that point of three successive waves. In experiments this 
cusp 1s tolerably well defined; and its position is the more im- 
portant, since it bears a very simple relation to the velocities wu 
and 2; in fact, we shall find that the distance of the cusp from the 
centre of the circle described by the jet has to the radius of that 
circle the same ratio that the velocity \ of propagation has to the 
velocity u with which the jet moves. 

14, For the sake of future applications, it will be more con- 
venient to deduce the form of the ripple above considered from 
the solution of the following more general problem. 

A jet which describes, with uniform velocity wu, a fixed circle 
with radius a, falls into a current whose velocity v and direction 
are the same at every point of its surface; required the form of 


the ripple. 


and their relation to the Velocities of Currents. 13 


Let the centre of the circle be taken as the origin of coordi- 
nate axes, one of which—the ordinate axis—is parallel to the 
direction of the current. To fix our ideas, let us suppose, too, 
that after having rotated for an indefinite period in the direction 
opposed to that of the hands of a clock, the jet has at length 
reached the position A (fig. 3) defined by the angle AO X=wW. 
The centre of the circular wave which the jet originated when in 
any position B, will have been carried with the current along 
the lme BC parallel to the ordinate axis, and its radius, from 
being zero, will have increased to a certaim magnitude C M. 


The arc A B, the line BC, and the radius CM being described 


in the same time, we shall clearly have the proportions 

AB: BC:CM=u:0:); 
so that, on representing the angle AOB by @, and the ratios 
= and ~ by « and # respectively, we shall have 


AB=ad, CM=aa¢d, BC=aBd; | 
and the coordinates &, » of the centre C of the circular wave 
will be a “8 
eel a ae t lea ptee hi) 
n=asin (—¢) + aB¢ ; 


whilst the equation of this wave will be 


[x —acos (y—$)]? + [y—asin (y—$) —a8o]?—a°a2g?=0. (21) 
The equation of the immediately succeeding wave will be ob- 
tained from this by changing ¢ into 6+d¢; the intersections 
of the two waves will be two points on the ripple, and their co- 
ordinates will clearly satisfy the equation (21), as well as its dif- 
ferential according to ¢. The equation of the ripple, therefore, 
at the moment the jet reaches the point A defined by the angle 
ar, will result from the elimination of ¢ between (21) and the 
equation 


[v—a cos (Yr—¢)]sin (—¢) —[y—asin (b}—¢) —a8 4] 

[cos p—)—B]+axe*M=0, . . . . « . (22) 
which is simply that of the chord of intersection of the two suc- 
cessive circular waves. In a similar manner, the equation of the 
chord of intersection of the second of the above waves, and a 
third, immediately following the same, will be found by putting 
o+d¢ in place of d in (22); and the coordinates of the point 
in which these two chords cut each other will satisfy both (22) 
and its differential according to @, which is 


[v—a cos (f—¢) ]eos (f—¢) + [y—a sin (—¢)— 489] 
sin (Wr —¢)+a[l1—a?+4 6?—28 cos (w—g]=0. . (23) 


14 T. A. Hirst on Ripples, 


If the three successive waves intersect in a point, the two chords 
will also pass through that point, and its coordinates will conse- 
quently satisfy, simultaneously, the three equations (21), (22), 
(23). The position of the cusps of the ripple at the moment 
the jet reaches A will be found, therefore, from the two 
equations which result from eliminating ¢ from the last three 
equations. These two equations will of course contain the 
angle yw which defines the position of the jet; if the latter be 
also elimimated, the resultimg equation will be that of the curve 
described by the cusps as the jet rotates. 

It will be at once observed that the elimination of w and @ 
from the above equations is equivalent to the elimination of the 
three variables sin (Wr—@), cos ar—@), and ¢ from those equa- 


tions in conjunction with 


sin? (r— d) + cos? (h—d) = 1; 
so that in the result all circular functions will disappear; that is 
to say, as the jet rotates, the cusps of the ripple will describe an 
algebraical curve. Particular cases excepted, the order of this 
curve is high; for instance, when the three velocities X, u, and v 
are equal, it reaches the eighth order ; when v vanishes, however, 
it becomes a circle (art. 20). 

If, lastly, we eliminate x and y from the equations (21), (22), 
(23), we shall obtain the relation between ¢@ and a which corre- 
sponds to the cusps at the moment under consideration, 27. e. 
when the jet reaches the position A. 

15. Before proceeding further, however, it will be useful to 
examine the locus (20) of the centres of the circular waves at the 
moment under consideration. On eliminating ¢ from the equa- 
tions (20), the equation of this locus will be found to be 


7—ab w= Ve—2—aR cos 


from which we learn that the curve undulates between the two 
lines £= +a parallel to the ordinate axis, and that the successive 
undulations are precisely similar, the length of each undulation 
being 27ra8. The form of each undulation differs according as 
£ is less than, equal to, or greater than 1, and in the following 
manner :—Firsi, when 6 <1, 7. e. when the velocity of the cur- 
rent is less than that of the jet, the curve consists of a series of 
loops, ABCDEF (fig. 5), the distances between the points 
B, D, F, where it touches the line X’F, as well as between the 
points C, EK, where it touches the lme XH, being 27a8. The 
branches BC and CD, however, are not symmetrical. As 8 
increases, the loops diminish until, secondly, when B=1, they 
become transformed into cusps B’, D', at which the tangents are 


and their relation to the Velocities of Currents. 15 


parallel to the abscissa axis. Lastly, when @> 1, the loops and 
cusps disappear, and are replaced by points of inflexion, H, K, 


which lie on the line €= — “. A somewhat clearer image of the 


ripple may be obtained by regarding it as the envelope of a circle 
whose centre M moves along one of the three curves of fig. 5 
and whose radius increases proportionally to the distance MN, 
measured along a parallel to the ordinate axis, between its centre 
and that portion X Y' X’ of the circumference of the circle whose 
concavity is turned in the same direction as that of the portion 
B’ MC’ of the curve along which the centre is moving. 

16. To return to the equations of the ripple : let us, for brevity, 


put 
sin (—d) =p, 00s (P—$) =¥3 
the equations (21), (22), (23) will then Rg 
(w—va)* + (y—pa—Roa)?— ap?" = ; 
| pla—va) + (8—v) (y—na— Roa) pert res 
v(@—va) + w(y—pa—Bda) + (l—2? + B?—2vB)a=0 


The first two equations, when solved for w and y, give 


ap+(B—v) /R 1 


Se ? | (25) 
Aw _ pe(B—v)FuvR | 
a u+6h ay * maaan go ee > | 
where 
i Pe 6 2B. a ie a eG) 


In these values of the coordinates of any point of the ripple the 
upper and lower signs correspond, and refer to the two distinct 
. branches into which the ripple divides itself. 

On eliminating 2 and y from the three equations (24), the 
result will be found to be | 

[a*— (1 —@y)?] 0°? — 2a8yRagd+(1+6?—28v)R?=0. (27) 
This is the equation, mentioned at the end of art. 14, which is 
satisfied by the values of ¢ corresponding to the cusps. 

17. When the value of ¢ is such as to make R=O, the two 
branches of the ripple meet, and from (25) the points of junction 
he in the curve represented by 

Plies ERB Ils ciel ihn ee alee 
y=ap+avd, 
which may be easily shown to be the involute of the circle formed 
by unwrapping the circle backwards from the point A, where the 


16 T. A. Hirst on Ripples, 


jet has reached. Further, if be the angle, opposite to the side 
Xr, in a triangle whose sides are respectively proportional to the 
velocities X, u, and v, we shall have the relation ; 


Mau2+v2—Qweoskh; . . . . (29) 
or, dividing by wu? and introducing the ratios « and @ (art. 14), 
a? =1+ B?—2B8 cos a 
This, compared with (26), shows that the condition R=O is 
satisfied when 


y=cosr, and w=+sind; . . . (30) 


so that the result of eliminating w, v, and @ from (28) and the 
equation R=O will be 


zcosh+y sin A=. 


This is the equation of the curve described by the junction points 
of the branches of the ripple as the jet describes its circle, which 
curve, as is at once seen, consists of two right lines touching 
that circle at points B and B’ (fig. 6), whose angular distances 


BOX, B’O X from the abscissa axis are each equal to a, Now, 


since an angle x fulfilling the condition (29) can always be found 
when the velocities A, wu, v form a triangle, that is to say, when 
any two of these velocities together exceed the third, we conclude 
that under these conditions the ripple will always break up into 
closed curves or loops, in consequence of the two branches of the 
ripple, which in other cases are always distinct, meeting each 
other. These meeting points describe the tangents (30) BC, B/C’ 
as the jet rotates, and their position at any moment is determined 
by the intersections C, C’, &c. with these tangents, of the involute 
ACC’ of the circle,—the latter being supposed to move with 
the jet. 

The physical character of these meeting points, as will be im- 
mediately shown, is that the ripple is there least prominent, so 
that the tangents (30) BC, B! C’ represent two lines along which 
the surface of the current is apparently least disturbed. If the 


angle between them, which is equal to 2\, were determined by 
experiment, and the velocity u of rotation were also known, the 
equation (29) would serve to determine either of the velocities 
» or v as soon as the other was given. 
18. The above results will be further elucidated by consider- 
ing the resultant relative velocity of the current and jet at any 
point A, fig. 4. This resultant will clearly be represented in 
direction and magnitude by the diagonal A R of a parallelogram 
whose sides A V parallel to O Y, and A U perpendicular to A O, 


respectively represent, in direction and magnitude, the velocities 


and their relation to the Velocities of Currents. 17 


of the current and jet. The angle at U being equal to the angle 
AOX=7, the magnitude of this resultant is expressed by 


(R)= Vu?-+v?—2uveosp, . . . . (381) 
and becomes equal to A, the velocity with which circular waves 


are propagated, when w=), that is to say, when the jet reaches 
either of the points B, B’ of the foregoing article (fig. 6). For 
all positions of the jet in the are B X Bb! the resultant (R) will be 
less than 2, and for all points in the arc B X! B’ greater; so that 
by art. 11, the jet will only commence producing a ripple when 
it reaches the point B, and will cease doing so as soon as it 
reaches the point B’. At these points, B and BY, the immediately 
adjacent circular waves of the incipient ripple touch each other,and 
the point of contact is very slightly elevated above the surface of 
the current at adjacent points (art. 11); further, since the centres 
of these waves proceed with the same uniform velocity down the 
eurrent, whilst their radii increase with the same velocity, they will 
clearly continue to touch each other along the line BC or B'C’; 
so that these lines, as above remarked, will be lines of least appa- 
rent disturbance. They do not in general touch the ripple; im fact, 
they do so only when the resultant velocity (R) =) coimcides in 
direction with that of the radius OB (or O B’), in other words, 
when v?=)?+ w?, as may be seen byaglance at fig. 4. This case 
of contact is represented in fig. 6, where A DCE represents the 
first closed loop of the ripple when the ject has reached the poimt 
A, and B!D,C, E, what this loop becomes when the jet reaches 
the point B’. The curve D'C' Hi! represents a portion of the 
second loop of the ripple corresponding to the position A; it is, 
in fact, a portion of what B’D,C,E, becomes as it floats down 
the current during the time that the jet is describing the 
are BBA. 

19. The law enunciated in art. 9 leads to a simple method of 
determining the velocity of a current ; to apply it, however, the 
velocity X must be first determined, and the velocity cf the cur- 
rent experimented upon must be greater than A. The formula 
(31), however, suggests two other methods of determining the 
velocity of a current, which do not require a previous determina- 
tion of X, and may be applied to all currents. They are briefly 
the following :— 

Ist. The jet having a known velccity uw, let the positions A 
and A! (fig. 4) be found at which the divergence between the 
branches of the ripple has a given magnitude, and call 2W the 
angle between the radii OA and OA!. The line bisecting this 
angle will be perpendicular to the direction of the current. Let 
the experiment be now repeated with a different velocity u,, and 
let 2, represent the angle now subtended at the centre of the 


Phil, Mag. 8. 4. Vol. 21. No. 137, Jan. 1861. C 


18 T. A. Hirst on Ripples, 


circle by the two positions of the jet at which the divergence 
between the branches of the rippleis the same as before. Then, 
since the divergences are the same in both experiments, it fol- 
lows from art. 10 that the resultant velocities (R) and (R,) will 
be equal; so that by (31) we have 
u? +0? —2Quv cosw=u,? +0? —2uyv cos Wy, 
whence we deduce 
eed ur —u,* 
°= 8 ucos ar—u, cosy 

2nd. Let the positions A and A! be found at which the angle 
between the branches of the ripple is bisected by the production 
of the radius. In this case the resultant velocity (R) will coin- 
cide in direction with the radius at each of the points A and A’, 
whose angular distance asunder is 2, and from fig. 4 we deduce 
at once the relation 

ean 
= C08 Ae 

20. The case alluded to in art. 13, where the jet describes a 

circle in still water, may now be easily disposed of by making 


v=0, and therefore 8=0, in the general case treated im art. 14. 
In this manner the equations (24) become 


(av)? + (yay)? —a2’g? =0, 
(c—av)u—(y—ap)v +a2a =0,} (32) 
(w—av)v + (y—ap)u+ (1-2? )a=0; 
or, by simplifying, 
a? + y* —2a(av + yp) + a? — a°a?g?=0, } 

xp— yv +a°ad =0, . . (33) 

rv+yp—oa =0; J | 
of which the first two represent the ripple, and all three are 
satisfied by the coordinates of its cusp. If, be the value of 


which corresponds to this cusp, we find immediately, by elimi- 
nating z and y from (82), 


pW ae i et 


which will always be real and positive when wu exceeds A. This 
same value of ¢ might be obtained from (27) by putting B=0; 
by means of it and the last of equations (33) the first becomes 


which is the equation of the circle described by the cusp as the 


and their relation to the Velocities of Currents. 19 


jet rotates. Putting r in place of Va?+y?, it leads to the 
relation 


Oe 5 MS ST ale et Je SEND 


expressed in art. 18. 

To obtain simple expressions for the coordinates 2,, y, of the 
cusp corresponding to a given position of the jet, it is merely 
necessary to observe that ie form of the present ripple does not 
alter as the jet rotates; so that we may refer its equation to co- 
ordinate axes which rotate with the jet,—the abscissa axis being 
at the angular distance AOX=d, behind the jet (fig. 7). By 
so doing w sand v become respectively sin (f; —¢) and cos(¢,— od); 
and the two last of the equations (33) give, on substituting for co) 


its value (34), 

yaar lab, t Ce aes Ge 
w= ea; 

so that if we call 0, the angular distance AOC of the cusp C 

behind the jet, we have, in virtue of (35), and sinceCOX=¢,—4,, 


sin (6—0,)=\/1—2?, cos ($,—9,) =e, 


ee i Me agg 24 


whence it follows that @, increases as « diminishes, in other words, 
as w Increases. 


Again, since the berigent to the ripple at any point coincides 
with the tangent to the circular wave which there touches it, we 
have from the first of equations (82), 

dy u—av 

pe Lape cante weet, he rome (38) 
With reference to our new coordinate axes, the values of y and uw 
' at the cusp are 1 and C respectively ; and these, together with 
the values in (86), give, when substituted in (38), 
=) KS aA—2, a MME Sea 

a Yy a 2, 

and show that the radius vector OC is the tangent at the cusp. 

The polar equation of the ripple, with reference to an axis 

passing through the jet and moving with it, is easily seen to be 
r?— ar cos (b— 0) =a7a*d?— a’, 
28 9 » e (39) 
r sin (b— 0) =2a7ad, 


C2 


20 Sir David Brewster on certain A ffections of the Retina. 


where 6 and ¢ are estimated in the same direction. To find the 
points A and B where the ‘ripple cuts the circle, » must be re- 
placed bya in these equations; on squaring and adding the results, 
it will be found that 


either $=0, or d=24, ; 
the former has reference to the point A, and the latter to the 


point B. Substituting the latter value of ¢ in (39), we have in 
virtue of (37), 


tan (26,—@) = pee ape 
eh? satan". —4) 


whence we conclude 0=26,; thatis to say, the radius OC to the 
cusp bisects the angle formed by the radu OA, OB to the two 
points where the ripple enters and leaves the circle. 

Lastly, when a=1 or X=u, the two first of equations (33) 
reduce themselves to the system (28), which, as we know, repre- 
sents the involute of the circle. This verification of the result 
contained in art. 13 may be most easily made by putting a=], 
/&=0, and hence R=0O, in the equations (25), which are equiva- 
lent to the system (33). 


II. On certain Affections of the Retina. 
By Sir Davip Brewster, K.H., D.C.L., F.RS* 


1 fa three articles published in the Philosophical Magazine for 

1834+, I have described several affections of the retina, 
which since that time I have frequently had occasion to study. 
Mrs. Mary Griffiths of New York had observed “a reticulated 
or network structure upon opening her eyes for the first time in 
the morning{. At one moment,” she says, “the meshes of 
the network were of a dull brickdust colour, and the spaces 
between were of a pale dingy yellow; and in the next moment 
the case was reversed—the meshes and intersections were of this 
pale dmgy yellow, and the spaces or interstices were of a dull 
brick-colour.” She describes the meshes “as generally the fifth 
of an inch in diameter,” but without telling us the distance of 
the surface upon which this measurement was made. 

Hlaving believed it possible to determine experimentally 
whether a beam of light was a continuous stream like a stream 
of water, or a stream in which the parts were at such a distance 
as to maintain a continued impression on the retina, I received 
a narrow beam of solar light upon a white ground, and made a 
strip of white card pass rapidly back and forwards across the beam, 


= tan (26,—28,), 


* Communicated by the Author. 
Tt Phil, Mag. 1834, pp. 115, 241, and 353. t Ibid. p. 43. 


Sir David Brewster on certain Affections of the Retina. 21 


comparing the luminosity of the dise which it reflects with that 
of the fixed circular spot upon the paper. In these experiments I 
cbserved two interesting facts,—that the reflected disc of ight 
exhibited different colours in different parts of it, and that it was 
more luminous than the beam received upon the white ground 
when no part of it was reflected by the moving card. 

Before I had examined these phenomena more minutely, I 
found that M. Benedict Prevost had published an interesting paper 
in the Mémoires de la Société de Physique et d’ Histoire Naturelle de 
Genéve*, and had anticipated me in the first of the above results. 
He agitated, to use his expression, a piece of white card across a 
sunbeam in a dark room, and he observed that the circular spot 
which it reflected, in place of being white, was white only in the 
centre. Around this white spot was a violet spot, growing deeper 
as it receded from the centre. The violet spot was surrounded 
with a zone of deep indigo, very well defined, and resembling the 
colour of the Viola tricolor. Round the indigo zone was one of 
greenish yellow, equally weil defined, and round it a red shade. 
He considers the ight as thus decomposed into seven principal 
colours ! 

“This phenomenon,” he adds, “is produced by a single pass- 
age of the card across the sunbeam, which proves that it 1s inde- 
pendent of the fatigue of the eye. Nor does it depend immedi- 
ately on the agitation or motion of the card, but only, without 
doubt, on some effect of this motion, and particularly on this, 
that the illuminated area strikes the eye only during a very short 
time ; for if the card is sufficiently large, so that the illuminated 
space does not go out of it, and notwithstanding the agitation 
of it the eye continues always to see it, it appears white as if 
it was seen at rest, and there is no longer any appearance of the 
decomposition of the light.” 

Reckoning from the centre of the disc, the colours observed 
by M. Prevost are as follow :— 


White. 

Violet. 

Deep indigo. 
Greenish yellow. 
Red shade. 

In the experiments which I made, I sometimes agitated a 
narrow slit, or a series of parallel slits, in a black card, across 
a circular aperture 1a another black card, or across an aperture 
in the window-shutter of a dark room; or I looked at a white 
surface, or a white disc through the slits of a revolving disc, as 
described in one of the papers already referred to. By these 


* Vol. mii part:2.) p.. 121. 


22 Sir David Brewster on certain Affections of the Retina. 


methods I found that the white disc, or aperture, was whitest in 
the centre at certain velocities, and when the light was strong, 
but that it was bluish when the light was moderate. The fol- 
lowing was the order and character of the tints, reckoning from 
the centre :— 


White or bluish. 

Darker blue. 

White. 

A dark ring, pretty well defined. 
White. 

Greenish yellow. 


Reddish. 


These colours vary, within certain limits, with the sensibility of 
the eye and the intensity of the light. I have sometimes observed 
the centre of the dise darkish blue, and sometimes yel/ow. When 
the velocity is great and the disc seen distinctly, there is not the 
slightest trace of colour. 

Phenomena somewhat analogous to these may be seen in the 
flame of a spirit-lamp, and in other flames, where the effect is 
caused by the shooting up of the flame, which produces success- 
ive impulses on the retina. At the top of the flame are seen 
several curves, convex upwards, like elongated parabolas. They 
are generally of a sap or olive-green colour ; and sometimes the 
most brilliant red tints appear where the uppermost curve opens 
at its vertex, and leaves two lateral and almost parallel branches. 

Colours similar to those discovered by M. Prevost have been 
recently observed by Mr. John Smith of the Perth Academy*, 
who draws from them what he justly calls many “ startling con- 
clusions.” M. Prevost and this writer have greatly misappre- 
hended the nature of these phenomena. While the Swiss phi- 
losopher considers them as “independent of the fatigue of the 
eye,” and as exhibiting a new decomposition of light by motion, 
Mr. Smith pronounces them to be “ produced by alternate light 
and shade in various proportions ;”” and he regards them “as 
proving the non-homogeneity of zether—as proving the undulatory 
hypothesis, but opposing the undulatory theory—as contrary to 
the idea of the waves of light having different lengths—as help- 
ing to explain many of the phenomena of polarization—and as 
giving a new explanation of prismatic refraction” different from 
that of Newton! 

Although we cannot adopt these conclusions, yet the phe- 
nomena, when carefully studied, as being the effect of suc- 
cessive impulses on the retina, acting in the manner which [ 


* “On the Production of Colour and the Theory of Light,’”’ Report of 
the British Association at Aberdeen, 1859, Trans. p. 22. 


Sir David Brewster on certain Affections of the Retina. 28 


have described in the Philosophical Magazine for 1834, have an 
interest of a different kind. When the luminous impressions 
succeed each other at a certain interval, the luminous disc, even 
when small, exhibits a reticulated structure like a mosaic pave- 
ment composed of distinct hexagons delineated in black lines 
(sometimes with a black spot in their centre), indicating that 
those portions of the retina are temporarily insensible to light. 
In order to see this phenomenon distinctly, we must employ 
a large dise uniformly illuminated, such as a glass globe ground 
on both sides, or a plate of ground glass. When the revolving 
dise has a particular velocity, the illumimated surface will be 
seen covered with the hexagonal pattern already mentioned ; and 
as the velocity diminishes, the pattern breaks up, exhibiting por- 
tions of circles and imperfect crosses, the exact forms of which 
it is difficult to describe. In daylight, when the light of the sky 
is used, the colours which accompany these phenomena are 
better seen, and also the variations which they undergo in refer- 
ence to the foramen centrale of the retina, as described in a former 
paper. 

When we maintain the revolving disc at that particular velo- 
eity which produces the hexagonal pattern, so that the retina 
may be greatly excited, a beautiful pattern of a very different 
kind makes its appearance, occasionally mixing itself with the 
first pattern, but most beautifully seen opposite the dark inter- 
vals between the slits of the disc when the velocity has become 
very slow, and the disc is nearly at rest. This pattern, which 
is too evanescent to permit it to be drawn, consists of a series of 

dark quadrangular spaces separated by a triple or multiple line of 

light. It has no relation whatever to the hexagonal pattern, and 
is never seen unless when the eye has been strongly impressed 
by the successive impulses of the luminous disc. 

When we observe these phenomena at different distances from 
the illuminated disc, the hexagons always subtend the same angle, 
which I have found to correspond with a space on the retina 
equal to the 420th part of an mch; and there can be no doubt 
that they are produced by a structure of a hexagonal character. 
In so far as the human retina has yet been studied, no structures 
of a hexagonal character have been discovered. In the choroid 
coat, however, in front of the retina nucleated cells of a slightly 
hexagonal form have been seen in man and in almost all mam- 
malia*; and it is not improbable that the parts of the retina 
immediately behind these hexagons may be so affected by them 
as to produce the hexagonal forms which we have described. 
With regard to the quadrangular pattern, in which the dark 


* Nunneley, ‘On the Organs of Vision,’ p. 171, and plate 2. fig. 7. 


24 Sir David Brewster on certain Affections of the Retina. 


quadrangles are separated by several parallel bright lines, it is 
obviously produced by some structure in the retina itself; and 
it is possible that it may arise from some regular arrangement 
of the rods in the columnar or bacillar layer which has not yet 
been detected by the microscope. 

The hexagonal pattern 1s very distinctly seen in the flame of 
a coal or a wood fire, at that particular part of it where the jets 
of ignited gas succeed each other at the proper interval. 

After making these experiments for some days in succession, 
I have found that the hexagonal pattern, and sometimes even the 

uadrangular one, is seen when the eye is accidentally directed 
to faintly illuminated surfaces. This fact seems to show that 
the pattern is rendered visible merely by the excitement of the 
retina with the action of hght, and not by its successive impulses, 
the black lines of the hexagons and the dark spaces of the triangles 
requiring a longer time to exiibit the action of the faint light 
than the other parts of the retina—a property which I have found 
at the foramen centrale, and at various points of the retina at or 
near the ora serrata, its anterior margin. 

As an inducement to optical observers to investigate any of the 
abnormal phenomena of vision which may come under their 
notice, I give the followimg lst of properties or structures in the 
retina which have been discovered, or are manifested, by optical 
observations. 

1. The polarizing structure which produces Haidinger’s brushes. 

2. The insensibility of the retina at the entrance of the optic 
nerve. 

3. The exhibition of the foramen centrale by its inferior sensi- 
bility to feeble light. 

4, The different sensibility to light possessed by different 
parts of the retina. 

5. The mability of the retina beyond the foramen to maintain 
a sustained vision of objects. 

6. The increased luminosity of objects seen indirectly, or by 
the parts of the retina beyond the foramen. 

7. The hexagonal and quadrangular structure described in 
the preceding pages. 

To these we may add the existence, in the vitreous humour, 
of the remains of vessels no longer required for its support, and 
the existence of cells in the same humour, as proved by the phe- 
nomena of Muscze volitantes, formerly described in this Ma- 
gazine. 


Allerly by Melrose, 
November 30, 1860. 


[ 2 | 


Ill. Proposal for a new reproducible Standard Measure of Resist- 
ance to Galvanic Currents. By M. Werner S1eMeEns*. 
[With a Plate. | 

HE want of a generally received standard measure of cur- 

rent resistance, and the great inconveniences thence arising, 

especially in technical physics, suggested to me some years ago 
the experiment I am about to describe. 

My original object was to procure for Jacobi’s stenienar a 
more eeneral introduction into the arts. I soon found, how- 
ever, that this could not be effected without convenience. On 
one occasion, several of Jaccbi’s standards that I had procured 
were so entirely at variance with each other, and their actual re- 
sistances agreed so little with what they ought to have been, 
that I should have been obliged to have had recourse to Jacobi’s 
original measure, only that it was not then at my disposal. In- 
dependently of this, however, I became convinced that a stand- 
ard measure of resistance is only adapted for general use when 
it is easily reproducible. Whether the resistance of a metal wire 
is altered by time, by the shaking of transport, by the passage 
of currents, or by any other cause, isnot yet absolutely decided. 
It is, however, very probable that some such alteration takes 
place, and it is therefore altogether inadmissible to take the re- 
sistance of such a wire as the unit-measure of resistance. More- 
over such standards being copies one of another, as must unavoid- 
ably be the case in the event of their general adoption, their 
deviation from accuracy would be continually mcreasing ; and 
for the purpose of researches which are to be conducted with 
improved instruments and with great accuracy, mere copies 
which are themselves inaccurate are useless. Besides, it would 
be very desirable and convenient to be able to unite a definite 
geometrical conception with the standard measure of resistance, 
which could never be the case with a metallic wire, since the 
resistance of a solid body depends greatly on its molecular state, 
and on the almost unavoidable impurity of the metal. 

The absolute standard measure appeared to me equally ill 
adapted to general use. It can only be reproduced by means of 
very perfect instruments, in places especially arranged for the 
purpose, and by those possessed of great manual dexterity; and 
moreover it is liable to the grave practical objection, that it does 
not exhibit itself in a physical form; and lastly, ae numbers it 
imvolves are exceedingly inconvenient on account of their mag- 
nitude. 

The only practicable method of establishing a standard mea-’ 
sure of resistance which should satisfy all requirements, and 


ee by Mr. I’, Guthrie from Poggendorff’s Annalen, No. 5, for 


26 M. W. Siemens on a new reproducible Standard 


especially which any one could reproduce with ease and with suf- 
ficient accuracy, seemed to me to be to adopt the resistance of. 
mercury as the unit. Mercury can easily be procured or ren- 
dered of sufficient, almost indeed of perfect purity. As long 
as it is fluid, it has no different molecular states affecting its 
conducting power; its resistance is more independent of tempe- 
rature than that of any other simple metal ; and finally, its specific 
resistance 1s very considerable, so that numerical comparisons 
founded on it as a standard are small and convenient. 

I therefore determined to try if it were possible, by means of 
the ordinary glass tubes of commerce and purified mercury, to 
obtain by suitable methods fixed standard measures of resistance 
of sufficient accuracy. The great difficulty seemed to be the 
impossibility of obtaining glass tubes of a form exactly cylin- 
drical. The diameter of the internal cavity of ordinary glass 
tubes generally varies irregularly. By gauging them, however, 
with a thread of mercury, some pieces of about 1 metre long 
may be selected out of a great number, the diameters of which 
vary almost uniformly. Such tubes as these may be regarded 
as truncated cones, the resistance of which ean be calculated. 
The volume of the cone filled with mercury can be determined 
with great ease and accuracy by weighing the metal contained. 

Let ABCD, Plate II. fig. 1, be such a truncated cone, rand 
R being the radu of its upper and lower circular extremities, and 
Zits length. Let MN be a section parallel to the flame AB, 
and at the distance # from it; let dx be the thickness of this 
section, and zits radius. Then,if W be the resistance of the 
cone in the direction of its axis, and dW the resistance of the 
element MN in the same direction, 


nh plac 2s 
Tz 
But m2 
o— Cer: a “fs 
i 
Therefore, differentiating with respect to 2, 
dz. dae 
a eS, 
whence 
a usp dz ; 
and by substituting this value of da in the first equation, we get 
De. te 


iy =e es 


(R—r)7 z 


Measure of Resistance to Galvanic Currents. 27 


whence, integrating with respect to z, 
alge dz l Ste 
w={ (Rr) 2? (R—r)r (-- 3) 


or l 

ee as ne te egal on a 
If, now, V be the volume of the truncated cone, G the weight 

of the mercury contained in it, and o its specific gravity, then 


V=(R?+Rr+7?) = 


3 ; 

and dividing both sides by Rr, we have 
Vv R +]+ Z ) i : 
Rr r Heo * 

Bret Sg 

or calling 72 Re bor, ae i 
EU ae; aati) an 

whence 71 es NE 3 


and putting for V its value = 


ip ss 2 


lire ‘s ig 
Peat 


which, substituted in equation (1), gives 


Thee RS lle eating daiat) 


The value of W found from this equation is obviously correct 
for every conductor of pyramidical form, as long as a represents 
the ratio of the greatest and least sections. It is moreover 
equally true when, instead of a single truncated cone of length 
/, any number of equal cones be substituted whose collective 
length is J, provided only that in each the ratio of the greatest to 
the least section, or its reciprocal, is a. , 

For in this case, if 
. l=" 
where A is the length of one of the cones, 


28 M. W. Siemens on a new reproducible Standard 


or oP Gad 
w- nro 1+/a+ /a 
or ¥ 1 
watt ptiala 
G 3 


When R and are nearly equal, the correction for the conical 
form of the conductor, viz. the factor 


differs little from unity ; whence every tube not accurately cylin. 
drical may be regarded as a truncated pyramid without netice- 
able error, the ratio a bemg determined from the greatest and 
least lengths of the mercury thread employed in gauging its 
capacity. 

By a series of experiments I now ascertained whether the cal- 
culated amount of the resistances of a number of tubes of very 
different mean sections agreed sufficiently well with the results 
of measurement. The method I pursued was as follows :— 

Glass tubes, from about 3 to 2 millims. internal diameter, were 
fastened to a long graduated scale, drops of mercury were intro- 
duced into them, and the length of the thread of mercury in the 
tube was measured. By inclining the tube under examination, 
the thread of mercury was made to pass gradually down its entire 
length; and thus every piece of tube of about 1 metre long 
which appeared most nearly cylindrical or uniformly conical, was 
detected. These pieces were then cut out of the tube, and, by 
means of a sinall apparatus constructed for that purpose by M. 
Halske, were reduced to the exact length of 1 metre. The tubes 
so prepared were then carefully cleaned. This was most conve- 
niently done by twisting together two thin German silver or steel 
silk-covered wires, inserting them through the tube, twisting a 
pad of clean cotton to the projecting end, and drawing it slowly 
and cautiously through the tube. This operation required to be 
performed with some care to avoid, breaking the tube. The tube 
was then filled with clean mercury and its contents weighed. This 
operation was conducted as follows :—One end of the glass tube 
was fastened, by means of a piece of vulcanized caoutchoue, to the 
opening of a small retort receiver, such as is used in chemical 
laboratories, so that the end of the tube projected ito the 
receiver. About the other end of the tube an iron collar was 
attached (fig. 2), by means of which a smooth iron plate could 


Measure of Resistance to Galvanic Currents. 29 


be screwed up against the mouth of the tube. The receiver was 
then properly secured and filled with clean mercury, which was 
suffered to run down the slightly inclined tube into a vessel 
placed below. When all the air-bubbles, which at first appeared 
adhering to the sides of the tube, seemed to be carried away by 
the descending stream of mercury, the lower orifice of the tube 
was tightly closed by means of the screw and plate; the tube 
was placed im a vertical position, and its upper end withdrawn 
from the caoutchouc covering. When this was done with care, 
the vertical tube was found entirely filled with a column of 
mercury which terminated in a projecting hemisphere of the 
metal. The upper orifice was next closed by pressing against it 
a glass plate ground flat, the superfluous metal being thus 
removed. The tube being then freed, by means of a brush, from 
any globules of mercury that might have adhered to its surface, 
was emptied into a glass vessel, and its contents weighed on an 
accurate chemical balance. When the precaution was taken of 
Jetting the mercury flow slowly from the tube by inclining it 
very slightly, and suffermg the air to enter gradually at the 
upper orifice, 1t was found that no globules were left behind in 
the tube, as is generally the case under other circumstances. 
Warming the tube when full by contact with the naked hands 
was of course avoided. The temperature at the time the tube 
was filled was observed, and the weight of the contents corrected 
for the difference of this above 0° C. Of the following Tables, 
Table I. gives the lengths of the threads of mercury observed in 
gauging the capacity of the tubes employed, and the ratio a of 
the greatest and least section thence determined. Table II. the 
weight of the mercury at the actual temperature, and the same 
as corrected for 0° C. 


Table I. 

1, a 3. 4 5. 6. 
125-0 | 101-2 48-2 143-0 115 111 
116-4 98-4 47-5 145-0 116 109 
115-3 96:9 450 146-0 119 107 
114-0 04:5 45-0 145 0 121 105 
112-0 94-0 44-8 143-5 121 105 
110-2 93°38 44-2 1425 122 103 
108-2 94:5 43-9 142°5 121 101 
107-0 95:7 43°7 140-0 | 120 100 
107-0 97-5 42-5 139-0 119 Lois | 
106-0 99-4 ANEOD PG 3.0536 ace ts 102 

101-1 AO cloarctin pela h a 100 
=e ie 125 | 101-2 48-2 | 146 122 | lil 
106; 933 | 401 | 139 | WS | Too 


30 M. W. Siemens on a new reproducible Standard 


And consequently the respective correction factors were-— 


| 1: 2, 3. 4. “d 6. 
| 1-:00225 | 1-00055]| 1-00282 | 1-000201] 1-000289] 1-000906 
Table IT. 
al, 2. 3. | 4, 5. 6. 


13-208 | 27-1915| 24-3825| 62-368 | 69-802 | 11-767 


13°210 | 27:1900) 24°3830| 62-366 | 69-796 | 11-768 
13:209 | 27-1915) 24-3840! 62-357 | 69°803 | 11:767 
13-209 | 27-1920) 24-3833 
at at at at at at 
Toes RE 4 RR 1S sb 1S B: 14°°7R) 15°29 


i | ee | | 


Weight in grammes at 0°. 


1. 2. 3. 4, ‘5. 6. 


13-2491 | 27:277 | 24457 | 62:774 70-057 | 11:808 


If in the formula (2) for the resistance, found above, viz. 


leh gt 
Ihrer LM ot Va 
& 3 ; 
we substitute the values of G (in milligrammes) and the correc- 
tion factor as determined by these Tables, and if we take for the 
specific gravity of mercury at 0° : 

C= 1B bod: 

and for the mean length of all the tubes 
Z=1000 millims., 


then we shall have the resistance of the tubes expressed in terms 
of the resistance of a cube of mercury 1 millim. each way. 
Table IIL. gives the values of W so calculated. 


W= 


Table IIT. 
1. 2. 3. 4, 5. 6. 
1025-54 | 497-28 | 555-87 | 216-01 | 193-56 | 1148-9 


Measure of Resistance to Galvanic Currents. 31 


The resistance of these tubes filled with mercury at 0° was 
next compared with one of Jacobi’s standards (B), by means of 
a Wheatstone’s bridge. As the bridge in question, in the form 
used by Halske and myself, is adapted to very accurate measure- 
ments, its more particular description will not be without interest. 

Fig. 3 is a perspective view of the bridge. AA is a brass 
frame on which the slide BB moves. The button C on the 
slide BB is provided with a toothed wheel, which works into a 
toothed rack attached to the frame. The slide-may therefore be 
moved either by direct pressure or by turning this button. 
Attached to the frame are the insulated pieces of metal HH, 
and the graduated scale mm divided into millimetres. Between 
the insulated pieces of metal EE, whose inner surfaces are per- 
pendicular to the scale mm, and are exactly 1000 millims. apart, 
a platinum wire of about 0°16 millim. in diameter is stretched. 
This wire, the ends of which correspond exactly with the division 
marks 0° and 1000 of the scale, is clasped by two small platinum 
rollers, whose axes are connected with the slide B by means of 
the springs G. The bodies whose resistances are to be compared. 
are inserted between the metallic band H, which can be con- 
nected by means of the contact lever I with one pole of the 
battery, and the two thick copper rods, L and L, which move 
freely in the eyes K and K. The other pole of the battery (a 
single-celled Daniell’s battery was generally employed) is con- 
nected with the slide B and the platinum roller. The eyes 
K K, and the insulated pieces EH, which serve as points of 
attachment for the platinum wire, are placed im perfect connexion, 
by means of thick copper rods, with the four plates of the plug 
reverser 8. By changing the plugs, the two resistances to be 
compared could be exchanged. The ends of the multiplying 
wire of the galvanometer employed are connected with the pieces 
of metal HH. In the following measurement I used a mirror 
galvanometer, with a round steel mirror 32 millims. in diameter, 
and 36,000 coils of a copper wire 0°15 muillim. thick. The 
distance of the scale divided into millimetres from the mirror 
was about 64 metres. 

The measurements obtained by means of this apparatus, which 
are collected together in the following Table, were for the most 
part determined by Dr. Esselbach. The method he pursued was 
as follows :— 

Hach end of the glass tube to be tested was inserted in a 
receiver, and retained there by means of a caoutchouc band. 
This receiver was so placed that the unused neck projected up- 
wards, and in this position it was, together with the tube, 
plunged into a trough filled with lumps of ice. One of these 
_ receivers was then supplied with clean dry mercury, which filled 


32 M. W. Siemens on a new reproducible Standard y 


the tube and ran through it into the other. By the time the 
mercury in the two vessels was at the same level, the tube was 
generally found free from air-bubbles. Thick amalgamated 
copper wires were now inserted into the mercury through the 
top of the receivers, and the resistance of the tube was compared 
with that of one of Jacobi’s standards by means of the bridge 
above described**. 

The resistance of the conducting rods was determined by 
plunging the amalgamated copper cylinder into a vessel filled 
with mercury. It was found to be quite evanescent in compa- 
rison with the resistance of the tubes. 

The experiments whose results are collected in the following 
Table were conducted as follows:—In the first position of the 
commutator, the slide BB was moved to such a position that, 
on lowering the contact lever I, the galvanometer exhibited no 
permanent deviation. The resistances to be compared were then 
changed by means of the commutator, and the slide was again 
adjusted. These two positions of the slide are given in the 
columns headed a and 6. If the observations were free from 
error, the sum of these magnitudes would be exactly 1000, 
which was gencrally the case, or very nearly so. We must here 
remark that, after establishing the equality of the currents, a 
small temporary deviation of several divisions, indicating a greater 
resistance on the part of the closely packed coils of Jacobi’s 
standard, was observed immediately on completing the circuit. 
As on breaking the circuit an opposite deviation of the same 
magnitude resulted, this phenomenon was obviously to be attri- 
buted to the extra current of the wire coil of the Jacobi’s stand- 
ard. It appeared, moreover, that on a long continuance of the 
current, the mercury in the tube began to grow warm, even 
though only a single cell of a Daniell’s battery was employed. 
On account of the slow oscillation of my mirror and the resist- 
ance encountered by its prolongations, the error arising from this 
cause was easily eliminated by allowing only short currents to 
traverse the instrument. The slide was always so placed that, 
immediately on completing the circuit, there was a shght move- 
ment towards the left, which, on the mercury becoming warm 
owing to the continuance of the current, gradually passed over 


* At first, instead of amalgamated copper wires, iron cylinders were used 
as conductors ; under these circumstances, however, we found that there was 
a very considerable resistance to the passage of the current from the iron 
to the mercury, even though the surface of the former was perfectly clean. 
This resistance, which was ralso considerable when unamalgamated copper 
wire was employed, was particularly strong when the cylinder had been 
some time exposed to the atmosphere after “having been cleaned, so that it 
is probable that this phenomenon is to be attributed to the gaseous con- 
densation on the surface of the metal. 


- 


Measure of Resistance to Galvanic Currents. 33 


into a deviation to the right. By again slightly altering the 
position of the slide, the first movement to the left could be 
rendered so small as to be imperceptible, and the effect of the 
change of temperature could thereby be entirely obviated. 


Table IV. 
SCE ae | 1 | ed eg 3 
a. b. a. b. a. b. 
605°7 394:3 429-1 570-9| 456 543°7 
Observed resist-] | -...... | ...... 429-0 571:1) 456-3 543-6 
Ee wot ol ld sesame. t yoteton te shecias 456°2 543°3 
epee bee) aes MPR < souk ee ee 456°2 543°6 
Mean value ...... 605°7 =| 894°3:'429-05 571:0 456-2 543°6 
DAS eS eee 1-536) ...... | OP. 0°8392 
eke anade\cns es TO16-52 |... 2 AOR 2S. ol Been: 55°38 
W 
er POOB Ys .355 HOGS PEN 1-:0008 
WwW, | | 
Ma cas. 4. | 5 | 6 
a. De | a. | b. | a. | b. 
247-6 | 752-6 227-4 | 772-8) 633-2 | 366-8 
@bseeved resist- |} i... | vce. 227°3 772°8| 633°15 || 366-85 
AMES aceon fee P| ek cnos Proce raise «Web oidae 633°10 | 366-90 
Mean value ...... 247-6 | 752-6 227-35 | 7728 633:15 | 366-85 
Ne 0-329) ...... O20 42 eon 1:726 : 
VU Re ae eee ZVITEA askces 194°7 | ee 1142-3 
W 
he O99? sn eC So 1-005 
W, | ‘ 


The line distinguished by the letter W, is found from the pre- 

ceding one by multiplication by 661°8, which number was fur- 
nished by comparing the calculated resistance of tube 2 with 
that of the Jacobi’s standard employed. The numbers in this 
line ought therefore to agree with the resistances as derived from 
calculation contained in Table ILI. The numbers in the line 
headed ue , which are the ratios of the calculated and observed 
esistomees, show that these magnitudes do not differ more than 
was to be expected. The most considerable crrors in our mea- 
surements arose from the fact that neither the temperature of the 
mercury nor that of the copper standard was constant. The 

Phil, Mag. 8. 4. Vol. 21. No. 137. Jan. 1861 D 


34 M. W. Siemens on a new reproducible Standard 


temperature of the ice-water varied between 0° and 2° C., and 
that of the standard between 19° and 22° C.; and as the con- 
ductibility of copper is diminished about 0°4 per cent. for every 
degree Centigrade, the differences in the above measurements, 
which are all under 1 per cent., are thereby fully accounted for ; 
and there can be no doubt that in this way standard measures 
of resistances can be reproduced of any degree of accuracy. 

The observed resistances in Table IV. ought strictly to have 
been diminished by the resistance of the mercury in the glass 
vessel to the spreading of the current, that is, by the resistance 
encountered by the current in passing from the orifice of the 
tube to the amalgamated copper conductors. This resistance 
may, without any considerable error, be taken as the resistance 
of a hemispherical shell, whose lesser radius is equal to the inner 
radius of the tube, and whose greater radius, on account of its 
comparative magnitude, may be taken as infinite. Now the 
resistance of a hemispherical shell of radius x and thickness dz 
being called dW, we have 


dx 


whence 
(ee) 
re { dx 1 r 


20° Qra Orta 

The resistance to the spreading of the current in the mercury at 
both ends of the tube is therefore equal to the resistance of a 
portion of the tube whose length is half its diameter. This 
resistance ought to be still further increased, because the surface 
of the mercury in the tube is flat and not hemispherical, as is 
assumed in the above calculation ; but these two sources of error 
are each of them so trifling, that their jomt effect may be 
neglected. 

The straight tubes used in the experiments hitherto described 
cannot be very conveniently employed as standards; I therefore 
got M. Giessler of Berlin to make me some spiral glass tubes, 
having their extremities turned up and provided with small ves- 
sels in which to receive the conducting wires. ‘These glass spirals 
were fastened, as shown in fig. 4, into the wooden cover of a 
broad glass vessel filled with water. The temperature of the water 
in the vessel was observed by means of a thermometer introduced 
through an opening in the cover. The glass spirals were easily 
filled with mercury, so as to be free from air-bubbles, in the follow- 
ing manner :—The orifice of the tube in one of the glass vessels 
was first stopped by means of a suitably shaped cork; the other 
vessel was then filled with mercury, the air being suffered to 
escape gradually by the cork at the other end, which was only 


Measure of Resistance to Galvanie Currents. 35 


removed when the mercury had slowly passed entirely through 
the windings of the tube. | 

As mercury is not to be found in the list of metals the altera- 
tion of whose specific resistance by heat has been determined by 
Arndtsen*, this deficiency had first to be remedied. This was 
effected by Dr. Esselbach, by means of the apparatus already 
described. The resistance of one of the spiral tubes was com- 
pared with that of the straight tube 2, first at the temperature 
of ice-water, and then when the temperature of the spiral was 
raised. If w represent the resistance of tube 2 (which according 
to Table III. is 498-7), and w, the resistance of the spiral tube, 
then, since the resistance of the conducting wires was rendered 
equal for both tubes, and was equivalent to that of 11 cubes of 
mercury 1 millim. each way, we had 


wt+ll oa 
w+ll 8 
where a and & represent the pieces of platinum wire of the bridge 


when no current passed through the galvanometer. This was 
the case when 


a_ 8113 
b- 688°7’ 
whence w = 219°4, 


The temperature of the straight tube was now maintained at 0° 
by means of melting ice, while the temperature of the water sur- 
rounding the spiral was raised. In the following Table, ¢ indi- 
cates the temperature of the straight, and ¢, of the spiral tube, 
a and b the lengths of wire read off when the currents were equal, 
y the required coefficient calculated according to Arndtsen’s 
formula, 

w(l+yt)+ll_a@ 

w(l+y)+ll 68 


Table V. 
te ae a. b. UP 
0 47-0 C. | 8204 679:5 | 0-000964 
0 34:5 318-0 682-0 | 0-000960 
0 165 3146 685-4 | 0:000981 


From this it appears that, of all simple metals, mercury is 
that whose resistance is least increased by an increase of tempe- 
rature. 

By means of the coefficient y, the resistances of the two other 
spirals A and B were determined, which were afterwards used 

* Poggendorff’s Annalen, vol. ci. p. 1. 
D2 


36 M. W. Siemens on a new reproducible Standard 


in constructing a standard of German silver wire. The resist- 
ance of spiral A at 0° was 514°45, that of B 673°9. 

German silver wire is very well adapted for standards of resist- 
ance, because its conducting power is very small, and varies little 
with the temperature; according to Arndtsen, only about ‘0004 
per cent. for a degree Centigrade. 

In the foregoing experiments, the resistance of a cube 1 millim. 
each way has been assumed as the unit. ‘or small resistances, and 
especially in calculation, this has many conveniences. It appears, 
however, more advisable that the measure of resistance should 
be in entire agreement with the ordinary metrical scale. I 
therefore determined to take as the unit of resistance,— 

The resistance of a prism of mercury 1 metre long and 1 millim. 
in section at the temperature O° C. 

If this proposal be generally acted on, all resistances can be 
at once reduced to the metrical seale. very experimenter will 
then be able to provide himself with a standard measure as accu- 
rate as his instruments permit or require, and to check the varia- 
tions of resistance of the more convenient metal standard. Of 
course also, in that case, the conducting power of mercury must 
be taken as the unit of conducting power, and not that of copper 
or silver. Unfortunately but few comparisons have been made 
between the conducting power of mercury and the solid metals, 
from which a table could be calculated in which the conducting 
power of mercury should be the unit; and in most of the com- 
parisons that have been made between the conducting power of 
the solid metals, it is not stated whether the wire employed was 
cold drawn or annealed. From the following Table, however, it 
appears that the conducting power of annealed wire is consider- 
ably greater than that of unannealed. 


a 2. 3. ° 4. 5. 6. 
Gaerne oe +, Weight in : : Conducting 
pecies of wire. Length in) ai. Specific Resistance! power, that 
millims, peace gravity. at 0° C. | of mercury 
TL Salver, hard ...5..0005: 4014:4 | 4884-9 | 10-479 | 614:55| 56-252 
Pe) BRNEDIED, ” chains. 4014°4 | 4889-1 | 10°492 537°2 64:38 
RS SC Ts Ge a ee -| 4014:4 | 3233-1 | 10502 896°1 58-20 
4° sa@nnealed Vin. 40144 | 8009°6 | 10:5132) 889-08} 63°31 
Se Coppers ard ss. ps0 oSss- 4014°4 | 3099-5 8-925 $90:5 527109 
A. MOTE coe. sajannees 4014-4 | 4409-1 8916 | 622-7 52-382 
” annealed ...... 4014-4 | 43855:2 89038 599-05 | 52-013 
5 ” BATE 3 cicccsesst 2007°2 | 1260-4 8-916 545'8 52°217 
” annealed ,..... 2007:2 | 1252-7 8-894 517 55°419 
eas |e ae ee RA 2007-2 | 1263-2 8 916 545°6 52:12] 
* annealed ...... 2007°2 | 1241°5 8-894 520°8 55°338 
7. Platinum, hard ......... 436-4 | 544-1 | 21-452 | 9106 8-244 
Bi. 354) hat ii. 436-4 | 550-1 | 21:452 897:7 8:27 
O..BPass; HAA o. yass ge sh: 1003°6 | 1406-1 8473 530°6 11-439 
»  annealed.........| 1003°6 | 1397°8 8:464 | 451:7 13:502 


Measure of Resistance to Galvanic Currents. 37 


It appears from this Table that the specific conducting power 
of annealed silver wire is ]0 per cent. greater than that of the 
same Wire unannealed; that of annealed copper wire on the 
average 6 per cent. greater. The difference of conducting power 
is especially great in the case of brass. As the density of wire 
depends on the amount it has been stretched since the last heat- 
ing, that, as well as the conducting power, must vary much even 
when the metal is perfectly uniform. The temperature to which 
the wire was raised, the duration of the operation, and the 
rapidity of the cooling, all affect its specific conducting power. 
Column 5 of the above Table was calculated by means of the 
formula 


Peal 
or Fg tt a+ Te 
ti eas ane 
Bat Sr I 
at/a+ ee : 
The eee the correction for the conicality of the 


conductor, may, in the case of metal wires, be almost always 
neglected, since it never differs sensibly from unity. This method 
is obviously much more exact than that hitherto employed, in 
which the mean diameter of the wire had to be determined by 
direct measurement; and the square of the magnitude so obtained, 
which was never exact, entered into the calculation. By my 
method all the data may be determined with great accuracy, 
especially the length of the wire, which alone enters in the 
square. 

_ If the above Table be compared with that of Arndtsen, it 
appears that the mean conducting power of unannealed platinum 
wire, viz. 8-257, and the smallest value found for unannealed 
silver wire, viz. 56°252, are exactly m the ratio given by Arndatsen ; 
while the resistance of copper wire according to Arndtsen, agrees 
pretty well with that of annealed copper in the above Table. As 
the silver and platinum wires employed both by myself and 
Arndtsen were chemically pure, I have in the following Table 
taken the resistance of platinum and hard silver as a standard. 
The values taken from Arndtsen’s Table are indicated by an A, 
those observed by myself by an 8S. 


38 Ona Standard Measure of Resistance to Galvanic Currents. 


Table VI. 


Conducting power of the metals at the temperature ¢ compared 
with that of mercury at 0° C. 


1 
Mercury . 1+0:00095 .z (S). 
5°1554 
Lead ° 2 e e ° ~ ° 1+0:00376.¢ (A). 
8:257 
Platinum : ° ° 3 < e 1+0-00376.t (A. S). 
8°3401 
Iron ss + + + + + 740:00413.¢4-0-0000082718 (A). 
10°532 
ae T£0-000887.4—0-000000557.2 (A): 
annealed 4:°137 (S). 
Brass, hard << 4...) -s gla ws): 
7, annealed. : >". “her oue tO) 
14249 em, 
A 2 © 1 -0'00166.4—8-00000208.F- . 
Anca 31°726 
wea 1 +0-003638.¢° 
Ceppe: T+0003682 ‘4: 
% us beards. soa ‘dst: D2 ROARS). 
Be uannedied.. ay 2s. «is. Do eoo Ws). 
Silver, hard . OO ES aac AG 


1+0-0003414:.z 
yr) wannedleds:: o;!. 64°38 (8S). 


For convenience I have given Arndtsen’s results, together 
with the coefficients for correcting the resistances for the tempe- 
rature. Whether these are the same for annealed and unannealed 
wires I have not been able to determine. The brass that I experi- 
mented on was found on analysis to consist of 29°8 per cent. 
zinc, and 70:2 copper. 

In conclusion I should mention, for the benefit of those who 
may wish to make standard measures of resistance in the manner 
here described, that it 1s necessary to warm the mercury to be 
employed for several hours under a covering of concentrated sul- 
phuric acid mixed with a few drops of nitric acid, to get rid of 
all metallic impurities, as well as the free oxygen, which greatly 
increase its conducting power. 


[ 389 ] 


IV. Remarks on Mr. Harley’s paper on Quintics. 
By G. B. JeRRarp. 


[Concluded from vol. xix. p. 274.] 


4, ‘ey my former paper I contented myself with showing, from 

a comparison of certain results at which Mr. Harley had 
arrived, that there were decisive marks of the existence of an 
error in his processes, leaving to him and Mr. Cockle the task 
of tracing the error to its source. But after the lapse of man 
months they have as yet failed to perform the part thus fitly 
assigned to them. ‘This is the more remarkable, as, in answer 
to an attempt made by the latter mathematician to infer the 
failure of my researches from the failure of theirs, I said at the 
time, in a postcript to my paper, what ought, I think, to have 
suggested to their minds the true origin of their error, and 
thence have shown them the irrelevancy of the objections urged 
against my method of solving equations of the fifth degree. 
Mr. Cockle, however, not seeing the meaning of my words, still 
adheres to his objections. I must now, therefore, abandoning 
suggestions the drift of which may escape observation, have 
recourse to statements of the plainest kind. 

d. If I were asked in what respect the method first explained 
by me in the Philosophical Magazine for June 1845, and after- 
wards given at greater length in Chapter II. of my ‘ Essay on 
the Resolution of Equations*,’ differed from all other methods 
constructed for the purpose of solving equations,—on what, while 
all these were seen to have failed, I grounded my hope of success, 
—I should answer by pointing to the theorem + 


Onflab)(ea) = 
EC, trae oH Ona, + Ux.) (ab) (¢ d) a8 
if On, Kad)(ea).. =45(O), ,) (ab) (ed) “e 


or 


(v) 


On, s(ab) (ed). = 


5 (aut Bayt Mo, +a, + oe)(ab) (ed) 


if On, “ab)(ea).. =U"(O,, ) (ab) (ed) one 


From this theorem we learn that, in constructing equations 


~ 3 r) 


* Published by Taylor and Francis, Red Lion Court, Fleet Street, 


London. 
t ‘Essay,’ p. 75. 


40 Myr. Jerrard’s Remarks on My, Harley’s paper on Quinties. 
between functions of the form 
On, f(ar)(e4) 


and those of the class 
u in 
(t,t Vagt. BeOS) aa 


a complex process of a peculiar character must take the place of 
the simple method of substitutions. 
Thus from (v,) we see that 


©, esas) =n, BE) (18): 


and analogously from (w,), that 


©0090) Ond Be) (12) § 


in each of which equations the © of one member is accented 
differently from the © of the other in consequence of a transfer 


of ©! and ©” from branch to branch for the affix (Be) (78). 
This shows the necessity of carefully distinguishing between 


On, gab)(ea).. and (@,, 7) (ab) (ed) tS 


if we would avoid admitting relations among the roots through 
equations of the class 


(BM AE)(1) = On, Be) (12)- 

I might go on to elicit other properties of the theorem (vy, w), 
but what I have already said is, I think, sufficient for my purpose. 

6. Turning now to Mr. Harley’s paper, I find that the very 
existence of the theorem (v, w) is ignored. No wonder then 
was it—where so much circumspection was needed, and such a 
safeguard against fallacies as the theorem (v, w) was flung aside 
—that he as well as Mr. Cockle fell into error. 

7. But Mr. Cockle, not reflecting that the functions 


Pn(L1, Lay + +25) Xn(#yy Loy +» 5) 

(wherein z,, 2,..@, are known to be such as not to involve any 
irreducible radical of the form 4/2, while z,, 2,..2, are not 
proved to be subject to any condition) do not come within the 
scope of Lagrange’s theory for expressing one of two hLomoge- 
neous functions of the roots of a given equation in rational terms 
of the other, attempts by means of that theory to apply cbjcctions 
drawn from the failure of the method given m Mr. Harley’s 

aper to the method of solution in my ‘ Essay.’ The nature of 
Mr. Cockle’s second error is now manifest. He implicitly assumes 


On the Principles of the Science of Motzon. 4] 


as a direct consequence of Lagrange’s theory, that he is permitted 
to express* 

Xn(@1s Lo; ++ Ws) 
as a rational function of 


PD, (21) Vay «+ Xs) 


Such an assumption is clearly inadmissible. It is not a little 
remarkable that a most striking confirmation of the validity of 
my method may be derived from that very theory +. 

8. Again, the objection which he urges against a statement of 
mine in reference to Taylor’s theorem, is founded on a misap- 
prehension of my meaning. The statement relates to equations 
of conditiont. But Mr. Cockle, ignoring their existence, speaks 
of a remainder. It would be easy, from what has been said in 
art. 7, to show the irrelevancy of the rest of his objections. It 
seems needless, however, to proceed further. 


December 1860. 


VY. On the Principles of the Science of Motion (Mechanics, 
Physics, Chemics)§. By J. 8. Stuart Guenniz, M.A. 


1. ii is proposed in the following paper to give a brief intro- 

ductory exposition of the conceptions by the analytical 
application of which it has been found that the laws and methods 
of mechanics can be more fully applied to the phenomena of 
physics and chemics. 

2. In order that mechanical principles may be rigorously ap- 
plied to physical and chemical phenomena, it seems clear that 
physical and chemical forces must be conceived in the same way 
as mechanical forces. Now a mechanical force, or the cause of 
a mechanical motion, we know to be, in general, the condition of 
a difference of pressure. Whether the motion is uniform, or 
accelerated, depends on whether the force, or difference, is in- 
stantaneous, or continuous. And whether that difference is 
between polar or extreme pressures, depends on whether the 
moved body transinits pressure with, or without, a tangential 
resistance. Hence the condition of the translation of a solid is 


* See his paper in the Philosophical Magazine for March 1860. The same 
error runs through all his subsequent papers on the subject of equations, 
and thus renders nugatory every objection based on Mr. Harley’s paper. 

+ Compare arts. 107; 112 of my ‘ Essay.’ 

~ See note on art. 44 of my paper for June 1845. 

§ Communicated by the Author, being a restatement of principles 
enounced in papers read at the two last Meetings of the British Associa- 
tion, and of which abstracts have been published in the ‘ Reports’ for 
1859 and 1860 (Trans, of the Math. and Phys. Section). 


42 Mr. J. S. Stuart Glennie on the 


a difference of polar pressures ; and of the motion of a fluid, a 
difference of maximum and minimum pressures; and similarly, 
it is evident that the causes of the other mechanical motions are, 
in fact, conditions of pressure. Thus, rotation is the effect of 
equal, a compound motion of translation and rotation of unequal, 
differences of polar pressures in opposite directions with respect 
to a line joining the points of application of each pair of polar 
pressures. It need hardly be said that it is not proposed that we 
should use the phrase “ differences of polar pressures” instead 
of the term “ forces.”” But, preparatory to a mechanical considera- 
tion of physical and chemical motions, it seems of importance 
clearly to see that, whatever force may be absolutely, whatever the 
unknowable ultimate cause of motion may be, or have been, the 
ordinary mechanical forces* called “a single force at the centre 
of gravity,” ‘a couple,” and “a single force not at the centre of 
gravity,” are, in fact, such conditions of pressure as above stated. 

3. Thus, as the cause of a mechanical motion is, in general, the 
condition of a resultant difference of the pressures on the moved 
body, and as the general law of the motion of the body is, that 
it is in the direction of the greater of the two opposed resultant 
pressures, if the great object of modern physical research is 
accomplishable, it must be attained by showing that physical 
forces are, like mechanical forces, conceivable as differences of 
pressure under certain characteristic but interchangeable con- 
ditions, and that, for instance, the movement of iron towards a 
magnet, or the movement of a paramagnetic body towards a 
place of stronger action, are motions in the direction of least 
resistance. And there is evidently this further condition of a 
general mechanical theory of physical and chemical phenomena 
—that pressure be, in physics and chemics, conceived, as in 
mechanics, as “a balanced forcey,” or “momentum virtually 
and not actually developedt.” Hence it appears that, if a 
general mechanical theory is possible, the ultimate property of 
matter must be conceived to be a mutual repulsion of its parts, 
and the indubitable Newtonian law of universal attraction be 
herefrom, under the actual conditions of the world, deduced. 

4. The general experimental condition of the fitness of the 
mechanical conception of pressure as the basis of a general phy- 
sical and chemical theory, evidently is that there be a plenum. 


did Toutefois, e’est une chose trés-remar quable, qu'un méme livre, écrit 
sur la science des forces, pourrait, sans cesser d’étre exact et de traiter régu- 
lerement laméme science, étre entendu de deux maniéres différentes, selon 
qu’on attacherait au mot de force Vidée d’une cause de translation, ou 
Vidée toute différente d’une cause de rotation.’’—Poinsot, Théorie Nou- 
velle de la Rotation des Corps, p. 13. 

+ Rankine, ‘ Applied Mechanics.’ 

{ Price, ‘Treatise on Infinitesimal Calculus,’ vol. iu. 


Principles of the Science of Motion. A3 


But such discoveries as that the tangential force of a resisting 
medium is given in the very formule of Encke’s comet*, and 
that of inductive action through contiguous particles, and not at 
a distance}, will, it is believed, cause this first postulate of the 
theory to be generally granted f. 

5. To give distinctness to this idea of the parts of matter as 
mutually repulsive, a molecule, or a body (an aggregate of mo- 
lecules), is conceived as a centre of lines of pressure ; the lengths 
and curves of these lines are determined by the relative pressure 
of the lines they meet ; and lines from greater, are made up of 
lesser molecules and their lines, and so on ad infinitum. 

In speaking of a molecule or body as such a centre of pres- 
sure, it will be convenient to have a technical name. Rather 
than coin a new term, it is proposed to use “atom” in this 
sense. In chemistry I shall use the term “ equivalent ” exclu- 
sively, and not, as at present, as more or less synonymous with 
“atom,” which I have thus ventured to appropriate for a new 
conception. Atoms, or mutually determining centres of lines 
of pressure, may also be defined, and their relations analytically 
investigated, as mutually determining elastic systems with cen- 
tres of resistance. 

6. This is the fundamental conception (not hypothesis) of the 
theory. What can at present be called hypothetical in the 
theory, is this only—that the application of analysis to the con- 
ception of elastic systems with such conditions, will in all cases 
give results corresponding with phenomena. An atom, as above 
defined, is the postulate of a conception, not of an agent, of a 
relation, not of an entity. And this conception, it is believed, 
distinguishes the theory from the many others of which the 
general object has been the same§. Butin this attempt to found 
a general theory cleared of ethers and fluids, of properties and 
virtues, the author owes whatever there may be of truth in its 
present imperfect form and incomplete application, chiefly to 
the discoveries of the immortal ‘ Experimental Researches ;’? and 
the constant endeavour has been to work out the theory in the 


* Ueber die Evxistenz eines widerstehenden Mittels im Weltraume, 
von J. F. Encke, p. 52. Berlin, 1858. 

+ Faraday, ‘ Experimental Researches,’ Series I., II., IV., IX., XI, 
XII., XIII. 

t See also on this point Humboldt, ‘ Cosmos,’ iii. 33; and compare 
Newton’s third letter to Bentley; the old aphorism, “‘ Nature abhors a 
vacuum,” and Grove’s remark thereon, ‘ Correlation of Physical Forces.’ 
And see Bacon, Nov. Org. i. 8. 

§ But compare the conception of an atom by Boscovitch, in his The- 
oria Philosophie Naturalis redacta ad unicam legem virium in Natura 
existentium. Venetiis, 1763; and Faraday, in his ‘ Experimental Re- 
searches,’ ili. 447. Also Seguin’s memoir, Sur l’origine et la propagation 
de la force, aud his Considérations sur les causes de la cohésion. 


4.4, Mr. J.S. Stuart Glennie on the 


spirit of such remarks as these :— What we really want is not 
a variety of different methods of representing the forces, but the 
one true’physical signification of that which is rendered apparent 
to us by the phenomena, and the laws governing them. Of the 
two assuraptions most usually entertained at present, magnetic 
fluids and electric currents, one must be wrong, perhaps both ave 

. It is evident, therefore, that our phy sical views ave very 
doubtful ; ; and I think good would result from an endeavour to 
shake ourselves loose from such preconceptions as are contaimed 
in them, that we may contemplate for a time the force as much 
as possible in its purity*.” 

7. Now, in asystem of atoms as above defined, let the centres 
be of equal mass, and at equal distances; there will be no dif- 
ference of pressure on any one centre, no moving force will be de- 
veloped, and the conditions of equilibrium will be satistied. But 
it is clear that forces will be developed, or the general conditions 
of motion be fulfilled, either (a) by a difference in the masses of 
the centres, or (8) by a difference in the distances of the centres, 
in consequence of a displacement of any one of them, or (y), 
supposing a state of dynamic equilibrium established in the 
system, by its being brought in contact'with another system in 
a different state of such equilibrium. 

8. Consider more particularly the first of these conditions of 
the development of a force, and with the postulate that the pres- 
sures of atomic lines are directly proportional to the mass of the 
atomic centre, and inversely to the square of the distance there- 
from. But observe that this last property is conceived to arise, 
not from an absolute change in any individual line, whatever its 
distance from the centre, but because, from the lateral expansion 
of these lines, fewer will, when such expansion is unresisted, be 
cut at a greater than at a lesser distance by the same surface. 

In a system of atoms in which there is a difference in the 
masses of any one or more centres, and in which the law of the 
pressure of the atomic lines is as above, any two masses, whether 
unequal or equal, will tend to approach. 

And first, let the masses be unequal. 

Then the pressure of the lines from the one is greater than 
that of the lines from the other; consequently these lines will 
be mutually deflected, and hence the centres approach. 

Let the two masses be equal. 

Then, if all the masses of the system were equal, and all at 
the same distance from each other, their mutual repulsions would 
be equal in all directions, and they would remain at rest. But 
if, though two masses may be equal, either has, on the other 
side of it, a mass of a greater size, or at a,greater distance than 

* Faraday, ‘ Experimental Researches,’ vol. ii. p. 5380. 


Principles of the Science of Motion. A5 


the other, it is evident that the mutual pressures of these two 
equal masses will, under such conditions, be unequal, and hence, 
as in the first case, they will approach. It is also evident that 
a body may thus cause the approach to itself of another body, 
whatever the number of interposed bodies. 

9. Thus, if the conception of atoms is applied to the unequal 
and unequally placed bodies of such a world as that presented 
to us, the law of universal attraction follows, and gravity 1s 
mechanically explained, that is, referred to a mechanical con- 
ception. 

But it must be understood that the above proposition is given 
rather to show that, as an actual law, universal attraction may 
be deduced from the theoretical conception of universal repulsion, 
than with any pretension to its being the best attainable form 
of an explanation of the law. It may, however, be remarked 
that such an explanation is in accordance with the chief charac- 
teristics of the force of gravity: it is not polar; and it seems to 
be so far different in kind from other physical forces, that it is 
not interchangeable with them, as they are among each other ; 
for the attraction of gravity is thus referred to difference of 
mass, either between the two attracted bodies, or in the system 
of which they are parts. And other attractions, as will presently 
appear, are referred to differences of tension, or of dynamic equi- 
librium ; and such conceptions do, though that of difference of 
mass does not, involve polarity. 

10. Consider now the second (8) of the above-stated (7) 
general conditions of the development of aforce. And, to fix our 
thoughts, let the system consist of three, and not of an indefinite 
number of bodies. That it must consist of at least three bodies, 
will be evident from the general reasoning of this theory; for 
the fundamental difference between the established and the pro- 
posed conception of a force is this:—a cause of motion is ordi< 
narily defined as “an action between two bodies ;” it is here 
conceived as a differential action between three bodies,—a concep- 
tion, it is submitted, equally defensible by metaphysical reason- 
ing and by physical experiment. 

11. The displacement of a molecule, conceived as an atomic 
centre, may be evidently under such physical and analytically 
expressible conditions as to cause such displacement to be per- 
manent or alternating. The first gives the conception of tension, 
by which electric and magnetic, the second that of vibration 
and undulation, by which optic and acoustic, phenomena are ex- 
plained. 

Let the conditions of the displacement of the molecular centres 
of lines of pressure be such that they are (and consequently, 
the body they constitute) in a state of tension. 


46 Mr. J. S. Stuart Glennie on the 


12. The theory of electricity here proposed is the develop- 
ment of the idea of the tension of atoms as above defined. Hence 
it is an immediate, not a mediate, mechanical conception of the 
phenomena ; for the conceptions of atoms or of centres of lines 
of pressure are not hypotheses, but convenient forms of the 
general conception of the parts of matter as mutually repelling. 
And the ground of the theory is this, that if matter is so con- 
ceived, experimental facts may themselves at once, and with- 
out the aid of hypothetical virtues or ethers, be mechanically 
conceived. For the theory has arisen from finding that the 
more simply facts were worded the clearer expressions they 
became of the general laws of motion; and that hypotheses 
only obscured the meaning and necessity of the relations of 
phenomena. It should therefore seem to be here sufficient 
briefly but clearly to express the conception of tension in its 
general relations, without entering into any detailed explanation 
of how it applies to different phenomena; for if there is any 
truth in the theory, such application ought at once to appear to 
those who can look at phenomena, and not at their hypothetical 
representations only, at least admissible. The clear proof that 
phenomena can be thus immediately (from a general conception of 
matter, and without aid of hypotheses) mechanically conceived, 
rests, of course with analysis, on the data of recorded and fur- 
ther experiments. 

13. Little more, therefore, will here be offered than prima 
facie evidence of the truth of the theory. The above considera- 
tions suggest that this may perhaps best be given by a state- 
ment of those general mechanical conceptions of (I.) the nature, 
(II.) the states, and (III.) the effects of electricity, which appear 
to be rather inductive generalizations of phenomena than hy- 
potheses by which they are to be explained. A few experi- 
mental facts will be recalled under each head, but rather as 
suggestive of others than as by any means exhaustive of those 
which might be cited in support of these generalizations. 

14, As to (I.) the nature of electricity: it is conceived as a 
permanent (not alternating) displacement of molecular centres of 
lines of pressure. Hence duality and polarity. For by such 
displacement there is evidently a tendency to produce motion 
of opposite characters in opposite directions ; the pressure of the 
lines being increased in the direction of displacement, and cor- 
respondingly diminished in the opposite direction. Hence also 
the identity of the various forms in which electricity may be de- 
veloped; the various conditions of such displacement differing only 
in intensity and quantity; and these being inversely as each other. 
For if intensity is conceived as amplitude of displacement, it is 
clear that, as the condition of a great displacement of a centre of 


Principles of the Science of Motion. A7 


lines of pressure is evidently the resistance or non-displacement 
of the centres of one or more of the limiting atoms in the direc- 
tion of displacement, the more equally and quickly displacement 
of one atomic centre causes displacement of all neighbouring 
centres, the less will be the amplitude attained by the originally 
displaced molecule. 

15. The fitness of the conceptions here offered of the nature 
and states of electricity will appear chiefly in the proof of the 
generalizations to which they lead of the effects of electricity. 
But the above view of the nature of electricity is also founded 
on such facts as these. The “sources de l’électricité*,”’? mecha- 
nical, thermal, or chemical, are all motions, or conditions of 
displacement. These motions are of different momenta. Com- 
pare facts as to the heterogeneousness of the bodies in frictional 
and thermal electricity ; and as to their compound character in 
chemical electricity, interpreted by the theory of the chemical 
constitution of bodies hereinafter enunciated. In reference to 
the above conception of the difference of electricities, compare 
facts proving “‘ the identity of electricities derived from different 
sources},” and, more particularly as to intensity, the various facts 
defining the correlative conceptions of insulation and discharge. 

16. (IL.) The states of electricity are thus conceived. (1) In 
a statically electrified body, the tension, or displacement of the 
molecular centres of pressure, is in closed curves forming the 
surface of the body, and the direction of displacement is either 
outwards (positive) or inwards (negative) ; and it seems demon- 
strable that there will be such a displacement only on the surface 
of the body. 

“17. Compare such facts as :—it is the least resisting of two 
rubbed bodies that is found negatively electrified ; if an elec- 
trified sphere is hollow, there will be little or no electricity on the 
inner surface, &c. 

18 Two conditions have been well distinguished by Ampéref 
in (2) dynamically electrified bodies—that of “ courant ouvert,” 
and that of “courant fermé.’”’ The former is conceived as a con- 
dition of longitudinal, the latter of transverse or spiral tension. 
Hence a polarity corresponding to the duality of statically 
electrified bodies. For electric poles are conceived as extremi- 
ties towards, and from, which molecular centres of lines of pres- 
sure have been moved, at which, therefore, there is not only a 
change in the mechanical relations to outward atoms of the lines 
of pressure from these extremities, but a change at the one ex- 
‘tremity of increase, at the other of diminution, of pressure. And 


* De la Rive, Traité de l Electricité, cinquiéme partie, 1. 456—828, 
ft Faraday, ‘ Experimental Researches,’ Series IV. 
t Ampére, Théorie des Phénoménes Electrodynamiques, Paris, 1826. 


48 Mr. J.S. Stuart Glennie on the 


thus a magnet is conceived as a body the molecular centres of 
pressure of which are transversely displaced about an axis 
joining its poles. 

19. As has been said, the fitness of conceptions of the nature 
and states of electricity is to be proved chiefly by their explana- 
tions of the effects of electricity; but note also, in support of 
these conceptions of current electricity, such facts, as to the 
origin of open currents, as that mere difference in the motions of 
metals in contact develope in them electric currents ; and, as to 
closed currents, note that the experimental conditions which de- 
fine a closed current, and the facts as to the molecular structure 
of magnets, however much they may still require investigation, 
seem already to justify a conception of magnetism wholly re- 
ferable to conditions of mechanical action and resistance—a 
conception the antithesis of that which “associates”? with bodies 
‘latent virtues’ and “neutral fluids,”’ and a conception which 
evidently differs also, though with respect, from the later 
theories in which mechanical principles are applied, not imme- 
diately to phenomena, but to, as it should seem, needless hypo- 
theses of “ zthers*.” 

20. (III). The effects of electricity may be generalized under 
these heads :—(A) induction; (a) msulation; (() discharge ; 
the latter distinguishable into (1) conduction ; (2) eleetrolytic 
discharge ; (3) disruptive discharge ; (4) convection, or carrying 
discharget: (B) motion (@ of bodies; conveniently classed as 
(1) ordinary attractions and repulsions; (2) paramagnetism 
and diamagnetism; (3) right- or left-handed deviations or ro- 
tations ; (8) motion of the medium, including heat and light, 
&c. vibrations. 

21. (A) Induction is conceived as the necessary mechanical 
consequence in a plenum of the displacement of centres of lines 
of pressure. For it is clear that, if the parts of matter are con- 
ceived as mutually repelling, and such repulsion is mechanically 
conceived in such forms as those above suggested—as the elas- 
ticity of atomic centres, or as lines of pressure from molecules, 
—the displacement of the molecules forming a line of centres 
of pressure implies a disturbance of the previously existing me- 
chanical relations, not only at the extremities of, but ail round 
such a line of displacement; and such a conception implies, 
further, that the character of such disturbance depends entirely on 
the relations between the direction and intensity of the original 


* T would desire more especially to express the diffidence and respect 
with which I venture to differ from Professor Challis as to the necessity 
or advantage of the fundamental hypothesis of his theory. See Phil. Mag. 
February, October, and December 1860. 

ft Faraday, ‘ Experimental Researches,’ Series VII. 1319. 


Prineiples of the Science of Motion. 49 


displacement and the varying resistance offered by the diverse 
conditions of motion and aggregation of opposed centres of lines 
of pressure. 

22. Now, as to the facts which justify the proposal of this 
conception as a true generalization by which mechanical principles 
ean be immediately applied to the phenomena of induction, it 
may be remarked that, as the full proof of such a conception 
depends on an experiraentally based, and analytically expressed, 
mechanical theory of the constitution of bodies, it is only sur- 
prising that, while so little has been done towards the establish- 
ment of such a theory, the general conclusions of researches on 
induction, independent of, or with wrong, theories of chemical 
constitution, should go so far to make induction mechanically 
conceivable. Among such conclusions, each of which will call 
up avast number of experimental facts, may be mentioned :— 
Induction is the origin and effect of all electrical phenomena; 
and is an action, not “at a distance,” but “through contiguous 
particles”’ in lines of any curve. Insulation and discharge, or 
conduction, are differences only of degree; and bodies have 
specific mductive capacities which are but degrees of resisting 
power. The degree to which particles are affected before dis- 
charge constitutes intensity; and; in order to discharge, inten- 
sity must be raised much higher for a solid than for a fluid, and 
higher for a fluid, than for a gaseous, dielectric. An electric 
current has not only polar, but lateral, inductive effects; and 
the “lines of force” about a magnet take the form of a 
“sphondyloid.” As to such facts as that gases, having the 
same inductive capacity, differ in insulating power, and that the 
effect of a magnet on a body without it is not affected by great 
rarefication of the medium (or a vacuum), their explanation more 
particularly depends on a mechanical theory of the constitution 
of bodies, and the principle that the character of inductive effect 
depends on the conditions of molecular motion and aggregation 
of the body acted on. 

23. The general principle by which this theory gives a common 
explanation of the above classified (B) («) motions of bodies in 
presence of an electrified or magnetized body, is that the mechant- 
cal motions of bodies in such circumstances are effects of differ- 
ential molecular displacement ; or, as it may be otherwise ex- 
pressed, if, of two bodies, one resists molecular displacement 
from a centre of disturbance less than the other, the former 
moves towards that centre as a direction of least resistance. 
For it is evident that if a force has its full effect in a molecular 
displacement, the body will, as far as the direct action of that 
force is concerned, remain at rest; and that if the molecules of 
a body resist displacement, the force will have its effect in the. 

Phil. Mag. 8. 4. Vol. 21. No, 187. Jan. 1861. 1D 


m4 


50 Mr.J.S. Stuart Glennie on the 


repulsion of the body. Molecular and bodily motion, or resist- 

ance thereto, are inversely as each other. Hence, if a force has 

more effect in producing molecular displacement in one body | 
than in another, the difference will be seen in a tendency to repel 

this second body, the reaction of which will evidently urge the 

first towards the centre of force. | 

24. A corollary of this theorem is, that electrified bodies 
of which either the molecular tension or the inductive lateral 
disturbance is in the same direction approach; or, as it may be 
otherwise more concretely expressed, opposite poles, and similar 
currents, attract. For it is evident that, when the directions of 
the molecular displacement of two bodies are in the same line, a 
point of increased, is opposite a point of diminished, molecular 
pressure. Hence, transmission of similar molecular displace- 
ment from the one is in this position less, in the opposite, more, 
resisted by the other than by the medium. And hence, as 
above, attraction in the former, and repulsion in the latter case. 

Further, it is evident that, according as two parallel currents 
or lines of tension are in the same, or in opposite directions, will 
their lateral disturbance of equilibrium be im the same, or in 
opposite directions inwards; and hence, that the reverse lateral 
motions, or at least tendencies to motion, cf the bodies, accord- 
ing as their currents are in the same, or opposite directions, are 
explicable in the same way as, above, the motions of bodies with 
the same, or opposite directions of molecular tension, that is, 
with opposite, or the same poles opposed. 

25. The special facts which seem to justify the advancing of 
the above theorem and its corollary as a true generalization and 
mechanical explanation of electric and magnetic motions, may be 
summed up under the following experimental conclusions :— 
Paramagnetism and diamagnetism are not absolute, but relative 
conditions of bodies. Paramagnets tend to pass from weaker to 
stronger, and diamagnets from stronger to weaker, places of 
action. ‘Two of either class repel, and one of each attract. These 
motions would be explicable as due to differences of conduction ; 
but magnetic, is quite different from electric, conduction. As to 
these facts, if their mechanical meaning is not from the foregoing 
sufficiently clear, remark that, the tension of a magnetized body 
being spiral, while that of a body with an “open current” is 
longitudinal, the directions of the lateral imductive actions of a 
magnet and an ordinarily electrified body will be different, and 
hence the molecular conditions which permit of electric, will be 
different from those which favour magnetic, conduction. And if 
differences of conduction, that is, of molecular displacement, are 
thus admitted in the explanation of paramagnetic and diamagnetic 
phenomena, it is evident, from what has been already said of the 


Principles of the Science of Motion. 51 - 


effect of differential molecular action, that a better conductor 
will, in moving in the direction of least resistance, pass to a 
‘stronger place of action. 

The above conclusions are Faraday’s*; but the theorem and 
corollary as generalizations rest also on the facts adduced by 
Ampére and his successors in support of his helix-theory of the 
magnet. 

A third most important class of facts by which the view here 
given of the mechanical conditions of the electric motions of 
bodies may be supported, is the disposition of iron filings about 
one or more electrified wires or magnets in various positions, 
and the information given by a moving wire as to magnetic 
forces. 

26. The fundamental importance of the conceptions of a force 
as, in general, a difference of pressures, and of polar attraction 
and repulsion as the effect of a differential molecular action, has 
induced me to give such disproportioned length to their illustra- 
tion, that it will be impossible within the brief limits of this 
paper todo more than note the other chief points of this general 
theory. 

What, therefore, has to be said on (B) (8) the effects of 
electricity as manifested in motions of the medium, must be 
referred to the paragraph on the correlation of forces. 

27. There will not, it is hoped, be thonght to be presump- 
tion in offering new views in theories which have been elaborated 
with such admirable genius as those of light and heat ; for the 
most strenuous supporters of the present form of the undulatory 
theory candidly admit that “there undoubtedly are several 
classes of phenomena which the wave theory has not merely 
failed to explain, but which are apparently at direct variance with 
its principles +.” 

It will be evident that the chief new view necessitated by this 
general theory (and which alone can be here noticed) resolves 
itself into a theory of the connexion of the elastic medium with 
the vibrating molecules in it. Now, though according to the 
present theory “it is certain that light is produced by undulations 
propagated with transversal vibrations through a highly elastic 
ether, yet the constitution of this ether, and the laws of its 
connexion (if it has any connexion) with the particles of bodies, 
are utterly unknown{.” But the theory here proposed implies 
such “laws of connexion.” For its practical result is, that the 
“ether” is conceived as the mutually determined lines of 

* But compare Tyndall’s Memoirs ‘‘ On the Reverse Polarity of Bis- 
muth” (Phil. Trans. 1855 and 1856). 

+ Baden Powell, ‘ Undulatory Theory,’ Introduction, p. xxiv. 

~ MacCullagh, ‘“ Laws of Crystalline Reflexion,” &c., Mem, R.I. A., 
Xvi. 38, 

K2 


52 Mr. J. S. Stuart Glennie on the 


pressure from molecules of the size to give by their vibrations 
the sensations of light and heat. 

It would seem that this conception of the “ ether” leads to 
the explanation of more than one difficulty in the egtablished 
theory ; but nothing can, of course, be advanced on such a point 
except as the result of analysis. | 

It will be understood that I thus speak of the conception of 
atoms, as above defined, as a mode of conceiving the “ther” of 
the undulatory theory, only in order to make clear the applica- 
tion to that theory of the fundamental conception of the general 
theory here proposed; and that this in nowise contradicts what 
has been above said as to the seeming needlessness of hypotheses 
of special fluids, or ethers, acting on, or through, matter. 

28. A general chemical theory is made up of two—a theory 
of the constitution, and a theory of the combination, of bodies. 
As to the constitution of bodies, the principal views here offered 
are :—Bodies are conceived as states of dynamic molecular equi- 
librium, that is, as states of molecular motion in which, while 
there is no decomposition, the intensity of motion is at all points 
equal. Hence, their differences are conceived as resulting from 
different conditions of molecular motion; and thus specific heat 
becomes one of the chief exponents of the nature of a body. 

The distinguishing mechanical characteristic of the gaseous, 
fluid, and solid, states of matter is degree of tangential resistance. 
In an absolutely perfect gas the molecules would be of equal 
mass and at equal distances: hence perfect equality of resist- 
ance in all directions. But let there be inequality either m the 
masses or distances of the molecular centres of pressures, it is 
evident, from the same reasoning as that above applied to the 
mechanical explanation of gravity, that there would be a cohesive 
force developed, the consequence of which would be inequality 
of resistance. Fluids, therefore, as opposed to solids, are con- 
ceived as bodies the molecules of which are of sensibly equal 
masses and at equal distances; and gases, as opposed to liquids, 
as bodies in which the distances of the molecules, though equal, 
are greater than in liquids. Hence the greater amplitude of their 
motion, or specific heat. 

The consideration of this theory of bodies with reference to 
that of Kronig* and Clausius+, cannot be at present entered upon. 

* “ Grundziige emer Theorie der Gase,” Poge. Ann. xcix. 315. 

+ “ Ueber die bewegende Kraft der Warme,”’ Poge. Ann. Ixxix. 394; and 
“ Ueber die Art der Bewegung welche wir Warme nennen,”’ ibid. c. 353. See 
also Prof. Maxwell’s “Illustrations of the Dynamical Theory of Gases,” Phil. 
Mag., January and July 1860. Dr. Tyndall’s discoveries and researches 
“On the Transmission of Heat of different qualities through Gases of 
different kinds ”’ (Proceedings of the Royal Institution, June 10, 1859), 


are of the greatest importance in such a dynamical theory of the constitu- 
tion of bodies, 


Principles of the Science of Motion. 53 


29. The combination of bodies, in whatever way it takes 
place, and not confining the meaning to the formation of salts*, 
is conceived as the establishment of a new state of dynamic 
equilibrium}. Hence there must necessarily be definite laws of 
- chemical combination. 

But as it is proposed to give the outlines of this mechanical 
theory of chemistry in a future paper or papers, it is unneces- 
sary to enter more fully upon it at present. A theory so im- 
portant has been introduced in a paper in which it must be so 
imadequately expressed, only to complete the general outline of 
the science of motion, and because a mechanical theory of 
chemistry is the necessary complement of the above-given 
mechanical theory of electricity. 

30. In such a theory of forces as that here proposed, the 
great experimental truth of the “ correlation of forces” t assumes 
an axlomaticclearness. specially is it to be noted that it gives 
an account of the difference of the correlation between electricity 
and magnetism, and that of either of these with light, heat, &c. 
The former is a correlation of coexistence, the latter of change 
of conditions. ) 

If I have been successful in making clear the conceptions 
offered in this theory of electricity and magnetism and of 
induction, it will be unnecessary here to say anything further 
of this correlation of coexistence ; for it 1s implied in the concep- 
tion of induction as a mechanical effect varying with resist- 
ance, and manifested at right angles to a longitudinal or trans- 
verse (spiral) line of tension, that is, of permanent (not alterna- | 
ting) molecular displacement. And if electricity is a permanent, 
light an alternating, molecular displacement, their correlation is 
evident, the conditions of their interchange assignable, and ana- 
lytically expressible. 

But not only is the correlation thus clear of physical motions 
among themselves, but also of these, as a class, with mecha- 
nical motions on one side, and chemical motions on the other— 
clear, that is, that the stopping of a mechanical, or the beginning 
of a chemical, motion implies more or less molecular displace- 
ment under such conditions as those above assigned for elec- 
tricity, light, and heat. But what is the proof of such a corre- 
lation of forces but the sublime “ persuasion that all the forces 


* Berthelot’s discoveries have definitively broken down the distinction 
between Inorganic and Organic Chemistry. See his Chimie Organique. 

tT Compare Williamson’s “ Theory of Etherification,” Chem. Soc. Quart. 
Journ. iv. 110. 

{ Grove. See also Helmholtz in Taylor’s Scientific Memoirs, 1853, 
p- 124; and compare Rendu’s “ circulation”’ of fire, light, electricity, and 
magnetism, Théorie des Glaciers de la Savoie, Memoirs of the Royal 
Academy of Sciences of Savoy, 1841, cited in Tyndall’s ‘ Glaciers of the 
Alps,’ p. 299, 


54: On the Principles of the Science of Motion. 


of nature are mutually dependent, have one common origin, or 
rather are different manifestations of one fundamental power* ” 
—become, at least for all the phenomena of Motion as distin- 
guished from those of Growth, a scientific truth ? 

81. For the sake of distinctly defining by its relations the 
Science of Motion, a few words may be added on the Classifica- 
tion of the Scicnces proposed by the author. The general di- 
visions of each of the two great classes—the Natural and Humane 
Sciences—are (A) the Systematic, (B) the Descriptive, and (C) 
the Historic Sciences. 

The Systematic Natural Sciences are the sciences of (I.) Mo- 
tion, (II.) Growth, (III.) Species (“the Classificatory Sciences” 
of Whewell) t+. 

The twofold subdivision of each of the three sciences of 
motion will be evident from the foregoing. 

Hach of these rational sciences, as well as those making up 
the Science of Growth, have a corresponding applied science. 

The Science of Motion, as a distinct science, and not as merely. 
a general name for the sciences of mechanics, physics, and che- 
mics, has a twofold division. 

Under the first, the general relations, laws, or principles of 
motion, without regard to the particular conditions of its cause, 
would be considered: such general principles, for mstance, as 
Galileo’s laws of Inertia, and of the Composition of Motions ; 
Newton’s law of the Equality of Action and Reaction ; its genera- 
lization in D’Alembert’s principle; Jean Bernoulli’s (?)¢ prin- 
ciple of Virtual Velocities; Varignon’s geometrical theorem on 
Moments; Poinsot’s theory of Couples ; Newton’s principle of the 
Conservation of the movement of the Centre of Gravity ; Kepler’s 
principle of Areas ; Laplace’s theorem on the Invariable Plane; 
Euler’s on Moments of Inertia, and Principal Axes ; Huygens’s 
principle of the Conservation of Vires vive; Daniel Bernoulli’s 
theorem on the Coexistence of small Oscillations, &c. 

The object of the second division cf the General Science of 
Motion would be the generalization of the conditions giving rise 
to the various Forces of Motion, mechanical, physical, and che- 
mical, and their correlations. This paper, therefore, has treated 
of the principles of but one division of the science. 

_ The divisions of the special science of Mechanics, that on 
Solids, and that on Fluids, would be conveniently considered in 
kinematical §, statical, and dynamical sections. 


* Faraday, ‘ Experimental Researches,’ 2702. 

t+ History of the Inductive Sciences, iii. p. 211. 

t Poisson, Traité de Mécanique, i. p. 654. 

§ See Ampére’s Essaz sur la Philosophie des Sciences ; Willis’s preface 
to his ‘ Principles of Mechanism,’ and the arrangement of Rankine’s 
‘Manual of Applied Mechanics’ (Encyc. Metrop.). 


Opacity of the Yellow Soda-Flame to Light of its own Colour. 55 


52. In conclusion, as every one of these theories is so de- 
pendent on every other, that it was necessary to give first a 
general outline of them all, it is hoped that allowance will be 
made for the imperfection, or even maceuracy, unavoidable in so 
brief an exposition of each. And lest, from imperfect expres- 
sion, the general principles themselves may be misunderstood, 
at may be added that the authors confidence in them arises 
only from their long-tested seeming accordance, not only with 
experimental gener aliza ations, but with scientific metaphysics. For 
every physical theory must be implicitly, or explicitly founded 
on metaphysical views as to the nature of Knowledge, as to the 
mode in which Matter and Force are to be eorieeived, and as to 
the meaning of Law. And the metaphysical bases of this phy- 
sical theory have been chiefly found in the Philosophy of Bacon, 
and of the Scottish School. 

The necessary limitation of human knowledge, the central 
doctrine of Sir Wiliam Hamilton’s system, and, indeed, the 
great result of the modern Critical School founded by Kant, 1s 
the citadel of those who would clear the Natural Sciences of 
absolute, and essentially distinct, force or forces acting on, 
associated with, or emanating from, matter. The fundamental 
conception of this theory—that of a force as a condition—is but 
a development of the doctrine of “ Forms,” “ the imvestigation of 
which is the principal object of the Baconian method of induc- 
tion*.” The conception of matter is in accordance with that of 
- substances, as ‘‘ corpora individua edentia actus puros individuos 
ex lege, ;” and that of a Law, as not an imposed rule to be 
discovered, but a relation to be expressed, seems to agree no less 
with the principles of Bacon, with whom “ the statement of the 
distinguishing character of the motion or arrangement, or of 
whatever else may be the form of a given phenomenon, takes the 
shape of a Law{,” than with the principles of Mill§. 

6 Stone Buildings, Lincoln’s Inn, 

10th Dee. 1860. 


VI. On the Opacity of the Yellow Soda-Flame to Light of its 
own Coiour. By Witt1amM Crooxes||. 


N thei remarkable investigations on the colours which certain 
substances impart to the flames in which they are heated, 
Professors Kirchhoff and Bunsen describe certain experiments by 
* Bacon’s Works, by Ellis and Spedding, i. p. 31. 
+ Ibid. t Ibid. p. 29. 
§ System of Logic, Ratiocinative and Inductive. 
|| Communicated by the Author. 


4 Chemical Analysis by Spectrum Observations. By Professors 
Kirchhoff and Bunsen. Phil. Mag. S. 4. vol. xx. p. 89. August, 1860. +5 _: 


56 Opacity of the Yellow Soda-Flame to Light of its own Colour. 


which they prove that the luminous lines which are produced in 
the spectrum of a spirit- or gas-flame, when salts of the alkalies 
or alkaline earths are caused to volatilize therein, become reversed 
(2. e. that the bright lines become changed to dark ones) when 
a source of light of sufficient intensity, and giving a continuous 
spectrum, is placed behind the coloured flame. 

During some researches on the spectra of artificial flames which 
I have been carrying on simultaneously with MM. Kirchhoff and 
Bunsen, one or two forms of experiment suggested themselves 
which, while they perfectly corroborate most of the facts men- 
tioned by them, seem to merit attention, from the facility with 
which they may be performed, and the striking manner in which 
the phenomena can be exhibited to several persons at once with- 
out the necessity of employing any optical apparatus. The 
atmosphere of the room—or rather that part of it in which the 
illustration is performed—is to be first impregnated with soda- 
smoke, by igniting a piece of sodium, the size of a pea, on wet 
blotting-paper. Any flame, whether of gas, spirit, a candle, &e., 
which may now be burning anywhere in that part of the room, 
will exhibit in a marked manner the well-known yellow soda- 
flame; and if the full amount of gas in an ordinary wire-gauze 
air-burner is turned on and ignited, it will give a uniformly 
brilliant yellow flame, upwards of a foot high and 3 inches in 
diameter. 

If a smaller flame be now moved in front of this large one, it 
will exhibit a curious phenomenon. Those parts of it which are 
ordinarily seen to be luminous will suffer no change, other than 
that slight dimimution in intensity which might be anticipated 
from their projection in front of a broad but not very brilliant 
source of light; but beyond these there will appear a sharply- 
cut and intensely black narrow border, closely surrounding the 
visible flame, and presenting the curious appearance of the latter 
being set in an opake frame. A closer scrutiny will show that 
the position of this black rim is not, as I at first supposed, in 
that outer cone in which the yellow soda-flame is most distinctly 
seen, but that it lies in the dark space immediately outside the 
luminous part of the flame, affording proof of the existence of 
another invisible cone of vapour. The flame from a tallow candle 
shows this appearance better than that of wax or sperm, pro- 
bably on account of its inferior luminosity. A small spirit- or 
gas-flame will also answer very well; but I think a tallow candle 
shows the phenomenon in a more striking manner. 

The fact of the cone of yellcw soda-flame being transparent, 
while the outer, non-luminous space is perfectly opake to the 
same kind of light placed behind it, appears worthy of attention. 
It seems to show that the yellow flame caused by the presence 


On the Laws of Absorption of Liquids by Porous Substances. 57 


of incandescent solid particles of a sodium compound has no 
very marked absorptive action on light of its own colour; but 
that to give rise to this kind of opacity it 1s necessary that the 
sodium compound should be in the state of vapour. It appears, 
moreover, to prove that it is not necessary for this vapour to be 
in the metallic state; for it could hardly be supposed that so 
highly combustible a vapour as that of metallic sodium could be 
present in that part of the flame which is seen to possess this 
great opacity. ‘T'hat soda salts are easily volatile at the tempera- 
ture of flame, is a fact abundantly proved by Bunsen*. The 
reason why the opacity is only exhibited by that part of the outer 
shell of vapour which is situated at the edge of the flame, and 
not by its entire extent, is owing to its thickness being insuffi- 
cient to produce sensible absorption on rays which traverse it 
perpendicularly ; an appreciable action taking place only when 
they pass as a tangent to the edge of the flame, and thus traverse 
a considerable extent of absorbing medium. 


VII. Experimental Researches on the Laws of Absorption of 
Lnquids by Porous Substances. By Tuomas Tate, Esq. 


[Continued from vol. xx. p. 510.] 
Il. On the Filtration of Liquids through different Porous 


Substances. 


ILTRATION is in general produced by the action of two 
forces, viz. by the force of absorption and that of pressure. 
Filters may be divided into two classes. The first class com- 
prises those substances which are highly porous, and which 
undergo little or no change during the process of filtration. 
The second class comprises “those substances with close pores, 
which under certain circumstances undergo a decided change 
during the process of filtration. The following laws (with cer- 
tain limitations) apply to both kinds of filters :— | 
1. The rate of filtration, other things being the same, varies 
directly as the area of the surface of the filter in contact with 
the liquid, and inversely as the thickness. 
2. The rate of filtration, other things being the same, increases 
in a high ratio with the increase of temperature. 
3. The rate of filtration, other things being the same, varies 
as the depth of the column of liquid upon the filter. 
And so on to other laws which will be hereafter illustrated. 
These experiments were, for the most part, made with the 
apparatus represented in the annexed diagram. 


* Phil. Mag. S. 4. vol. xviii. p. 513. 


« 


58 Mr. T. Tate’s Experimental Researches on the 


AB awide glass tube, containing the liquid, 
about 2 feet.in length, graduated into units 
of cubic inches, or into units of half cubic 
inches, as the case may be; © and D two 
equal plates of polished slate having equal 
orifices bored through their centres; the 
plate C is cemented (with a resmous cement) 
to the bottom of the tube, and the filter e 
is cemented to both plates, so that all lateral 
discharge from the filter is stopped, and at 
the same time the filter presents a surface, in 
contact with the liquid, equal to the section 
of the orifices of the plates. All liquids, 
before being used in the filtrometer, were 
twice filtered through ordinary filtering 
paper, and the top of the filter tube AB was 
covered during the experiment to prevent any 
dust from falling intothe hquid. The tube 
AB was filled up, with the liquid, to a cer- 
tain point of the graduation, and then the 
time at which the liquid, in its descent, ar- 
rived at the different points of the gradua- 
tion was duly noted. 


Heperiment XVI. 

The filter used in this experiment was common wood-charcoal 
half an inch in thickness. The liquid was distilled water. The 
diameter of the orifice of the plate was ;4ths of an inch. The 
filter-tube was graduated into 8 units, each contaming half 
a cubic inch, and the 8 divisions measured 9:2 inches. The 
temperature was 56° throughout the experiment. The results 
recorded in the third column of the following Table are obtained 
by dividing the unit of space by the mean of the times taken in 
describing the two consecutive units of space; thus the velocity 


epee 46+55 1 
at 4= 1 + ————_ = —.. 
2 50 
| | 
i : Val f 
Hig of loony tine| Gomer | EEE, | vaso 
liquid, “Dp > descent, ee Ah ; by formula 
h, 7 | v. ~ 203 (4). 
vied aa ee — 
| 8 0 | fe 0 
7 27 Z5 25 26°5 
‘ - ae s 57°5 
5 94 at a5 | 94-0 
‘ oe 35 2s 139-0 
3 195 Se oe 196°0 
2 272 | xt a 277-0 
1 | 400 | 415-0 


Laws of Absorption of Liquids by Porous Substances. 59 


The near coincidence of the results im the third and fourth 
columns shows that the velocity of discharge varies digectly as the 
height of the column of liquid upon the filter. 

Let S! = the whole depth of the liquid at the commencement 
of the experiment, in umits of the divisions of the filtrometer ; 
S =the descent of the liquid in the time T; v = the corre- 
sponding velocity of descent ; «, y, p = constants ; then we have 
generally, 

T=a—ylog (S'+p—S). ... . (1) 


By differentiation, we get 


dS __ log.10,, 
7 (S’-+e—S) ; 
2°30258 
= orice e -@ . ° ° ° ° (3) 


2°30258 1 
~ 2037 

relation of time and space is expressed by the formula 
T= 415:74— 460'4 log fea cn 2s) (A) 


This experiment, upon being repeated, gave a slight diminu- 
tion in the velocity of descent of the liquid, showing that the 
- filter had undergone only a very slight change during the pro- 
cess of filtration. This observation applies to the filters used in 
the three following experiments. 


Experiment XVII. 


The filter in this experiment was coke, ;4,ths of an inch in 
thickness. The liquid was distilled water. The diameter of the 
orifice of the plate was 7/j;ths of an inch. The filter-tube was 
the same as in the last experiment, and the temperature was 57° 
throughout the experiment. 


In the foregoing experiment, p=0, 


e 


Height of Cc : Corresp. Value of v 
column of |Corresp- 4ME€! velocity of | by formula 
liquid, oo sceoude, descent, h 

h. +3 a v. v= 205. 
8 0 Pe os 
7 27 29 29 
6 59 Ba Bq 
+ 99 40 ar 
4 139 = sr 
3 195 es os 
2 279 wh zis 

1 460 


60 Mr. T. Tate’s Experimental Researches on the 


Here it will be observed that the liquid followed the same law 
of descent as that of the preceding experiment. 

Reducing the coke filter to the same thickness and diameter 
of orifice as in the case of the charcoal filter, we find, under the 
Same circumstances of pressure, &c., the filtering power of the 
charcoal to be 33 times that of the coke. 


Experiment XVIII. 


The filter in this experiment was stout woollen cloth. The 
liquid was distilled water. The diameter of the plate was ~>ths 
of an inch. Each half cubic inch graduation of the filter-tube 
measured on an average 1:55 inch, so that the height of the 
liquid column at the commencement of the experiment was 15°5 
inches. 


Height of é Corresp. Value of v 
column of |©rresp. time | velocity of | by formula 

liquid, dn seconds, descent, h 
Ah. T. Ve v= 208° 

10 0 
9:5 nce os sr 
9-0 22 ‘ ae 
8:5 Be aa oa 
8-0 46 ; 
Popa Ha Lenina ae 
6°5 cee 3a so 
6-0 106 ie 
o°5 a a ca 
5-0 143 te sp 
45 uae ay 1 
4-0 190 et 
35 eee SO B50 
3-0 250 : 
2-5 ie se re 
2-0 330 Ss es 
SS awe eh ara ae 


Here the results of the third and fourth columns show that 
the velocity of discharge varies according to the same law as in 
the two foregoing experiments. 


Experiment XIX. 


In this experiment the filter was sponge plugged tight into 
the bottom of the filter-tube, which was the same as that of the 
last experiment. 


Laws of Absorption of Liquids by Porous Substances. 61 


Beat cece | Geral Seas 
liquid, seconds, descent, h 
h. ts wu. u= 303° 
agen eit abe e 
105 a - 
93 «(«| (8 2 = 
8 5 03 S 
Be | gag oo Ph ae 
o8 174 * ny 
25 225 * e 
45:1. 986 pelea ae 
Biol Lapa yior|. > - Pain a 
25 «(| (G6 aa 
Bee gape ah FT | 


The results of this experiment show that, for the first nine 
units of descent, the velocity of discharge varies almost exactly 
as the height of the column of liquid. For the last two units, 
the rate of discharge considerably exceeded that which the for- 


mula v= = would give, showing that the effect of the absorb- 


ent power of the filter greatly exceeded that which would be due 
to the pressure alone. 

This experiment was repeated with little or no variation in 
the results. 

Similar results were obtained from filters formed of plugs of 
different sorts of soft porous material ; also from a filter formed 
of fine sea-sand laid upon a perforated plate. 

The followmg experiment was made to determine the variation 
of the rate of filtration due to increase of temperature. 


Experiment XX. 


The liquid used in this experiment was distilled water, and 
the filters were those employed in Experiments XVI. and XIX. 

With the charcoal filter under a constant pressure, the time 
required to discharge one cubic inch of liquid at 52° tempera- 
ture was 114 seconds; whereas at the temperature of 90° it only 
required 65 seconds. In this case an increase of 38° of tem- 
perature increased the rate of discharge 12 times; that is, the 


62 Mr. T. Tate’s Hxperimental Researches on the 
rate of discharge was nearly doubled by the addition of 38° of 


temperature. ; 
With the sponge-filter the following results were obtained :— 


Time in seconds to discharge 1] eubic inches of water. 
At 50°, At 80°. At 90°. At 100°, 


420" 286" 246" 204! 


Here an increase of temperature from 50° to 90° caused the 
rate of discharge to be increased ]:707 times, a result nearly 
coinciding with that determined for the charcoal filter. At 100° 
temperature the rate of discharge is a little more than double the 
rate at 50°. These results further show that, for equal volumes 
of discharge, the decrements of time are for the most part propor- 
tional to the increments of temperature. 

The following experiment was made to determine the rates of 
filtration of different liquids as compared with that of water. 


Experiment XX1. 


The filter used in this experiment was charcoal; and the 
liquids compared were distilled water, and three different solu- 
tions of carbonate of soda. Solution No. 1 contained 2 per cent. 
of carbonate of soda; No. 2 contained 4 per cent.; and No. 3 
contained 8 per cent.; that is to say, the per-centage of the salt 
in these different solutions were in the geometrical progression 
2,4, 8. The discharge in each case was produced under the 
pressure of a column of 9:2 inches of the liquid. 


Time in minutes to discharge 
one cubic inch of the liquids. 


Water .fieit ets. 27 o= Zo 1S 

Now 2 2.  P87=17%8 x 108" nega 
Occ: nick alts Aderd) CRUG Rao sa ae 
IN Ops veins « larga ere aoe 


Here it will be observed that the rates of discharge are very 
nearly in geometrical progression. This property of filtration is 
analogous to that of absorption, as shown in connexion with ex- 
periments XI.and XII. Thus it appears that the chemical com- 
position of aliquid affects its relative rate of filtration. 

In general the rate of filtration or filtrativeness of a liquid 
seems to depend mainly upon its viscosity, and not so much 
upon its specific gravity. Alcohol, oils, &c., which have a less 
specific gravity than water, have a low rate of filtration. Solu- 
tions of sugar and starch, even when much diluted, have very 
low rates of filtration as compared with that of water; whilst 
diluted acids and weak solutions of alkaline salts, for the most 
part, have a rate of filtration nearly equal to that of water. In 


rc Se 


Laws of Absorption of Liquids by Porous Substances. 638 


these respects the law of filtration is analogous to that of absorp- 
tion; at the same time it must be observed that the relative ab- 
sorbent power of a substance does not always correspond to its 
filtermg power. 

The filters used in the following experiment belong to the 
second class of filters. 


Experiment XXII. 


The filter used in this experiment was thick unsized paper, and 
the liquid was spring water. The diameter of the orifice of the 
plate was ;4,ths of aninch. The filter-tube was the same as that 
of Experiment XVI. At the commencement of the experiment 
the liquid stood at the eighth division of the tube measured from 
the filter. The temperature was 64° throughout the experiment. 


| Value of v 


Descent of | C . time} Velocity per | 

the liquid, ‘a keconds, | cco | yy foreuala 
Ss. | v. ara 
0 0 Bo 30 
1 20 
I 97 1 12 1 7) 8 
1i 125 
2 225 140 TAG 
21 260 
3 400 FOO T5D 
34 450 
4 620 Eo DED 
41 685 
5 870 os ahs 
BL 960 
6 1360 Eo 49a 
62 1480 | 
7 1990 giv sto 
72 2160 | 


The formula expressing the relation between the time T and 
space S of descent is 


A G2"3 (185 bey tell eid in 5 Vo hie Gal) 

It will be seen how very nearly the velocity of descent of the 
liquid is represented by the formula v= - .1:3557°; showing 
that af the spaces of descent be taken in arithmetical progression, 


the corresponding velocities of descent will be in geometrical pro- 
gression. ‘Vhe common ratio of the velocities in this experiment 


=: 
eo 355 
The relation of T and S for both kinds of filters may be repre- 


” 


64 On the Laws of Absorption of Liquids by Porous Substances. 


sented by the general formula 
T=a(6°—1) —y log (S!+p—8), 
where a, @, y, and p are constants. 


When 8=1, this formula becomes the same as equation (1) ; 
and when y=0, or very small, it becomes 


Taa(S 3), o3. 2. a 


which is the general formula applying to the second class of 
filters. 
By differentiation, we find 


1 -s 
Sa peaeatie ne a = 904 pee 
v a log, 8 B ? ( ) 
which is a general formula for the rate of descent of the liquid. 
In the foregoing experiment, a=262°3, 8=1°355, and 


= ga b855™*. kt 2g 


Towards the close of the experiment the velocity of descent 
became exceedingly small, showing that the adhesion of the hquid 
to the bottom of the filter-tube interfered with the law of velo- 
city expressed by equation (8). 

This experiment being immediately repeated, it was found 
that the rate of filtration had sensibly diminished, showing that 
the filtermg power of the paper had undergone a decided change 
during the process of filtration. This change, as will be here- 
after shown, is progressive, being in proportion (within certain 
limits) to the quantity of liquid filtered. But after the filter had 
been dried, it somewhat regained its original power. 

In this manner various experiments were made, which gave 
precisely similar results. 

Although the liquid in these experiments had been carefully 
filtered through ordinary filtermg-paper, yet it is possible that 
certain minute particles may have passed through the filter, suffi- 
cient to deteriorate the filtering power of a small filtering surface 
such as that used in the foregoing experiment. 

The following experiments were made on upward filtration. 


Experiment XXIII. 


In this experiment the filter was immersed in a jar of liquid 
to the depth of 7 units of the filter-tube. As the liquid rose in 
the tube through the filter, the liquid in the jar was maintained 
at a constant level. The filter was the unsized paper of the last 
experiment, the diameter of the plate being ;4ths of an inch. 
The liquid was a diluted solution of carbonate of soda. 


Prof. Challis on a Theory of Mayietie Force. 65 


Depth of the Corresp. Value of v 


column of |Corresp. time velocity by formula 
liquid, = a of ascent, rig: 
h. , v. = 8°69. 
1 
6 0 | tease re 
OnE Se Seman 1 L | 
5 1:58 ae ates A 
AL Pere | 
Be ssanine 1°93 1°93 
ed 3°51 L oe 
ns oS 2°4 2°48 
3 5°91 ‘ : 
{ oe a os ae 3°35 3°49 
Ae 9-26 
IL wes a 
= Nd RQR eee 5°65 579 
1 14-91 | ‘ ‘ 
a aes 17°84 17°38 
| 0 32°75 


The near coincidence of the results in the third and fourth 
columns shows that in this case the rate of filtration varies directly 
as the pressure upon the filter. 

With a double filter the rate of discharge was found to be 
reduced to one-half very nearly ; and with a filter of =2;ths of an 
inch diameter, that is, one-fourth of the surface of the filter in 
the above experiment, the rate of discharge was found to be 
reduced to one-fourth of that of the above experiment. Hence 
we conclude that the rate of filtration varies directly as the areas 
of the surface of the filter in contact with the liquid, and iversely 


as the thickness. 
[To be continued. | 


VIll. A Theory of Magnetic Force. 
By Professor CuHauiis, F.R.S* 


ps my last communication, containing a theory of galvanism, 

no allusion was made to thermo-electric phenomena. This 
omission I propose to supply before proceeding to the theory of 
magnetism, the fact that galvanic currents may be produced by 
heat, being confirmatory of the explanation given by hydro- 
dynamics of the generation of secondary currents generally, 
whether electric, or galvanic, or magnetic. 

1. It isassumed in that explanation that in the neighbourhood 
of the earth’s surface there are steady etherial currents, which 
eventually may be found to be secondary with respect to other 
more general currents, but for considerable spaces may be con- 
sidered to be uniform as to velocity and density. These currents 
are supposed to flow freely through the interior of bodies, with 
only such modifications as may result from the arrangement of 

* Communicated by the Author. 


“Phil, Mag. S, 4. Vol. 21, No, 137, Jan. 1861. F 


66 Prof. Challis on a Theory of Magnetic Force. 


the atoms, and the contraction of the channel by the atomic 
occupation of space. At the parts of the boundary of any sub- 
stance where the stream enfers, there will be a sudden mcrement 
of velocity, and at the parts where it zssues, a sudden decrement ; 
but not to a large amount, because there is reason to conclude 
that even in dense bodies the space occupied by atoms is very 
small compared to the vacant space. Under all circumstances 
the motion remains steady, if there be no extraneous force, and 
no variation of the primary current. If, throughout the interior 
of the body, the atoms within a given space (as one thousandth 
of a cubic inch) occupy a portion of it which has a constant ratio 
to the vacant space, they produce no acceleration or retardation 
_ of the velocity of the stream. But if from any cause there should 
be a gradation of internal density of the atoms, the atomic com- 
position remaining the same throughout, secondary streams will 
be produced in the following manner :—Conceive the external 
primary current to be cut at right angles by a plane in a given 
position. Then since it is supposed to be steady and uniform, 
the velocity will be always the same at all points of the plane. 
Hence, tracing two contiguous and equal filaments of the stream 
into the interior of the body, it will be seen that if the density 
of the atoms be greater at certain portions of the course of one 
filament than at the adjacent portions of the course of the other, 
the velocity will be greater in any element of the former portions, 
than in the adjacent element of the datter, assuming, as may be 
done, that in other respects the channels of the two filaments 
are at adjacent parts of equal dimensions. Hence by the general 
hydredynamieal equation for steady motion, the density and 
pressure of the ether will be /ess in the former elements than in 
the latter. Consequently there will be an accelerative force of 
the fluid always tending from the rarer to the denser parts of 
the body, and taking effect, whatever be the direction of the 
original stream, in the directions of normals to surfaces of equal 
density, because in these directions the change of density of the 
atoms in a given space is greatest. These accelerative forces 
produce secondary currents, the velocities of which will depend 
on the magnitudes of the forces, and on the extent through 
which they act. Considering the vast elasticity of the ether, as 
shown by the rate of the propagation of light, a difference of its 
density equal to a ten-millionth part of the whole density would 
correspond to an enormous difference of pressure. 

2. According to these views it might be expected that a lamina 
of metal, heated unequally at the two extremities, would become 
electro-dynamic, as Volta found to be the case with a lamina of 
silver. In this stance the heat produces local disturbances of 
the condition of superficial atoms, and from these disturbances 


Prof. Challis on a Theory of Magnetic Force. 67 


probably the internal gradation of density chiefly results, as in 
a body subject to the influence of electricity by induction. Ifa 
closed circuit of any metal be heated at any point, currents, 
according to this theory, will be generated in consequence of the 
different degrees of expansion of the metal at different points, 
and, flowing in opposite directions, will neutralize each other if 
they be equal. But if by any mechanical means they be made 
unequal, as by contortions of the metallic circuit, a galvanic 
current should result, as is found to be the fact by experiment. 
When the circuit is formed by two metals soldered together at 
their extremities, and heat is applied at one of the positions of 
junction, inequality of the opposite currents might be expected 
to arise from difference of the capacity of the two metals for 
generating currents, owing to difference of their atomic constitu- 
tion; and accordingly it is found that under these circumstances 
a galvanic current is produced. I proceed now to the theory of 
magnetism. 

3. In the preceding theories the generation of secondary 
etherial currents has been ascribed to a disturbance of the 
atomic condition of bodies by external agency,—ain electricity, by 
friction ; in galvanism, by the mutual molecular actions of dis- 
similar substances in contact; and in thermo-electricity, by 
heat. In the theory of magnetism it must be assumed that 
there are substances in which a gradation of interior density 
exists independently and permanently,—that iron, for instance, 
is found in this state in nature; that the same state may be 
induced in steel by mechanical means, with different degrees of 
permanence ; and that it may be momentarily induced in soft 
iron. Also it must be supposed that the direction of the grada- 
tion of density depends on the form of the magnetized body. 
These suppositions rest immediately on facts of experience, the 
explanations of which, since they relate to qualities of the bodies, 
and not to the agency by which magnetic phenomena are pro- 
duced, are not now under consideration. 

4. Let us take the case of a bar of magnetized steel of the 
form of a long rectangular parallelopiped, and let it be assumed 
that there exists permanently a uniform decrease of its atomic 
density from the end A to the end B. . By the argument in art. 
1, on the supposition of a steady and uniform primary current, 
there will be impressed on the ether within the bar a uniform 
accelerative force, acting throughout its length from B towards A. 
To the accelerative force in that half of the bar which lies towards 
B, may be ascribed the effect of overcoming the inertia of the 
ether in motion within and without the bar on the side of B, 
and to the accelerative force in the other half, the effect of over- 
coming the resistance opposed to the flow of the current by the 


68 Prof. Challis on a Theory of Magnetic Force. 


inertia of the ether on the side of A. Thus the motion will be 
maintained so as to be symmetrical with respect to a neutral 
position N, mid-way between A and B, the partial streams con- 
verging towards the parts about B, and diverging in like manner 
from the parts about A. The velocity of the ether will be 
greatest, and its density least, at N, and the velocity will de- 
crease, and the density increase, in both directions from this 
position by the same gradations. Hence the atoms, assumed 
to be of finite dimensions, will be urged on both sides towards 
N, by reason of the excess of pressure on the halves of their sur- 
faces turned from N, and the total moving forces in the opposite 
directions will be equal. Consequently the theory not only 
accounts for the weil-known fact, that the magnetism of a steel 
bar is equal and opposite on the opposite sides of a middle neutral 
line, but explains also why terrestrial magnetism, being supposed, 
for reasons that will be hereafter adduced, to act as the primary 
current of the theory, produces no perceptible motion of 
translation of the bar. These mferences will not be altered when 
the dynamic effect of the motion in the secondary streams 1s taken 
into account, as will be shown in a subsequent part of the theory. 

5. It also follows, conformably with experience, that if a 
magnetized bar be divided into two or more parts by being cut 
transversely, each part becomes a magnet, because it may be 
assumed that the gradation of density from end to end is the 
same, and in the same direction, in each, as when it formed a 
part of the whole bar. 

6. The theory of the action between two magnets requires the 
investigation of the mutual influence of two steady streams, 
having separate origins and interfering courses. The following 
laws, which may be admitted on hydrodynamical principles, will 
suffice for my present purpose. The resultant of two interfering 
steady streams is steady. Where two streams meet, the velocity 
is in general less, and consequently the density greater, than 
that which would be due to either stream flowing separately. 
When two streams unite in the same course, the velocity is 
greater, and the density less, than in either of the component 
streams. When the courses of two streams cross at right angles, 
the gradations of density in the directions of the courses are very 
nearly the same as in the separate streams. 

7. Conceive, now, that two bar-magnets, BN A, BIN'A!, are 
brought near each other, with their axes in the same straight 
line; and, for distinctness, let the axes be in the plane of the 
magnetic ‘meridian, and let A, A!’ be the ends from which the ° 
secondary streams always issue. The two currents under these 
circumstances will interfere with each other, so that the sym- 
metrical distribution of density with reference to the neutral 


Prof. Challis on a Theory of Magnetic Force. 69 


positions N and N! will be destroyed, and the disturbance will 
be in greater degree as the distance between the magnets is less. 
Also the consequences of the disturbance will be different accord- 
ine to the different directions of the currents. First, let B and 
A! be adjacent ends. Then the streams, always flowing towards 
A and A’, will be in the same direction. Hence, by hydrody- 
namics, the density and pressure of the fluid are diminished by 
the junction of the streams, in greatest degree in the space in- 
tervening between B and A’, and in N B and N/A! to a greater 
degree than in N A and N’B!. Thus the increment of density 
from the neutral lines towards the ends is less rapid in the 
adjacent halves, than in the remote halves. Hence the moving 
force of the xther urging the individual atoms towards the 
neutral lines is in excess in the remote parts, causing the mag- 
nets to move towards each other as if they were attracted. The 
same effect would be produced if the adjacent ends were B’ and A, 
because the two currents would still be in the same direction. 

Next, let A and A’ be adjacent. In this case, the streams 
issue from the magnets in contrary directions towards the space 
between A and A’, and by their meeting the ether is condensed 
in such a manner that the decrements of density towards the 
neutral positions are more effective in the nearer halves of the 
magnets than in the more remote. The magnets consequently 
move from each other, or are apparently repelled. Lastly, let B 
and B’ be the adjacent ends. The streams now flowing from 
B towards A and from B! towards A’, a diminution of velocity 
and consequent increment of density, result from their contrary 
tendencies between B and B’. The increase of density in this 
case may be conceived to be produced by the accelerations of the 
ether resolved in directions perpendicular to the common axis of 
the magnets, the resolved parts, in both streams and on both 
sides of the axis, conspiring to produce motion ¢owards that line. 
Thus by the same reasoning as 1m the preceding case, the magnets 
will be repelled. Consequently the known law, that like poles 
mutually repel and unlike poles mutually attract, is accounted for 
on the principles of the hydrodynamical theory. 

I take occasion to add that the above considerations respect- 
ing the mutual influence of opposing and conspiring magnetic 
streams, equally apply to the streams to which in the theory of 
electricity the attractions and repulsions of electrified bodies 
were attributed, and may be regarded as supplementary to the 
explanations given in arts. 18, 19, and 20 of the communication 
to the Number of the ‘ Philosophical Magazine’ for last October. 

8. In a similar manner the mutual action between magnets 
and galvanic currents may be explained. In the theory of gal- 
vanism, reasons were given for concluding that the movement of 


70 Prof. Challis on a Theory of Magnetic Force. 


galvanic currents relative to an electrode is composed of uniform 
motions parallel to the electrode, and of uniform circular motions 
about its axis. (See art. 10 of the communication to the ‘ Phi- 
losophical Magazine’ for December.) The theory I am about to 
give of the mutual action between magnets and galvanic currents, 
essentially depends on the existence of the circular motion: but 
it is remarkable that the facts to be explained require that the 
direction of this motion should be always the same; that is, if 
the electrode be parallel to the earth’s axis, and the current flow 
from south to north, the cireular motion must be in the same 
direction as that of the earth’s rotation about its axis. Ido not 
at present profess to account antecedently either for the circular 
motion, or for its having a determinate direction; but I can 
conceive that both these characteristics of the theoretical gal- 
vanic currents may be referable to the primary currents, which, 
as I shall hereafter attempt to show, have their origin im the 
earth’s rotation. 

9. Assuming galvanic currents to be such as are described 
above, suppose a straight horizontal electrode to be placed in 
the plane of the magnetic meridian, and the current to flow from 
south to north; and let a horizontal magnetic needle be placed 
directly underneath the electrode at a small distance from it. 
Since the needle and electrode are parallel, if the galvanic cur- 
rent were wholly longitudinal, there would seem to be no cause 
of disturbance of the needle, because the circumstances of the 
eether would be alike on the opposite sides of the plane of the 
magnetic meridian. But suppose the motion of the ether along 
the electrode to be accompanied by a circular motion about its 
axis in the direction from above towards the mght hand of a 
person looking northward; and calling the end of the needle 
which points to the north A and the other end B, let A designate, 
as heretofore, that end from which the magnetic streams asswe in 
curved diverging courses; also, abstract for the present from 
the longitudinal motions both galvanic and magnetic. Then 
the circular motion produces a stream which crosses the magnet 
from east to west. This stream meets the parts of the issuing 
magnetic streams resolved in the horizontal direction, on the 
east side of the north portion of the needle, and flows with them 
on the west side. There is consequently an increase of density 
and pressure on the east side, and a diminution of density and 
pressure on the west side, and the needle is consequently urged 
towards the west. About the end Band the sowth portion of the 
needle, where the entering streams converge in curved courses, 
the parts resolved horizontally conspire with the circular streams 
on the east side, and oppose them on the west side. The greater 

density of the ether is therefore on the west side, and the south 


Prof. Challis on a Theory of Magnetic Force: 71 


end of the needle is consequently urged towards the east. As 
the actions on the opposite halves of the needle are equal and in 
contrary directions, the total effect is simply a motion of rotation, 
and the north end of the needle deviates towards the west, the 
direction of the galvanic current being from south to north. 

If the direction of the current be reversed, the circular stream 
passes across the magnet from west to east, and consequently by 
the same reasoning as before, the north portion of the needle is 
urged eastward, and the south portion westward. It is clear that 
the directions of the deviations of a needle above the current are 
the opposite to those of a needle below, the direction of the 
effective parts of the circular streams being opposite. 

This directive action of the galvanic current vanishes when the 
axis of the needle is transverse to the direction of the current. 
If the current acts simultaneously with the earth’s magnetism, 
the needle must take a position intermediate to the transverse 
position and the plane of the magnetic meridian. 

All these inferences from the theory are in accordance with 
well known results of experiment. 

10. The curvilinear paths of the etherial streams in the above 
theory of the magnet, correspond to Faraday’s lines of magnetic 
force, and points of greater or less velocity correspond to points 
of greater or less magnetic intensity. 

11. The explanation of the reciprocal action of magnets on 
galvanic currents on the same principles appears to be as follows. 
In the case first supposed, the magnet being under and parallel 
to the galvanic current, let the electrode be moveable about a 
vertical axis, and the magnet be fixed. Then the moving force 
which urges the magnet when moveable, reacts upon the circular 
current, and disturbs its uniformity. It has been previously 
argued that the circular movement is necessary for maintaining 
the galvanic current, by preventing its flowing towards the axis 
of the electrode. Hence under this disturbance there will be a 
tendency of the fluid to rush to the parts towards which the flow 
of the circular stream is impeded by the partial interruption, that 
is, to the west side of the north portion of the electrode. This 
impetus, being unopposed, will cause the electrode to deviate 
towards the east. Like considerations would show that the 
south portion of the electrode is made to deviate towards the. 
west. ‘Thus the magnet and electrode will have the same relative 
positions as when the former was moveable. Similar explanations 
may be given in the other cases. In general, it may be said that, 
as the galvanic current always tends to maintain itself by a 
uniform circular motion about the axis of the electrode, it tends 
also to impress on the electrode a movement by which the 
uniformity of the circular motion, when interrupted, may be 
most readily restored. 


72 Prof, Challis on a Theory of Magnetic Force. 


12. The directive action of terrestrial magnetism on galvanic 
currents admits of the following explanation. Let the current 
flow in a circular electrode moveable about a vertical axis, and 
let the electrode be so placed in the plane of the magnetic 
meridian, that the direction of the current at the lowest part may 
be from north to south. A diameter to the circle being drawn 
in the direction of the terrestrial current, that is, from south 
towards north in the line of the dipping needle, at and near the 
south extremity of the diameter this current will be cenfluent 
with the circular movement about the electrode on the easé side, 
and opposed to it on the west side. Hence on the latter side 
there will be an excess of pressure which will tend to move the 
electrode eastward. At the other end of the diameter the 
terrestrial current flows with the circular stream on the west side 
and opposes it on the east side, and consequently tends to move 
the electrode westward. Hence on the whole the electrode will 
rotate in the direction which accords with observation, till it 
takes a position perpendicular to the plane of the meridian. 

13. The directive action of terrestrial magnetism on the 
dipping needle is explained as follows. When the needle is in its 
normal position, the extremity A directed northward, the secon- 
dary streams flow longitudinally in the same direction as the 
primary terrestrial stream, and their transverse motions are 
perpendicular to the latter. There is consequently no tendency 
of the needle to move from this position. Now let the axis of 
the magnet be inclined to its normal position in any given 
direction. The secondary streams will not be altered by this 
change, because, as before explained, the accelerative forces to 
which they owe their origin are independent of the direction of 
the primary stream. But in the new position the two streams 
will influence each other so as to give rise to dynamic action on 
the needle. Conceive, for the sake of distinctness, the end A of 
the needle to deviate about 30° from the normal position towards 
the west. Then resolving both the primary and the secondary 
streams in the directions perpendicular and parallel to the needle, 
the respective perpendicular streams along the north portion of 
the needle (this being the portion from which the secondary 
streams zssue) will be opposed to each other on the west side of 
the needle, and conspire on the east side. Thus the needle will 
be urged eastward. Onthe south portion of the needle, at which 
the secondary streams are confluent, the perpendicular compo- 
nents are opposed to each other on the eas¢ side and conspire on 
the west side, and that portion is consequently urged westward. 
As the two actions are equal and opposite, the needle has simply 
a motion of rotation, and the directive action is always éowards the 
normal position. 

14, It follows that the directive force of the earth’s magnetism 


C. W. Siemens on a new Resistance Thermometer. 73 


is a measure of the velocity of the terrestrial current, that is of 
the total intensity of the magnetic force. According to the 
theory, this force may be supposed to be the resultant of hori- 
zontal and vertical components, and the ratio of the latter to the 
former is the tangent of the Inclination. 
Cambridge Observatory, 
December 22, 1860. 
[To be continued. | 


IX. On anew Resistance Thermometer. 


To Professor John Tyndall, F.R.S., &c., Royal Institution. 
3 Great George Street, Westminster, S.W. 
My pear Sir, December, 1860. 

hehe will probably be interested to hear about a very direct 

application of physical science to a purpose of considerable 
practical importance, which I had lately occasion to make. Having 
charge, for the British Government, of the Rangoon and Singapore 
telegraph cable, in so far as its electrical conditions are concerned, 
I was desirous to know the precise temperature of the coil of 
cable on board ship at different points throughout its mass, 
having been led by previous observations to apprehend spontane- 
ous generation of heat. As it would have been impossible to 
introduce mercury thermometers into the interior of the mass, 
I thought of having recourse to an instrument based upon the 
well-ascertained fact that the conductivity of a copper wire 
increases in a simple ratio inversely with its temperature. The 
instrument consists of a rod or tube of metal about 18 inches 
long, upon which silk-covered copper wire is wound in several 
layers so as to produce a total resistance of, say 1000 (Siemens) 
units at the freezing temperature of water. The wire is covered 
for protection with sheet india-rubber, inserted into a tube and 
hermetically sealed. The two ends of the coil of wire are brought, 
by means of insulated conducting wires, imto the observatory, 
where they are connected to measuring apparatus, consisting of 
a battery, galvanometer, and variable resistance coil. The 
galvanometer employed has two sets of coils, traversed in oppo- 
site directions by the current of the battery. One circuit is 
completed by the insulated thermometer coil, and the other bya 
variable resistance coil of German silver wire. Instead of the 
differential galvanometer, a regular Wheatstone’s bridge arrange- 
ment may be employed. 

You will readily perceive that if the thermometer coil before 
described were placed in snow and water, and the variable re- 
sistance coil were stoppered so as to present 1000 units of resist- 
ance, the currents passing through both coils of the differential 
galvanometer would equal one another, and produce, therefore, 
no deflection of the needle. If, however, the temperature of the 


74: C. W. Siemens on a new Resistance Thermometer. 


water should rise, say 1° Fahr., its resistance would undergo an 
increase of 1000 x 002] =2°1 units of resistance, necessitating 
an addition of 2°1 units to the variable resistance coil m order 
to re-establish the equilibrium of the needle. 

The ratio of increase of resistance of copper wire with increase 
of temperature may be regarded as perfectly constant within the 
ordinary limits of temperature ; and being able to appreciate the 
tenth part of a unit in the variable resistance coil employed, I 
have the means of determining with great accuracy the tem- 
perature of the locality where the thermometer resistance coil 
is placed. Such thermometer resistance coils I caused to be 
._placed between the layers of the cable at regular intervals, con- 
necting all of them with the same measuring apparatus in the 
cabin. 

After the cable had been about ten days on board (having left 
a wet tank on the contractors’ works), very marked effects of 
heat resulted from the indications of the thermometer coils 
inserted into the interior of the mass of the cable, although the 
coils nearer the top and bottom surfaces did not show yet any 
remarkable excess over the temperature of the ship’s hold, which 
was at 60° Fahr. The increase of heat in the interior progressed 
steadily at the rate of about 3° Fahr. per day, and having reached 
86° Fahr., the cable would have been inevitably destroyed in the 
course of a few days, if the generation of heat had been allowed 
to continue unchecked. 

Considering the comparatively low temperature of the surface 
of the cable, much incredulity was expressed by lookers-on re- 
specting the trustworthiness of these results; but all doubts 
speedily vanished when large quantities of cold water of 42° 
temperature were pumped upon the cable, and found to issue 72° 
Fahr. at the bottom. 

Resistance thermometers of this description might, I think, 
be used with advantage in a variety of scientific observations,— 
for instance, to determine the temperature of the ground at 
various depths throughout the year, or of the sea at various 
depths, &c. &c. In the construction of this instrument, care 
has to be taken that no sensible amount of heat is generated by 
the galvanic currents in any of the resistances employed. 

By substituting an open coil of platinum wire for the insulated 
copper coil, this instrument would be found useful also as a 
pyrometer. 

But, finding this letter already exceeds its intended limits, I 
shall not enlarge upon these applications, which, no doubt, are 
quite obvious to you. 

I am, dear Sir, 
Yours very truly, 
- C. Wo, SIEMENS. 


pores. 
X. Proceedings of Learned Societies. 


ROYAL SOCIETY. 
(Continued from vol. xx. p. 550.] 
March 22, 1860.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 


‘PHE following communications were read :— 
“On the Insulating Properties of Gutta Percha.” By Flee- 
ming Jenkin, Esq. 

The experiments described in this paper were undertaken with the 
view of determining the resistance opposed by the gutta-percha 
coating of submarine cables at various temperatures to the passage 
of an electric current. 

The experiments were made at the works of R. 8. Newall and Co., 
Birkenhead. ‘The relative resistance of the gutta percha at various 
temperatures was determined by measuring the loss on short lengths 
immersed in water. These experiments are described in the first 
part of the paper. The absolute resistance of gutta percha has been 
calculated from the loss on long submarine cables. These experi- 
ments and calculations are described in the second part of the 
paper. 

Part I. 

The loss of electricity was measured upon three different coils, 
each one knot in length. One was covered with pure gutta percha; 
the two remaining coils were covered with gutta percha and Chat- 
terton’s compound. The coils were kept at various temperatures 
by being covered with water in a felted tub ; and the water was main- 
tained at a constant temperature for twelve or fourteen hours before 
each experiment. 

The loss or current flowing from the metal conductor to earth 
through the gutta-percha coating was measured on a very delicate 
sine-galvanometer. The loss from the connexions when the cable 
was disconnected, was measured in a similar manner. The electro- 
motive force of the battery employed was on each occasion measured 
in the manner described by Pouillet. Corrections due to varying 
electromotive force and loss on connexions were made on the result 
of each experiment. 

A remarkable and regular decrease in the loss was observed for 
some minutes after the first application of the battery to the cable; 
a phenomenon, which the author thinks may be due to the polariza- 
tion of the molecules of gutta percha, or of the moisture contained 
in the pores of the gutta percha. The loss was therefore measured 
from minute to minute for five minutes, with each pole of the 
battery. 

Nineteen tables containing the results, with the reductions and 
curves representing the results, accompany the paper. The following 
results were obtained from the first coil; this was prepared with 
Chatterton’s patent compound. With a negative current between 
the limits of 50° and 80° Fahrenheit, the decrease of resistance is 
sensibly constant for equal increments of temperature; and the 
increase of resistance due to continued electrification is also nearly 


76 Royal Society :— 


constant. At 60° the resistance increases about 20 per cent. im five 
minutes from this cause. With a positive current, similar results 
appear between the temperatures of 50° and 60°; but the resistance 
is somewhat greater than with the negative current. ‘The extra 
resistance due to continued electrification is unchanged by a change 
in the sign of the current. Above the temperature of 63° great 
irregularities occur in the observations, which could not even be 
included in regular curves. The difference in the resistance of the 
gutta-percha coating when the copper is positively and negatively 
electrified, may be caused by the contact between the resinous com- 
pound and the copper: no such difference was observed when pure 
gutta percha was in contact with the copper. 

The curves resulting from the experiments on the second coil, 
which was covered with pure gutta percha, present an entirely dif- 
ferent character from those resulting from the first coil. The copper 
and gutta percha were of the same size in these two coils. The re- 
sistance of pure gutta percha at low temperatures is greater than 
that of the compound covering. At 65° the resistance of the two 
coverings is equal; at higher temperatures the resistance of pure 
gutta percha diminishes extremely rapidly. The curves obtained 
with positive and negative currents are identical up to about 75°; a 
slight difference occurs above this temperature, which may have been 
accidental. ‘I'he extra resistance 1s less with pure gutta percha than 
with the compound; it increases slightly at high temperatures, and 
is not affected by a change in the sign of the current. 

The curves derived from the experiments on the third coil, which 
contained a smaller proportion of Chatterton’s compound than the 
first coil, appear in some respects intermediate between those derived 
from the first and second coils. ‘The extra resistance due to con- 
tinued electrification was still greater in this coil than in the others. 
40 per cent. of the entire resistance is at 70° due to this cause. 
This increase is believed to be due to the greater mass of gutta 
percha used in covering this coil, which was of larger dimensions 
than the two others. 


Parr II. 


Professor Thomson has supplied an equation expressing the law 
which connects the resistance of a cylindrical covering, such as that 
of a cable, with the resistance of the unit of the material forming the 
covering. 

Let S be the specific resistance of the material, or the resistance 
of a bar one foot long, and one square foot in section; let G be the 


resistance of the cylindrical cover of a length of cable L; let 5 be 
the ratio of the external to the internal diameter of the covering ; 
then 


27LG 
= Bo ee 


log Z 


The resistance G was calculated from cables of various lengths, 
lying in iron wells at the works of R. S. Newall and Co., Birkenhead. 


Mr. Jenkyn on the Insulating Properties of Gutta Percha. 77 


The cables were not wet; but direct experiment proved that cover- 
ing a sound iron-covered cable with water has no effect on the loss. 
The details of this experiment are given in the paper. 

The résistance G was obtained in the following manner. The 
copper conductor of the cable to be tested was arranged so as to form 
a complete metallic are with a battery of 72 cells and a tangent gal- 
yanometer : the deflection on this galvanometer was read and entered 
as the continuity test. Deflections were then read on the same gal- 
vanometer with the battery and several known resistances in circuit, 
for the purpose of measuring the resistance and electromotive force 
of the battery, in the manner described by Pouillet. The deflection 
caused by the loss was next read on a second tangent galvanometer : 
the same battery was used. This deflection was entered as the insu- 
lation test. The temperature of the tank containing the cable was 
observed by means of a thermometer inserted in a metal tube, ex- 
tending from the circumference into the mass of the coil. 

The relative delicacy of the galvanometers was ascertained by 
experiment, or, in other words, the coefficient was found by which 
the tangents of the deflections of the first were multiplied to render 
them directly comparable with the tangents of the deflections of the 
second galvanometer. 

The resistances of the galvanometer coils, of the artificial resistance 
coils, and of the copper conductor of the cable were measured by 
Wheatstone’s differential arrangement. Special experiments were 
made by means of this differential arrangement to determine the 
change of resistance of the copper conductor in the cable, produced 
by a change of temperature. 

The equation (No. 2) R=7r(1+0-00192¢) gives the value of the 
resistance R of the copper wire at any temperature ¢+ a in function 
of the resistance 7 at any temperature a (Fahrenheit). The length 
and temperature of any coil being known, the resistance of the 
copper wire was thus at once obtained from the resistance of one 
knot at 60°, which was very carefully determined. 


Now let G=resistance of cylindrical coating. 
D=deflection called the continuity test. 
d=deilection called the insulaticn test. 
C=coefiicient expressing the relative delicacy of the two 
galvanometers. 
BR=resistance of the battery. 
'T,=resistance of the coil of first galvanometer. 
T,=resistance of the coil of second galvanometer. 


C tan DX (BR+T,4+) WV 
Then (aise alla alta a at (3) 


tan d 
G having been thus obtained in any desired units, S, the specific 
resistance of the material, can be at once obtained by equation No. 1, 
which appears from several experiments to give constant values for 
S when calculated from cables of different dimensions. In extreme 
eases, however, the influence of extra resistance would render the 
formula defective, especially after continued application of the cur- 


78 | Royal Society. 


rent: thus the resistance of a foot-cube would be very different to 
that of an inch-cube. 

The values of G for the covering of the Red Sea cable, after con- 
tinued ‘electrification for periods of one, two, three, four, and five 
minutes, were calculated in Fhomson’s Absolute British Units, from 
four sets of tests made specially for this purpose on four different 
cables, each about 500 knots long. Tables containing the results of 
these calculations accompany the paper. 

A Table is also given of the resistance of the Red Sea covering 
after one minute's electrification, and after five minutes’ electrification, 
at each degree of temperature, from 5U° to 75° Fahrenheit. This 
Table was formed by means of the temperature curves described in 
the first part of the paper: this Table is here annexed (No. 1). 

Similar Tables were given for the covering of the two experimental 
coils mentioned in the first part of the paper. The coil composed 
of pure gutta percha, gave very regular and complete results. An 
abbreviation of the Table is annexed. 

It was remarked that in the tests of the cable in the iron tanks, 
the resistance after five minutes’ electrification was invariably 
greater with zinc than with copper to cable, whilst the reverse was 
the case with the single knot covered by water. The length of the 
cable, and the condition of immersion or non-immersion, have pro- 
bably some influence on the phenomenon of extra-resistance. This 
phenomenon appears to the author to be of much importance, and 
to demand further investigation. 

The values of G were also calculated from the daily tests of the 
cables during manufacture at many temperatures. These values 
agreed with those given in the Tables above described. The general 
results of the experiments may be summed up as follows. 

The relative loss at various temperatures through pure gutta 
percha has been pretty accurately determined for all ordinary tem- 
peratures, Toa less extent the same knowledge has been gained 
concerning two other coatings containing Chatterton’s compound. 
The latter appears superior at high, and inferior at low temperatures. 

Attention has been drawn to the considerably increased resistance 
which follows the continued electrification of gutta percha and its 
compounds. Some of the laws of this extra resistance have been 
determined, and some suggestions made as to the cause of the 
phenomenon. 

The bounds have been pointed out within which formule may 
be used, which consider gutta percha as a conductor of the same 
nature as metals. 

The resistance of gutta percha has been obtained in units, such as 
are employed to measure the resistance of metals; and by the use of 
Professor Thomson’s formula, the specific resistance of a unit of the 
material has been fixed with some accuracy. 

The resistance of other non-conductors, such as glass and the 
resins, may probably, by comparison with gutta percha, be obtained 
in the same units. 

Incidentally, the increase of resistance in copper with increased 
temperature has been given from new experiments; and it has been 


Intelligence and Miscellaneous Articles. 79 


shown that the insulation of a sound wire-covered cable is little, if at 
all, affected by submersion. 

Finally, tables and formule are given by which the resistance of, 
or the loss through any new cable coated with gutta percha, may be 
at least approximately estimated :— 


TaBte_e I, 


Specific Resistance in Thomson’s Units of the Red Sea Covering at 
various Temperatures. 


Zinc to cable. Copper to cable. 


Tempera- /After electrification|After electrification||After electrification|Af er electrification 
ture. for one minute. for five minutes. for one minute. for five minutes. - 


60° 2162 «1017 3330 x 1017 2239 x 1017 3405 x 1017 

65 1810x ,, 2947 ,, 1720 ,, W770 

70 1460~x ,, AS 78'>< «5; ISis>s< ;, DA er a 

79 1160~x ,, BSS <5 1000~x ,, L7a9 <>, 
Taste II. 


Specific Resistance in Thomson's Units of pure Gutta Percha at 
various Temperatures. 


Zinc to cable. Copper to cable. 

Tempera- /After electrification|After electrification|/After electrification|After electrification 
ture. for one minute. for five minutes. for one minute. for five minutes. 
50 41131017 5663 x 1017 4113 x 10!” 5663 x 1047 
55 2917x ,, 3636X ,, 2917 ,, 3636X ,, 

60 2163X ,, 2549 ,, 2163x ,, 2549X ,, 
65 1634 ,, 1858x ,, 1634X ,, 1858 ,, 
70 1162x ,, 1291x ,, 1192 ,, 1291x ,, 
75 805x ,, S71 X os 780% -53 866 ,, 
80 566x ,, 613.X< 5; 548 X ,, agi xX. 5, 


“Qn Scalar and Clinant Algebraical Coordinate Geometry, intro- 
ducing a new and more general Theory of Analytical Geometry, in- 
cluding the received as a particular case, and explaining ‘imaginary 
points,’ ‘intersections,’ and ‘ Lines.’ ”’ By Alexander J. Ellis, Esq., 
BA; F.C.P.S. 


XI. Intelligence and Miscellaneous Articles. 


THE LITHIUM SPECTRUM. 
To the Editors of the Philosophical Magazine and Journal. 


GENTLEMEN, 
ERMIT me through you to ask MM. Kirchhoff and Bunsen, or 
other experimentalists in this country who may be in possession of 
the requisite apparatus, whether the “ very weak yellow line Lif,” 


80 Intelligence and Miscellaneous Articles. 


described by them* as accompanying the brilliant red line Lia, re- 
quires any extraordinary precautions to render it visible. Two 
specimens of lithium salts which I have examined in a very perfect 
apparatus, somewhat similar to the one described by them+, have 
failed to give the slightest evidence of its presence, although I have 
repeatedly examined them with that object; and as I know that 
other experimentalists in this country have been equally unsuccess- 
ful, it is possible that the presence of this line in the spectrum given 
by MM. Kirchhoff and Bunsen’s specimens of lithia may really be 
due to the presence of another element hitherto unknown. The 
spectrum of the new alkali metal Cesium (which it may be of interest 
to know I have detected in some highly concentrated mother-liquors 
from sea-water) is in no respect similar to it. It will bea sufficient 
proof of the delicacy of my apparatus, to say that it is constructed 
principally of quartz, and that it easily separates the double line D. 
I remain, Gentlemen, 
Your obedient Servant, 
WiLuiAM CROOKES. 


A CONSTANT COPPER-CARBON BATTERY. BY JULIUS THOMSEN. 


In the ordinary galvanic apparatus, zinc usually officiates as posi- 
tiveelement. ‘This metal is, however, readily attacked by acid if it is 
not either chemically pure or well amalgamated. if the sulphuric 
acid is not greatly diluted, the zinc cylinders are strongly attacked 
by continuous use, in spite of the amalgamation, by which a great loss 
of metal is caused ; if, on the other hand, the acid is much diluted, it 
is soon saturated, and the action of the apparatus is enfeebled. 

In my investigations I use a galvanic apparatus consisting of cop- 
per in dilute sulphuric acid.(1 part acid and 4 parts of water) as positive 
element, and, as a negative element, carbon in the mixture of bichro- 
mate of potass, sulphuric acid, and water, recommended by Wohler 
and Buff. (Buff uses 100 parts water, 12 of bichromate, and 25 of 
sulphuric acid.) The electromotive force of this combination is ;%,ths 
of that of a Daniell’s battery. 

Its advantages are as follows :—The copper is not at all attacked 
by the acid when the circuit is open ; the resistance of the sulphuric 
acid, from its being so little diluted, is a minimum: the sulphuric acid 
is so strong that it can be used for months without becoming satu- 
rated. As, further, the mixture of chromate of potass and sulphuric 
acid is inodorous, this combination is very convenient for working 
with in closed spaces. 

This combination is very interesting theoretically ; for as copper 
cannot decompose dilute sulphuric acid, the copper-carbon element 
is an example of a powerful apparatus in which chemical action and 
the disengagement of electricity are quite inseparable.—Poggendorff’s 
Annalen, October 5, 1860. 


* Phil. Mag. S. 4. vol. xx. p. 96, August, 1860. 
t+ Ibid, p. 90. 


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PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FOURTH SERIES.] 


FEBRUARY 1861. 


XII. Note respecting Ampére’s Experiment on the Repulsion of 
a Rectilinear Klectrical Current on itself. By James D. 
Forses, D.C.L., V.P.R.S.E., Principal of the United College, 
St. Andrews, late Pr ofessor of Natural Philosophy in the Uni- 
versity of Edinburgh*. 

[With a Plate. ] 

p a communication to the Royal Society of Edinburgh, on 

the 3rd of January, 1859, I related some experiments on 
the vibrations of metallic bodies and of carbon, produced by the 
passage of electricity through them+. I learned soon after, 
from a paper by Dr. Tyndall{, that these vibrations had been 
already described by Dr. Page of the United States§. The 
analogy of the experiment to that of Mr. Trevelyan, on the 
vibrations of metallic bodies by heat, led me to suspect that the 
resistance to the propagation of heat in the first case, and of 
electricity in the second, in its passage from the one to the 
other of the bodies in contact, was the cause of a sensible me- 
chanical repulsion. So strongly was I persuaded of this, that 
twenty-seven- years ago, when making my experiments on the 

“Trevelyan” bars, I attempted to set them in motion by elec- 

tricity, though then ineffectually. 

[Tam aware that the idea of the idio-repulsive quality of the 

heat-current has not been favourably received, and that the high 

authority of Mr. Faraday is still given for an explanation of the 


* Communicated by the Author, having been read to the Royal Society 
of Edinburgh, January 7, 1861. 

t Proceedings of the Royal Society of Edinburgh, vol. iv. p. 151; and 
Phil. Mag. vol. xvii. p- 308. 

is Phil. Mag. vol. xvi. p. 358. 

§ Silliman’s Journal (1850), vol. ix. p. 105. 


Phil. Mag. 8, 4. Vol. 21. No. 188, Fed, 1861. G 


82 Prof. J. D. Forbes on the Repulsion of 


phenomena founded on the familiar laws of conduction and ex- 
pansion alone. Dr. Tyndall thinks that the effects of electri- 
city are also to be ascribed to the indirect action of the heat which 
it produces, in the way of expansion. I lave never been satisfied 
with either of these explanations. The conviction to which I 
still hold is that the alleged expansion and contraction cannot 
sensibly operate in the almost infinitely short periods of succes- 
sive contact and separation, and that the effect must be due to 
a molecular impulse of a far more sudden and instantaneous 
character*. We seem to be sufficiently conversant with such im- 
pulses in galvanic, and especially in secondary induced currents. 

This inquiry, however, into the effects of an electrical current 
upon itself, and upon the different portions of one and the same 
conductor conveying it, is one of extraordinary difficulty. We 
cannot fail to be struck by the hesitation with which that great 
Master of this branch of science, Mr. Faraday, expresses himself 
in different parts of his writings respecting them J. 

There is one experiment, quoted m modern treatises on elec- 
tricity, which might seem to throw light on the subject ; and that 
is Ampére’s experiment on the repulsion of one portion of an 
electrical current upon another portion which is a continuation 
of it in the same right line. This repulsion appeared to be the 
necessary complement of Ampére’s theory of the mutual action 
of currents placed in different positions relatively to one another. 
He considered it to be sufficiently demonstrated by the following 
experiment :—A and B (Plate II. fig. 5) are two little troughs 
filled with mercury, or rather a single trough divided lengthwise 
into two by the glass partition CD. Two straight pieces of 
copper wire a,b, united by the bridge c, float on the mercury, 
which, however, they are everywhere prevented from touching 
metallically by means of a coating of sealing-wax, except at the 
extreme ends nearest to A and B, where they are amalgamated, 
and of course touch the mercury. The two poles of a powerful 
battery being imserted in the mercury troughs near the letters 
A, B, the cireuit is evidently completed through the wire acb. 
It is stated that when this is done, the floating wire is repelled 
from the vicinity of the terminal wires of the battery. This 
repulsion is ascribed to the reaction of a rectilinear current from 
A to a through the mercury, upon the continuation of the cur- 
rent in the copper conductor a,.and to a similar action on the 


side 0B. 


* That the electrical vibrations go on during the copious affusion of the 
apparatus with cold water, and that they take place with remarkable energy 
in an almost inexpansible substance like carbon (see my paper cited above), 
are direct arguments in favour of this conclusion. 

tT See particularly the Ninth and Thirteenth Series of his ‘ Researches.’ 


a Reetilinear Klectrical Current on itself. 83 


This remarkable experiment has been circumstantially de- 
scribed in more places than one by Ampere himself*; but the 
description is in all essentially alike, and the accounts, being 
nearly contemporaneous, may be assumed to refer to one and 
the same trial, which was made, it appears, at Geneva, and in 
the presence of M. Auguste De la Rive. This last is a circum. 
stance of some importance; for it would perhaps be difficult to 
establish that it has ever been successfully repeated since. The 
authors whom I have consulted usually content themselves with 
the barest citation of Ampére’s authority. The only exception 
which I know of is in Miiller’s Lehrbuch der Physik (vol. u. 
p- 318), where the writer notes the difficulty he found in repeat- 
ing the experiment: ‘“ Ferner muss noch angefiihrt werden dass 
dieser Versuch keineswegs zu den leicht gelingenden gerechnet 
werden kann.” From which I infer that the writer had not suc- 
ceeded in repeating it. He also raises doubts (which seem to be 
reasonable) as to whether, supposing it successful, the conclusion 
of Ampére could with certainty be legitimately drawn from it. 

It appeared to me to be a matter of some interest in connexion 
with the experiment of electrical vibration, to repeat the obser- 
vation of Ampére. I had an apparatus made for the purpose, 
but circumstances have hitherto prevented me from using it; 
and I have requested my successor in the Chair of Natural 
Philosophy, Professor Tait, to make trial of it when he happens 
to have a powerful voltaic battery in action. I did, however, 
attempt the experiment in a different form, and, as it appears to 
me, in one both more sensitive in its indications, and less ambi- 
guous in its interpretationy. 

I fitted up a Coulomb’s torsion apparatus (one that had been 
used for experiments on diamagnetism) in the following way. It 
is represented in outline in fig. 6. A moderately fine platinum 
wire A, about 18 inches long, was used to suspend a wooden 
torsion-rod BC, near one end of which (laid on a piece of paste- 
board fastened to the rod) was poised a copper wire bent in the 
form of a horseshoe, as shown in the figure at ab{. Two strong 
copper wires P,N, the terminals of a Grove’s battery of four 
moderate-sized pairs in good action, were brought into the 
position indicated in the figure, so as to be exactly opposite to, 
and in continuation of, the limbs of the horseshoe. The termi- 
nals P, N were kept firmly in their place, and the extremities a, d, 

* Recueil d’ Observations Electro-dynamiques, 8vo, pp. 285, 318. Also 
Bibliotheque Universelle, vol. xxi. p.47; and Ampére’s Théorie, p. 39 
(this last citedby Dr. Roget in his ‘ Electro-Magnetism,’ art. 187). 
app hus following experiments were made in December 1858 and January 

{ The distance a6 might be half an inch, and the distance from the 
suspension wire was relatively sear than the figure indicates, 


84. Prof. J. D. Forbes on the Repulsion of 


of the horseshoe were adjusted by moving it on the pasteboard 
shelf until simultaneous contact of the two limbs with the fixed 
Wires was obtained on moving the graduated head of the torsion 
wire A from right to left. The completion of the current was 
effected without much difficulty by gently pressing the rough 
extremities of the wires into contact by the help of the torsion 
head. 

I found it convenient to increase the tension of the current 
by introducing into the cireuit an ordinary electrodynamic coil 
of stout wire, with or without a core of iron wires. 

So far from finding anything like repulsion of the moveable 
horseshoe on the continuation of the circuit, I soon observed 
that attraction took place, resisting the force of twist of the 
platinum wire exerted through a considerable are, when it tended 
to produce separation. This attraction continued to subsist even 
after the current was withdrawn. 

With a horseshoe composed of two straight limbs, a and 4, of 
bismuth, the connexion c being of copper, a still more decided 
attraction was the result; and it continued to subsist after with- 
drawing the current of electricity, even if only one of the poles 
touched the horseshoe. 

When the terminals P, M were somewhat flatly rounded (as 
in fig. 6a), and the extremities of the horseshoe also carefully 
rounded and polished, I was unable to obtain electrical contact 
by the pressure due to mere torsion. ‘The current did not pass 
until the extremities were touched with nitrate of mercury and 
wiped dry, when it passed readily ; and a marked adhesion took 
place while the current lasted, and for some time after it stopped. 
While the electricity passed, a fizzing noise was audible from the 
extremities of the wires. This might possibly be due to an in- 
sensible vibration. It thus appears that the irregularitics of 
surface of the wires at the points of contact im the first form of 
the experiment was favourable to the electrical propagaticn, as 
it is in the case of ordinary frictional electricity. 

A current from a very powerful Ritchie’s mduction coil, ex- 
cited by four pairs of Grove’s, was next passed through the ap- 
paratus last described. Distinct adhesion took place of the ends 
in contact, opposing a force amounting to 90° or more of tor- 
sion. It continued while the current passed, and for some time 
after. By and by they separated through the effect of torsion. 

This experiment was very instructive. If it commenced when 
the terminations were a little apart, the high-tension electricity 
passed readily in the form of sparks from P and N to the horse- 
shoe—the horseshoe steadily approaching—the sparks getting 
shorter and finally vanishing at both contacts, the attraction 
continuing and facilitating electrical contact. Apparently the 


a Rectilinear Electrical Current on itself. 85 


very same process, of polarity preceding conduction, obtains in 
the ordinary galvanic current. 

The form of the terminals P, N was again altered to a ham- 
mer-shape, as in fig. 6; and now electrical contact with the 
copper horseshoe was even more difficult to obtain than before. 
Though for intensity eight pairs of Grove’s battery and a coil 
were used, the current did not pass without amalgamation, and 
also decided pressure being used; then the adhesion became 
strong, amounting to 140° of torsion of the suspending wire. 

A similar result was obtained when the current was passed 
from one of the hammer-shaped poles A (fig. 7) through a 
straight wire B, laid on the torsion-rod and terminating in a 
small trough of mereur y C, connected with the opposite pole of 
the battery. The adhesion and other phenomena were in all 
respects the same as before. 

I think it will not be doubted that these experiments are far 
more delicate tests than Ampére’s floating wire, of the mutual 
action of two portions of one and the same current, and also 
that the first form is free from the ambiguity which ‘the intro- 
duction of a fiuid conductor occasions. At the same time the 
result, with reference to Ampére’s theory, would be more satis- 
factory if the two rectilinear currents whose mutual action is 
examined were independent of one another, and not parts of one 
and the same current ; for the break in the conductor, necessary 
to the mobility of the parts, mtreduces a peculiarity due rather 
to the force required to propagate the current at all, than to the 
reciprocal action of two currents propagated independently. 

It is needless to add that the result of these experiments is 
not fayourable to the cause which I have assigned to the elec- 
trical vibrations ; but I have not the less thought it desirable to 
record the result, though it leaves that experiment, In my opinion, 
more in need of ‘explanation than ever. 

I have not overlooked the probability of the maintaiing power 
of electricity in the rocking-bar being due to instantaneous in- 
duction currents (Faraday’s) excited at the two points of, con- 
tact of the bar and block round which the rocking takes place ; 
but some experiments made on this supposition led to no result. 

I would, before concluding this paper, direct the attention of 
electricians to another of those isolated experiments connected 
with this subject which require confirmation: I mean the pro- 
duction of “ Davy’s cones,” said to occur when two terminals of a 
very powerful battery, coated with sealing-wax and naked only at 
the ends, are introduced, parallel and vertically, through the bot- 
tom of acup filled with mercury, and reach to within a little space 
of the surface of that fluid. On two occasions—once with 500 
or 600 pairs of the Royal Institution battery, and again with 


86 I. W. and A. Dupré on the existence of a 


Mr. Pepys’s gigantic single galvanic pair at the London Institu- 
tion—cones of mercury rose over the general level of the fluid 
and above the polar wires*. Even Mr. Faraday has failed in re- 
peating the experiment, which is remarkable since, though he 
only used 100 pairs, the electromotive power of modern batteries 
vastly exceeds that of those used in Davy’s time, and the suc- 
cess with Pepys’s apparatus shows that intensity is not indispen- 
sablet. Mr. Faraday thinks that Davy’s cones and Ampeére’s 
repulsion experiment are due to one and the same cause. But 
T incline to believe that Davy’s cones intimate an attraction, and 
not repulsion, and so far concur with the results of my experi- 
ments with the torsion-balance. 

I have had Davy’s apparatus constructed and placed in the 
Natural Philosophy Class Collection in Edinburgh, where I hope 
that it may one day be tested with an adequate power. 


Pitlochry, N. B., 
July 11, 1860. 


Postscript. —Soonafter writing the preceding notice, Irequested — 


Professor A. De la Rive to give me any confirmation which his 
memory could supply, of the success of Ampére’s experiment ; 
and this he has kindly done with all the precision which might 
be expected from him. He adds that the motion could not be 
due to the action of the earth’s magnetism, as it was independent 
of the direction of the current. 


United College, St. Andrews, 
November 26, 1860. 


22 January 1861.—I have just learned from Professor Tait 
that he has succeeded in repeating Ampére’s experiment. 


XIII. On the existence of a Fourth Member of the Calcium group 
of Metals. By F. W. and A. Durret. 


URING our recent examination of London waters by the 

beautiful method of Kirchhoff and Bunsen, we several times 
noticed a faint biue line not due to strontium or potassium, or to 
the lately discovered cesium. Having since worked with larger 
quantities of the deep well-water which had given this line most 
distinctly, we believe we are now justified in stating that the 
group of calcium, strontium, and barium, like that of the alkali- 
metals, contains a fourth member. ‘This new metal gives but 


* Sir H. Davy in Philosophical Transactions for 1823. Compare Mr. 
Faraday’s ‘ Researches m Electricity,’ Ninth and Thirteenth series, arts.1113 
and 1609. 

+ Mr. Faraday’s ‘ Researches,’ as above cited. 

{ Communicated by the Authors. 


i ee 


aT a os “ 


Fourth Member of the Calcium group of Metals. 87 


one blue line*, situated between the lines Sr d+ and K £8, about 
twice as far from the former as from the latter. In brightness 
and sharpness of definition it is quite equal to the line Sr6. 
The method which, after repeated trials, we found most advan- 
tageous for obtaining it in a state of comparative purity is the 
following. The deposit formed by boiling the water was dissolved 
in hydrochloric acid, and a small quantity of sulphuric acid added 
to the clear solution. The precipitate formed, consisting prin- 
cipally of sulphate of calcium, but containing some sulphate of 
barium, sulphate of strontium, and sulphate of the metal under 
consideration, was collected, washed, dried and fused with car- 
bonate of sodium. The fused mass was then boiled with water, 
and the insoluble carbonates of the above-named metals collected 
and treated several times successively in the same manner as the 
original deposit. By these means the lime was gradually re- 
moved, the carbonates becoming proportionally richer in barium, 
&c. Owing to the small quantity of substance at our command, 
we did not attempt to remove the lime entirely. The carbonates 
finally obtained were once more dissolved in hydrochloric acid, 
and the solution, after considerable dilution, mixed with a few 
drops of sulphuric acid. After standing at rest for twenty-four 
hours, the slight quantity of deposit formed, consisting of almost 
pure sulphate of barium ft, was filtered off, and some alcohol added 
to the filtrate, by which a further deposit was obtained, com- 
posed chiefly of the sulphates of strontium and the new metal, 
though not quite free from sulphate of calcium. These sulphates 
were again converted into carbonates, which were then dissolved 
in hydrochloric acid, and the solution evaporated to dryness. 
When a portion of this dry residue was brought into the flame 
of the apparatus, the spectra of calcium and strontium appeared ; 
and, in addition, beyond the line Sr 6, in the position indicated 
avove, a blue line, rivalling the strontium-line in brilliancy and 
distinctness of outline. 

As far as we have been at present able to ascertain, the car- 
bonate, oxalate, and sulphate of the new metal are insoluble in 
water, the last-named possessing about the same insolubility as 
sulphate of strontium. The chloride of the metal does not seem 
to be hygroscopic, resembling in this respect that of barium 
rather than those of strontium and calcium. 


* Having been unable to separate it completely from calcium and stron- 
tium, we are not quite positive whether or not it gives any lines at the red 
end of the spectrum. 

T In our last communication there is a typographical error, Sry being 
. put for Sr 6d. 

{ We have detected the presence of barium in several London waters 
since the publication of our notice in the November Number of the Phi- 
losophical Magazine, 


88 Prof. Schcenbein on the Insulation of Antozone. 


We hope soon to be in possession of a sufficient quantity of 
some salt of this metal to give a fuller account of its pro- 
perties. 

In reference to the letter of Mr. Crookes in the last Number 
of this Magazine, stating his inability to recognize the yellow 
line Lif, we may say that all the different specimens of lithium- 
salts we have experimented with have shown this line distinctly. 
Since the publication of his letter, we have examined some very 
pure specimens of lithium-salts, all of which gave the yellow 
line Li 8 with equal distinctness, though showing no other lines 
except Lia and. The red line may certainly be recognized 
with quantities of lithium-salt much smaller than are required 
to exhibit the yellow line. 

The apparatus we use is one similar to that described in 
Kirchhoff and Bunsen’s paper, and we find no particular pre- 
cautions necessary to exhibit the line in question, beyond using a 
comparatively large quantity of lithium-salt, say J) to 35 of a 
grain, and a thin ‘platinum wire of about + millim. diameter. 

We may here mention imeidentally, that we have found it 
advisable to discontinue the use of a brass Bunsen’s burner, to 
prevent the occasional appearance of a series of green and blue 
lines, due to copper. A Bunsen’s burner made of steatite is 
quite free from any such defect. The flame of the burner should 
also be regulated in such a manner as to have the part placed 
opposite the slit free from any marked blue tint, as otherwise a 
number of Ines, one green and three blue being the most con- 
spicuous, make their appearance. The blue or lower part of 
the flame of a candle or of an oil-lamp shows precisely the 
same lines. 


—— 


XIV. On the Insulation of Sea ee a Tete to Professor 
 Farapay. By Professor Scua@NnBEIN*. 

| HAVE been working very hard these many months to obtain 

the ‘‘antozone,”’ or @, in its insulated state, and I flatter myself 
that I have succeeded, at least to a certain extent. Youare aware 
that, from a number of facts, notably from the reciprocal deoxi- 
dizing influence exerted by many oxy-compounds upon each 
other, I drew the inference that there existed two series of oxides, 
one of which contains ©, the other @©,—the ozonides and ant- 
ozonides. The mutual deoxidation of those compounds I made 
dependent upon the depolarization or neutralization of @ and O 
into O. Now © and 0 being capable of being transformed into 
O, I thought it possible, even probable, that the contrary might 
be effected, 2. e. the chemical polarization of O into © and 0; 
and you know that in the course of the last and present year I 

* Communicated by Professor Faraday. 


Prof. Schoenbein on the Insulation of Antozone. 89 


have ascertained a great number of facts that speak, as far as I 
can see, highly in favour of that idea. As the typical or funda- 
mental fact of this chemical polarization of O, I consider the 
simultaneous production of O and HO+@ which takes place 
durmg the slow combustion of phosphorus. This simultaneity is 
such, that ozone never makes its appearance without its equivalent 
HO+0. Allthe metals which oxidize slowly, HO being present, 
such as zine, lead, iron, &c., give rise to the formation of HO+@; 
and so do a great number of organic substances, such as ether, 
the tannic, gallic, and pyrogallic acids, hamatoxidine, &c.; and 
even reduced indigo, associated with potash, &c., makes no excep- 
tion to the rule. The same simultaneity takes place during the 
electrolysis of water; never ozone without peroxide of hydrogen. 
I admit therefore that O, on being brought into contact with an 
oxidable substance and water, undergoes that change of condition 
which I call ‘chemical polarization;” 7. e. is converted into O and 
@, the latter of which combines with HO to form HO+ ®, whilst 
© is associated to the oxidable matter, such as phosphorus, zine, 
&e. In the preceding statements you have only a very rough 
outline of my late researches on the chemical polarization of 
neutral oxygen: the details on that subject are contained in a 
number of papers lately published, and of which your English 
periodicals have as yet not taken any notice. Havimg gone so 
far, I could not but be very curious to try whether it was not 
possible to obtain © in its insulated or free state. I directed 
of course my attention to that set of peroxides which I call 
“antozonides,” and tried in different ways to eliminate from 
them that part of their oxygen which I consider to be ®. Years 
ago I remarked, in accordance with an observation made by M. 
Houzeau, that the oxygen disengaged from the peroxide of 
barium by means of the monohydrate of SO%, exhibits an 
ozone-like smell, and the power of turning my ozone test-paper 
blue. Not having at that time a notion of two opposite active 
conditions of oxygen, I was inclined to ascribe these proper- 
ties to the presence of minute quantities of ozone in the said 
gas; but on examining it more closely, 1 found it to be neutral 
oxygen mixed up with a very small portion of antozone, or @. 
A most important and distinctive property of antozone is the 
readiness with which it unites with water to form peroxide of hy- 
drogen, whilst ozone, like neutral oxygen, is entirely incapable 
of domg so. Hence it comes to pass that the oxygen disengaged 
from BaO +, under certain precautions, becomes inodorous on 
being shaken with water, and that this fluid contains HO”. The 
simple cause of the minute quantities of Oobtained from BaO + 0, 
is the heat disengaged during the action of SO® upon the per- 
oxide, by which most of the © eliminated is transformed into O. 


90 Mr. J. Cockle’s Note on the Remarks of Mr. Jerrard. 


Now, what do you say to the extraordinary fact, that the anti- 
pode of ozone has these many thousand years been ready formed 
and incarcerated, only waiting for somebody to recognize and 
let it loose out of its prison? <A dark blue species of fluor-spar 
has for years been known by the German mineralogists, being 
distinguished by its property of producing a peculiarly disagree- 
able smell on being triturated. Many conjectures were made 
as to the chemical nature of the odorous matter emitted from 
the spar: chlorine, iodine, and even ozone were spoken of, but 
it turned out to be a different thing. 

M. Schafhaeutl of Munich sent me, a month ago, some hun- 
dred grammes of the said fluor-spar (occurring within the veins 
of a granitic rock at Wulsendorf, a Bavarian village near Am- 
berg), asking me to try my luck in ascertaining the nature of 
the smelling matter; and I think I have fully sueceeded in 
making out what itis. Surprising as it may sound to you, and 
unique as the fact certainly is, that matter happens to be nothing 
but my insulated antozone. ‘ But how do you prove that ?” you 
will ask me. Inthe first place, it smells exactly like © disengaged 
from BaO?. “ But smells are fallacious tests.” They are. You 
shall have another proof that will irresistibly carry conviction 
with it: on triturating the fluor-spar with water, peroxide of 
hydrogen is formed, not in homceopathic, but very perceptible 
quantities. When I first found out this extraordinary fact (I 
think it was on the 17th of November last), I could not help 
laughing aloud, though I happened to be quite alone in my la- 
boratory. I laughed because [ strongly suspected my foe to be 
hidden in the spar, and I broke his mask under water with the 
view of catching him by that fluid. Indeed, it was to me as if I 
had caught a very cunning fox, long sought after, in a trap put 
up for him. To show you that in saying this I have neither 
been joking nor dreaming, I shall send you, as soon as I can, a 
sample of the wonderful spar, with which you may easily satisfy 
your curiosity and convince yourself of the correctness of my 
statenents. I must not omit to tell you that, according to some 
previous experiments of mine, the fluor-spar of Wulsendorf 
contains =;5,th part of antozone—a quantity, as you see, not at 
all homeeopathic. How that subtle matter got into the spar I 
cannot tell. 


XV. Note on the Remarks of Mr. Jerrard. 
By Jams Cocxin, Esq. 
[Concluded from vol. xix. p. 332. ] 
HE sequel to Mr. Jerrard’s important ‘ Essay’ may remove 
the new doubts and difficulties which arise upon his 
‘Remarks,’ and which, numbered in conformity with his para- 


0 


Mr. J. Cockle’s Note on the Remarks of Mr. Jerrard. 91 


graphs, are here briefly noticed. Mr. Jerrard has to meet the 
additional objections that— 

1, 2,4. There is no error in Mr. Harley’s processes. The 
error of inferrmg the sextic to be an Abelian I have already 
traced to its source (vol. 3 XIX, up 197 et seq.). 

3. If the functions ,&, .=, 3,5, and ,= are not extraneous, 
let two quintic surds be expelled, as reducible, from them and 
from >=. Then, according to Abel’s theorem, all the roots of 
(ab) are roots of (ac). Denote (ac) and (ab) by 


==0;) e=0 


E=i(Bz—t {Pie .) })- 
But what is the form of €? Certainly not f, for the root & + 


is common to (ab) and (ac). Unless Mr. Jerrard shows that ¢ 
cannot be replaced by f(Be); his conclusion is vitiated by an 


respectively. Then 


error in comparing (ab) and (ac). 

5. The complex process need not supersede the simple method 
of substitutions when we are dealing with symmetric functions 
of @ and ©". Such functions are Mr. Jerrard’s = 5, or 


0; oe 0, “i @;° a ©,, 
and my @, or 
54@, ©, O, O,. 
To take a simple example, 
®n.09(2) t On.a9)(8)= Ons On) BEI): 

6. It can scarcely be said that Mr. Jerrard’s theorem 1s 
ignored by Mr. Harley. That theorem is inapplicable to the 
processes dealt with in Mr. Harley’s paper, into which no 
symbol corresponding to P enters. 

7. Actual calculation shows that & and @ are similar func- 
tions (fonctions semblables). And if in my function y we sub- 
stitute & for @, the result is an equation which, combined with 
(ac), shows that, if the latter be an Abelian, the root of a general 
quintic can be expressed without quintic surds. 

8. If, in expanding a function of two independent quantities, 
we do not obtain an expression symmetric with respect to those 
quantities, and such as to admit of an interchange between them, 
I cannot consider the expansion as algebraically (rigorously) 
true. 

In generalizing the theory of transcendental roots which I 
have sketched, and partially developed, in these pages, we may 
start from 

2” —ne + (n—1)a=0, 


92 Prof, Challis on a Theory of Magnetic Force. 


We next deduce an n-ic in y, in which 


dz 
y= (1 a") Ta? 


and, hence, we pass to an n-ic in 2’, in which 
a'=P+Qy+ Ry?+ .. + Ty”, 
where m is not greater than n—1, and P, Q, R,.. T are so de- 
termined that the n-ic in 2! is of the form 
ai” —nz' + (n—I1)a'=0. 
Irom the equations in 2 and a! we obtain | 
L—= oi, 2 = 0 B= 00", 2.1 tO= one 
whence the form of ¢ is to be sought. 

Mr. Jerrard’s trinomial transformation indicates that this 
process is applicable (primd facie) to equations as high as the fifth 
degree inclusive. Beyond that degree a trimomial cannot be a 
general equation. But possibly the properties of trinomial equa- 
tions, or of equations involving only one parameter, may enable 
us to extend the process further by obtainmg the n-ic in a’, 


4 Pump Court, Temple, London, 
January 12, 1861. 


XVI. A Theory of Magnetic Force. 
By Professor Cuaruis, /R.S, 


[Continued from p. 73.] 


N art. 6 of the foregoing part of the Theory of Magnetic 
Force, certain laws of the motion of an elastic fluid, essential 
both to that theory and to the previous theories of electric and 
galvanic forces, were enunciated without being supported by 
mathematical evidence. Before proceeding further with the ex- 
planation of magnetic phenomena, I.propose to adduce the 
mathematical investigation of those laws. 

15. It was stated that the resultant of the composition of 
steady motions is steady motion. The proof of this theorem is 
as follows :—For cases of steady motion, the general hydrody- 
namical equation which expresses constancy of mass, viz. 

dp ai. pu, d.pvd. pu 
Be de dy dz 
becomes, to the second order of approximation, 
du, dv , dw 


—+—_+-—=0 
da pate ; 


because for that kind of motion dp =0(0, an dp dp dp 


de pd? py? plz 


Prof, Challis on a Theory of Magnetic Force. 93 


each of the order of the square of the velocity, as is shown by 
the general differential equations involving the pressure, no 
extraneous force being supposed to act. Nowif w, v,, w,; 
Up) Voy Wo, &e. be velocities due to different disturbances acting 
separately, and each set of valucs satisfy separately the second 
of the above equations, it is evident that if w=u,+u + &ce., 
v=v,+2,+ &e., w=w,+w.+ &e., u,v, w will satisfy the same 
equation. From this reasoning it follows that when several 
causes of steady motion coexist, the velocity they produce con- 
jointly at any point, is the resultant of the velocities which they 
would produce at the same point by acting separately. Hence 
since the component motions, being steady, are constant in 
magnitude and direction at each point, the resultant motions 
will be constant in magnitude and direction at each point; that 
is, the whole motion will be steady. 

16. Hence in the general hydrodynamical equation applicable 
strictly to steady motion, when no extraneous force acts, viz. 


2 


a* Nap. log p= c-¥ 


we may assume, since terms involving the square of the velocity 
have been taken into account, that V is the resultant of several 
velocities, v', vo’, &c., given in magnitude and direction. Take, 
for instance, the two velocities v! and v”, and suppose their direc- 
tions to make an angle a with each other. Then 
V2=0? +y!? + 20'v! cos a. 

From this equation it is seen that if the value of C be given, 
the velocity is greatest and the density and pressure least, where 
a=0, that is, where the two streams coincide in direction; and 
that the velocity is least, and the density and pressure greatest, 
where a=7 and the two streams are in opposite directions. 

In general the constant C will be different for different lines 
of motion. But in the cases of convergent streams flowing from 
an unlimited distance, and divergent streams flowing to an un- 
limited distance, at remote points p=1 where V=0, and con- 
sequently C=O for each of the lines of motion. 

17. The hydrodynamical theorems above demonstrated are 
those which have been used in accounting for electric attrac- 
tions and repulsions, the mutual action between two electrodes, 
that between an electrode and a magnet, and the mutual attrac- 
tions and repulsions of magnets. It is to be remarked that in 
these explanations the moving forces of the ether acting on the 
ultimate atoms of bodies have been supposed to be due to varia- 
tions of its density, producing statically differences of pressure 
at different points of each atom. But if motion resulted solely 
from variation of the density of the ether from point to point 


94 Prof. Challis on a Theory of Magnetic Force. 


of space, there would seem to be no reason why a magnet should 
not move various substances as an electrified body does. In the 
one case, as in the other, variation of pressure is produced, accord- 
ing to the theory, by etherial streams. What, then, is the reason 
that an electrified body acts indifferently on many kinds of sub- 
stances, whilst a magnet acts in a special manner on certain sub- 
stances, which from this peculiarity have been named magnetic ? 

18. In answering this question, it is first to be considered 
that, according to the hydrodynamical theory of electricity, an 
electrified body has had its superficial atoms forcibly disturbed, 
and that this state of disturbance gives rise to vibrations of the 


ether, the dynamic effect of which on a neighbouring body is to © 


put its superficial atoms also into a state of disturbance, and 
thus to induce electricity. It was explained in the theory referred 
to, that this state of induced electricity coexists with a gradation 
of internal density, which generates the secondary currents to 
which electric attractions and repulsions are attributable. But 
in a magnet there is nothing corresponding to that superficial 
disturbance, the internal gradation of density bemg an inde- 
pendent property of the body. Hence there are no vibrations 
to disturb the superficial atoms of adjacent bodies, the magnet 
acting dynamically wholly by currents, and consequently, as is 
known by experience, it is incapable of inducing electricity. At 
the same time, between a magnet and a body partially or induc- 
tively electrified, there must be interference of cetherial currents, 
and consequently mutual action, as is found experimentally to 
be the case. 

Still it may be argued that magnetic streams, varying from 
point to point of space as to density and velocity, must act 
dynamically on the atoms of bodies of all kinds, independently 
of their electric or magnetic states. That such action does 
really take place to a sensible amount under the influence of 
powerful magnets, will be made apparent by the following con- 
siderations applied to the class of facts discussed experimentally 
by Faraday in the Twentieth and Twenty-first Series of his ‘ Re- 
searches in Electricity’ (Phil. Trans. part 1. 1846). 

19, It has been already stated that, according to hydrody- 
namics, a single spherical atom, subject to the action of a uniform 
steady current, suffers no change thereby of a condition either 
of rest or of uniform motion, But this is no longer true if, the 
stream being steady, the lines of motion are not parallel, to each 
other, because in that case there will be inequality of the pres- 
sures on opposite hemispherical surfaces of the atom. Also when 
such a stream enters into any substance, the partial convergences 
or divergences of its course, which must result from its encoun- 
tering an aggregation of atoms, may materially influence its 


>, =) ee, 


Prof. Challis on a Theory of Magnetic Force. 95 


dynamic action on any given atom. We have not the data for 
inquiring what that action may be in any particular substance, 
because for that purpose we require to know its composition and 
the magnitudes and arrangement of its atoms. I shall there- 
fore assume, asa result of the experiments above referred to, 
that divergent and convergent magnetic streams act dynamically 
in different manners and in different degrees on a great variety 
of substances which they permeate. 

20. If the substance be iron, the moving force of the mag- 
netic streams on its individual atoms, apart from any action 
resulting from interference with secondary streams, tends along 
the lines of motion towards the poles of the magnet. ‘The fol- 
lowing remarkable experiment by Faraday (2368) establishes 
this law. Cylindrical glass tubes containing ferruginous solu- 
tions of different degrees of strength were suspended with the 
axes vertical in a ferruginous solution of given strength between 
the poles of the magnet. If the solution in the tube was stronger 
than that of the surrounding fluid, the tube was attracted to- 
wards either pole; and if weaker, it was repelled. Both these 
effects may be explained on the assumption that the magnet 
attracts the solutions in proportion to the quantity of iron they 
contain. The tube was drawn towards the poles in the first 
case, because the contained fluid being more ferruginous, was 
more attracted than the surrounding fluid. In the other case, 
the hydrostatic pressure of the surrounding fluid, due to the 
assumed magnetic attraction towards the poles, is greater on 
the side of the tube nearest either pole, than on the opposite 
side, and this difference of pressure, not being wholly counter- 
acted by the attraction on the contained weaker solution, causes 
a repulsion of the tube. The cases are exactly analogous to 
those of a body specifically heavier than water smking in it, 
and a body specifically lighter rising in it, by the action of 
gravity. Now it is true that the magnetic forces here assumed 
have the same directions as those which the variation of the 
pressure of the ether would of itself produce. But if the 
action were either wholly or chiefly due to this cause, no reason 
appears why the observed motions should depend, not upon the 
difference of the specific gravities of the fluids within and without 
the tube, but upon one being more or less ferruginous than the 
other. ‘The experiment, therefore, allows us to infer theoreti- 
eally, that etherial streams, flowing through ron, and affected 
by the number, size, and state of aggregation of its atoms, 
exert on each atom an accelerative force, which is in the direc- 
tion of the current where it is convergent, and in the direction 
contrary to that of the current where it is divergent. The 
atoms being by hypothesis spherical, it may be inferred from 


96 Prof, Challis on a Theory of Magnetic Force. 


hydrodynamical considerations, that converging and diverging 
streams impress upon them the same moving forces, if the velo- 
cities be the same, and the degree of convergency be equal to 
that of divergency; but the forces will be in opposite direc- 
tions with respect to the course of the streams. Hence, under 
those circumstances, if one magnetic pole be attractive, the 
other will be attractive also, and in the same degree. This 
result experience confirms. 

21. If a bar of bismuth be suspended either horizontally or 
vertically between the poles of a magnet, it is found to be im- 
pelled in the directions of the lines of motion from the poles. 
The action is therefore opposed to that which results from va- 
riation of density of the ether. The same effect took place when 
the bismuth was broken into very small pieces. Also it appeared 
that two pieces of bismuth subject to the action of magnetic 
streams, exerted no influence on each other; that is, no se- 
condary streams were generated. From these facts it must be 
concluded theoretically, that convergent and divergent magnetic 
streams, when they enter bismuth and substances of the same 
class, and are modified by the number, size, and arrangement 
of the constituent atoms, impress on the individual atoms acce- 
lerative forces, which impel them along the lines of motion from 
the magnetic poles. For the same reason as that above given 
in the case of iron, the action is alike from both poles, and in 
the same degree, although the streams diverge from one and 
converge towards the other. 

22. It is found by experiment that aw and gases are not 
sensibly acted upon by magnetic streams. This fact may be 
explained by the theory on the supposition that such substances, 
on account of their small density, do not perceptibly, by the 
state of aggregation of their atoms, modify the etherial streams, 
which consequently act on each atom as if it were alone. Now 
in that case a divergent stream impels the atom in the direction 
of the course, and a convergent stream draws it in the direction 
contrary to the course, and it is possible that these actions may 
be just counteracted by the opposite effects of the variation of 
density of the ether. 

23. Since the magnetic streams attract one class of substances 
(the magnetic) towards the poles, and repel another class (the 
diamagnetic) from the poles, we might expect to meet with 
other substances which are neither attracted nor repelled, or are 
only acted upon very fecbly. This appears to be the case with 
copper. ‘The peculiar phenomena (Faraday, 2309, &c.) which 
this metal exhibits when placed between the poles of a magnet, 
seem to admit of explanation on the principles of this theory, 
by supposing its atoms to be easily moveable from their normal 


—_— ~ — 


ee a 


Se Se ee eee 


_—* a ee a 


Prof. Challis on a Theory of Magnetic Force. 97 


positions,—a property to which it may perhaps owe the facility 
with which it conducts galvanic currents. Iron and bismuth, 
which are not good conductors of galvanism, present very dif- 
ferent phenomena, in consequence, probably, of a great degree 
of fixity of their atoms, by reason of which, and of atomic ar- 
rangement and constitution, the magnetic streams permeating 
them may be so modified as to become respectively attractive 
and repulsive. <A bar of copper, when first. acted upon by the 
magnetic streams, begins to move as if it were a magnetic body, 
this motion being probably due only to the variation of pressure 
from point to point of the streams. But quickly its atoms, on 
account of their mobility, will be moved by that pressure into 
new positions, which may be such as to render it for a brief 
interval diamagnetic, so that the incipient motion 1s stopped, the 
atoms finally settling into positions for which the bar is neither 
magnetic nor diamagnetic. These are positions of constraint, in 
which they are held by the dynamic action of the pressure of 
the magnetic streams. When the streams are interrupted, the 
atoms, by the proper molecular action of the copper, return to 
their normal positions; and in the mean time the reaction of 
the ether on the bar produces the observed revulsion. The 
magnetic streams continuing in action, if an impulse be given 
to the bar tending to move it into a position of greater mag- 
netic action, for the same reason as above an increment of dia- 
magnetic force is generated, and a momentary excess of diamag- 
netic action, arising from the atoms being carried by their 
momentum beyond the positions in which they finally settle, 
stops it; and if it be moved into a position of less magnetic 
action, a momentary defect of diamagnetic action, also due to 
_ the momentum of the atoms in taking up new positions, equally 
stops it. The sluggish motion of the bar may be thus accounted 
for. The movement which occurs when the streams commence, 
would not take place if the bar were placed in the axial or equa- 
torial direction, because the initial magnetic action would .be 
symmetrical with respect to each of these directions. If the 
copper were of the form of a globe, with its centre on the axial 
direction, the sluggishness would still exist, because any move- 
ment of it about a vertical axis would bring each point into a 
position of either greater or less magnetic action. 

24, Since it appears from the foregoing discussion that, inde- 
pendently of the dynamic effect of magnetic streams resulting 
from gradations of the density of the ether, they exert, when 
they enter a magnetic body, a particular moving force due to 
their divergence or convergence as affected by the atomic con- 
stitution of the body, this force ought to be taken into account 
in the theory of the magnet (art. 4), and in the explanation 

Phil, Mag. 8. 4, Vol. 21. No, 138, Feb, 1861 H 


98 Prof. Challis on a Theory of Magnetic Force. 


of the mutual action between two magnets (art. 7). As the 
two kinds of force act along the same lines in the same direc- 
tions, the consideration of this second force will not alter the 
conclusion arrived at in art. 4, as, in fact, is stated at the 
conclusion of that article. With respect to the manner in 
which the mutual action of two magnets is affected by the 
motion of the xtherial streams within them, it is to be remarked 
that divergence and convergence are increased by the opposi- 
tion of two streams, and diminished by their confluence; and 
that the particular force under consideration is always towards 
positions from which the streams diverge, or towards which they 
converge. Hence this additional force, being some function 
of the degree of convergency or divergency, produces effects 
exactly like those of the pressures considered in art. 7, and the 
conclusion there drawn remains the same when both kinds of 
force are taken into account. 

25. The following theory of magnetic induction rests on the 
foregomg views. It is found that when a bar of soft iron is 
placed in the plane of the magnetic meridian, it is magnetized 
inductively, the magnetism disappearing when its axis is placed 
perpendicular to that plane. ‘The induced magnetism is greatest 
when the axis coincides with the direction of the dippmg-needle ; 
and the magnetism of its north end is the same as that of the 
north end of the needle. These facts admit of beg explained 
on the supposition that the primary terrestrial stream in its 
passage through the bar exerts a force on the atoms in the di- 
rection from south to north, so as to produce a gradation of 
density of the bar towards the north end. ‘This force may ori- 
ginate in the circumstance that when the stream enters the 
bar its velocity is increased by the contraction of the channel by 
the atoms, and, the density and pressure bemg consequently 
diminished, the surrounding fluid is drawn towards the axis of 
the stream. ‘Thus there will be lines of motion without and 
within the bar converging northward, and consequently, from 
what is argued in art. 20, a force will be generated proper for 
producing the increment of density towards the north end. The 
same effect would be produced even if the streams were parallel, 
because as divergent streams fiowmg through iron, draw the 
atoms towards the quarter from which they flow, @ fortiori, 
parallel streams would do the same. Thus the bar is converted 
intoa magnet. But itis to be observed that the atoms retain their 
positions m consequence of the counteraction of this disturbing 
force by the molecular repulsion of the iron due to the variation 
of its density. Hence when the bar, by being put intoa position 
transverse to the magnetic meridian, ceases to be under the in- 
fluence of the terrestrial current, the atoms return to their normal 
positions, and the bar ceases to be a magnet. It is clear that this 


Prof. Challis on a Theory of Magnetie Force. 99; 


induction of magnetism will be greater, the more directly the 
primary stream flows through the bar, as is known to be the case 
by experiment. 

26. When a coil of wire in the form of a helix surrounds a 
cylinder of soft iron, and a galvanic current is sent through the 
wire, magnetism is found to be induced in the iron. This fact 
is explained by the theory as follows. The turns of the helix 
being supposed to be very little apart, each turn will be nearly 
in a plane perpendicular to the axis of the cylinder. Hence the 
circular motions, which, according to the theory of galvanism, 
take place about the wire, will be very nearly in planes passing 
through that axis. Suppose the course of the current to be 
from the end B towards the end A of the cylinder, and the 
turns of the helix to proceed from the left hand, over the ecylin- 
der, to the right hand of a person looking from B towards A. 
Then, since the circular motion about any portion of an elec- 
trode in which the current is conceived to flow parallel to the 
earth’s axis from south to north is always in the direction of 
the earth’s rotation, it follows, in the case supposed, that if the 
circular motion within the cylinder be resolved into parts par- 
allel and perpendicular to its axis, the former will all be in the 
direction from B towards A, and the latter will very nearly 
destroy each other. Thus the result will be a longitudinal stream 
from B towards A, the velocity of which, if the helix be pretty 
close to the cylinder, will be greatest along its axis. The ex- 
planation of the manner in which this stream induces mag- 
netism in the iron core, is precisely the same as that applied in 
the preceding article to induction by terrestrial magnetism. The 
pole A of the magnetized cylinder corresponds to that pole of a 
magnetic needle which points northward. The contrary would 
plainly be the case if the helix, instead of being dextrorsum, as 
supposed above, had been sinistrorsum. All these results agree 
with well known experimental facts. 

27. The theory I now proceed to give of terrestrial magnetism 
rests on no other hypotheses than those on which the general 
physical theory is based. It will be assumed that the earth and 
all the bodies of the solar system are composed of spherical 
inert atoms, of different magnitudes, and in different states of 
aggregation, and that the ether pervading their interiors is in 
the same state of density as in the external spaces. Any in- 
vestigation of the motions impressed on the ether by the known 
motions of the bodies of the solar system, must, in order to be 
consistent with the whole preceding argument, set out from these 
hypotheses. The following considerations will, I think, show 
that they lead to conclusions which are in accordance with ob- 
served facts of terrestrial and cosmical magnetism. 


H 2 


100 Prof. Challis on a Theory of Magnetic Force. 


We are to assume that the mass of the earth consists of dis- 
erete spherical atoms, and that the whole of its interior, excepting 
the space occupied by atoms, is filled with ether in the same 
state of density as in the external regions of space, with only 
such variations of density as are produced by its motion. The. 
same assumption is to be extended to the sun, the moon, and 
all the planets. In the first place, let us endeavour to ascertain 
what kind of movement is impressed on the ether by the earth’s 
rotation ; and for the sake of distinctness, I shall, at first, suppose 
that the earth has no motion of translation, and that it is per- 
fectly symmetrical with respect to its axis and its equatorial 
plane. Then as the terrestrial atoms will impress a part of their 
velocity on the ether, a rotatory motion of the latter will be 
produced, which by its centrifugal force will tend to draw the 
fluid from the earth’s axis. This tendency cannot give rise to a 
stream from one pole to the other, because there is no reason 
why it should flow in one direction rather than the other. 
Neither can streams be generated setting from the equaterial 
parts towards the poles, because as the velocity will be greatest 
in and near the plane of the equator, the fluid would rather be 
urged towards this plane, and circulate by return currents along 
the axis towards the poles. The tendency of the centrifugal 
force to draw off the fluid from the axis of rotation, will be 
counteracted by accelerative forces due to increments of den- 
sity of the ether which result from the resistance of its mertia 
to the centrifugal movement. These forces, acting always 
towards the axis, cause the circular motion immediately im- 
pressed by the atoms to extend into the ether beyond the 
earth’s surface. But it is evident that so long as the terrestrial 
atoms have greater velocity than the ether contiguous to them, 
the centrifugal force is on the increase, and the permanent state 
is reached only when there is no motion of the atoms relative 
to the ether. The opposite forces then maintain a steady 
motion at all points, there bemg no reason why the motion 
should not be steady at one point rather than at another. Con- 
sequently in the earth’s interior, and at the surface, and sensibly 
to considerable heights above, the ether, like the atmosphere, 
partakes of the earth’s rotation. This gyratory motion must 
spread to remote distances, the velocity decreasing with the di- 
stance according to a law which eventually may be found to 
admit of mathematical investigation on hydrodynamical prin- 
ciples. As the motion of rotation must be combined with the 
circulating currents above mentioned, the total motion is spiral. 

28. Now let the earth be supposed to have a motion of trans- 
lation, either uniform or variable. Then on the principle that 
there can be neither gain nor loss of the momentum of the ether 


Prof. Challis on a Theory of Magnetic Force. 101 


due to the earth’s rotation, it may be asserted that the gyratory 
motion is transferred without alteration through space with the 
earth. It may not be that the motion of a given particle of the 
fluid remains the same; but the motion is constantly the same 
im positions which in successive instants are the same relative to 
the earth’s centre and equatorial plane. Coexistent with the 
gyrations of the «ther, motions of translation must be impressed 
upon it, having constant relations to the earth’s motion. With 
respect to that portion of ether which has sensibly the same 
rotation as the earth, the most probable supposition is that it 
has also very nearly the same motion of translation, and that 

consequently the relative motion of the earth’s atoms and the 
ether in its interior is very small. 

These conclusions apply to the other rotatory bodies of the 
solar system. All are consequently centres of gyratory motions, 
which, according to the reasoning in art. 15, may coexist in the 
cosmical spaces without interfering with each other. 

29. But it is not true, as supposed, that a earth is symme- 
trical with respect to its axisand equatorial plane, the superficial 
distribution of land and water showing that this is not the case. 
On the supposition cf symmetry, the centrifugal force of the 
earth’s rotation would induce a variation of its internal density, 
proper, according to the theory, for generating secondary streams 
under the influence of a primary current. But as by reason of 
the symmetry equal and opposite effects would be produced on 
every diameter of the earth, no streams would become sensible. 
For the same reascn no streams result from the increase of the 
earth’s density towards the centre by the effect of ee In 
the actual case of deviation from symmetry, the motion of the 
ether cannot be wholly in symmetrical gyrations as above 
inferred, although it will be approximately such. There must 
be motion relative both to the equator and the axis, steady in its 
character, as depending on constant causes, and constituting a 
primary stream, which flowing through the earth, put into an 
unsymmetrical state of restraint by the centrifugal force, will 
give rise to secondary streams. The primary current : may be of 
feeble intensity, and yet by originating accelerative forces which 
act through large spaces, may generate streams of great intensity, 
The earth’s magnetic streams may be regarded as resulting from 
a combination of the primary and secondary streams. According 
to these views the deviations of the earth’s form and matter from 
symmetry determine the directions of the magnetic streams, which 
appear from experiment to enter the earth on the north side of the 
magnetic equator, and to zssue from it on the south side. The earth 
is thus a vast magnet, the streams of which are of constant intensity, 
excepting so far as they may be disturbed by cosmisal influences: 


102 Prof. Challis on a Theory of Magnetic Force. 


The terrestrial streams probably circulate, those which issue 
nearly perpendicularly to the earth’s surface in the antarctic 
regions, after rising to great heights; turning back in curved 
courses distant from the earth, so as to enter again nearly per- 
pendicularly in the arctic regions. To this circulation must be 
added that spoken of in art. 27, which conspires with the ant- 
arctic streams and opposes the arctic, and thus probably accounts 
for the observed excess of antarctic magnetic intensity. 

30. If the earth had been symmetrical with respect to its axis, 
but not with respect to its equator, the magnetic streams would 
also have been symmetrical with respect to the axis. But the 
actual irregular distribution of land and sea is opposed to this 
law, and it is found in fact that there is an approximation to 
two magnetic poles as well in the arctic as the antarctic regions. 
Also it is established by observation that these poles have not 
fixed positions on the earth’s surface. Taking account of this 
circumstance, and of the character of the irregularities to which 
the theory ascribes the generation of the currents, we might 
infer that the magnetic poles would be unsymmetrically situated 
with respect to the earth’s poles, that the streams would be 
disposed unsymmetrically about them, and that in their move- 
ment they would not retain the same relative positions. These 
inferences observation appears to countenance. 

31. The arches and streamers of the Aurora Borealis and the 
Aurora Australis are portions of terrestrial magnetic streams 
made visible by particular disturbances. According to my view 
of the undulatory theory of light, I should have no difficulty in 
admitting that etherial streams that are steady, and on that 
account emit no light, become luminous upon being disturbed. 

32. We have now to consider the disturbances which the 
steady terrestrial currents may undergo from cosmical influences. 
And in the first place it may be stated, as a deduction from 
hydrodynamical principles, that the steady streams to which 
magnetic force has been attributed, and the vibrations which 
were assumed to exist in the theory of the force of gravity, may 
coexist without mutual interference, so that the two kinds of force 
act independently of each other. 

33. The effect which any motion of translation which the 
earth’s atoms may have relatively to the ether, may be presumed 
to be the same, in respect to generation of secondary currents, 
as that of a current within the earth at rest. In the mvestiga- 
tion of such effect, the motion of translation of the solar system 
would have to be taken into account, together with the motion 
of the earth in its orbit. As observation has not detected a 
variation of terrestrial magnetism corresponding to the law of 
the variation of velocity which would result from the combina- 


Prof. Challis on a Theory of Magnetic Force. 103 


tion of these motions, it must be concluded, in conformity with 
what is said in art. 28, that there is no perceptible effect from 
motion of translation of the atoms relative to the ether. 

34, The terrestrial streams will be disturbed by the streams 
due to the gyratory motion about the sun, and the direction and 
amount of the resultant, at a given place, of the combination of 
the solar and terrestrial streams, will vary with the time of day. 
Hence there will be a diurnal variation of magnetic intensity, as 
is also known from observation. The epoch of maximum in- 
tensity will depend in part on the position of the place relative 
to the magnetic poles. 

35. The amount of the variation of intensity on a given 
day will depend on the sun’s declination, and therefore will be 
subject to an annual variation, being in north latitudes greatest 
at the summer solstice, and least at the winter solstice. These 
results are confirmed by observation. 

It may deserve to be considered whether the magnetic in- 
tensity is sensibly affected by currents which must be produced 
in the atmosphere by solar heat, setting in all directions from 
the parts of the atmosphere most heated by the sun. The effeet 
of these currents would be subject to diurnal and annual varia- 
tions, and if of considerable amount, would have an influence on 
the local hour of maximum intensity. 

36. There will also be an annual variation of intensity inde- 
pendent of the sun’s declination, being due solely to the change 
of the velocity of the solar gyrations, caused by change of the 
-earth’s distance from the sun. Such a variation has been 
detected ; but its amount is very small. 

37. Through the telescope the sun presents itself to our view 
asa globular body, surrounded by a thick envelope consisting 
of matter which accumulates and divides, floatmmg and whirling 
most probably by the action of an atmosphere, and which is 
separated from the interior solid globe by an intervening space. 
‘We cannot be far wrong in calling such matter cloud. It is 
then reasonable to suppose that the observed changes are attri- 
butable to the action of galvanic or magnetic streams, generating 
and precipitating from time to time the cloudy matter. But 
changes can hardly be attributed to the proper magnetic streams 
of the sun, because these, as in the case of the earth, will most 
probably be of a constant character. The changes are rather 
due to disturbances of the solar streams by external influence, as 
‘by the gyratory streams of the planets. It is therefore quite 
in accordance with this theory to find, as has been done lately, 
that observations indicate periods of maxima and minima of 
solar spots. 'These periods will be determined by changes of the 
combined action of the gyratory motions about the planets, as 


104: Prof. Challis on a Theory of Magnetic Force. 


resulting from changes of their positions relative to the sun ; and 
it is therefore not surprising to find that one of them (that of 
111 years) differs little from the periodic time of Jupiter, the 
influence of this planet bemg likely to be predominant on 
account of his large size and rapid rotatory motion. The 
periodicity of the magnetic action of any planet must clearly 
depend in part on the position of the plane of its equator, the 
gyratory motion being at a maximum in this plane. 

38. If the preceding account of the periodicity of the maxima 
of solar spots be true, it will be seen to be a necessary conse- 
quence that the planetary gyrations produce disturbances of 
terrestrial magnetism, having in the long run a reguiar and 
periodic character. The researches of General Sabine, applied to 
magnetic observations taken at various positions on the earth’s 
surface, have in fact conducted him to the result that magnetic 
storms are pericdic, and led him to assign to them a period of 
ten years. Considering that the same planetary magnetic 
streams must operate on the earth as on the sun, and that the 
sun’s position is central with respect to the earth’s orbit, it 
might have been anticipated, on theoretical grounds, that a like 
periodicity of effects would be detected, and that the periods in 
the two cases would not greatly differ. Possibly the period of 
the magnetic storms may eventually be found to be in some 
degree variable, and the mean period inferred from observations 
extended over a longer interval, to be somewhat different from 
ten years. 

39. The theory, by giving to extraordinary magnetical disturb- 
ances a planetary origin, accounts for their occurrmg simul- 
taneously at places on the earth’s surface widely distant. But 
the amounts of disturbance at the same instant may differ 
ereatly at different places, owing to difference of latitude, and 
difference of position relative to the magnetic poles. Consider- 
ing, however, the changes of the configurations of the planets, 
the amounts of disturbance, regarded as functions of the time 
of day, may be expected in the long run to follow the same law 
at different places. This is found to be the case, although, as 
might have been anticipated, the Iceal hours of the maximum 
values are different. | 

40. The fact of there being local hours of maximum disturbance, 
in the case of the planetary as in that of the solar disturbances, 
seems to be referable to the circumstance that the disturbances 
of the superior planets will be greatest when they are in opposi- 
tion, or about midnight, they being then least distant from the 
earth, and the disturbances of the inferior planets will for the same 
reason be greatest when they are in inferior conjunction, or about 
mid-day. If this explanation ke true, we should expect to find 


Prof. Challis on a Theory of Magnetie Force. 105 


a set of maxima prevailing in hours of the night, and another 
set in hours of the day, and that the directions of the deviations 
of the needle in the two cases would be opposite, the directions 
of the gyratory streams of the superior and inferior planets 
being opposite for their positions of maximum disturbance. 
These laws General Sabine has in fact detected by a discussion of 
numerous observations taken at Kew and Hobarton. (See 
‘ Proceedings of the Royal Society,’ vol. x. No. 41, p. 632.) 
41. The facts relating to the movements of the earth’s mag 
netic poles do not appear to be sufficiently well ascertained to 
allow of applying the theory to explain them. Conceive, for 
the sake of illustration, that there are two north magnetic poles 
at the same distance from the earth’s pole, and 180° from each 
other, that the currents converging to them are of the same 
intensity, and that they have the same uniform movement from 
east to west. On these supnositions it is evident that when the 
poles are on the great circle passing through the pole of the 
earth and a given place, the Inclination is at a maximum, and 
the Declination is changing from east to west. When they 
have passed over 90° the Declination will have gone through a 
western maximum, and be on the point of changing from west 
to east, because the needle, being equally acted upon by the two 
poles in the new positions, must point exactly between them. 
At the same time the Inclination will be at a minzmum. After 
the poles have advanced 90° further, the needle will have gone 
through a maximum eastern Declination, and returned to its 
original position, and the Inclination will again be at a maximum: 
and soon. ‘These hypothetical circumstances are, perhaps, not 
so far different from the actual as to prevent our concluding 
from them that neither the direction nor the amount of the 
motion of the magnetic poles can be inferred with any certainty 
from mere observations of “pomts of convergence” of the 
horizontal needle—at any rate not with so much certainty as 
the direction of the movement may be inferred from the direc- 
tion in which the Declination is changing when it is passing 
through zero at any place, as London or Paris, ¢f at the same 
time the Inclination is near its maximum at the same place. 
Now early observations at Paris show that the Declination was 
zero there about the year 1663, and was changing from east to 
west, and observations both at Paris and London indicate a 
constant diminution of Inclination from that date, while, accord- 
ing to Hansteen’s Isoclinal lines, the Inclination was less in 
1600 than in 1700. It may therefore be inferred that a 
maximum of Inclination occurred between those two epochs, 
and consequently, from the above argument, that the motion of 
one of the north magnetic poles is from east to west, If this 


106 Prof. Challis on a Theory of Magnetic Force. 


law should eventually be found to be true of all the magnetic 
poles, the theory will account for it in this manner, The 
north magnetic streams may be supposed to descend into the 
earth from heights at which the gyratory motion of the ether is 
sensibly less than at the earth’s surface, and the south magnetic 
poles to issue from the earth to heights at which the same 
circumstance prevails. Thestreams being supposed to circulate 
from south to north in courses distant from the earth’s surface, 
that diminution of the velocity of gyration will cause them to 
lag behind the earth in rotatory motion, and thus to draw the 
magnetic poles westward. 


I have now completed an outline of a general physical theory, 
of which the leading idea is that all quantitative physical laws 
may be mathematically deduced from a few fundamental facts, 
distinct conceptions of which may be formed from sensation and 
experience. The hypothetical facts on which the theory rests 
are, that all substances consist of minute spherical atoms, of 
different, but constant, magnitudes, and of the same intrinsic 
inertia, and that the dynamical relations and movements of 
different substances are determined by the motions and pres- 
sures of a uniform elastic medium pervading all space not 
occupied by atoms, and varying in pressure in proportion to 
variations of its density. Iam well aware that many of the 
explanations I have given of physical phenomena on these 
hypotheses are expressed in general terms, and are too little 
supported by exact analytical or numerical calculation, Some 
of the explanations, requiring a knowledge of the interior con- 
stitution of bodies, could not be conducted in an exact manner 
in the present state ‘of science. Still so comprehensive a theory, 
resting on so few hypotheses, could hardly fail of meeting with 
contradictions in the attempt to explain facts, unless the hypo- 
theses were true. The number and the variety of the explana- 
tions of physical phenomena which have been drawn from them 
without the support of symbolical calculation, seem almost of 
themselves to justify the conclusion that the ultimate atoms of 
bodies are really such as they have been assumed to be, and 
that the physical forces are modes of action of a single elastic 
medium. 

But no doubt the general theory and the explanations 
derived from it are not fully established till they have borne 
the test of numerical verification. And here I take occasion to 
add that every complete physical theory is necessarily mathe- 
matical. Observation and experiment are essential for furnish- 
ing facts both for the foundation and for the verification of a 
theory, and may also discover laws and relations of facts; but 


On an Alloy to be used as a Standard of Electrical Resistance. 107 


the theory is not complete till all facts not fundamental, and 
all laws, have been referred by mathematical calculation to 
the fewest possible fundamental facts. These principles have 
been admitted in physical astronomy, and belong equally to 
other departments of physical science. Hence if the hypothesis 
of the existence of the «ther as the sole source of physical 
power be true, the mathematical investigation of the motions of 
an elastic fluid become essential ; and the new principles of the 
application of partial differential equations to the determination 
of fluid motion, which I have proposed, will have the same 
relation to the future progress of theoretical physics, as the dis- 
covery by Newton of the principles of the application of differen- 
tials in dynamics had to the progress of physical astronomy. 
On account of the important applications those principles may 
eventually receive, I purpose, as soon as I shall be able, to bring 
them again under the notice of mathematicians. 


Cambridge Observatory, 
January 17, 1861. 


XVII. On an Alloy which may be used as a Standard of Electrical 
Resistance. By A. Matruizssen, Ph.D* 


tn expression of electrical resistances in the absolute 
measure proposed by Webert is, and probably will 
always remain, the best ; but its determination requires so much 
apparatus and room, as well as so much skill in manipulation, 
that it is placed beyond the means of most experimenters. 
I have therefore deemed it worth while to test some alloys, to 
see whether I should not be able to find one— 
I. Whose resistance will remain the same, whether it be made 
of absolutely pure or commercially pure metals; in other words, 
that such an alloy may be made by any chemist or assayer, and 
its conducting power will always be the same. 

II. That its conducting power will not be altered by the 
process of annealing. 

III, That its conducting power will not vary much with an 
increase or decrease of temperature. 

IV. That the alloy will not alter by exposure to the atmo- 
sphere. | 

The great difficulty in obtaining absolutely pure metals, 
together with the fact that the smallest traces of impurity 
materially increase the electrical resistance of most metals, pre- 


* Communicated by the Author. 
+ Pogg. Ann. vol. Ixxxu. p. 337, 


1 


108 Dr. Matthiessen on an Alloy which may be used 


clude the use of them as standards, and make it desirable that, 
instead of comparing, as heretofore, the conducting powers of 
metals, alloys, &c. with that of silver, copper, or, as has lately 
been proposed, with mercury*, they should in future be com- 
pared with an alloy having the properties mentioned above. 

The alloy best adapted for a standard of resistance for 
galvanic currents, is that composed of 

2 parts by weight of gold +, 

chau i 4) silvers 
for on looking at the curve which expresses the conducting 
powers of the gold-silver alloys{, we find part of it almost at a 
straight line ; that is to say, to the alloy containing 50 volumes 
per cent. of gold (which is the middle point of the straight line) 
one or two per cent. more or less gold may be added without 
altering its conducting power to any great extent. 

In order to test the first condition, I have had the alloys 
made in different parts of the world; and my best thanks are 
due to those gentlemen who kindly undertook the making and 
procuring of them. The following order was given :— 

Take 6 grammes proof, or purest gold, and 3 grammes 
proof, or purest silver; fuse and cast three times§, and then 
draw into wire of about 0°5 millim. diameter. The wire to be 
hard-drawn. 

The alloys experimented with were :— 

No. 1. Made of pure gold and silver by Mr. R. Smith, in Prof, 
Percy’s laboratory. Drawn by Messrs. Watts and Son, of Karby 
Street. These wires were annealed in a red-hot crucible. 

No. 2. Made and drawn in Brussels. Procured for me by my 
friend Mr. G. C. Foster, through the kindness of Prof. Stas. 
Annealed on wire-gauze over a four Bunsen burner. 

No. 8. Made and drawn in New York. Procured through my 
friend Mr. C. M. Warren. Annealed in the same way as No. 2. 

No. 4. Made and drawn in Paris. Procured through Mr. 8, 
Reuter. This wire came to hand already annealed ; therefore no 
determinations of the hard-drawn wire could be made. 


* Siemens, Phil. Mag. (Jan. 1861); Schroder von der Kolk, Poge. Ann. 
vol. ex. p. 452. It should be borne in mind that the use of this metal as 
a standard is open to the following grave objection: viz. that the copper 
wires cr plates dippmg in the mercury will after a time make it im- 
pure ; and as traces of foreign metals (0°1 er 0'2 per cent.) cause a decre- 
ment inthe conducting power of pure mercury (not as stated by Siemens, 
an increment), it would become necessary often to change it, thereby 
requiring a large supply of chemically pure metal. 

+ Corresponding nearly to equal volumes of gold and silver. 

+ Phil. Trans. 1860. 

§ It would have been better to have added, fuse with a little berax and 
dalipelre, 


as a Standard of Electrical Resistance. 109 


No. 5. Made and drawn in Frankfort. Procured through my 
friend Dr. Dupré. These wires were annealed on a wire-gauze 
over a Bunsen’s glass-blower’s lamp. 

No. 6. Made of proof-gold and silver, by Messrs. Johnson 
and Matthey, of Hatton Garden, and drawn by them. These 
wires were annealed in the same manner as No. 2. 

No. 7. Made and drawn by myself, of proof-gold and silver, 
lent me by Professor Hofmann. Annealed in the same manner 
as No. 2. 

No. 8. Made and drawn by myself, of pure gold and silver. 
Annealed as No. 2 was. 

In Table I. are given the values found for conducting power 
of the above alloys. ‘They have been compared with a hard- 
drawn silver wire, whose conducting power has been taken 


= 100 at 0° C. 


Table I. 
No. of alloy. Mean reduced to 0° C. 
Oe Hard-drawn. Temp. Annealed. Temp. Hard-drawn. Annealed. 
0. 1. vs 
BUA cose nea caiines . 1499 145C. 15:02 15-0C. 
PERIOD civewiv savas 14°87 15:0 14:92 15:2 15:08 15°13 
Mean ..... wee Slee  ~ Lares 1497" tart 
No. 2. 
PARE oe elena e 14:98 9°8 15:02 10°0 
meme. sisi. 14:95 9°6 1504 10°4 15°06 15°14 
RICAN vceacesie  L4°96 9°7 15-03 10°2 
No. 3. 
Ro ae ed 14:60 16°8 14°66 17:0 
ae a a Bere BAST Dx. LOD 14-82 17-4 14°85 14°92 
RTCAD. .s.000 14°68 16°5 4-74 17:2 
-No. 4 
1 wire Slidarciase eases : 14:94 6:0 
PEMUMEED? Aicrarnedtes eeu 15°02 9°8 Mn 15:06 
lean ‘id des Seeks 14°98 7 
No. 5 
i Wetbeers he... 15°02 8°5 15:06 9-0 
yp WATE) cite. isiciven 14°99 9°2 15°03 9°8 15:09 15°14 
WEAN -ciheceie’» ; 15°00 8°38 15°04 9°4 
No. 6 
BONWIEE) We Saccwoes ve 14°87 148 14:82 16-0 
PO WEROT Me Ursvde ss vice TAGS? NED 14:86 15°0 14:99 15°00 
1 a 14:83 16°0 14°84 15:5 
No.7 
Lac ere 14:94 14:0 14:99 16:2 
PERE. iva ociein Cas 14:91 16-2 1497 U2. 107 15°16 
UE one 14:92 © York 1498 167 
No. 8 
Eyres, Senter: i 14°86 18°4 14:92 18°2 
PURE oes oc anise 1488 166 14-90 17°70 15°05 15°10 
Mean.....00s ‘ IAS 1 1e'3 14°91 i 


Meanseseees 15°03=100 15:08=100°3 


110 Dr. Matthiessen on an Alloy which may be used 


Calling the mean of the values at 0° of the hard-drawn wires 
100, we find that, as Table IL. shows, the differences between 
the conducting powers of the alloys are very small, in fact, that 
the greatest is only 1:6 per cent. 


Table IT. 
No, of alloy. Hard-drawn. Difference, Annealed. Difference. 

Lacishesdsttins 100°3 + 03 edd Wavat 1006 + 03 
) eon 1DO*2. | hag AO 3. vi ceen cents be 100-7. +. © 

abatenencdcd O85 *) pets eee ence 992 — Ill 
2 RECN ACHE Mul COSee SeeweT Sivenciswences . 100°'2 — O71 
Dnt ten fahcee 100°45))--. 0G 7G. HAS 100°7 + O04 
Bs Bear cmecias 99°F = Ro) oe sents : 998 — 08 
Wis. cSacaateee cs 100°3.. WO ea ae eas 100°8 + 0° 
Siastccericls: TOR ee esc certenae 1004 + O1 


The great concordance in the above results is partially due to 
the wire drawing so very well. It draws as well as, if not better 
than, any wire | have as yet tried. 

For the sake of comparison, I will give in Table III. the values 
found by different experimenters for the metals with which the 
others are usually compared. 


Table ITI. 
Becquerel *. Siemensf. Matthiessen. 
Lenz}. 
Seal Annealed, vicina Annealed. Has | Annealed. 
HLVED ska ns 100°0| 107:0 100°0 10070; 108-8 | 100°0; 110-0 
Copper ...| 95°3 97°8 73°3 89°7 95:2 99°35; 102°0 
Gald. «.... 68°9 70°0 58°'5 dances D hshes ee 78°0 80°0 
Mercury... 1:86 3°42 at 18°°7 1°72 1:63 at 22°°8 


When no temperature is given, the observations have been 
made at 0° C. 3 | 

Part of these differences may be due to the silver, which in 
some cases may not have been chemically pure; but if any of the 
others be taken as unit, we do not arrive at any better result. 

Table LV. shows the differences between annealed and hard- 
drawn wires,—the annealed being the better conductor, accord- 
ing to— 


‘ Table IV. 


7 
2 
1 


Becquerel, 


a 


0 per cent. 
‘6 per cent. 
‘6 per cent. 


Siemens. 


8°8 per cent. 
6°1 per cent. 


eee ee estes eeeee 


Matthiessen, 
Holzmann §. 


10-0 per cent. 
2°5 per cent. 
2°6 per cent. 


* Ann. de Chim. et de Phys. vol. xvii. (1846), p. 242. 
t+ Pogg. Ann. vol. xxxiv. p. 418, and vol. xlv. 105. 
TOG, BAe. § Phil. Trans. 1860 


i 


as a Standard of Electrical Resistance. 11 


The gold-silver alloy, however, only varies 0°3 per cent.,— 
another reason why the alloy may be drawn by anybody, and 
still have the same conducting power. 

The following experiments show the effect of an increase of 
temperature on the conducting power of this alloy. The details 
of the experiments, together with the apparatus employed, will 
be published shortly in a paper by Dr. von Bose and myself, 
“ On the Conducting Power of the Metalloids, Metals, and Alloys 
at different temperatures.” Our results at present do not agree 
with those of Arndtsen and Siemens, who state that the resist- 
ances of most metals vary in direct ratio with the increase 
of temperature, but with those of Lenz, who calculates the 
conducting powers for different temperatures by the formula 
N=a+yt+ z 7%, where x is the conducting power at 0° C., 
y and 2 constants. I may also mention that the metalloids 
conduct better on being heated, being the reverse of that which 
the metals do. | ets 

An annealed wire of No. 1 alloy was heated in a glass tube 
placed in a water-bath (a), and afterwards heated in an oil- 
bath (4). Its conducting power was determined at different 
temperatures ; and the values found are given in Table V. The 
values found for an annealed wire of No.5 alloy (c), heated in 
an oil-bath, are also added. 


Table V. 
(4.) (d.) (e.) 
Conducting Conducting Conducting 
T. power. T. power. T. power. 
0°4=15°053 9:°1=14°954 6°1=15:088 
19°5=14°854 30°9=14°728 33°3 =14:798 
41°3=14°626 java — 14°50) 51°6=14°607 
60°6=14°431 71°4=14°325 73°3=14391 
82°7=14°219 95°'1=14:094 96°7 =14°162 
100:0= 14°052 69°'4=14°342 73°3= 14391 
79°3 = 14°251 47°9=14°550 51°4=14°609 
59°1=14°453 30°8 = 14°730 31:7=14°811 
39°3=14'647 10°5=14°939 10°3=15°039 
17°9=14°865 


0°-7=15-049 


The diameter of (a) was 0°539 millim. and its length 683 
millims., and that of (c) 0-915 millim. and its length 987 
millims. 

Taking the mean of the two temperatures and conducting 
powers, and calculating (by the method of least squares) the 
probable values for 2, y, z for the formula X=2-+ yt+ 2é?, where 
A= conducting power z at ¢ degrees, 2 conducting power at 0° C., 
yand z constants, we find, ) 


112 


for 


Dr. Matthiessen on an Alloy which may be used 
(a2) N=15:059 —0:01077 ¢ + 0:00000722 72, 


(6) X=15-052—0-01074 ¢ + 0:000007 L4 2?. 
(ce) N=15°152 —0:01098 ¢ + 000000774 2?. 
Table VI. gives the mean of the observed conducting powers, 
those calculated from the above formule, and their differences. 


Table VI. 
(a.) (d.) 
Observed | Calculated Observed | Calculated 
conducting | conducting Diff, conducting | conducting Diff. 
power. | power. ul power. power. 
0-6=15:051 | 15:053—0-:002 || 98=14-946 | 14-947—0-001 
18:7 =14:860 14°860 0:000 30°8 = 14°729 14:728+0°001 
40°3= 14-637 | 14-638—0:001 50°7=14526 | 14:526 0-000 
59°8 = 14°442 14°441+-0°001 70°4 = 14°333 14°331+0-002 
81°0=14°235 14°234+0°001 95°1=14:094 14°:096 — 0-002 
100:0 = 14:052 14:054—0°002 
(e.) 
Observed | Calculated 
T. conducting | conducting Diff, 
power. power. 
8°2=15°063 15063 0:°000 
32°5 = 14°800 14°803—0:003 
51°5=14°608 147608 0:000 
73°3=14°391 14°389-+-0:002 
96°7 =14'162 147162 0:000- 


If we now take the conducting power at 0° = 100°3, being 
the mean of the observed conducting powers (see Table II.), 
we find 
for (a2) X=100°3—0-07216 ¢+0:0000484 7, 

(6) X=100°3—0:07196 ¢+0:0000478 7, 

(ce) N=100°3—0:07247 ¢+0:-0000511 7; 

and taking the mean of the mean of a and 0 (this being the same 
wire) and c, we find the conducting power of the annealed wire 
at different temperatures 


= 100°3—0:07226 ¢ 4+ 0:0000496 72. 


The next step was to determine the conducting powers 
of hard-drawn wires for different temperatures: but here we had 
to contend with great difficulties; for when a hard-drawn wire 
is heated to 100°, a different conducting power is generally 
found on cooling; and to obtain concordant results, it is neces- 
sary to heat the wire several times ; but when once obtained, the 
values found will remain the same, no matter how often the wire 
may be heated, showing that the apparatus and method are not 


as a Standard of Electrical Resistance. 113 


faulty, whether by letting the wire remain for a length of time 
it will gradually assume its original conducting power or not is 
a question now under consideration. With annealed wires this 
is also the case, but in a much less degree. All the above 
wires, as well as the following, were heated several times before 
concordant results were obtained. I cannot at present state 
the cause of this behaviour; but experiments are now being 
made on the subject by Dr. von Bose and myself. 

Hard-drawn wires of No. 5 (a) and No. 3 (8) alloys were 
heated, (a) in a glass tube in a water-bath, (4) in an oil-bath. 
The values found are given in Table VII. 


Table VII. 
(a.) (d.) 
| 
Conducting Conducting 
power. power. 

0°0=15°075 9°3=14°870 
20°9=14°858 35°6 = 14:608 
46:5 =14°605 50°8 = 14°460 
76°4=14°318 67°6=14:300 
100°0=14:094 98:1=14°011 
71°6=14°370 70°-4=14:278 
51°4=14°566 54:4 = 14°426 
23°8 = 14°838 35°2=14°613 
0°0=15:075 14°1=14°824 


The diameter of (a) was 0°616 millim., and its length 876 
millims., and that of (6) 0°551 millim., and its length 348 millims. 
Taking, as before, the mean of the two temperatures and con- 
ducting powers, and calculating the values of w, y, z from them, 
we find 


for (2) X=15:074—0-01012 ¢+0°00000829 7, 
(6) X=14°964—0-01011 ¢+0°00000410 22. 

Table VIII. gives the mean of the observed conducting 
powers, and those calculated from the above formule, with their 


differences. 


Table VIII. 
(a.) (d.) 

Observed | Calculated Observed | Calculated 

conducting | conducting conducting | conducting 
T. power. power. Diff. T. power. power. Diff. 
0°0=15°075 15:074-+-0:001 11:7=14°847 14:847 0-000 
22°3=14°848 14°850—0-002 35'°4=14°610 14°611—0°001 
49:0 =14:586 14°586 0°000 52°6 =14°443 14443 0°000 
74°0=14:344 14°343-+-0°001 69°0= 14:287 14°286+0:001 
100°0 =14°094 14:095—0:001 98:1=14°011 14011 0-000 

Phil. Mag. 8. 4. Vol. 21. No. 138. Feb, 1861. I 


114) On an Alloy to be used as a Standard of Electrical Resistance. 


Taking the conducting power at 0°=100, we have 


for (a), X=100—0:06714¢ + 0:0000218 7?, 
(6), N=100—0:06753 ¢ + 0-:0000274 2?, 
mean A=100—0:06734¢ + 0:0000246 2, 
which shows there is a difference in the conducting powers at 
different temperatures between annealed and hard-drawn wires 
of this alloy. 

A similar difference we have already found between hard- 
drawn and annealed silver wires. 

Although the values found for x and y do not agree very well 
with each other, yet for all purposes it will not make much dif- 
ference which is used, as they will lead to the same results ; 
thus, if we calculate the conducting power for the highest ordi- 
nary summer temperature (in a room), say 30°C, we find it in 
the one case to be 

98:005, and in the other 97-999. 


In Table IX., I have given the differences in the conducting 
powers of some metals between O° and 100°, taking the con- 
ducting power at 0°=100. 


Table IX. 
Silver iahs sshageaeeeasinde 28°5 per cent. (annealed). 
GOpper «osc 0pendejsenasseani 29°0 per cent. (annealed). 
GOld: cn iesapsnayenacnssesss 28°0 per cent. (annealed). 
MBrCar ysis ins cccsesvanpes sss 8°7 per cent. (Siemens). 
The gold-silver alloy...... 6°5 per cent. (hard-drawn). 


6°7 per cent. (annealed). 


From the foregoing Table it will be seen how well the alloy is 
adapted for use as a standard to compare the resistances of 
other metals. . 

Whilst making these experiments, I have found that as soon 
asmost of the pure metals are alloyed with traces of any other, 
these differences rapidly decrease, in fact, almost in the same 
proportion as the conducting power of the metals themselves. This 
may explain why the copies of Weber’s standard vary so much 
one from another. For imstance, I have tested a commercial 
copper wire whose conducting power only varied between O° and 
100° 7 per cent (about), whilst pure copper varies 29 per cent. 
Now, suppose a wire of that copper whose conducting power 
only varies 7 per cent. between O° and 100° be compsred with 
one of Weber’s standards at a certain temperature, and then with 
a pure copper wire at another temperature, say 20° difference, it 
is obvious that the pure copper wire will not have the same re- 
sistance as the original standard. It has as yet been generally 
assumed that the conducting power of all copper wire, whether 


On the Laws of Absorption of Liquids by Porous Substances. 115 


pure or commercial, varies with an increase of temperature to the 
same degree, which, however, is far from true, and should be - 
borne in mind when constructing a resistance thermometer as 
described by Siemens*. The fourth condition needs no com- 
ment. It is too well known how gold-silver alloys behave when 
exposed to the atmosphere. 

With regard to the expense, the 9 grammes alloy cost, drawn 
into wire, about.£1 4s., but the gold im it is always worth about 
15s. ; so that the real expense is very small. Care must, of course, 
be taken to prevent the alloy coming in contact with mercury, 
which amalgamates readily with all gold-silver alloys. The best 
way to prevent any such accident is to varnish the wires. 

In having this alloy made, it would be advisable always to 
have two made by different parties, so as to be sure no mistake 
has occurred. 

I therefore propose that all those who study the electrical re- 
sistance of metals, should compare one of their metals with this 
alloy, calling its conducting power 100 at 0° (hard-drawn 
wire of 1 millim. length and 1 millim. diam.) ; for then we should 
be able to compare the results obtained by different experimenters 
with one another. ” 

I am sorry that I am not in a position to give the value of 
the absolute resistance of this alloy in terms of Weber’s standard; 
for if this be once determined, we shall, of course, be able to 
reproduce an alloy of known resistance in absolute measure. 

1 Torrington Street, January 1861. 


XVIII. Haperimental Researches on the Laws of Absorption of 
Liquids by Porous Substances. By Tuomas Tatu, Esq. 
[Concluded from p. 65. ] 
we ea following experiments were made with filters of larger 


surfaces. 
Experiment XXIV. 


_ This experiment was made with upward filtration, as in the 
foregoing experiment. ‘The filter was unsized paper, presenting 
a surface of =%ths of an inch in contact with the water. The 
temperature was 43° throughout the experiment, other things 
being the same as in the last experiment. 

The velocity of ascent of the liquid in the filter-tube for the 
first five units was found to be correctly represented by the 
formula h 

ieee 
Towards the close of the experiment, however, it was observed. 
* Phil, Mag. January 1861. 
I2 


116 Mr. T. Tate’s Experimental Researches on the 


that the filtering power of the paper had sensibly decreased ; but, 
owing to the rapidity of the process, the effect arising from this 
cause had not materially interfered with the normal law of 
filtration. 

Upon repeating the process, it was found that the velocity of 
ascent followed, for the most part, the law expressed by the 
general equation (7). 

Hence it would appear that the normal law is, that the rate 
of filtration varies directly as the pressure upon the filter, the 
deviations from this law bemg due to the change which takes 
place in the molecules of the filter during the process. 

The following experiment shows that by alternating the direc- 
tion of the current of filtration, the original power of the filter 
may be maintained nearly unimpaired. 


Experiment XXV. 


The filter in this experiment was coke, presenting an interior 
surface of half an inch in contact with the water, and an exterior 
surface of about two inches, other things being the same as in 
the last experiment. | 

By upward filtration, the law of ascent of the liquid was 
accurately expressed by the formula © 

h 
144’ 
where v is the velocity per second, 2 being the column of liquid 
pressure on the filter expressed in units of the graduation of 
the tube. 

The water thus filtered into the tube was allowed to be dis- 
charged by downward filtration. In this case the liquid followed 
nearly the same law of descent ; but upon repeating this process 
of downward filtration, the velocity of descent was found to fol- 
low the law expressed by equation (7). Upon reversing the 
direction of the current of filtration, the law of ascent was found 


C= 


to be accurately expressed by the formula = And so on 


to other alternations. 

Similar results were obtained with wood-charcoal filters. 

The following experiment was made to determine the rate of 
change which takes place in the filter during the process of 
filtration under a constant pressure. 


Experiment XXVI. 


This experiment was made with a close coke filter about an 
inch and a quarter in depth, and presenting three-fourths of an 
inch of surface in contact with the water, which had been care- 


Laws of Absorption of Liquids by Porous Substances. 117 


fully filtered through ordinary filtering-paper. The discharge 
was produced by downward filtration, the exterior portion of the 
filter being exposed to the air. The pressure on the filter, 
throughout the experiment, was produced by a column of 15 
inches of the liquid; and the temperature was carefully main- 
tained at 51° throughout the experiment. The successive inter- 
vals of time requisite for the discharge of one cubic inch of 
water were noted, and recorded in the following Table of results. 


Succession of |corresp. time in Value of T by 
cubic inches minutes for each formula 
Heehateed, puemeh; piled = 3°16 x 1497 1 
1st cub. in. 3°16 3°16 
2nd .,, 4:56 4:49 
and ,; 6°36 6°37 
Ath ,, 9:00 9-05 
BSth. 5, 13°50 12-85 
6th ,, 18:00 18°24 
Pulte 55 26:00 25°91 
Sih. ,; 33°00 36°80 


Here the near coincidence of the results in the second and 
third columns shows that, under a constant pressure on the filter 
(within certain limits), the times requisite to produce equal suc- 
cessive quantities of discharge are in geometrical progression. 

At or near to the eighth cubic inch of water discharged the 
progression seemed to have reached its limit; for the time required 
for the diseharge of the succeeding cubic inch was found to be 
nearly the same as that of the eighth cubic inch. 

The experiment, as above recorded, extended over a period of 


two hours nearly, and during that time the rate of filtration had 


changed from seth of a cubic inch per minute to s.rd of a 


cubic inch; that is, the rate of filtration had decreased eleven 
times nearly. 

I offer no hypothesis on these remarkable results, beyond the 
mere statement of the fact that during the process of filtration 
these filters undergo a progressive molecular change, causing the 
rate of filtration to decrease according to a general law expressed 
by the formula T,,_,;=a B"—1, where « and B are constants for 
each particular filter, and 'T,_, is the time required to filter the 
nth unit of water. 

At the close of the foregoing experiment, the water being dis- 
charged, the tube was filled with water by upward filtration, and 
then, this water being allowed to discharge itself by downward 
filtration, it was found that one cubic inch of water was dis- 
charged in 156 minutes, showing that by thus reversing the 


118 =Mr. T, Tate’s Experimental Researches on the 


direction of the current of filtration, the filter had to a consider- 
able extent regained its original power. 

Precisely similar results were obtained with filters of wood- 
charcoal and unsized paper. 

As it is scarcely possible to obtain filters, especially of char- 
coal and coke, of precisely the same internal structure, different 
filters, even of the same substance, vary yery much with respect 
to the value of the ratio expressing the change in their filtermg 
power. The rate of change of the filter in the foregoing ex- 
periment was unusually great. 

The results recorded in Experiment XXI. were no doubt to 
some extent affected by the progressive deterioration of the 
filterimg power of the-coke; but it must be observed that this 
filter, having been previously tested, underwent an exceedingly 
small change during the process. 

The following experiments were made to determine the analogy 
subsisting between the filtration of liquids through porous sub- 
stances, and the discharge of liquids through small perforations 
made in thin plates. 

The results of these experiments showed that the velocity of 
discharge through the orifices of ‘thin plates varies according to 
a certain power of the column of liquid pressure, that is, v ac A”, 
where the exponent z 1s constant for orifices of the same dia- 
meter, but for orifices of different diameters it varies between the 
limits n= and n=1. 

For orifices less than +,th of aninch diameter, n=4 ; that is, 
the velocity of discharge, in this case, varies as the square root 
of the column of liquid pressure. 

For orifices about ;45th of an inch diameter, n=1, that is, 
the velocity, in this case, varies as the depth of the column of 
liquid pressure. 

Moreover it was found that the velocity of discharge increases 
in a high ratio with the increase of temperature, especially for 
the smallest orifices, and also that it varies with the adhesiveness, 
and even, in some cases, with the chemical composition of the 
liquids. 

Hence it would appear that the laws of filtration are, in some 
respects, analogous to the discharge of liquids through minute 
perforations not exceeding ;4,,th of an inch diameter. 


Experiment XXVII. 


In this experiment the liquid was discharged from a small 
orifice z,th of an inch in diameter, made in a thin plate cemented 
to the bottom of the filter-tube of the foregoing experiments. 


Laws of Absorption of Liquids by Porous Substances. 119 


Depth of the Corresp. time | value of T by 
column of liquid,| in seconds, formula (9) 
T, . 


h. 

6 0 0 

5 33 32°6 
4 68 68:0 
3 108 108-2 
2 173 1790 
1 218 218-0 
0 378 368°0 


The formula expressing the relation between T and A is 


T= 868 150M a SS 89) 
Hence we find 


1 


h2 
v= 75 > OR aS Seta eae (10) 


that is to say, for orifices of this diameter, the velocity of discharge 
varies directly as the square root of the depth of the column of 
liquid. 
In general it has been found that 
Weal. ccc ie srdewe yh whieh nia eh Ws weed 


By integrating the equation v= ee 


7p We find 
T=a—yh'-, & e e ° e ® e (12) ! 
1S tial | 
where y= aoe 


In formule (9) and (10), n=4, e=74, and y=150. When 

n=1, we find from equation (11), 
Peay los hy te iore: «vis! eoeey G19) 

2°30218 
aoe 

This formula represents the law of descent of the liquid in the 
following experiment. 

Experiment XXVIII. 

In this experiment the diameter of the orifice was ~4 5th of 

an inch nearly. 


where y= 


Depth of the | Corresp. time | value of T by 
column ofliquid,} in minutes, formula (14). 
h. T. 


120 Chemical Notices :—M. Pasteur on Fermentation. 


In this case the formula expressing the relation between T 
and h is 
T=883:95—50logh, “. «4 s «> 
and | 
ops OAGR Sry g a a yO 


that is, the velocity of discharge varies directly as the depth of the 
column of liquid. 


XIX. Chemical Notices from Foreign Journals. By Ki. ATKIN- 
son, Ph.D., F.C.S., Teacher of Physical Science in Cheltenham 


College. 
[Continued from vol. xx. p. 523.] 


PASTEUR has for a considerable length of time been 
: e engaged in a research on the nature of alcoholic 
fermentation, a complete account of which he has published in 
the Annales de Chimie et de Physique. Some of the results 
have already appeared in this Journal ; but the importance of the 
subject induces us to lay before our readers the following brief 
summary of the whole investigation, taken from the Répertoire 
de Chimie. : 

According to Pasteur, alcoholic fermentation is the peculiar 
transformation which sugar experiences under the influence of 
beer yeast ; the author shows that glycerine and succinic acid 
are products of the alcoholic fermentation, and treats of their 
estimation and scparation. 

When the fermentation is terminated, the fermented liquid is 
passed through a weighed filter; the increase in weight of the 
filter after being dried at 100°, gives the weight of the yeast 
which has collected at the bottom of the vessel. The filtered 
liquid is then gradually evaporated until it is reduced to a small 
bulk, and the evaporation is terminated in vacuo. This residue 
is exhausted with a mixture of alcohol and rectified ether, which 
dissolves out succinic acid and glycerine. This liquid is evapo- 
rated first on the water-bath, and then, water having been 
added, the evaporation is continued over a gentle flame in 
order to get rid of the ether. The liquid is next exactly 
neutralized by milk of lime, carefully evaporated, and exhausted 
by a mixture of alcohol and ether, which only dissolves the 
glycerine. The residue, which consists of impure succinate of 
lime, is digested with alcohol of 80°; this dissolves the foreign 
matters and leaves the succinate of lime, which is dried and 
- weighed. 

The alcoholic liquid, which contains glycerine, is also evapo- 
rated in the water-bath, and finally 2x vacuo, where it must not 


M. Pasteur on Fermentation. 121 


‘remain more than two or three days ; for it loses weight in vacuo, 
even at the ordinary temperature, when free from water. The 
glycerine is then weighed. 

Using a very small quantity of yeast to produce the fermenta- 
tion, Pasteur finds that the weight of succinic acid obtained 
exceeds the total weight of the soluble matters contained in the 
yeast. The same is the case with the glycerine, as compared 
with that of the yeast. 

Glycerine, succinic acid, alcohol, and carbonic acid are not the 
only products of fermentation. The yeast assimilates something 
from the sugar: in one experiment 100 grms. of sugar gave up 
1} grm. to the yeast; doubtless the cellulose of the new glo- 
bules produced in the fermentation forms part of this increase. 

The equation 

Coe OM 2 CH O24 C0 
by which the alcoholic fermentation was formerly expressed, 
does not exactly represent the change. The quantity of car- 
bonic acid formed is less than that required by the equation. 
Hence a certain quantity of sugar disappears without being 
accounted for. 

Pasteur assumes that this portion of sugar is resolved into 
succinic acid, glycerine, and carbonic acid, and he represents 
the change by the equation 
49(C??H" OM) +109 HO=12(C®H® 08) +. 72(C°H8 O°) + 60CO2, 

. Succinic acid. Glycerine. 
Succinic acid and glycerine are constant and necessary products 
of alcoholic fermentation. 

Lactic acid is an accidental production of the fermentation. 
Whenever it occurs (and it is very rare), the yeast must have 
contained some lactic ferment. Hach of the ferments effects its 
usual transformation, and then the fermented liquid contains, 
besides succinic acid and glycerine, lactic acid and mannite, as 
well as a new acid. 

In the second part of his research the author examines what 
becomes of the yeast in the fermentation. He shows that the 
nitrogen of the yeast is never changed into ammonia during 
alcoholic fermentation. Far from forming ammonia, that sub- 
stance disappears; for yeast is formed in a mixture of sugar, an 
ammoniacal salt, and phosphates. 

The globules of yeast are formed of small vesicles with elastic 
sides, full of a liquid containing a soft substance more or less 
granular and vascular. This is usually near the side; but in 
proportion as the globule becomes older, it tends towards the 
middle of the cell. 

The globules are reproduced by means of gemmation, as M,. 


122 M. Pasteur on Fermentation. 


Cagniard Latour showed. The translucent globules without 
granular contents gemmate most rapidly; there are more gra- 
nulations in proportion as the globule is older, less active, and 
less capable of gemmation. 

Mitscherlich supposed these globules to burst and discharge 
their granules, dispersing seminules in the liquid, which increase 
and become globules of ordmary yeast. Pasteur does not agree 
with this. 

It has been usually thought that, in the fermentation of solu- 
tion of sugar, the ferment, far from being destroyed, is developed 
by gemmation ; a close examination has shown the author that, 
in the fermentation of sugar in the presence of albuminous sub- 
stances, neither more nor less yeast is produced than when the fer- 
mentation takes place with pure solution of sugar, 

In all cases of the fermentation of pure solution of sugar, the 
weight of nitrogenous matter dissolved in the fermented liquid, 
added to the weight of the yeast, perceptibly exceeds the total 
weight of the original yeast. The increase amounts from 1:2 to 
1‘5 per cent. of the weight of the sugar. 

The disappearance of the yeast in certain cases is merely ap- 
parent. less yeast is obtaimed than was taken for fermentation 
because the quantity dissolved is greater than the weight of the 
new globules which are formed. In the fermentation of solutions 
of sugar containing albuminous matters, about 1 per cent. (of 
- the sugar) of yeast and soluble products is formed, and therefore 
a little less than in working with yeast already formed, and with 
pure solution of sugar. 

Hence the result is the same whether albuminous substances 
are present or not; the small difference observed arises doubt- 
less from the fact that the globules, formed in a medium where 
the nitrogenized aliment is in excess, are more active, and for the 
same weight decompose more sugar than those formed in a 
medium poor in mineral or nitrogenized aliments. 

Hence yeast, placed in solution of sugar, lives at the expense 
of the sugar and of its nitrogenous matter, which is dissolved or 
which becomes soluble from the changes taking place during 
fermentation between the principles which it contains. Fermen- 
tations which take place in the presence of excess of sugar are 
virtually of indefinite duration. This is readily conceived, for 
there is no destruction of nitrogenized matter; only displace- 
ments or modifications of this substance occur; and it remains 
in the complex state in which we are accustomed to meet with it 
in these products. ‘The soluble part of the nitrogenous matter 
becomes partially fixed in the globules in an insoluble state. 
But the power of organization which these globules possess is 
such that the old globules can yield their nitrogenized matter in 


M. Pasteur on Fermentation. 123 


the soluble state to serve as food for the recent globules; and 
thus this fermentation continues for a long time. 

The nitrogen of the yeast diminishes during fermentation from 
two reasons :—first, because the yeast increases in weight during 
- fermentation by assimilating the elements of sugar, which con- 
tains no nitrogen; secondly, in consequence of the solubility of 
certain nitrogenized principles of the yeast. 

In all alcoholic fermentation, part of the sugar becomes fixed 
on the yeast in the form of cellulose. When the yeast is formed 
in amedium consisting of pure sugar, of phosphates, and of an 
ammoniacal salt, it is clear that the cellulose is formed from the 
elements of the sugar, and that the ammonia combines with 
another part of the sugar to form the soluble and insoluble albu- 
minous matters in the globules. 

Are the phenomena analogous in the case in which sugar 
ferments in the presence of alouminous substances? Hxperi- 
ment proves that there is more cellulose in the yeast after than 
before the fermentation ; so that it is very probable, if not certain, 
that all the cellulose of the yeast-globules is formed from the 
elements of sugar. But, besides the formation of cellulose, a per- 
ceptible quantity of sugar doubtless becomes assimilated by the 
yeast; for the weight of the yeast taken, added to the weight 
of the cellulose fixed during ‘fermentation, does not equal the 
total weight of the yeast and of its soluble part, such as is found 
when the fermentation is terminated. 

The weight of the cellulose increases considerably during fer- 
mentation, which furnishes a further proof of the vitality of the 
yeast during this act. 

In every alcoholic fermentation, part of the sugar becomes 
assimilated to the yeast in the form of fatty matter. If solution 
of pure sugar be mixed with an aqueous extract of yeast which 
has been repeatedly extracted by alcohol and ether, and also with 
an imponderable weight of fresh globules, a few grammes of 
yeast are obtained containing one to two per cent. of its weight of 
fatty bodies, which are readily saponifiable, forming crystallizable 
fatty acids. This fat is formed from the elements of sugar; for 
yeast prepared in a mixture of water, sugar, ammonia, and phos- 
phates also forms fatty matter. 

Permanent Vitality of Yeast.—When yeast is mixed with a 
proportionally small quantity of sugar, after the latter has been 
decomposed, the activity of the yeast continues, but is turned 
upon its own tissues with an extraordinary energy and rapidity ; 
a weight of alcohol and carbonic acid is thus obtained, exceeding 
that which the sugar could yield. Under these conditions the 
following facts are observed :— 

lst. The action of the yeast is at first exerted on the sugar. 


124 M. Kekulé on Derivatives of Suecinic Acid. 


2nd, The yeast reacts on itself when the sugar has been com- 
pletely destroyed. 

3rd. The effect produced by the yeast on itself is not pro- 
portional to the weight of the yeast. 

The author assumes that the globules formed by the fermen- 
tation of the sugar cannot attain their complete development for 
want of sufficient sugar, and that the young globules needing 
this nourishment live at the expense of the parent globules,— 
which produces a secondary fermentation, or the yeast destroys 
itself. 

Lastly, M. Pasteur speaks of the application of some of the 
results to the composition of fermented liquors. 

Since glycerme and succinic acid are constant products of 
the alcoholic fermentation, they ought to be fouhd in wine, 
beer, cider, &c. This the author has already shown to be the 
case. 

He terminates his memoir by the following passage, contain- 
ing the fundamental conclusion which he draws from his im- 
portant researches :—‘“ As to the interpretation of the whole of 
the new facts which I have met with in my researches, I think 
that whoever considers them impartially will see that fermentation 
is a correlative act of life, and of the organization of globules, 
and not of death or the putrefaction of these globules; still less 
does it appear to be a phenomenon of contact, where the trans- 
formation of sugar proceeds in the presence of the ferment with- 
out yielding anything to it, or taking anything from it.” 


Kekulé has described* a mode of preparing the brominated 
derivatives of succinic acid, which is simpler than the methods 
hitherto employed. 

To obtain bibromosuccinic acid, C4 H* Br? 04, he heats in 
sealed tubes (at 150°—180°) twelve parts of succinic acid with 
thirty-three parts of bromine and twelve parts of water. After 
the reaction is complete, the whole mass is changed into small 
greyish crystals, and on opening the tube a large quantity of 
hydrobromic acid escapes. The crystals are purified by washing 
with cold water, solution in boiling water, and treatment with 
animal charcoal. Bibromosuccinic acid is formed in all cases in 
which a small quantity of water is taken, even when the propor- 
tion of bromine is such as to form monobromosuccinic acid. 

Monobromosuccinic acid, C* H° Br 04, is obtained by heating 
succinic acid with bromine and with a larger quantity of water. 
It is purified in a similar manner, but, being more soluble, it 
crystallizes less easily. 


* Bulletin de la Société Chimique, p. 208, 


MM. Léwig and Scholz on a new Sulphur Compound. 125 


Butlerow* has investigated the action of ammoniacal gas on 
dioxymethylene+: these substances act on each other with great 
energy, and the mixture becomes ultimately converted into a 
magma of granular crystals, which, when purified, present the 
appearance of colourless, transparent, lustrous rhombohedra. 
This body can be sublimed when heated slowly. It has distinctly 
basic properties; it forms with hydrochloric acid a compound 
which crystallizes in long prismatic needles. The composition 


of the base is C° H!? N4, and its hydrochlorate is €° H!* N* HCL. 


2(€ H?) N 
He considers that it has the rational formula 2(¢ H’) N +N, de- 
2(C H?) N 
rived from the type NH°, in which three atoms of hydrogen are 
replaced by three atoms of dimethylenammonium. He names 
it hexamethylenamine. Its nearest congener is Debus’s glycosine. 
Like that body, Butlerow’s new base is formed with elimina- 
tion of water, according to the equation 


3C? H*O?44NH3=€o H!? N44 6H? 0. 
Butlerow has also found that diacetate of methylglycol, when 


heated with an excess of water in a sealed tube, is converted into 
dioxymethylene and free acetic acid. 


The amalgam of sodium and mercury, obtained by adding 
sodium in small quantities to mercury, is very convenient for 
applying sodium in many reactions ; in most cases it simply acts 
by dividing the sodium and increasing its surface. 

Lowig and Scholzt have investigated the action of this amal- 
gam on a mixture of sulphide of carbon and iodide of ethyle. 
A very brisk reaction took place, and the vessel in which it was 
effected required cooling; the product was then treated with 
ether, which dissolved out a new body, as well as the excess of 
iodide of ethyle and bisulphide of carbon. The etherial solution, 
mixed with water, was distilled in the water-bath to drive off the 
ether, the excess of iodide of ethyle, and of the bisulphide of 
carbon ; on cooling, the new body collected under water in the 
form of a yellow oil with a penetrating alliaceous odour. When 
this was fractionally distilled, it was found to consist principally 
of mercaptan, and of a new body which boiled at 188°, the ana- 
lysis of which led to the composition C°H°S*%. It is formed 
thus :— 


C+ H®1T+C28*+2Na=C® H® S?+Nal+NaS8. 
It is a sulphur-yellow liquid, very fluid, and highly refracting. 
* Bulletin de la Société Chimique, p. 221. 


+ Phil. Mag. vol. xvii. p. 287. . 
{ Journal fiir Prakt. Chemie, vol. lxxix. p. 441. 


126 M. Landolt on Phasphuretted Hydrogen. ~ 


Its density is 1-012 at 15°. It has a very disagreeable odour ; it is 
insoluble in water, but soluble in alcohol, ether, and sulphide of 
carbon. Nitric acid attacks it violently, as also do chlorine, bro- 
mine, and hypochlorite of lime. Its alcoholic solution, mixed 
with an alcoholic solution of bichloride of mercury, gives a white 
precipitate which dissolvesin hotalcohol. It consists of the new 
body combined with 6 equivalents of bichloride of mercury. 


Léwig* has examined the action of sodium on oxalic ether. In 
the presence of water, sodium acts on oxalic ether, liberating 
carbonic oxide and forming carbonic ether. The mass becomes 
coloured, and a new acid is formed which the author calls myrinic 
acid. 

With a pulverized sodium amalgam the action is quite differ- 
ent ; oxalate of soda is deposited, only a few bubbles of carbonic 
oxide are disengaged, and not a trace of carbonic ether is formed. 
Treated with water, a colourless solution is formed, which, agi- 
tated with ether, gives up a neutral body of a bitter taste, which, 
on evaporation of the ether, is left as a syrupy colourless liquid. 
In two or three days this deposits beautiful white crystals, which 

have the crude formula C* H? O°. 
Neither baryta water nor subacetate of lead act in the cold on 
the aqueous solution of these crystals; but on the application of 
heat, a white precipitate is formed which contains no oxalic acid. 


Graham showed long ago that phosphuretted hydrogen, which 
is not spontaneously inflammable, is made so by admixture with 
a very small quantity of nitrousacid. Tandolt describest a con- 
venient mode of performing this experiment. Phosphuretted 
hydrogen, which is not spontaneously inflammable, is generated 
by heating phosphorus with concentrated soda lye, to which 
about double its volume of alcohol has been added, and is passed 
through some nitric acid placedina porcelain dish. Ifthe nitric 
acid is about 1°34, and has been previously freed from hyponi- 
tric acid by boiling, the bubbles of gas burst without inflaming. 
But if now a few drops of fuming nitrie acid be added, each 
bubble takes fire, forming the usual rings. The spontaneous 
inflammability is again destroyed by an excess of hyponitric acid, 
for then the phosphuretted hydrogen is destroyed in the liquid. 
The hyponitric acid doubtless causes the formation of a small 
quantity of the spontaneously inflammable liquid compound 
PH?. At the same time the nitric acid plays some part; for 
water to which hyponitric acid has been added produces no 
such effect. 
* Journal fiir Prakt. Chemie, vol. lxxix. p. 453. 
tT Liebig’s Arvnalen, November 1860. 


ner 9 


XX. Note on the ivumbers of Bernoulli and Kuler, and a new 
Theorem concerning Prime Numbers. By J. J. SYLVESTER, 
M.A., F.R.S., Professor of Mathematics at the Royal Academy, 
Woolwich*. 


Be the accepted continental notation, I denote by 


Bt the positive value of the coefficient of 7?” in 


aon ge 
multiplied by the continual product 1.2.3...7. 

The law which governs the fractional part of B, was first 
given in Schumacher’s Nachrichten, by Thomas Clausen in 1840 ; 
ahd almost immediately afterwards a demonstration was freien 
by Professor Staudt in Crelle’s Journal, with a reclamation of 
priority, supported by a statement of his ‘having many years pre- 
viously communicated the theorem to Gauss. 

The law is this, that the positive or negative fractional residue 
of B, (according as n is odd or even) is ‘made up of the simple 
sum of the reciprocals of all the prime numbers which, respect- 
ively diminished by unity, are contained in 2n. The proof, which 
is of an inductive kind, is virtually as follows: Suppose the law 
holds good up to (n—1) ‘inclusive ; if we expand & (#)?” under the 


form — am, we shall evidently obtain aoe +B,, under the 


Ge 
form of a finite series, of which the terms are numerical mul- 
tiples of the products of powers of # by the Bernoullian num- 
bers of an order inferior to the nth. If, now, we make x equal 
to the product of all the primes which, diminished by unity, are 
contained in 2n, it will at once be seen (on inspection of the 
series) that all its terms become integer numbers, and con- 


27 
sequently at +B, becomes an integer; and therefore the law 


will hold good up to n, since it may easily be shown, by an 
application of Vermat’s theorem and elementary arithmetical 
considerations, that if N be the product of any prime numbers 
whatever, and if p is the general name of such . them as dimi- 


nished by unity are factors of w, then aoe 


EEO integer. 


Hence, since the law holds good forn= x , it is universally true. 


* Communicated by the Author. 

+ Were it not for the general usage being as stated in the text, I cer- 
tainly think it would be far more convenient to use a notation agreeing 
with the continental method as to sion, and nearly, but not quite, with 


Myr. DeMorgan’s as to quantity, viz. to understand by Bz the coefficient of 
et 


i” in it an taken positively, so that Bn should be equal to zero for all 


the odd values of n, not excepting n=1, 


128 Prof. Sylvester on the Numbers of Bernoulli and Kuler, 


This theorem, then, of Staudt and Clausen, inter alia, gives a 
rule for determining what primes alone enter into the deno- 
minators of the Bernoullian numbers when expressed as frac- 
tions in their lowest terms; it enables us to affirm that only 
simple powers of primes enter into those denominators, and to 
know @ priort what those prime factors are. This note is 
intended to supply a law concerning the numerators of the Ber- 
noullian numbers, which I have not seen stated anywhere, and 
which admits of an instantaneous demonstration, to wit, that the 
whole of 2 will appear im the numerator of Bn, save and except 
such primes, or the powers of such primes, as we know by the 
Staudt-Clausen law must appear in the denominator. 

I am inclined to believe that this law of mine was not known, 
at all events, in 1840, from the circumstance that in Rothe’s 
Table, published by Ohm in Crelle’s Journal in that year, which 
gives the values of B, up to n=81, the numerators are, with one 
exception {about to be named), all exhibited in such a form as 
to show such low factors as readily offer themselves, but for By. 
the fact of the divisibility of the numerator by 23 is not in- 
dicated. This numerator is 596451111598912163277961, 
which in fact =23 x 25982657025822267968607. It is obvious, 
indeed, under my law, that whenever p is a prime number other 
than 2 and 8, the numerator of B, must contain p, because in 
such case p—1 cannot be a factor of 2p. When p=3 or p=2, 
2 p always contains (p—1), so that 2 and 8 are necessarily con- 
stant factors of the Bernoullian denominators, and can there- 
fore never appear in the numerators. In Schumacher the law of 
the denominator is given as “a passing” (or chance ?) ‘ speci- 
men” of a promised memoir by Clausen on the Bernoullian 
numbers, which I shall feel obliged if any of the readers of this 
Magazine will inform me whether anywhere, and if so, where it 
has appeared. Now for my demonstration of the law of the nu- 
merators. 


By definition, B,, =II(2n) x coefficient of ¢?”-! in a Let 


pw be any integer number; then + (u?”—1)B,=TII(2n) x coeffi- 

: bi at bb 
cient of ¢2"-! in eT ay == 
(—1) — (eH -DF 4 eH—DEL ,, +e?) 


evt— J ‘ 


——, or 1n 
ef —]? 


or in 
elu 2)t 1 Qelu—S)E4t + (w—2)eh+ (u—1) 
si eM—Di+4 eH—24 .., tet] ; 


But obviously, by Maclaurin’s theorem, the coefficient of ¢?"~1 in 


and a new Theorem concerning Prime Numbers. 129 


the expansion of this last generating function will be of the form 


ie tl my 1) yg to , where [ is an integer, and therefore B,, will 
2Qnl 
be of the form pe (ue="— 1)" 
Suppose now, when sca i. is reduced to its lowest 


wees (we? — 1) 

terms, that p (a prime contained in 2n) does not appear in the 
numerator, this can only happen by virtue of p being contained 
in w??—1(w2"— 1); let now yw be taken successively 2,3,4,...(u—1), 
then »?”—1 im all these cases is divisible by p; and therefore, 
by an obvious inverse of Fermat’s theorem, (p—1) must be con- 
tained in 2n, i. e. y must be a factor of the denominator of b, 
under the Staudt-Clausen law, which proves my theorem. 

As a corollary to the foregomg, using Herschel’s transforma- 
tion, we see that if w be taken any intecer whatever, 


Qn (1 + A)*? +2(1-+ A)? 4... + (u—1) on 


a oy eat 
be 7S ag ar Nae 7 Beas ir, Ne 
L k. = —l 
2 a K—3 ‘iad 
Rete Pitt BE AN ee BES - 
=" on 2 


ay = ny 

id AY At 2+ pe ee iis Ee 3 Ae 
and if we write 0°"*’ instead of 0°”, the result vanishes. For 
the case of w=2, this theorem accords with one well known. 
As this subject is so intimately related to that of the Herschelian 
differences of zero, I may take this occasion of stating a proposi- 
tion concerning the latter, which (simple as it is) appears to have 


A’0” +7 


escaped observation, viz. that is in fact the expression 


\r 
for the sum of the homogeneous products of the natural num- 
bers from 1 to 7, taken n and z together. For 


1 
(v—n)(v7—n+1)...(¢%—l1)z 


las 
Bae We Nn writer beter ieee 4th 
Ilr lLa—n  (e—n4+1) ° (v—n+2) or 


Hence obviously 


1 | ey (Oe VAG 3 rl a) Ye 
im? —r(r7—1)"4+r. 5 (r—— 2)" + se, }, 
Phil. Mag. 8. 4, Vol. 21, No, 188 Feb, 1861. K 


130 Prof. Sylvester on the Numbers of Bernoulli and Euler, 


1. @. 
og ag ; Lee i 
I) = coefficient of git in Go hj\G=n+l) Gon+l) ee 


= the sum of the (n—r)ary homogeneous products of 
1 ee ace ae 


Thus, then, we are able to affirm, from what is known concerning 
Ao" ™ 


(see Prof. De Morgan’s Calculus), that the r-ary homoge- 


neous product-sum of 1, 2, 3... (which is of the degree 2r 
in n) always contains the algebraic factor n(n+1)...(n+7). 


Addendum.—Since sending the above to press, I have given 
some further and successful thought to the Staudt-Clausen 
theorem. Staudt’s demonstration labours under the twofold 
defect of indirectness and of presupposing a knowledge of the law 
to be established. In it the Bernoullian numbers are not made 
the subject of a direct contemplation, but are regarded through 
the medium of an alien function, one out of an infinite number, 
in which they are as it were latently embodied; and the proof, 
like all other mductive ones, whilst it convinces the judgment, 
leaves the philosophic faculty unsatisfied, inasmuch as it fails to 
disclose the reason (the title, soto say, to existence) of the truth 
which it establishes. I present below an immediate and a direct 
proof of this beautiful and important proposition, founded upon 
the same principle as gives the law of the necessary factor in the 
numerators (viz. the arbitrary decomposition of the generating 
function of Bernoulli’s numbers into partial fractions), and rest- 
ing upon a simple but important conception, that of relative as 
distinguished from absolute integers. 

I generalize this notion, and define a quantity to be an integer 
relative to 7 (or, for brevity’s sake, to be an 7** integer) when it 
may be represented by a fraction of which the denominator 
does not contain 7. 

The lemma* upon which my demonstration rests is the fol- 

* This lemma is the converse of a self-evident fact, and it virtually em- 
bodies a principle respecting an arithmetical fraction strikingly analogous 
to a familiar one respecting an algebraical one; viz. in the same way as a 
rational algebraical function of 2 can be expressed in one, and only one, way 
as an integral function augmented by a sum of negative powers of linear 
functions of 2, so a rational arithmetical quantity can be expressed in one, 


and only one, way as an integer augmented by the sum of negative powers 
of simple prime numbers multiplied respectively by numbers less than such 


: : : ‘ 2 . c 
primes. In drawing this parallel, the arithmetical quantity pe where 


2 es 
(aw+b)’? 


4 
c<p, is regarded as the analogue of the algebraical one 


and a new Theorem concerning Prime Numbers. 131 


lowing, which is itself an immediate corollary from the arith- 
metical theorem that if a,b,c, ... 1, with or without repetitions, 
are the distinct prime factors of the denominator of a fraction, 
the fraction itself may be resolved into the sum of simple frac- 
tions, 


ete By oC L 
ee a OT 


(itself a direct inference from the familiar theorem that if 
P; 7 be any two relative primes, the equation pa—qy=c is 
soluble in integers for all values of c). The lemma in question 
is as follows: If the quantity above described is representable 
under the several forms, 

al ; b i! 

ot an (a) integer yet 8 (6*) inteser-e zeta (A) integer, 
then it is equal to 


ahs: Bl i 
epage th et ad absolute integer. 

From what has been already shown, it is obvious that « being 
any prime number, the highest power of « which can enter into 
the denominator of (u?”—1)B, is y?”, and consequently y?"B is 
an integer relative to uw. Also it is clear that only those values 
of ~ can appear in the denominator of B, which, diminished by 
unity, are factors of 2n. We have, moreover, 


1 
(—)"*(w"—1)B, =I (2n) x coefficient of #2”! in wt ea 


2. e. coefficient of ¢2"-! in eri Ae where 


N =I (2n)(e™—Dé4 eu—2#4 ... +e’—(u—1)) 
=V,t +57 + eee + Vol?” + &e., 


as is quite proper, for both of them are fractions in their simplest forms, 
which would not be the case for the former were ¢ equal to or greater than p, 


since in such case S could be more simply expressed under the form 
me sy. 

This principle amounts to an affirmation that the equation in positive 
integers, 

(0...kl)e+(ab...2y+...+(ab...k)t—(ab...klu=N, 

where a, b,..k,/ are relative primes, and N<(ad... hi), always admits of a 
solution, which may be termed the primitive one, and which will be unique, 
that namely in which 2, y,...2, ¢ are respectively less than a, b,..k, 1. 


132 Prof. Sylvester on the Numbers of Bernoulli and Kuler, 
where obviously v,, Vg)». « Von are all integers, and the last of them 
Gy 1) eee J 24 128, 
Suppose now that 2n contains (u—1), then by Fermat’s theorem 
Von = (u—1) [mod p]. 


Again, avery slight consideration* will serve to show that when 
1s any prime other than 2, e““—1 is of the form 


w(t + m0, t? + pdotF + 0.6. + Mb2n 12"! + &e.), 
where 6), 59, ..« Oon_) are all integers relative to wu. Now suppose 


N 
aT =YoH t+ Got? + oe 6 + gan; 


then by multiplication and comparison of coefficients we obtain 
the identities following: 
Fo=Vx VAM HVey Yat #191 + HYo0a = Vg + +s 
Gon—1 + MYon—10, + «+ MYod2n—1 =Von > 


obviously therefore g2,-)=4X (an integer relative to “) + Von. 
Hence 


(—1)"B,=(an integer relative to w) — 5 
: 1 
= (an integer relative to w) + a 
pe 


* Yor » being a prime number greater than 2, if we put T(r) (the coeffi- 


cient of ¢” in e«t—1) under the form of (an integer gud ») Xp’, we have 


r r r 
i=r—E-—E- > —E7;- &e, 
pe lH 


va T : 2 
= Of ty Oe >1 when r > 2; also when r=2, (=-2—-h 


When p=2, this would be no longer true; and in fact it is easily seen that 
in this case, whenever r is a power of 2, z will be only equal to J. 

For the benefit of my younger readers, I may notice that the direct proof 
of the theorem that the product of any 7 consecutive numbers must con- 
tain the product of the natural numbers up to 7, or, in other words, that 


ih oh, IIn : : 
the trinomial coefficient Fp 4,7 Where »+»'=2 is an integer, is drawn 


from the fact that this fraction may be represented as an integer gud mp (any 
prime) multiplied by p#, where 


A y p\ as n y yp! 
oes — hee | he hs = — i 
i=(2 —E 1D ae 7 -E=-E :)+ &e 


(Ez meaning the integer part of x), so that 2 is necessarily either zero or 
positive, because the value of each triad of terms within the same paren- 
thesis is essentially zero or positive. This is the natural and only direct 
procedure for establishing the proposition im question, 


and a new Theorem concerning Prime Numbers. 133 


And this relation obtains for any value of yu other than 2, which 
(or a power of which) could be contained in 2n. When p=2, 
the & series wiil nof all of them be the doubles of relative inte- 
gers to 2; but the v series, on account of the factor I1(2n), will 
obviously, up to v2,—, inclusive, all contain 2 and ».,=13; conse- 
quently go, will be twice (an integer gud 2)+1, and B,, will still 


be (an integer relative to ~) + : as before. Hence it follows from 


the lemma that (—1)"B,,=an absolute integer + 2 or 


1 
B,= an integer +(—)”"= ie 


which is the equation expressed by the Staudt-Clausen theorem*. 

My researches in the theory of partitions have naturally in- 
vested with a new and special interest (at least for myself) every- 
thing relating to the Bernoullian numbers. I am not aware 
whether the following expression for a Bernoullian of any order 
as a quadratic function of those of an inferior order happens to 
have been noticed or not. It may be obtained by a simple pro- 
cess of multiplication, and gives a means (not very expeditious, 
it is true) for calculating these numbers from one another with- 
out having recourse to the calculus of differences or Maclaurin’s 
theorem, viz. 


Be. igo B, Biot . 2 Pat et 
Ten ~~) irey’ Tren—s tray enw 
Bos B. 
Qn—4 At LM Se tae 2S 
et... + (2 —)it@n—4) 114 
+ (227-2 1) Bra =i 


Tl(2n—2) 112’ 

in which formula the terms admit of being coupled together from 

end to end, excepting (when n is even) one term in the middle. 
To illustrate my law respecting the numerators of the num- 

bers of Bernoulli, and its connexion with the known law for 

the denominators, suppose twice the index of any one of these 


* I ought to cbserve that in all that has preceded I have used the word 
imteger in the sense of positive or negative integer, and the demonstration - 
I have given holds good withcut assuming B, to be positive. That thisis 
the case, or, in other words, that the signs of the successive powers of ¢ 


. et—] ate 
at alternately positive and negative, may be seen at a glance by 
z 4 


putting t=2’/ — 16, and remembering that all the coefficients in the series 


for tan @ in terms of 6 are necessarily positive, because (a) tan 6 obvie 


ously only involves positive multiples of powers of (tan @) and (sec 6). 


134 Prof. Sylvester on the Numbers of Bernoulli and Euler, 


numbers to contain the factor (p—1)p*, where p is any prime; 
then this number will contain the first power of p in its deno- 
minator; but if the factor piis contained in double the index in 
question, but (p—1) not, then p‘ will appear bodily as a factor 
of the numerator. 

It has occurred to me that it might be desirable to adhere to 
the common definition of “ Bernoulli’s numbers,” but at the same 


time to use the term Bernoulli’s coefficients to denote the actual 
os 
coefficients in — ; so that if the former be denoted in 


2(e! 

general by B,, and the latter by @,, we shall have 

Bon= (—)"'B,, 

comin —! 0 
In the absence of some such term as I propose, many theorems 
which are really single when affirmed of the coefficients, become 
duplex or even multifarious when we are restrained to the use 
of the numbers only. 


Postscript.—The results obtained concerning Bernoulli’s num- 
bers in what precedes, admit of being deduced still more suc- 
cinctly; and this simplification is by no means of small im- 
portance, as it leads the way to the discovery of analogous and 
unsuspected properties of Huler’s numbers (namely the coeffi- 


cients of 


in the expansion of sec @), and to some very re- 
n 


markable theorems concerning prime numbers in general. 

In fact, to obtain the laws which govern the denominators and 
numerators of Bernoulli’s numbers, we need only to use the fol- 
lowing principles :—(1) That « being a prime, 2u”=0, or = —1 
to the modulus jz, according as ~—1 is, or is not, a factor of m, 
—the second part of this statement being a direct consequence 
of Fermat’s theorem, the first part a simple inference from its 
inverse. (2) That e“*—1 is of the form pt-+p72?T, where T is 
a series of powers of ¢, all of whose coefficients are integers rela- 
tive to ~, except for the case of ~=2, when e“*—1 is of the form 
2¢+2T. We have then (u2”—1)(—)"~"B, = —II(2n) x coeffi- _ 
ele Wey e(h—2)t 4 wn & 

ett — ] 


virtue of principle (2)) =I— , where I is an integer relative to 


cient of ¢?”-! in a by actual division (in 


#, containing n, and —R= -< (Vt Oe +(e — 1) 


Hence (—)"B,= an integer relative to w or to such integer + 


and a new Theorem concerning Prime Numbers. 135 


according as 2n does not or does contain (w—1), which proves 
the law for the numerators; and so if pw‘ is a factor of n, but 


(u—1) not a factor of 2n, x will vanish, and 2”—1 will not con- 


tain “; hence (u?”—1)B,, and consequently B,, will be the pro- 
duct of «* by an integer relative to ~, which proves my nume- 
rator law. 

So by extending the same method to the generating function 


ef + 


Q4 Q2n 


secO=H,+E + Baya ga te t En pa gay t he 


6? 
IT, 2° +E 
every prime number yp of the form 4n+1, such that (u—1) isa 
factor of 2n, will be contained in H,,; and every such factor, when 
p is of the form 4m—1], will be contained in H,+(—)"2. 

I call the numbers E,, E,,... HE, EHuler’s Ist, 2nd,...nth 
numbers, as Kuler was apparently the first to brmg them into 
notice. In the Institutiones Caleuli Diff. he has calculated their 
values up to H, inclusive: in this last there isan error, which is 
specified by Rothe in Ohm’s paper above referred to; had Kuler 
been possessed of my law this mistake could not have occurred, 
as we know that H,+2 ought to contain the factors 19 and 7, 
neither of which will be found to be such factors if we adopt 
Kuler’s value of Ky, but both will be such if we accept Rothe’s 
corrected value. But in still following out the same method, I 
have been led, through the study of Bernoull’s and the allied 
numbers, and with the express aid of the former, to a perfectly 
general theorem concerning prime numbers, in which Bernoulli’s 
numbers no longer take any part. Fermat’s theorem teaches us 
the residue of g“~! in respect to w, viz. that it is unity; but I 
am not aware of any theorem being in existence which teaches 


, : #— lo] aia 
anything concerning the relation of Fe Be ty (or, which is 


the same thing, of the relation of gu—-1 to the modulus ?). I have 
obtained remarkable results relative to the above quotient, which 
[I will state for the simplest case only, viz. that where q¢ as well 
as # is a prime number. I find that when q is-any odd prime, 


Lo a 


be w—l 


where ¢,, Co, Cs). --Cy—1 are continually recurring cycles of the 
numbers 1, 2, 3,...7, the cycle beginning with that number 7! 


Co C3 Cu—1 
Sy se ae aes ks 3 


136 On a new Theorem concerning Prime Numbers. 
which satisfies the congruence pr! =1(modr). Since we know 


1 i! pie : 
maa ae aa wine eee — — . ] 
that aa Danger a pra +9 = 0 (to mod. yw) in place 


of the cycle 1, 2, 3,...7, we may obviously substitute the re- 
duced cycle 

r—l r7—o 
“9? ae “9? @oe 


r—3 r—l 
—1,0,1,..— “== 


2 2 


oodies 
Thus, ea. gr., , when pw is of the form 6n+ 1, 


aia 1 1 1 
Fay 8 + a go ee 
and when wp is of the form 6n—1, 
—1 1 1 1 


tee ee) Maen ae Ee 
When g is 2, the theorem which replaces the preceding is as 


.—1,to mod. p. 


Q-1_] 
follows: » when p is of the form 4n +1, 
: po 
1 1 1 1 a 1 
See eg eb fad ae ee ee 
foal pk p—d poo 5 
i} 1 1 


and when p is of the form 4n—1, 


a0), dalton oan Be aT ac 
— por lo pp? pd ph pS 


1 | sa il 
+ eae + re, + &c., to mod. p. 

When q is not a prime, a similar theorem may be obtained by 
the very same method, but its expression will be less simple. 
The above theorems would, I think, be very noticeable were it 
only for the circumstance of their involving (as a condition) the 
primeness as well of the base as of the augmented index of the 
familiar Fermatian expression g#~1,—a condition which here 
makes its appearance (as I believe) for the first time in the 
theory of numbers. 


ptise:. 4 


XXI. On a new Method of arranging Numerical Tables. By 
W. Dirrmar, Assistant in the Laboratory of Owens College, 
Manchester*. 

[ With a Plate. | 


HE use of numerical tables constructed in the ordinary 
manner is, for obvious reasons, inseparably connected with 
interpolation calculations. Such calculations, although by no 
means difficult, involve, as every practical mathematician knows, 
much loss of time, and often give rise to mistakes. This is 
especially the case when, from a given value of a dependent vari- 
able, the corresponding value of the independent, or of another 
dependent variable has to be found. It is obvious that all inter- 
polations could be avoided by giving all the values which can 
possibly be required; this, however, is in most cases practically 
impossible, as the tables w ould thus become inconyeniently volu- 
minous, and the chance of typographical error would be greatly 
increased. I believe that the completeness thus attainable can 
be arrived at by the use of the following graphical method, 
- while at the same time the size of the table will not extend 
beyond the ordinary limits. Let it be required to construct 
a table giving the values of several functions y, z,w...of a 
variable x. Draw a system of vertical parallels, and call them 
respectively the zw, y, z,w... line. On each of the verticals 
construct a scale, and let every point on each of the scales be the 
symbol for a number equal either to the number of divisions (and 
in general cne fraction of a division) contained between the 
origin and that point, or to a simple multiple of this number ; 
so that the marks on each scale represent the terms of an arith- 
metical series. These several scales must be so constructed that 
the corresponding values of all the variables are found in one 
and the same horizcutal line. It is true that, strictly speaking, 
this can only be the case when all the functions are linear ones ; it 
is, however, easy to show that, practically speaking, the problem 
can always be solved with any degree of exactitude required, 
provided that the functions are continuous. The mode of con- 
struction and use of such tables will perhaps be best explained 
by an example. 

Tig. 1, Plate III. represents the commencement of a Table of 
logarithms and. reciprocals, which is intended to afford about the 
same degree of exactitude as a common 4-place logarithmic table. 
Calumn UH. contains. the logarithm-scale; each of the divisions 
is 4 millims. in length, and represents a logarit thmic increment 
of 0-001; each point in this scale has a twofold meaning ; it 
stands, namely, both for the mantissa v=), and for the (posi- 


* Communicated by the Author. 


138 On anew Method of arranging Numerical Tables. 


tive) mantissa of : which equals 1—d. When this scale had 


been drawn, the integral numbers from 100 to 1000 were marked 
on the other two columns by drawing horizontal lines opposite 
to the corresponding logarithms; the numbers up to num. 
(mant. =*5000) were placed in column I. beyond this number 
in column III, Lastly, the interval between every two such 
marks was divided into ten equal parts. Since, now, within the 
intervals « = 100 to e= 101, e=101 to x=102, &c. the 
A (log x) 
Aw 


quotients may in our case safely be taken as a con- 


stant, any Alog@ within such an interval may, together with its 
Az, be graphically represented by one and the same straight 
line, as is in fact done in the Table. It is now clear that any 
horizontal line will cut the verticals. in points which (whether 
they coincide with marks or not) are symbols for respectively a 
certain number z, log #, and a number having the same succes- 


sion of figures as = The above will afford complete informa- 


tion for the AOA use of the Table*. The division of the 
spaces between the marks on the scales 1s to be made by the eye. 
With some practice an error greater than one-tenth of an interval 
in the logarithm-scale will rarely be made; the position of the 
marks themselves may be by far more accurately determinedt ; 
the error accompanying any logarithm taken out of the Table 
will therefore scarcely ever exceed 0: 0001, and. any number 
found by its help will be correct within about S000 Of its value. 
The reliability of the results is not so dependent upon the exacti- 
tude of the drawing as one might at first sight be disposed to 
think, as only that 4 portion of every number is really graphically 
determined which in an ordinary 4-place table is found by compu- 
tative interpolation. ‘The Table is particularly handy for finding 
the values of reciprocals, as these may be obtained directly with- 


* Let us suppose the logarithm and the reciprocal of 1°0653 were to be 
found. Divide the interval between the marks 106°5 and 106°6 on the 
a-scale (in your mind) into ten equal parts, and through the third point 
from 106°5 draw a horizontal line, which is best done by bringing a straight 
line etched on one side of a piece of plate-glass into the right position. This 
line will cut the log-scale in the point ‘0274 = mant. 10653, and the 


] 1 1 
77scale in the point 938°7=1000 x T9G53- At the same time log 7-pgRy 
may be read off directly, the point of intersection in the log-scale standing 
also for mant. 10653 = 9/26. 


+ When great exactitude is required, the figure may be drawn on a cop- 
per plate by help of a dividing engine, and copies printed from the copper. 


‘ 
, 
’ 
« 
‘ 
" 


es he 


Mr. W. Dittmar on Graphical Interpolation. 139 


out the intervention of logarithms. It will therefore be especi- 
ally useful in chemical calculations, as, for instance, in converting 
specific grayities into specific volumes, for reducing per-centage 
compositions to the unit of weight of one constituent, &c. The 
general applicability of this method is evident. For the sake of 
illustration I append figs. 2 and 8, giving respectively the be- 
ginning of a general interpolation- and of a densimetric Table. 
The mode of construction and use of these Tables will be under- 
stood from the description given of the Table of logarithms. 


XXII. On Graphical Interpolation. By W. Dittmar, Assistant 
in the Laboratory of Owens College, Manchester*. 


et principles laid down in the preceding article for the 

construction of numerical tables may also be employed for 
the purpose of carrying out graphical interpolations. Let us 
suppose that the corresponding values x¥o, 2)Y1 %eYo-++ be- 
longing to an unknown function y=/(z) are given by obser- 
vation, and that it is required to complete the series of vari- 
ables. It is clear that the direct results of observation may be 
registered in a graphical table in the manner described above. 
For this purpose itis only necessary to draw a straight line, and 
to construct on one side of it a scale with a constant unit of 
length, the points of which are considered as representatives of 
the values of y, while on the other side of the line marks made 
opposite to the points 7, ¥;, Ya,--. are taken as symbols of the 
respective values of 2, 1. €. %, 2, Zq,...&c. The question now 
is, how can the gaps on the w-scale be filled up by graphic inter- 
polation? This may be accomplished in the following way :— 
When there are reasons for supposing that f(z) does not differ 
much from a linear function, all the divisions on the x-scale may 
be made equal to one another, and each so long that the points 
corresponding to 2%, #,, &c. coincide as nearly as possible with 
those signifying respectively 7, y,, &c. on the y-scale. This is 
best done by dividing the distance between the two furthest 
points on the z-scale into the requisite number of equal parts, 
drawing lines from the points thus obtained to one point situated 
at some distance, and by moving the y-scale along in this system 
of lines parallel to the line dividedy, till a position is found in 
which the points of intersection of the radu with the y-scale 
yield an w-scale which agrees as closely as possible with the 
observed values. 


* Communicated by the Author. 
7 A sharp-edged drawing measure is most conveniently employed for 
this purpose. 


140 Mr. W. Dittmar on Graphical Interpolation. 


If a satisfactory result cannot be obtained im this way, it is 
best to try whether /(z) can be practically represented by an 
expression of the form A+ Bz+Ca?, where A, B, and C signify 
constants. If this be the case, we have* 

Y=AS BOTs ee ies ss. 8 oc 
y— Ay=A-+ B(@—Az) + C(e#—Az)?. 
Ay=BAz-—C(Az)?+(2CAz)z.. . . . » (IL) 


Ax Yen —BAx—C(Aa)?+ (2CAz) G + = (IIL) 

2,—X, 2 

Comparing equation (III.) with (II.), we see that In In Nz 

Lx, 

is equal to this Ay, the graphical representative of which is con- 

tained between the two points in the 2-scale corresponding to 
x +x, + Az Bidets tenn At _ A, 
—— ease : 


the numbers 


From the equations (II.) and (III.) the following method for 
constructing the z-scale may be found :—Combine the observed 
pairs of variables by twos, and find from every combination, with 
the help of equation (III.), a certain Ay, the graphical represen- 
tative of which is contained between the two points which in the 
z-scale mean z—~Az and x ‘Then construct a rectangular 
system of coordinates, and represent the values of x thus obtained 
(with an arbitrary unit of length) as abscissc, the corresponding 
values of Ay as*ordinates, using for the latter that length as unit 
which represents Ay=1 in the y-scale. Next draw a straight 
line which passes as nearly as possible through the extreme 
points of the ordinates. The ordinates of this line correspond- 
ing respectively to Aw, 2Az, 3Az,..., when put together in the 
right order, give the required z-scale. In order to obtain exact 
results, it is advisable to choose first such a large value for Ax 
that only a few points of the w-scale are obtained, and to deter- 
mine the intermediate pomts by new constructions. As soon as 
so many points are determined that two successive intervals do not 
differ perceptibly in length, the subdivisions of each interval may 
be made equal to one another. Should the indications of a scale 
thus obtained not agree quite satisfactorily with the observed 
data, it may often be improved by slightly changing the unit of 
length used in the construction, and by altering its position with 
respect to the y-scale. A convenient method for doing this has 
been already described. 

* g and y mean any values of the variables belonging together; xp, yp, 
and @n, Yn mean particular pairs of variables; Av stands for the constant 
numerical difference corresponding to one division in the a-scale; Ay for 
the corresponding variable increment of y. 


Royal Society. 141 


If an interpolation of the second degree proves to be insufli- 
cient for representing the observations, the series of values given 
is divided into several intervals, and each of these is then treated 
in the manner described. 

In some cases it will be advisable to represent, not y, but some 
function of y like y”, logy, &c., on a scale with equal divisions. 

The advantages which the method of graphical interpolation 
described appears to me to possess, as compared with the usual 
one of drawing a curve in a rectangular system of coordinates, 
are the following :— 

1. All the lines drawn are straight lines; the personal error in 
the drawing is therefore reduced to a minimum. 

2. The drawing can be executed with less trouble and greater 
exactitude, and it takes up less space than in the ordinary way. 

3. When the drawing is finished, the value of y belonging to 
any given z may be read off at once, and vice versd. 


XXIII. Proceedings of Learned Societies. 


ROYAL SOCIETY, 
{Continued from p. 79.]| 
March 22, 1860.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 

HE following communications were read :— 

** Qn the Theory of Compound Colours, and the Relations of 
the Colours of the Spectrum.” By J. Clerk Maxwell, Esq., 
Professor of Natural Philosophy, Marischal College and University, 
Aberdeen. 

Newton (in his ‘ Optics,’ Book I. part ui." prop. 6) has indicated a 
method of exhibiting the relations of colour, and of calculating the 
effects of any mixture of colours. He conceives the colours of the 
_ Spectrum arranged in the circumference of a circle, and the circle so 
painted that every radius exhibits a gradation of colour, from some 
pure colour ef the spectrum at the circumference, to neutral tint at 
the centre. The resultant of any mixture of colours is then found 
by placing at the points corresponding to these colours, weights 
proportional to their intensities; then the resultant colour will be 
found at the centre of gravity, and its intensity will be the sum of 
the intensities of the components. 

From the mathematical development of the theory of Newton’s 
diagram, it appears that if the positions of any three colours be 
assumed on the diagram, and certain intensities of these adopted as 
units, then the position of every other colour may be laid down from 
its observed relation to these three. Hence Newton’s assumption 
that the colours of the spectrum are disposed in a certain manner in 
the circumference of a circle, unless confirmed by experiment, must 
be regarded as merely a rough conjecture, intended as an illustration 
of his method, but not asserted as mathematically exact. From the 


142 Royal Society :— 


results of the present investigation, it appears that the colours of the 
spectrum, as laid down according to Newton’s method from actual 
observation, lie, not in the circumference of a circle, but in the 
periphery of a triangle, showing that all the colours of the spectrum 
may be chromatically represented by three, which form the angles of 


this triangle. 
Wave-length in millionths of Paris inch. 


DeHPlebe Hak Sere 2328, about one-third from line C to D, 
Green........ 1914, about one-quarter from E to F, 
Blue ........ 1717, about half-way from F to G. 


The theory of three primary colours has been often proposed as 
an interpretation of the phenomena of compound colours, but the 
relation of these colours to the colours of the spectrum dees not 
seem to have been distinctly understood till Dr. Young (Lectures on 
Natural Philosophy, Kelland’s edition, p. 345) enunciated his theory 
of three primary sensations of colour which are excited in different 
proportions when different kinds of light enter the organ of vision. 
According to this theory, the threefold character of colour, as perceived 
by us, is due, not to a threefold composition of light, but to the 
constitution of the visual apparatus which renders it capable of being 
affected. in three different ways, the relative amount of each sensation 
being determined by the nature of the incident light. If we could 
exhibit three colours corresponding to the three primary sensations, 
each colour exciting one and one only of these sensations, then since 
all other colours whatever must excite more than one primary sensa- 
tion, they must find their places in Newton’s diagram within the 
triangle of which the three primary colours are the angles. 

Hence if Young’s theory is true, the complete diagram of all colour, 
as perceived by the human eye, will have the form of a triangle. 

The colours corresponding to the pure rays of the spectrum must 
all lie within this triangle, and all colours in nature, being mixtures 
of these, must lie within the line formed by the spectrum. If 
therefore any colours of the spectrum correspond to the three pure 
primary sensations, they will be found at the angles of the triangle, 
and all the other colours will lie within the triangle. 

The other colours of the spectrum, though excited by uncom- 
pounded light, are compound colours; because the light, though 
simple, has the power of exciting two or more colour-sensations in 
different proportions, as, for imstance, a blue-green ray, though not 
compounded of blue rays and green rays, produces a sensation com- 
pounded of those of blue and green. 

The three colours found by experiment to form the three angles 
of the triangle formed by the spectrum on Newton’s diagram, may 
correspond to the three primary sensations. 

A different geometrical representation of the relations of colour 
may be thus described. ‘Take any point not in the plane of Newton’s 
diagram, draw a line from this point as origin through the point 
representing a given colour on the plane, and produce them so that 
the length of the line may be to the part ent off by the plane as the 
intensity of the given colour is to that of the corresponding point on 


Prof. Maxwell on the Theory of Compound Colours. 148 


Newton’s diagram. In this way any colour may be represented by 
a line drawn from the origin whose direction indicates the quality of 
the colour, and whose length depends upon its intensity. The 
resultant of two colours is represented by the diagonal of the paral- 
lelogram formed on the lines representing the colours (see Prof. 
Grassmann in Phil. Mag. April 1854). 

Taking three lines drawn from the origin through the points of 
the diagram corresponding to the three primaries as the axes of 
coordinates, we may express any colour as the resultant of definite 
quantities of each of the three primaries, and the three elements of 
colour will then be represented by the three dimensions of space. 

The experiments, the results of which are now before the Society, 
were undertaken in order to ascertain the exact relations of the 
colours of the spectrum as seen by a normal eye, and to lay down 
these relations on Newton’s diagram. The method consisted in 
selecting three colours from the spectrum, and mixing these in such 
proportions as to be identical in colour and brightness with a constant 
white light, Having assumed three standard colours, and found the 
quantity of each required to produce the given white, we then find 
the quantities of two of these combined with a fourth colour which 
will produce the same white. We thus obtain a relation between the 
three standards and the fourth colour, which enables us to lay down 
its position in Newton’s diagram with reference to the three standards. 

Any three sufficiently different colours may be chosen as standards, 
and any three points may be assumed as their positions on the 
diagram. The resulting diagram of relations of colour will differ 
according to the way in which we begin; but as every colour-diagram 
is a perspective projection of any other, it is easy to compare diagrams 
obtained by two different methods. 

The instrument employed in these experiments consisted of a dark 
’ ehamber about 5 feet long, 9 inches broad, and 4 deep, joined to 
another 2 feet long at an angle of about 100°. If light is admitted 
at a narrow slit at the end of the shorter chamber, it falls on a lens 
and is refracted through two prisms in succession, so as to form a 
pure spectrum at the end of the long chamber. Here there is 
placed an apparatus consisting of three moveable slits, which ean be 
altered in breadth and position, the position beimg read off on a 
graduated scale, and the breadth ascertained by inserting a fine 
graduated wedge into the slit till it touches both sides. 

When white light is admitted at the shorter end, light of three 
different kinds is refracted to these three slits. When white light is 
admitted at the three slits, light of these three kinds in combination 
is seen by an eye placed at the slit in the shorter arm of the instru- 
ment. By altering the three slits, the colour of this compound light 
may be changed at pleasure. 

The white light employed was that of a sheet of white paper, placed 
on a board, and illuminated by the sun’s light in the open air; the 
instrument being in a room, and the light moderated where the 
observer sits. 

Another portion of the same white light goes down a separate 


144 Royal Society :— 


compartment of the instrument, and is reflected at a surface of 
blackened glass, so as to be seen by the observer in immediate contact 
with the compound light which enters the slits and is refracted by 
the prisms. 

Each experiment consists in altering the breadth of the slits till 
the two lights seen by the observer agree both in colour and brightness, 
the eye being allowed time to rest before making any final decision. 
In this way the relative places of sixteen kinds of light were found by 
two observers. Both agree in finding the positions of the colours to 
lie very close to two sides of a triangle, the extreme colours of the 
spectrum forming doubtful fragments of the third side. They differ, 
however, in the intensity with which certain colours affect them, 
especially the greenish blue near the line F, which to one observer is 
remarkably feeble, both when seen singly, and when part of a mixture; 
while to the other, though less intense than the colours in the 
neighbourhood, it is still sufficiently powerful to act its part in com- 
binations. One result of this is, that a combination of this colour 
with red may be made, which appears red to the first observer and 
green to the second, though both have normal eyes as far as ordinary 
colours are concerned; and this blindness of the first has reference 
only to rays of a definite refrangibility, other rays near them, though 
similar in colour, not being deficient in intensity. Foran account of 
this peculiarity of the author’s eye, see the Report of the British 
Association for 1856, p. 12. 

By the operator attending to the proper illumination of the paper 
by the sun, and the observer taking care of his eyes, and completing 
an observation only when they are fresh, very good results can be 
obtained. The compound colour is then seen in contact with the 
white reflected light, and is not distinguishable from it, either in hue 
or brilliancy ; and the average difference of the observed breadth of a 
slit from the mean of the observations does not exceed =), of the 
breadth of the slit if the observer is careful. It is found, however, 
that the errors in the value of the sum of the three slits are greater 
than they would have been by theory, if the errors of each were 
independent ; and if the sums and differences of the breadth of two 
slits be taken, the errors of the sums are always found greater than 
those of the differences. This indicates that the human eye has a 
more accurate perception of differences of hue than of differences of 
illumination. 

Having ascertained the chromatic relations between sixteen colours 
selected from the spectrum, the next step is to ascertain the positions 
of these colours with reference to Fraunhofer’s lines. This is done 
by admitting light into the shorter arm of the instrument through 
the slit which forms the eyehole in the former experiments. A pure 
spectrum is then seen at the other end, and the position of the fixed 
lines read off on the graduated scale. In order to determine the wave- 
lengths of each kind of light, the incident light was first reflected 
from a stratum of air too thick to exhibit the colours of Newton’s 
rings. The spectrum then exhibited a series of dark bands, at 
intervals increasing from the red to the violet. The wave-lengths 


Prof. Maxwell on the Theory of Compound Colours. 145 


corresponding to these form a series of submultiples of the retarda- 
tion ; and by counting the bands between two of the fixed lines, whose 
wave-lengths have been determined by Fraunhofer, the wave-lengths 
corresponding to all the bands may be calculated ; and as there are 
a great number of bands, the wave-lengths become known at a great 
many different points. 

In this way the wave-lengths of the colours compared may be 
ascertained, and the results obtained by one observer rendered 
comparable with those obtained by another, with different apparatus. 
A portable apparatus, similar to one exhibited to the British 
Association in 1856, is now being constructed in order to obtain 
observations made by eyes of different qualities, especially those 
whose vision is dichromic. 


PosTscRIPT. 
Account of Experiments on the Spectrum as seen by the Colour-blind. 


The instrument used in these observations was similar to that 
already described. By reflecting the light back through the prisms 
by means of a concave mirror, the instrument is rendered much 
shorter and more portable, while the definition of the spectrum is 
rather improved. The experiments were made by two colour-blind 
observers, one of whom, however, did not obtain sunlight at the 
time of observation. The other obtained results, both with cloud- 
light and sun-light, in the way already described. It appears from 
these observations— 

I. That any two colours of the spectrum, on opposite sides of the 
line “ F,” may be combined in such proportions as to form white. 

II. That all the colours on the more refrangible side of F appear 
to the colour-blind “ blue,”’ and all those on the less refrangible side 
appear to them of another colour, which they generally speak of as 
*‘yellow,”’ though the green at E appears to them as good a repre- 
sentative of that colour as any other part of the spectrum. 

Ii. That the parts of the spectrum from A to E differ only in 
intensity, and notin colour; the light being too faint for good experi- 
ments between A and D, but not distinguishable in colour from E 
reduced to the same intensity. The maximum is about 2 from D 
towards EK. 

IV. Between E and F the colour appears to vary from the pure 
“yellow”? of E to a “neutral tint”? near F, which cannot be distin- 
guished from white when looked at steadily. 

V. At F the blue and the “yellow” element of colour are in equi- 
librium, and at this part of the spectrum the same blindness of the 
central spot of the eye is found in the colour-blind that has been 
already observed in the normal eye, so that the brightness of the 
spectrum appears decidedly less at F than on either side of that line ; 
and when a large portion of the retina is illuminated with the light 
of this part of the spectrum, the limbus luteus appears as a dark 
Spot, moving with the movements of the eye. The observer has not 
yet been able to distinguish Haidinger’s “‘ brushes’ while observing 
polarized light of this colour, in which they are very conspicuous to 
the author. 


Phil. Mag. 8. 4. Vol. 21. No. 183. Feb. 1862. = 


PAB re 0 bury BRagal Baeidly Been TT Rot 

- VI. Between F anda point 4 from F towards G, the colour appears 

to vary from the neutral tint to pure blue, while the brightness in- 

creases, and reaches a maximum at 2 from F towards G, and then 

diminishes towards the more refrangible end of the spectrum, the 
urity of the colour being apparently the same throughout. 

VII. The theory of colour-blind vision being “‘ dichromie,”’ is con- 
firmed by these experiments, the results of which agree with those 
obtained already by normal or “ ¢richromic’’ eyes, if we suppose the 
‘red’ element of colour eliminated, and the “green” and ‘ blue” 
elements left as they were, so that the “red-making rays,” though 
dimly visible to the dichromic eye, excite the sensation not of red 
but of green, or as they call it, ‘‘ yellow.” 

VIII. The extreme red ray of the spectrum appears to be a suf- 
ficiently good representative of the defective element in the colour- 
blind. When the ordinary eye receives this ray, it experiences the 
sensation of which the dichromic eye is incapable; and when the di- 
chromic eye receives it, the luminous effect is probably of the same 
kind as that observed by Helmholtz in the ultra-violet part of the 
spectrum—a sensibility to light, without much appreciation of colour. 

A set of observations of coloured papers by the same dichromic 
observer was then compared with a set of observations of the same 
papers by the author, and it was found— 

1. That the colour-blind observations were consistent among them- 
selves, on the hypothesis of two elements of colour. 

2. That the colour-blind observations were consistent with the 
author’s observations, on the hypothesis that the two elements of 
colour in dichromic vision are identical with two of the three elements 
of colour in normal vision. | 

3. That the element of colour, by which the two types of vision 
differ, isa red, whose relations to vermilion, ultramarine, and emerald- 
green are expressed by the equation 


D=1-198V +0:078U—0:276G, 


where D is the defective element, and V, U and G the three colours 
named above. 


April 26.—Sir Benjamin C. Brodie, Bart., President, in the Chair. 
The followmg communication was read :— 


** Note on Regelation.”” By Michael Faraday, D.C.L., F.R.S. &e. 
_ The philosophy of the phenomenon now understood by the word 
Regelation is exceedingly interesting, not only because of its relation 
to glacial action under natural circumstances, as shown by Tyndall 
and others, but also, and as I think especially, in its bearmgs upon 
molecular action ; and this is shown, not merely by the desire of dif- 
ferent philosophers to assign the true physical principle of action, 
but also by the great differences between the views which they have 
taken. 
Two pieces of thawing ice, if put together, adhere and become 
one ; at a place where liquefaction was proceeding, congelation sud- 
denly occurs. ‘The effect will ke place in air, or in water, or in 
vacuo. It will occur at everypoint where the two pieces of ice 


Pxof. Faraday on Regelation. 147 
touch ; but rot with ice below the freezing-point, 7. e. with dry ice, 
or ice so cold as to be everywhere in the solid state. 

Three different views are taken of the nature of this phenomenon. 
When first observed in 1850, I explained it by supposing that a 
particle of water, which could retain the liquid state whilst touching 
ice only on one side, could not retain the liquid state if it were 
touched by ice on both sides; but became solid, the general tem- 
perature remaining the same*. Professor J. Thomson, who dis- 
covered that pressure lowered the freezing-point of water‘, attributed 
the regelation to the fact that two pieces of ice could not be made 
to bear on each other without pressure ; and that the pressure, how- 
ever slight, would cause fusion at the place where the particles 
touched, accompanied by relief of the pressure and resolidification of 
the water at the place of contact, in the manner that he has fully 
explained in a recent communication to the Royal Society{. Profes- 
sor Forbes assents to neither of these views ; but admitting Person’s 
idea of the gradual liquefaction of ice, and assuming that ice is 
essentially colder than ice-cold water, 7. e. the water in contact with 
it, he concludes that two wet pieces of ice will have the water be- 
tween them frozen at the place where they come into contact$. 

Though some might think that Professor Thomson, in his last 
communication, was trusting to changes of pressure and tempera- 
ture so inappreciably small as to be not merely imperceptible, but 
also ineffectual, still he carried his conditions with him into all the 
eases he referred to, even though some of his assumed pressures 
were due to capillary attraction, or to the consequent pressure of the 
atmosphere, only. It seemed to me that experiment might be so 
applied as to advance the investigation of this beautiful pomt in 
molecular philosophy to a further degree than has yet been done; 
even to the extent of exhausting the power of some of the principles 
assumed in one or more of the three views adopted, and so render 
our knowledge a little more defined and exact than it is at present. 

In order to exclude all pressure of the particles of ice on each 
other due to capillary attraction or the atmosphere, I prepared to 
experiment altogether under water ; and for this purpose arranged a 
bath of that fluid at 32°F. A pail, surrounded by dry flannel, 
was placed in a box; a glass jar, 10 inches deep and 7 inches wide, 
was placed on a low ‘tripod in the pail; broken ice was packed be- 
tween the jar and the pail; the jar was filled with ice-cold water to 
within an inch of the top ; a glass dish filled with ice was employed 
as a cover to it, and the whole enveloped with dry flannel. In this 
way the central jar, with its contents, could be retained at the un- 
changing temperature of 32° F. for a week or more; for a small piece 
of ice floating in it for that time was not entirely melted away. All 
that was required to keep the arrangement at the fixed temperature, 
was to renew the packing ice in the pail from time to time, and also 


* Researches in Chemistry and Physics, 8vo. pp. 373, 378. 
+ Mousson says that a pressure of 13,000 atmospheres lowers the temperature 
of freezing from 0° to —18° Cent. 
~ Phil. Mag. vol. xix. p. 391. 
-§ -Proceedings of the Royal Society of Edinburgh, April 19, 1858. — 
L 2 


148 Royal Society :— 


that in the basin cover. A very slow thawing process was going on 
in the jar the whole time, as was evident by the state of the indi- 
cating piece of ice there present. 

Pieces of good Wenham-lake ice were prepared, some being blocks 
three inches square, and nearly an inch thick, others square prisms 
four or five inches long: the blocks had each a hole made through 
them with a hot wire near one corner ; woollen thread passed through 
these holes formed loops, which being attached to pieces of lead, 
enabled me to sink the ice entirely under the surface of the ice-cold 
water. Each piece was thus moored to a particular place, and, be- 
cause of its buoyancy, assumed a position of stability. The threads 
were about 13 inch long, so that a piece of ice, when depressed 
sideways and then left to itself, rose in the water as far as it could, 
and into its stable position, with considerable force. When, also, a 
piece was turned round on its loop as a vertical axis, the torsion 
force tended to make it return in the reverse direction. 

Two similar blocks of ice were placed in the water with their 
opposed faces about two inches apart; they could be moved into 
any desired position by the use of slender rods of wood, without 
any change of temperature in the water. If brought near to each 
other and then left unrestrained, they separated, returning to their 
first position with considerable force. If brought into the slightest 
contact, regelation ensued, the blocks adhered, and remained ad- 
herent notwithstanding the force tending to pull them apart. They 
would continue thus, even for twenty-four hours or more, until they 
were purposely separated, and would appear (by many trials) to 
have the adhesion increased at the points where they first touched, 
though at other parts of the contiguous surfaces a feeble thawing 
and dissecting action went on. In this case, except for the first 
moment and in a very minute degree, there was no pressure either 
from capillary action or any other cause. On the contrary, a 
tensile force of considerable amount was tending all the time to 
separate the pieces of ice at their points of adhesion ; where still, I 
believe, the adhesion went on increasing—a belief that will be fully 
confirmed hereafter. 

Being desirous of knowing whether anything like soft adhesion 
occurred, such as would allow slow change of position without sepa- 
ration during the action of the tensile force, I made the following 
arrangements. The blocks of ice being moored by the threads 
fastened to the lowest corners, stood’ in the water with one of the 
diagonals of the large surfaces vertical; before the faces were 
brought into contact, each block was rotated 45° about a horizontal 
axis, In opposite directions, so that when put together, they made a 
eompound block, with horizontal upper edges, each half of which 
tended to be twisted upon, and torn from the other. Yet by placing 
indicators in holes previously made in the edges of the ice, I could 
not find that there was the slightest motion of the blocks in rela- 
tion to each other in the thirty-six hours during which the experi- 
ment was continued. This result, as far as it goes, is against the 
necessity of pressure to regelation, or the existence of any condition 
like that of softness or a shifting contact; and yet I shall be able to 


, ee ee ee SS lS Se 


© od i te ee 


Prof. Faraday on Regelation. 149 


show that there is either soft adhesion or an equivalent for it, and 
from that state draw still further cause against the necessity of pres- 
sure to regelation. 

Torsion force was then employed as an antagonist to regelation. 
The ice-blocks, being separate, were adjusted in the water so as to be 
parallel to each other, and about 1} inch apart. If made to ap- 
proach each other on one side, by revolution in opposite directions 
on vertical axes, a piece of paper being between to prevent ice con- 
tact, the torsion force set up caused them to separate when left to 
themselves; but if the paper were away and the ice pieces were 
brought into contact, by however slight a force, they became one, 
forming a rigid piece of ice, though the strength was, of course, very 
small, the point of adhesion and solidification being simply the con- 
tact of two convex surfaces of small radius. By giving a little 
motion to the pail, or by moving either piece of ice gently in the 
water with a slip of wood, it was easy to see that the two pieces were 
rigidly attached to each other; and it was also found that, allowing 
time, there was no more tendency to a changing shape here than in 
the case quoted above. If now the slip of wood were introduced 
between the adhering pieces of ice, and applied so as to aid the 
torsion force of one of the loops, 7. e. to increase the separating force, 
but unequally as respects the two pieces, then the congelation at the 
point of contact would give way, and the pieces of ice would move 
in relation to each other. Yct they would not separate; the piece 
unrestrained by the stick would not move off by the torsion of its 
own thread, though, if the stick were withdrawn, it would move 
back into its first attached position, pulling the second piece with it ; 
and the two would resume their first associated form, though all the 
while the torsion of both loops was tending to make the pieces 
separate. 

If when the wood was applied to change the mutual position of 
the two pieces of ice, without separating them, it were retained for a 
second undisturbed, then the two pieces of ice became fixed rigidly 
to each other im their new position, and maintained it when the 
wood was removed, but under a state of restraint; and when suffi- 
cient force was applied, by a slight tap of the wood on the ice to 
break up the rigidity, the two pieces of ice would rearrange them- 
selves under the tersion force of their respective threads, yet remain 
united ; and, assuming a new position, would, in a second or less, 
again become rigid, and remain inflexibly conjoined as before. 

By managing the continuous motion of one piece of ice, it could 
be kept associated with the other by a flexible point of attachment 
for any length of time, could be placed in various angular positions 
to it, could be made (by retaining it quiescent for a moment) to 
assume and hold permanently any of these positions when the ex- 
ternal force was removed, could be changed from that position ito 
a new one, and, within certain limits, could be made to possess at 
pleasure, and for any length of time, either a flexible or a rigid attach- 
ment to its associated block of ice. 

So regelation includes a flexible adhesion of the particles of ice, 
and also a rigid adhesion. The transition between these two states 


150 Royal Society :—- 


takes place when there is no external force like pressure tending to 
bring the particles of ice together, but, on the contrary, a force of 
torsion is tending to separate them ; and, if respect be had to the 


mere point of contact on the two rounded surfaces where the flexible 


adhesion is exercised, the force which tends to separate them may 
be esteemed very great. The act of regelation cannot be considered 
as complete until the junction has become rigid; and therefore I 
think that the necessity of pressure for it is altogether excluded. 
No external pressure can remain (under the circumstances) after the 
first rigid contact is broken. All the forces which remain tend to 
separate the pieces of ice; yet the first flexible adhesions and all the 
successive rigid adhesions which are made to occur, are as much effects 
of regelation as those which occur under the greatest pressure. 

’ The phenomenon of flexible adhesion under tension looks ver 
much like sticking and tenacity ; and I think it probable that Pro- 
fessor Forbes will see in it evidence of the truth of his view. I 
cannot, however, consider the fact as bearing such an interpretation ; 
because I think it impossible to keep a mixture of snow and water 
for hours and days together without the temperature of the mixed 
mass becoming uniform; which uniformity would be fatal to the 
explanation. My idea of the flexible and rigid adhesion is this :— 
Two convex surfaces of ice come together; the particles of water 
nearest to the place of contact, and therefore within the efficient sphere 
of action of those particles of ice which are on both sides of them, 
solidify ; if the condition of things be left for a moment, that the 
heat evolved by the solidification may be conducted away and dis- 
persed, more particles will solidify, and ultimately enough to form 
a fixed and rigid junction, which will remain until a force sufficiently 
great to break through it is applied. But if the direction of the 
force resorted to can be relieved by any hinge-like motion at the 
point of contact, then I think that the union is broken up among the 


particles on the opening side of the angle, whilst the particles on the. 


closing side come within the effectual regelation distance ; regelation 
ensues there and the adhesion is maintained, though in an apparently 
flexible state. The flexibility appears to me to be due to a series of 
ruptures on one side of the centre of contact, and of adhesion on the 
other,—the regelation, which is dependent on the vicinity of the ice 
surfaces, being transferred as the place of efficient vicinity is changed. 
That the substance we are considering is as brittle as ice, does not 
make any difficulty to me in respect of the flexible adhesion ; for if 
we suppose that the point of contact exists only at one particle, still 
the angular motion at that point must bring a second particle into 
contact (to suffer regelation) before separation could occur at the 
first ; or if, as seems proved by the supervention of the rigid adhesion 
upon the flexible state, many particles are concerned at once, it is not 
possible that all these should be broken through by a force applied 
on one side of the place of adhesion, before particles on the opposite 
side should have the opportunity of regelation, and so of continuing 
the adhesion. | 

It is not necessary for the observation of these phenomena that a 
earefully-arranged water-vessel should be employed. The difference 


Prof. Faraday on Regelation. 151 


between the flexible and rigid adhesion may be examined very well in 
air, _ For this purpose, two of the bars of ice before spoken of, may 
be hung up horizontally by threads, which may be adjusted to give 
by torsion any separating force desired ; and when the ends of these 
bars are brought together, the adhesion of the ice, and the ability of 
placing these bars at any angle, and causing them to preserve 
that angle by the rigid adhesion due to regelation, will be rendered 
evident ; and though the flexible adhesion of the ice cannot in this 
way be examined alone, because of the capillary attraction due to the 
film of water on the ice, yet that is easily obviated by plunging the 
pieces into a dish of water at common temperatures, so that they are 
entirely under the surface, and repeating the observations there. All 
the important points regarding the flexible and rigid junction of ice 
due to regelation, can in this way be readily investigated. 

It will be understood that, in observing the flexible and rigid state 
of union, convex surfaces of contact are necessary, so that the contact 
may be only at one point. If there be several places of contact, 
apparent rigidity is given to the united mass, though each of the 
places of contact might be in a flexible and, so to say, adhesive con- 
dition. It is not at all difficult to arrange a convex surface so that, 
bearing at two places only on the sides of a depression, it should 
form a flexible joint in one direction, and a rigid attachment in a 
direction transverse to the former. 

it might seem at first sight as if the flexible adhesion of the ice 
gave us a point to start from in the further investigation of the prin- 
ciple of pressure. Ifthe application of pressure causes ice to freeze 
together, the application of tension might be expected to produce the 
contrary effect, and so cause liquidity and separation at the flexible 
jomt. This, however, does not necessarily follow ; nor do I intend to 
consider what might be supposed to take place whilst theoretically 
contemplating that case. I think the changes of temperature and 
pressure are too infinitesimal to go for anything; and in illustration 
of this, will deseribe the following experiment. Wool is known to 
adhere to ice in the manner, as I believe, of regelation. Some wool- 
len thread was boiled in distilled water, so as thoroughly to wet it. 
Some clean ice was broken up small and mixed with water, so as to 
produce a soft mass, and, being put into a glass jar clothed in flan-, 
nel that it might keep for some hours, had a linear depression made 
in the surface, so as to form alittle ice-ditch filled with water ; in this 
depression some filaments of the wetted wool were placed, which, 
sinking to the bottom, rested on the ice only with the weight which 
they would have being immersed in water; yet in the course of 
two hours these filaments were frozen to the ice. In another case, a 
small loose ball of the same boiled wool, about half an inch in 
diameter, was put on to a clean piece of ice ; that into a glass basin; 
and the whole wrapped up in flannel and left for twelve hours. At 
the end of that time it was found that thawing had been going on, 
and that the wool had melted a hole in the ice, by the heat conducted 
through it to the ice from the air. The hole was filled with the 
water and wool, but at the bottom some fibres of the wool were 
frozen to the ice. : 


152 Royal Society :— 


Is this remarkable property peculiar to water, or is it general to 
all bodies? In respect of water it certainly seems to offer us a glimpse 
into the joint physical action of many particles, and into the nature 
of cohesion in that body when it is changing between the solid and 
liquid state. I made some experiments on this point. Bismuth was 
melted and kept at a temperature at which both solid and liquid 
metal could be present; then rods of bismuth were introduced, but 
when they had acquired the temperature of the mixed mass, no adhe- 
sion could be observed between them. By stirring the metal with 
wood, it was easy to break up the solid part into small crystalline 
granules ; but when these were pressed together by wood under the 
surface, there was not the slightest tendency to cohere, as hail or 
snow would cohere inwater. The same negative result was obtained 
with the metals tin and lead. Melted nitre appeared at times to 
show traces of the power; but, on the whole, I incline to think the 
effects observed resulted from the circumstance that the solid rods 
experimented with had not acquired throughout the fusing tempera- 
ture. Nitre is a body which, like water, expands in solidifying; and 
it may possess a certain degree of this peculiar power. 

Glacial acetic acid is not merely without regelating force, but 
actually presents a contrast to it. A bottle containing five or six 
ounces, which had remained liquid for many months, was at such a 
temperature that being stirred briskly with a glass rod crystals began 
to form in it; these went on increasing in size and quantity for eight 
or ten hours. Yet all that time there was not the slightest trace of 
adhesion amongst them, even when they were pressed together ; and 
as they came to the surface, the liquid portion tended to withdraw 
from the faces of the crystals ; as if there were a disinclination of the 
liquid and solid parts to adhere together. 

Many salts were tried (without much or any expectation),—cerystals 
of them being brought to bear against each other by torsion force, 
in their saturated solutions at common temperatures. In this way 
the following bodies were experimented with :—Nitrates of lead, 
potassa, soda; sulphates of soda, magnesia, copper, zinc; alum; borax; 
chloride of ammonium; ferro-prussiate of potassa; carbonate of soda; 
acetate of lead; and tartrate of potassa and soda; but the results with 
all were negative. 

My present conclusion therefore is that the property is special for 
water; and that the view I have taken of its physical cause does not 
appear to be less likely now than at the beginning of this short 
investigation, and therefore has not sunk in value among the three 
explanations given. 

Dr. Tyndall added to one of his papers*, a note of mine “On ice 
of irregular fusibility ”’ indicating a cause for the difference observed 
in this respect in different parts of the same piece of ice. The view 
there taken was strongly confirmed by the effects which occurred in 
the jar of water at constant temperature described in the beginning 
of the preceding pages, where, though a thawing process was set up, 
it was so slow as not to dissolve a cubic inch of ice in six or seven 
days. The blocks retained entirely under water for several days, 


* Philosophical Transactions, 1858, p. 228. 


Prof. Faraday on Regelation. 153 


became so dissected at the surfaces as to develope the mechanical 
composition of the masses, and to show that they were composed of 
parallel layers about the tenth of an inch thick, of greater and lesser 
fusibility, which layers appear, from other modes of examination, to 
have been horizontal in the ice whilst in the act of formation. They 
had no relation to the position of the blocks in the water of my ex- 
periments, or to the direction of gravity, but had a fixed position in 
relation to each piece of ice. 


ADDENDUM. 


The following methed of examining the regelation phenomena above 
described may be acceptable. Take a rather large dish of water at 
common temperatures. Prepare some flat cakes or bars of ice, from 
half an inch to aninch thick ; render the edges round, and the upper 
surface of each piece convex, by holding it against the inside of a 
warm saucepan cover, or in any other way. When two of these pieces 
~ are put into the water they wiil float, having perfect freedom of motion, 
and yet only the central part of the upper surface will be above the 
fluid; when, therefore, the pieces touch at their edges, the width of 
the water-surface above the place of contact may be two, three, er 
four inches, and thus the effect of capillary action be entirely removed. 
By placing a plate of clean dry wax or spermaceti upon the top of a 
plate of ice, the latter may be entirely submerged, and the tendency 
to approximation from capillary action converted into a force of 
separation. When two cr more of such fioating pieces of ice are 
brought together by contact at some point under the water, they 
adhere ; first with an apparently flexible, and then with a rigid adhe- 
sion. When five or six pieces are grouped in a contorted shape, as 
an S, and one end piece be moved carefully, all will move withi 
rigidly ; or, if the force be enough to break through the joint, the 
rupture will be with a crackling noise, but the pieces will still adhere, 
and in an instant become rigid again. As the adhesion is only by 
points, the force applied should not be either too powerful or in the 
manner of a blow. I find a piece of paper, a small feather, or a 
camel-hair brush applied under the water very convenient for the 
purpose. When the point of a floating wedge-shaped piece of ice ig 
brought under water against the corner or side of another floating 
piece, it sticks to it like a leech; if, after a moment, a paper edge be 
brought down upon the place, a very sensible resistance to the rupture 
at that place is felt. If the ice be replaced by like rounded pieces of 
wood or glass, touching under water, nothing of this kind occurs, nor 
any signs of an effect that could by possibility be referred to capillary 
action ; and finally, if two floating pieces of ice have separating forces 
attached to them, as by threads connecting them and two light pen- 
dulums, pulled more or less in opposite directions, then it will be seen 
with what power the ice is held together at the place of regelation, 
when the contact there is either in the flexible or rigid condition, by 
the velocity and force with which the two pieces will separate when 
the adhesion is properly and entirely overcome. 


154 _ Geological Society :— 


GEOLOGICAL SOCIETY. 
[Continued from vol. xx. p. 486.] 
November 21, 1860.—L. Horner, Esq., President, in the Chair. 


The following communication was read :— 

“On the Geology of Bolivia and Southern Peru.” By D. 
Forbes, Esq., F,R.S., F.G.S. With Notes on the Fossils by Prof. 
Huxley, F.R.S., Sec.G.S. . and J. W. Salter, Esq., F.G.S. 

After some observations on the previous researches by others, and 
on the general features of the region, the author proceeded to de- 
scribe the Post-tertiary formations of the maritime district. ‘These 
beds, containing existing species of shells, occur at various heights 
up to 40 feet above the sea-level. Guano deposits are frequent 
along the coast, and deposits of salt also in raised beaches a little 
above the sea. ‘The author could not verify Lieut. Freyer’s state- 
ment of Balani and Millepore being attached high up the side of the 
Morro de Arica, a perpendicular cliff at the water's edge ; indeed, 
from the state of old Indian tumuli along the beach, and other cir- 
cumstances, the author believes that no perceptible elevation has. 
here taken place since the Spanish Conquest, although such an alter- 
ation of level has occurred in Chile. The sand-dunes of the coast, 
and their great mobility during the hot season, were noticed. From 
Mexillones to Arica the coast is steep and rugged, formed of a chain 
of mountains, 3000 feet high, consisting of rocks of the Upper Oolitic 
age. At Arica the high land recedes, leaving a wide plain formed 
of the débris of the neighbouring mountains; and in the middle of 
this area was observed stratified volcanic tuff contemporaneous with 
the formation of the gravel. 

The saline formations were next treated of as three groups, ac- 
cording to their height above the sea-level, and were shown to be 
much more extensive than generally supposed, extending over the 
rainless regions of this coast for more than 550 miles. They are 
mostly developed, however, between latitudes 19° and 25° South. 
These salines are supposed to have originated in the evaporation of 
sea-water confined in them as lagoons by the longitudinal ranges of 
hills separating them from the ocean. ‘The nitrate of soda had, in 
the author’s opinion, resulted from the chemical reactions of sea-salt, 
carbonate of lime, and decomposing vegetable matter (both terrestrial 
and marine). The borate of lime, occurring with the nitrate, is 
connected with the yolcanic conditions of the district, and was pro- 
duced by fumaroles containing boracic acid. Where the highest 
range of salines extend bey ond the rainless region, they are much 
modified in the rainy season, and generally take the form of salt 
plains encircling salt lakes or swamps. 

The great Bolivian plateau, having an average elevation of 13,000 
or 14,000 feet above the sea, consists of great gravel plains formed 
by the spaces between the longitudinal ranges of mountains being 
filled up by the débris of these mountains. The most western 
of these consists of Oolitic débris with volcanic tuff and scorie; 
it bears the salines above-mentioned, and is nearly destitute of 
water. The central range of plains, formed from the disintegration, 


Mr. D. Forbes on the Geology of Bolivia and Southern Peru. 155 


of red sandstones and marls, with some volcanic scoriz, is well 
watered. ‘The third range consists of plains made up of the débris 
of Silurian and granitic rocks, and is auriferous. The thickness 
of this accumulation of clays, gravel, shingle, and boulders is, 
at places, immense. At La Paz it is more than 1600 feet. Con- 
temporaneous trachytic tuff was found also in these deposits. In 
freshwater ponds on this plateau, at a height of 14,000 feet (lat. 
15° 8.), Mr. Forbes found abundance of Cyclas Chilensis, formerly 
considered to be peculiar to the most southern and coldest part of 
Chile at the level of the sea (lat. 45° to 50° S.). 
_ The volcanic formations were next noticed. Volcanic action has 
continued certainly from the pleistocene age to the present. The. 
line of volcanic phenomena is nearly continuous N. and S$. Cones 
are frequent, some of them 22,000 feet high and upwards; but 
craters are rare. Volcanic matter, both in ancient times and at 
present, has in a great part been erupted from lateral vents, often of 
great longitudinal extent; recent trachytic lavas from such orifices 
have covered in some cases more than 100 miles of country. Be- 
sides trachyte, there are great tracts of trachydoleritic and felspathic 
lavas. On the whole, in these South American lavas silex abounds, 
and it las been the first element in the rock to crystallize; whereas 
apparently in granite quartz is the last to crystallize and form the 
state of so-called ‘‘ surfusion.” Diorites (including the so-called 
«« Andesite”) occur in force along two parallel N. and S. lines of 
eruption in this region, reaching through Chile, Bolivia, and Peru, 
for more than 40 degrees of latitude. These diorites, and more espe- 
cially the rocks which they traverse, are metalliferous; and the 
author looks upon the greater part of the copper, silver, iron, and 
other metallic veins of these countries as directly occasioned by the 
appearance of this rock. | 
Shales and argillaceous limestones, with clay-stones, porphyry- 
tuffs, and porphyries, form the mass of the Upper Oolite formation 
of Bolivia, equivalent to Darwin’s Cretaceo-Oolitic Series of Chile, 
At Cobija these are traversed in all directions by metallic veins, 
chiefly copper, and which, as before mentioned, appear to emanate 
from the diorite. : 
Red and variegated maris and sandstones, with gypsum and cu- 
riferous and yellow sandstones and conglomerates, come next in 
order; they have a thickness of 6000 feet, and are much folded and 
dislocated. ‘These are considered by the author to resemble closely 
the Permian rocks of Russia. Fossil wood is not uncommon in some 
of these strata, which extend for at least 500 miles N. and 8. 
Carboniferous strata occur chiefly as a small, contorted, basin- 
shaped series of limestones, sandstones, and shales, with abundant 
characteristic fossils. Cle 
The quartzites which are generally supposed to represent the De- 
vonian formation in Bolivia, but which the author is rather disposed 
to group as Upper Silurian, are really not of very great thickness, 
but are very much folded, and perhaps are about 5000 feet thick. ~ 
The Silurian rocks (perhaps 15,000 feet thick) are well developed 
over an area of from 80,000 to 100,000 miles of mountain coun- 


bd * 


156 Geological Society. 


try, including the highest mountains of South America, and giving 
rise to the great rivers Amazon, &c. These slates, shales, grau- 


wackes, and quartzites yield abundant fossils even up to the highest © 


point reached, 20,000 feet. ‘The problematical fossils known as 
Cruziana or Bilobites occur not only in the lower beds, but (with 
many other fossils) in the higher part of the series. 

Lastly, the differences between the sections made by M. D’Or- 
bigny, M. Pissis, and the author were pointed out, though for the 
most part difficult of explanation. D’Orbigny makes the mountain 
Illimani to be granite; it is slate according to the author. M. 
Pissis describes as carboniferous the beds in which Mr. Forbes found 
Silurian fossils,—and so on. 


* On a New Species of Macrauchenia (M. Boliviensis).” By Prof. 
By ot. Huxley. vor, wet, re. ce. 

Some bones, fully impregnated with metallic copper, which had 
been brought up from the mines of Corocoro in Bolivia were sub- 
mitted to Prof. Huxley for examination. ‘The mines referred to are 
situated on a great fault; and the bones were probably part of a 
carcass that had fallen in from the surface,—the copper-bearing 
water of the mines having mineralized them. A cervical and a 
lumbar vertebra, an astragalus, a scapula, and a tibia show com- 
plete correspondence in essential characters with those bones of the 
great Afacrauchenia Patachonica described by Prof. Owen in the 
Appendix to the ‘ Voyage of the Beagle ;’ but the relative size and 
proportions of the vertebra, the tibia, and the astragalus indicate a 
distinct species, much smaller and more slender ; and in some points 
of structure this new form (M. Boliviensis) approaches more nearly 
to the recent Auchenide than to the larger and fossil species. The 
fragments of the cranium show some peculiarities of form, but, on 
the whole, it has many resemblances to that of the Vicugna. 

Prof. Huxley pointed out that this slender and small-headed Ma- 
crauchenia may have been the highland-contemporary of the larger 
M. Patachonica ; just as now-a-days the Vicugna prefers the moun- 
tains, whilst its larger congener the Guanaco roams over the Pata- 
gonian plains. 

Lastly it was remarked that as Macrauchenia was an animal com- 
bining, to a much more marked degree than any other known recent 
or fossil mammal, the peculiarities of certain artiodactyles and perisso- 
dactyles, and yet was certainly but of postpleistocene age, it presents 
a striking exception to the commonly asserted doctrine that ‘ more 
generalized”’ organisms were confined to the ancient periods of the 
earth’s history. For similar reasons, the structure of the Macrau- 
chenia is also inimical to the idea that an extinct animal can always 
be reconstructed from a single tooth or a single bone. 


** On the Paleozoic Fossils brought by Mr. D. Forbes from Bo- 
livia.” By J. W. Salter, Esq., F.G.S. 

The Fossils of Carboniferous age brought home by Mr. Forbes 
are the well-known species described by D’Orbigny. Several are 
identical with Kuropean forms (as Productus Martini, &c.), and are 


cosmopolitan ; others are peculiar to the district (as Spirifer Condor, 
Orthis Andii, &c.). 


Intelligence and Miscellaneous Articles. 157 


Mr. Forbes has brought a “Devonian” trilobite (Phacops latifrons 
or Ph, Bufo), in a rolled pebble, from Oruro: it is a widely-spread 
species. Another allied form was found by Mr. Pentland, many 
years back, at Aygatchi. In other respects the “ Devonian” evidence 
is scanty. 

In Mr. Forbes’s fine collection of Silurian fossils none of D’Or- 
bigny’s ten Silurian species occur ; nearly all are such as are met 
with in Lower Devonian and in Upper Silurian rocks—Homalonotus, 
Tentaculites, Orthis, Ctenodonta, Pileopsis (2), Strophomena, Bellero- 
phon. South Africa and the Falkland Isles yield a similar fossil 
fauna. 

The Bilobites in this collection differ, some of them probably ge- 
nerically, from D’Orbigny’s figured species. A little Beyrichia from 
the upper part of the Silurian series in Bolivia appears to be like a 
North American form figured by Emmons as Silurian. 


XXIV. Intelligence and Miscellaneous Articles. 


ON THE POLARIZATION OF LIGHT BY DIFFUSION. BY G. GOVI, 


oe polarization of atmospheric light has long since proved that 

gases, as well as solid and liquid bodies, have the property of 
_ polarizing light; but I am not aware that any direct experiments 
have been made to prove the presence of polarizing power in the 
case of gases. 

I was led to the consideration of this question by the polariscopic 
study of the hght of comets; and the idea occurred to me to inves- 
tigate how a pencil of light would be affected by being transmitted 
through a certain thickness of a gaseous medium in which it was re- 
flected or diffused. 

The experiment was made in the following manner:—A thick 
pencil of the sun’s rays, reflected from a heliostat, was allowed to 
pass into a dark room, through a hole in the window-shutter. ‘This 
light was principally reflected from metal, and showed very feeble 
traces of polarization. A large quantity of smoke was then pro- 
duced by burning incense ; and the pencil immediately expanded and 
formed a large cylinder, which diffused white light in all directions. 
This light, when investigated by a polariscope, was found to be po- 
larized even when the cylinder was viewed at right angles to its 
axis; but the intensity of the polarization was truly extraordinary 
when the direction of the visual ray, on the side of the source of light, 
formed a somewhat small angle with the axis of the cylinder: one 
would have said that the phenomenon was caused by the action of 
a solid or liquid body on the molecules of the ether. Viewing the 
cylinder in this direction, the polarization perceptibly decreased on 
approaching the source of light or removing from it. The light pro- 
ceeding from the column of smoke seen by reflexion upon the 
aperture was only feebly polarized. 

Iixcepting in its intensity, the above phenomenon presents nothing 
extraordinary; but for a physicist the circumstance appears to me 
important, that the light polarized by diffusion does not seem to arise 
from a simple reflexion from gas moiecules, for its plane of polar- 


158 Intelligence and Miscellaneous Articles. 

ization is at right angles to the plane in which the reflexion ought 
to occur. For on examining the cylinder of light round its axis in 
the direction of the maxima of polarization, it was found that the 
light proceeding from it was polarized tangential to that point of the 
surface of the cylinder towards which the polariscope was directed. 
Whether the plane of polarization becomes removed by its repeated 
reflexions from the gas molecules, or whether the action of gases 
under certain circumstances is analogous to that of refracting bodies, 
are questions which hitherto I have not been able to decide by ex- 
periment. 

I endeavoured to depolarize the light completely on its entry into 
the dark room, by allowing it to pass through a thin sheet of white 
paper; but the phenomena, with the exception of the intensity of 
the light, were quite the same. 

Light polarized by reflexion from a black glass experienced no 
perceptible change by the action of the smoke, and its plane of 
polarization always retained its original direction. 

It is possible, by suitably regulating the incident quantity of po- 
larized light, to succeed in finding a limit to the action of the gas 
molecules, beyond which the original polarization of the pencil pre- 
ponderates over the molecular forces of the medium which the light 
has to penetrate. 

The relations which these facts may possibly bear to the pheno- 
mena of atmospheric polarization, and perhaps also to fluorescence 
and the peculiar colour of bodies, have induced me to publish these 
observations, spite of their incompleteness. 

Some days after the preceding experiments had been laid before 
the Academy, I repeated them with more sensitive polariscopes, and I 
found exactly the same facts; I can further state that the plane of 
polarization of diffused light suddenly rotated 90°, on passing the 
direction in which I had seen all trace of polarization disappear in my 
previous experiments. 

Thus on receiving in the polariscope the rays emanating from the 
luminous track produced by the passage of the sun’s light, or of the 
electric light, through the smoke of incense, it is found that under a 
small inclination (the angles being measured from the luminous 
source) the polarization of diffused light is already very perceptible ; 
that it increases up to a certain angle, which is the maximum; it then 
decreases, and at the normal it is almost nil. Up to this point the 
plane of polarization is perpendicular to the plane which passes 
through the source of light, the place observed, and the eye or the 
polariscope. Above 90°, the polarization, although very feeble, reap- 
pears, but its plane is then perpendicular to the first plane. Still 
further it diminishes very rapidly, and the diffused light soon shows 
no sensible traces of polarized rays. 

I have investigated the smoke of tobacco in the same way; and 
the results were the same, though the angle at which I found the 
neutral point and the reversal of the plane of polarization was perhaps 
a little less than with the smoke of incense. 

It is possible that the nature of the diffused particles has an ap- 
preciable influence on these phenomena, and that different gases (if 
gases do diffuse light), vapours, and powders may in this manner be 


‘ Intelligence wnd Miscellaneous ‘Articles. 159 


distinguished. I propose to undertake a series of experiments 
froni this point of view, the results of which I shall lay before the 
Academy.:—Comptes Rendus, Sept. 3, and Oct. 29, 1860. 


ON BLECTRIC ENDOSMOSE. BY M. C. MATTEUCCI. 

Having recently had occasion to examine into the construction 
and operation of the galvanic batteries used in our telegraph offices, 
I have been led to make certain original experiments on the subject 
of electric endosmose, a short description of which, as they seem to 
throw some light on the true nature of the phenomenon in question, 
I beg to lay before the Academy. MM. Porret and Becquerel were 
the first who called attention to the fact that a liquid mass, sepa- 
rated into two compartments by a porous diaphragm, and traversed 
by an electric current, appears to be transported in the direction of 
that current; that is to say, the level of the liquid is lowered in the 
compartment that contains the positive pole, and raised in that which 
contains the negative pole. ‘The determination of the law of this 
phenomenon is due to M. Wiedemann, who proved that the quantity 
of water transported is directly proportional to the intensity of the 
current and the electric resistance of the liquid. M. Wiedemann 
seems to have regarded this mechanical effect of the current as a 
different phenomenon from its electrolytic action; while other phy- 
Sicists have considered that the transportation of the liquid was only 
‘a secondary effect of electrolysis. I should mention also that 
MM. Van Breda and Logemann have in vain endeavoured to as- 
certain whether, in the absence of a diaphragm, there is any displace- 
ment of the electrolysed liquid, or whether a very light moveable 
diaphragm is itself displaced in the direction of the current. Theo- 
retical considerations, which easily suggest themselves to the mind, 
and which I need not here specify, founded on the equality of the 
electrolytic effects, whether endosmose be produced or not, give 
probability to the conclusion that these phenomena are caused by 
some secondary action of electrolysis. The following experiments 
seem to show that this supposition is correct. 

I divided a rectangular vessel of varnished wood into six com- 
partments, by means of diaphragms of porous porcelain. All these 
compartments were filled to the same height with well-water, the 
level of which was indicated by a line of white varnish. A platinum 
plate of the same size as the diaphragms was placed in each of the 
end compartments, Through this apparatus I caused a current to 
pass, produced sometimes by 10, sometimes by 15, and sometimes by 
20 cells of a Grove’s battery. ‘The endosmose became apparent after 
the current had lasted for some hours, and in every case the first 
effect produced was as follows :—The level of the liquid was raised 
in the compartment that contained the negative electrode, and was 
lowered in the compartment next to it, while it was lowered in the 
compartment that contained the positive electrode (though to a less 
degree than it was elevated in the compartment at the opposite ex- 
tremity), and raised in the adjoining compartment. These effects 
were invariably produced, notwithstanding the change of the dia- 
phragm and the reversal of the position of the vessel with respect ta 


160 Intelligence and Miscellaneous Articles. 


the electrodes. Floats may be put in all the compartments, except 
_those containing the platinum plates, in which the liquid is too much 
agitated by gaseous bubbles due to electrolysation; and on viewing 
these floats with a glass, the displacements I have described become 
sensible much earlier. In the intermediate compartments the liquid 
remains stationary,for several hours; but after a certain time the 
liquid begins to rise in the compartments towards the positive pole, 
and to fall in those towards the negative pole. I shall mention but 
one precaution which must not be neglected in these experiments, 
namely, that the diaphragms must be as equal as possible. 

In a second series of experiments I closed one end of each of two 
glass tubes with a porcelain diaphragm fixed with mastic. Each 
of these tubes was then placed in a glass vessel, and both vessels 
and tubes were filled to the same height with well-water. The same 
current passed through both tubes, in each case passing from the water 
in the vessel to that in the tube, the only difference being in the 
position of the platinum electrodes, which in the one case were very 
near the diaphragm, while in the other they were placed at the 
greatest possible distance from it. Under these circumstances I in- 
variably found that the electric endosmose made its appearance much 
sooner, and with much greater intensity in the first case than in the 
second. 

I shall not stop to discuss the consequences of these experiments, 
since they appear to me to be obvious, and to prove that the phenome- 
non in question is no other than that mentioned above, that is to say, a 
case of endosmose produced by changes in the composition of the liquid 
in contact with the two electrodes. I should mention here that the 
liquid round the positive electrode always acquires an acid reaction, 
while that round the negative electrode becomes alkaline, and that 
these effects are produced even when distilled water is employed. I 
did not content mysclf with the ancient experiments of Dutrochet, 
which prove that there isa current of endosmose from an acid liquid 
to water, from water to an alkaline liquid, and from an acid to an 
alkaline liquid. I repeated the experiment with the two liquids 
which had been in contact with the electrodes as described above, 
sometimes making use of both of the liquids, sometimes testing each 
of them separately with pure water. I invariably found that there 
was endosmose from the liquid that had been in contact with the 
positive electrode to pure water, and from pure water to the liquid 
that had been in contact with the negative electrode. It appears 
therefore that the conditions for the production of ordinary endosmose 
are undoubtedly present in the phenomenon called electric endos- 
mose. I should, however, observe that the amount of displacement 
by endosmose is much less when the liquids which have been in 
contact with the electrodes are experimented on simply without 
any electric current, and that it is hardly perceptible in the case of 
electrolysed distilled water. Without attempting to explain all the 
phenomena of electric endosmose, it seems natural to suppose that 
the presence of electricity, and the peculiar state in which the ele- 
ments of electrolysation are produced, give to these products pro- 
perties which influence the effect of endosmose, and which cease 
with the cessation of the current.—Comptes Rendus, Dec. 1860, 


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[FOURTH SERIES.] 


MARCH 1861. 


XXV. On Physical Lines of Force. By J. C. Maxweut, Pro- 
fessor of Natural Philosophy in King’s College, London*. 


- Part 1—The Theory of Molecular Vortices applied to Magnetic 
Phenomena. 


i all phenomena involving attractions or repulsions, or any 

forces depending on the relative position of bodies, we have 
to determine the magnitude and direction of the force which 
would act on a given body, if placed in a given position. 

In the case of a body acted on by the gravitation of a sphere, 
this force is inversely as the square of the distance, and in a 
straight lme to the centre of the sphere. In the case of two 
attracting spheres, or of a body not spherical, the magnitude 
and direction of the force vary according to more complicated 
laws. In electric and magnetic phenomena, the magnitude and 
direction of the resultant force at any point is the main subject 
of investigation. Suppose that the direction of the force at any 
point is known, then, if we draw a line so that in every part of 
its course it coincides in direction with the force at that point, 
this line may be called a line of force, since it imdicates the 
direction of the force in every part of its course. 

By drawing a sufficient number of lines of force, we may 
indicate the direction of the force in every part of the space in 
which it acts. 

Thus if we strew iron filmgs on paper near a magnet, each 
filmg will be magnetized by induction, and the consecutive 
filings will unite by their opposite poles, so as to form fibres, 
and these fibres will indicate the direction of the lines of force. 
The beautiful illustration of the presence of magnetic force 
afforded by this experiment, naturally tends to make us think of 


* Communicated by the Author. 
Phil. Mag. 8. 4. Vol. 21. No. 189. March 1861. M 


162 Prof. Maxwell on the Theory of Molecular Vortices 


the lines of force as something real, and as indicating something 
more than the mere resultant of two forces, whose seat of action 
is at a distance, and which do not exist there at all until a mag- 
_net is placed in that part of the field. We are dissatisfied with 
/ the explanation founded on the hypothesis of attractive and 
repellent forces directed towards the magnetic poles, even though 
we may have satisfied ourselves that the phenomenon is in strict 
accordance with that hypothesis, and we cannot help thinking 
_ that in every place where we find these lines of force, some phy- 
sical state or action must exist in sufficient energy to produce the 
actual phenomena. 

My object in this paper is to clear the way for speculation in 
this direction, by investigating the mechanical results of certain 
states of tension and motion in a medium, and comparing these 
with the observed phenomena of magnetism and electricity. By — 
pointing out the mechanical consequences of such hypotheses, 1 
hope to be of some use to those who consider the phenomena as 
due to the action of a medium, but are in doubt as to the relation 
of this hypothesis to the experimental laws already established, 
which have generally been expressed in the language of other 
hypotheses. 

I have in a former paper* endeavoured to lay before the mind 
of the geometer a clear conception of the relation of the lines of 
force to the space in which they are traced. By making use of 
the conception of currents in a fluid, I showed how to draw lines 
of force, which should indicate by their number the amount of 
force, so that each line may be called a unit-line of force (see 
Faraday’s ‘ Researches,’ 3122) ; and I have investigated the path 
of the lines where they pass from one medium to another. 

In the same paper I have found the geometrical significance 
of the “ Electrotonic State,” and have shown how to deduce the 
mathematical relations between the electrotonic state, magnetism, 
electric currents, and the electromotive force, using mechanical 
illustrations to assist the imagination, but not to account for the 
phenomena. 

I propose now to examine magnetic phenomena from a mecha- 
nical point of view, and to determine what tensions in, or motions 
of, a medium are capable of producing the mechanical pheno- 
mena observed. If, by the same hypothesis, we can connect the 
phenomena of magnetic attraction with electromagnetic phe- 
nomena and with those of induced currents, we shall have found a 
theory which, if not true, can only be proved to be erroneous by 
experiments which will greatly enlarge our knowledge of this 
part of physics. 

* See a paper “ On Faraday’s Lines of Force,’’ Cambridge Philosophical 
Transactions, vol. x. part 1. 


applied to Magnetic Phenomena. _ 163 


The mechanical conditions of a medium under magnetic in- 
fluence have been variously conceived of, as currents, undula- 
tions, or states of displacement or strain, or of pressure or stress. 

Currents, issuing from the north pole and entering the south 
pole of a magnet, or circulating round an electric current, have 
the advantage of representing correctly the geometrical arrange- 
ment of the lines of force, if we could account on mechanical 
principles for the phenomena of attraction, or for the currents 
themselves, or explain their continued existence. 

_ Undulations issuing from a centre would, according to the cal- 
culations of Professor Challis, produce an effect similar to attrac- 
tion in the direction of the centre; but admitting this to be true, 
we know that two series of undulations traversing the same space 
do not combine into one resultant as two attractions do, but pro- 
duce an effect depending on relations of phase as well as intensity, 
and if allowed to proceed, they diverge from each other without 
any mutual action. In fact the mathematica! laws of attractions 
are not analogous in any respect to those of undulations, while 
they have remarkable analogies with those of currents, of the 
conduction of heat and electricity, and of elastic bodies. 

In the Cambridge and Dublin Mathematical Journal for 
January 1847, Professor William Thomson has given a “ Mecha- 
nical Representation of Electric, Magnetic, and Galvanic Forces,” 
by means of the displacements of the particles of an elastic solid 
in a state of stram. In this representation we must make the 
angular displacement at every point of the solid proportional to 
the magnetic force at the corresponding point of the magnetic 
field, the direction of the axis of rotation of the displacement 
corresponding to the direction of the magnetic force. The abso- 
lute displacement of any particle will then correspond in magni- 
tude and direction to that which I have identified with the elec- 
trotonic state; and the relative displacement of any particle, 
considered with reference to the particle in its immediate neigh- 
bourhood, will correspond in magnitude and direction to the 
quantity of electric current passing through the corresponding 
point of the magneto-electric field. The author of this method 
of representation does not attempt to explain the origin of the 
observed forces by the effects due to these strains in the elastic 
solid, but makes use of the mathematical analogies of the twe 
problems to assist the imagination in the study of both. 

We come now to consider the magnetic influence as existing 
in the form of some kind of pressure or tension, or, more gene- 
rally, of stress in the medium. 

Stress is action and reaction between the consecutive parts of 
a body, and consists in general of pressures or tensions different 
in different directions at the same point of the medium. 


M2 


164 Prof. Maxwell on the Theory of Molecular Vortices 


The necessary relations among these forces have been in- 
vestigated by mathematicians; and it has been shown that the 
most general type of a stress consists of a combination of three 
principal pressures or tensions, in directions at right angles to 
each other. 

When two of the principal pressures are equal, the third be- 
comes an axis of symmetry, either of greatest or least pressure, 
the pressures at right angles to this axis being all equal. 

When the three principal pressures are equal, the pressure is 
equal in every direction, and there results a stress having no 
determinate axis of direction, of which we have an example in 
simple hydrostatic pressure. 

The general type of a stress is not suitable as a representation 
of a magnetic force, because a line of magnetic force has direc- 
tion and intensity, but has no third quality indicating any dif- 
ference between the sides of the line, which would be analogous 
to that observed in the case of polarized light*. 

We must therefore represent the magnetic force at a point by 
a stress having a single axis of greatest or least pressure, and all 
the pressures at right angles to this axis equal. It may be 
objected that it is inconsistent to represent a line of force, which 
is essentially dipolar, by an axis of stress, which is necessarily 
isotropic ; but we know that every phenomenon of action and re- 
action is isotropic in its results, because the effects of the force 
on the bodies between which it acts are equal and opposite, 
while the nature and origin of the force may be dipolar, as in 
the attraction between a north and a south pole. 

Let us next consider the mechanical effect of a state of stress 
symmetrical about an axis. We may resolve it, in all cases, into 
a simple hydrostatic pressure, combined with a simple pressure 
or tension along the axis. When the axis js that of greatest 
pressure, the force along the axis will be a pressure. When the 
axis is that of least pressure, the force along the axis will be a 
tension. 

If we observe the lines of force between two magnets, as in- 
dicated by iron filings, we shall see that whenever the lines of 
force pass from one pole to another, there is attraction between 
those poles; and where the lines of force from the poles avoid 
each other and are dispersed into space, the poles repel each 
other, so that in both cases they are drawn in the direction of 
the resultant of the lines of force. 

It appears therefore that the stress in the axis of a line of 
magnetic force 1s a ¢ension, like that of a rope. 

If we calculate the lines of force in the neighbourhood of two 
gravitating bodies, we shall find them the same in direction as 

* See Faraday’s ‘ Researches,’ 3252. 


applied to Magnetic Phenomena. 165 


those near two magnetic poles of the same name; but we know 
that the mechanical effect is that of attraction instead of re- 
pulsion. The lines of force in this case do not run between the 
bodies, but avoid each other, and are dispersed over space. In 
order to produce the effect of attraction, the stress along the 
lines of gravitating force must be a pressure. 

Let us now suppose that the phenomena of magnetism depend 
on the existence of a tension in the direction of the lines of force, 
combined with a hydrostatic pressure; or in other words, a pres- 
sure greater in the equatorial than in the axial direction: the 
next question is, what mechanical explanation can we give of 
this inequality of pressures in a fluid or mobile medium? The 
explanation which most readily occurs to the mind is that the 
excess of pressure in the equatorial direction arises from the 
centrifugal force of vortices or eddies in the medium having their 
axes in directions parallel to the lines of force. 

This explanation of the cause of the inequality of pressures 
at once suggests the means of representing the dipolar character 
of the line of force. Hvery vortex is essentially dipolar, the two 
extremities of its axis being distinguished by the direction of its 
revolution as observed from those points. 

We alsc know that when electricity circulates in a conductor, 
it produces lines of magnetic force passing through the circuit, 
the direction of the lines depending on the direction of the cir- 
culation. Let us suppose that the direction of revolution of our 
vortices is that in which vitreous electricity must revolve in order 
to produce lines of force whose direction within the circuit is the 
same as that of the given lines of force. 

We shall suppose at present that all the vortices in any one 
part of the field are revolving in the same direction about axes 
nearly parallel, but that in passing from one part of the field to 
another, the direction of the axes, the velocity of rotation, and 
the density of the substance of the vortices are subject to change. 
We ‘shall investigate the resultant mechanical effect upon an 
element of the medium, and from the mathematical expression 
of this resultant we shall deduce the physical character of its 
different component parts. 

Prop. I.—If in two fluid systems geometrically similar the 
velocities and densities at corresponding points are proportional, 
then the differences of pressure at corresponding points due to 
the motion will vary in the duplicate ratio of the velocities and 
the simple ratio of the densities. 

Let / be the ratio of the linear dimensions, m that of the velo- 
cities, n that of the densities, and p that of the pressures due to 
the motion. Then the ratio of the masses of corresponding por- 
tions will be /°n, and the ratio of the velocities acquired in 


166 ~~ Prof. Maxwell on the Theory of Molecular Vortices 


traversing similar parts of the systems will be m; so that /®mn 
is the ratio of the momenta acquired by similar portions in 
traversing similar parts of their paths. 

The ratio of the surfaces is /?, that of the forces acting on 
them is /*p, and that of the times during which they act is 


l : me 
3 80 that the ratio of the impulse of the forces is —, and we-. 
have now eck ot 
m 
or 
mn=p ; 


that is, the ratio of the pressures due to the motion (p) is com- 
pounded of the ratio of the densities (n) and the duplicate ratio 
of the velocities (m*), and does not depend on the linear dimen- 
sions of the moving systems. 

In a circular vortex, revolving with uniform angular velocity, 
if the pressure at the axis is po, that at the circumference will be 
Pi=Po+4pv’, where p is the density and v the velocity at the 
circumference. The mean pressure parallel to the axis will be 


Pot gp" =Po- 

If a number of such vortices were placed together side by side 
with their axes parallel, they would form a medium in which 
there would be a pressure p, parallel to the axes, and a pressure 
p; in any perpendicular direction. If the vortices are circular, 
and have uniform angular velocity and density throughout, then 


Pi —Po= apr" 
If the vortices are not circular, and if the angular velocity and 
the density are not uniform, but vary according to the same law 
for all the vortices, 

P1—Po= Cpr’, 
where p is the mean density, and C is a numerical quantity de- 
pending on the distribution of angular velocity and density in 


the vortex. In future we shall write = instead of Cp, so that 


1 
Pi—Pa= Gp, RE) 


where w is a quantity bearing a constant ratio to the density, and 
v is the linear velocity at the circumference of each vortex. 

A medium of this kind, filled with molecular vortices having 
their axes parallel, differs from an ordinary fluid in having dif- 
ferent pressures in different directions. If not prevented by 
properly arranged pressures, it would tend to expand laterally. 
In so doing, it would allow the diameter of each vortex to expand 


applied to Magnetic Phenomena. 167 


and its velocity to diminish in the same proportion. In order 
that a medium having these inequalities of pressure in different 
directions should be in equilibrium, certain conditions must be 
fulfilled, which we must investigate. | 

Prop. I1.—If the direction-cosines of the axes of the vortices 
with respect to the axes of x, y, and z be-/, m, and n, to find the 
normal and tangential stresses on the coordinate planes. 

The actual stress may be resolved into a simple hydrostatic 
pressure p, acting in all directions, and a simple tension p, —po, 
or rae acting along the axis of stress. 

Hence if py», Pyy, and pzz be the normal stresses parallel to 
the three axes, considered positive when they tend to increase 
those axes; and if p,,, Pex, and p,, be the tangential stresses in 
the three coordinate planes, considered positive when they tend 
to increase simultaneously the symbols subscribed, then by the 
resolution of stresses*, 


1 
Psa= Ty hh Pr 
1 Qin 
Pyy= nee 1 ay 
i 2,2 
pe ge UE 
Pyz= ipeemn 
1 2 
Pz 7 nl 


1 
Pay = Fe poorlm. 


If we write 
| a=vl, B=vm, and y=v, 
then 
! ] 
Pes= go MO — Py Pyz= G BBY | 
oe Cie 
Py = rate —Pi Paa= Ge we} (2) 
ae. a Sate 
Pas eehY TP Pay= go Mob. j 


Prop. I11.-—To find the resultant force on an element of the 
medium, arising from the variation of internal stress. 


* Rankine’s ‘ Applied Mechanics,’ art. 106. 


168 — Prof. Maxwell on the Theory of Molecular Vortices 
We have in general, for the force in the direction of 2 per unit 
of volume by the law of equilibrium of stresses*, 
d d d 
X= 7 Peat dyP* ae zee . . . . . . . (3) 
In this case the expression may be written 


d (poe) de dp, 
X= 7 da iki aga 
d(wy) eS . 


d(u) 
ani nee aa 


ne 


4- 


zs dz ie 


d 
Remembering that aes ee Was de ata +6? +97), this 
becomes 
sa aa Ag? 43 d d Dae ; 
K=ai(£ (mex) + dy HP) + aS (uy) +3 he Lg + 6? + 7°) 


pS dB du 1 i= dy\ _ dp, 

we (5. a) +HY Ga \de 7 da). deen 
The expressions for the forces parallel to the axes of y and z may 
be written down from analogy. 

We have now to interpret the meaning of each term of this 
expression. 

We suppose «, 8, y to be the components of the force which 
would act upon that end of a unit magnetic bar which poits to 
the north. 

/ represents the magnetic inductive capacity of the medium 
at any point referred to air as a standard. pa, wB, wy represent 
the quantity of magnetic induction through unit of area perpen- 
dicular to the three axes of a, y, 2 respectively. 

The total amount of magnetic induction through a closed sur- 
face surrounding the pole of a magnet, depends entirely on the 
strength of that pole; so that if dw dy dz be an element, then 


which represents the total amount of magnetic induction out- 
wards through the surface of the element dx dy dz, represents 
the amount of “imaginary magnetic matter” within the element, 
of the kind which points north. 

The first term of the value of X, therefore, 


LP ad d ) 
ape(S.net oS om pth 
may be written 


ame bk) ita elt.niqe i 


* Rankine’s ‘ Applied Mechanies,’ art. 116. 


applied to Magnetic Phenomena. 169 


where « is the intensity of the magnetic force, and m is the 
amount of magnetic matter pointing north in unit of volume. 

The physical interpretation of this term is, that the force 
urging a north pole in the positive direction of # is the product 
of the intensity of the magnetic force resolved in that direction, 
and the strength of the north pole of the magnet. 

Let the parallel limes from left to right in fig. 1 represent a 
field of magnetic force such as that of the earth, sv being the 
direction from south to north. The vortices, according to our 
hypothesis, will be in the direction shown by the arrows in fig. 3, 
that is, in a plane perpendicular to the lines of force, and revolv- 
ing in the direction of the hands of a watch when observed from 
s looking towards n. The parts of the vortices above the plane 
of the paper will be moving towards e, and the parts below that 
plane towards w. . 

We shall always mark by an arrow-head the direction in which 
we must look in order to see the vortices rotating in the direc- 
tion of the hands of a watch. The arrow-head will then indicate 
the northward direction in the magnetic field, that is, the direc- 
tion in which that end of a magnet which points to the north 
would set itself in the field. 

Now let A be the end 


of a magnet which points Big) 

north. Since it repels the i a 
north ends of other mag- —————_+_|__7 > 
nets, the lines of force will pemCN IY 4 Su 
be directed from A out- § CS ee m 
wards in all directions. | Bt 

On the north side the line ‘ ) a ca 
AD will be in the same e a 
direction with the lines of 

the magnetic field, and the Fig. 2. 

velocity of the vortices will a 
be increased. On the south Ne ee ag 
side the line A C will be in 2 MG WS ee 
the opposite direction, and MS ie Oe Vee 


the velocity of the vortices Oss h es 
will be diminished, so that 
the lines of force are more 
powerful on the north side 
of Athan on the southside. 
We have seen that the 
mechanical effect of the 
vortices is to produce a 
tension along their axes, 
so that the resultant effect 


VEY 


170 ~~ Prof. Maxwell on the Theory of Molecular Vortices 


on A will be to pull it more powerfully towards D than towards 
C; that is, A will tend to move to the north. 

Let B in fig. 2 represent a south pole. The lines of force 
belonging to B will tend towards B, and we shall find that the 
lines of force are rendered stronger towards E than towards F, 
so that the effect in this case is to urge B towards the south. 

It appears therefore that, on the hypothesis of molecular vor- 
tices, our first term gives a mechanical explanation of the force 
acting on a north or south pole in the magnetic field. 

We now proceed to examine the second term, 


| aeti 
Sg sp (a? + 8? + 97). 


Here «?+ 87+? is the square of the intensity at any part of 
the field, and w is the magnetic inductive capacity at the same 
place. Any body therefore placed in the field will be urged 
towards places of stronger magnetic intensity with a force depend- 
ing partly on its own capacity for magnetic induction, and partly 
on the rate at which the square of the intensity increases. 

If the body be placed in a fluid medium, then the medium, as 
well as the body, will be urged towards places of greater intensity, 
so that its hydrostatic pressure will be increased in that direc- 
tion. The resultant effect on a body placed in the medium will 
be the difference of the actions on the body and on the portion 
of the medium which it displaces, so that the body will tend to 
or from places of greatest magnetic intensity, according as it has 
a greater or less capacity for magnetic induction than the sur- 
rounding medium. 

In fig. 4 the lines of force are represented as converging and 
becoming more powerful towards the right, so that the magnetic 
tension at B is stronger than at A, and the body AB will be 
urged to the nght. If the capacity for magnetic induction is 
greater in the body than in the surrounding medium , it will move 
to the right, but if less it will move to the left. 


Fig. 4, Fig. 5. 
D 
A B 
Cc 


We may suppose in this case that the lines of force are con- 
verging to a magnetic pole, either north or south, on the right 
hand. 

In fig. 5 the lines of force are represented as vertical, and be- 


applied to Magnetic Phenomena. 171 


coming more numerous towards the right. It may be shown 
that if the force increases towards the right, the lines of force 
will be curved towards the right. The effect of the magnetic 
tensions will then be to draw any body towards the right with a 
force depending on the excess of its inductive capacity over that 
of the surrounding medium. 

We may suppose that in this figure the lines of fores are 
those surrounding an electric current perpendicular to the plane 
of the paper and on the right hand of the figure. 

These two illustrations will show the mechanical effect on a 
paramagnetic or diamagnetic body placed in a field of varying 
magnetic force, whether the increase of force takes place along 
the lines or trausverse to them. The form of the second term 
of our equation indicates the general law, which is quite inde- 
pendent of the direction of the lines of force, and depends solely 
on the manner in which the force varies from one part of the 
field to another. 

We come now to the vee term of the value of X, 


Jot 
OY Tanda dy)" 

Here uf is, as before, the quantity of magnetic induction through 
unit of area perpendicular to the axis of y, and Ene Is a 
quantity which would disappear if adx-+ @dy+ydz were a com- 
plete differential, that is, if the force acting on a unit north pole 
were subject to the condition that no work can be done upon 
the pole in passing round any closed curve. The quantity repre- 
sents the work done on a north pole im travelling round unit of 
area in the direction from +z to +y parallel to the plane of zy. 
Now if an electric current whose strength is 7 is traversing the 
axis of z, which, we may suppose, points vertically upwards, then, 
if the axis of w is east and that of y north, a unit north pole will 
be urged round the axis of z in the direction from 2 to y, so 
that in one revolution the work done will be = 47rr. Hence 
7 = — a) represents the strength of an electric current 
parallel to z through unit of area; and if we write 


1 (dy =*)= eet —\-- 1) = ~(% - a) an 
ale - dz) ~ aa\dz~ da) ~? Ga\de dy ae) 
then p, g, r will be the quantity of electric current per unit of 
area perpendicular to the axes of x, y, and z respectively. 

The physical interpretation of the third term of X, —r, is 


that if w8 is the quantity of magnetic induction parallel to y, and 
r the quantity of electricity flowing in the direction of z, the 


172 Prof. Maxwell on the Theory of Molecular Vortices 


element will be urged in the direction of —z, transversely to the 
direction of the current and of the lines of force; that is, an 
ascending current in a field of force magnetized towards the north 
would tend to move west. 

To illustrate the action of the molecular vor- Fig. 6. 
tices, let sm be the direction of magnetic force ~ n 
in the field, and let C be the section of an 
ascending magnetic current perpendicular to 
the paper. The lines of force due to this current ,, 
will be circles drawn in the opposite direction 
from that of the hands of a watch ; that is, in the 
direction nwse. At e the lines of force will be 
the sum of those of the field and of the current, 8 
and at w they will be the difference of the two 
sets of lines; so that the vortices on the east side of the current 
will be more powerful than those on the west side. Both sets 
of vortices have their equatorial parts turned towards C, so that 
they tend to expand towards C, but those on the east side have 
the greatest effect, so that the resultant effect on the current is to 
urge it towards the west. 

The fourth term, 

1 (de 
+m {Fe oat or +uyg, . . + (10) 
may be interpreted in the same way, and indicates that a current 
g in the direction of y, that is, to the north, placed in a magnetic 
field in which the lines are vertically upwards in the direction of 
z, will be urged towards the east. 

The fifth term, 

dp, 

Fa tue ho athe a 
merely implies that the element will be urged in the direction in 
which the hydrostatic pressure p, diminishes. 

We may now write down the expressions for the components 
of the resultant force on an element of the medium per unit of 
volume, thus: 

ie 4 d, . 
X=am+ ws (%)—wOrt+pyg—S3, . . (12) 
Losi d 
Y=@m+ Sa ay Hw + mar — 7 :  % hae 


gpg d, 
Z=ym+ 3- wo (v*)— pag +mBp — 2. wore (lp 


The first term of each expression refers to the force acting on 
magnetic poles. 


applied to Magnetic Phenomena. 173 


The second term to the action on bodies capable of magnetism 
by induction. 7 

The third and fourth terms to the force acting on electric 
currents. 

And the fifth to the effect of simple pressure. 

Before going further in the general investigation, we shall 
consider equations (12, 13, 14,) in particular cases, corresponding 
to those simplified cases of the actual phenomena which we seek 
to obtain in order to determine their laws by experiment. 

We have found that the quantities p, g, and r represent the 
resolved parts of an electric current in the three coordinate 
directions. Let us suppose in the first instance that there is no 
electric current, or that p, g, and rvanish. We have then by (9), 

dy dB da dy dB da _ s 

perce > ge ae ae ap ne 
whence we learn that 

eer eyed. 6 el suits Met we) eh e@lO) 


is an exact differential of ¢, so that 


tO oy hea beashesen eV 


oe he’ ay dee 
p is proportional to the density of the vortices, and represents the 
“ capacity for magnetic induction” in the medium. It is equal 
to 1 in air, or in whatever medium the experiments were made 
which determined the powers of the magnets, the strengths of 
the electric currents, &c. 

Let us suppose constant, then 


1/d d iy, ) 
m= 5 (7, (ue) + 5 (HB) + oe (on) 
_ 1 (ad , a , dd 
= (Ss + dy? + dz? ° ° ° ° e (18) 
represents the amount of imaginary magnetic matter in unit of 
volume. That there may be no resultant force on that unit of 


volume arising from the action represented by the first term of 
equations (12, 13, 14), we must have m=0, or 


FD IEE 2.6) 3 nn ag EE 


da® * ay? * dz? 

Now it may be shown that equation (19), if true within a given 
space, implies that the forces acting within that space are such 
as would result from a distribution of centres of force beyond 
that space, attracting or repelling inversely as the square of the 
distance. 


174 ~—Prof. Maxwell on the Theory of Molecular Vortices 


Hence the lines of force in a part of space where is uniform, 
and where there are no electric currents, must be such as would 
result from the theory of “imaginary matter” acting at a di- 
stance. The assumptions of that theory are unlike those of ours, 
but the results are identical. 

Let us first take the case of a single magnetic pole, that is, 
one end of a long magnet, so long that its other end is too far 
off to have a per ceptible influence on the part of the field we are 
considering. The conditions then are, that equation (18) must 
be fulfilled at the magnetic pole, and (19) everywhere else. The 
only solution under these conditions is 


m I 
ae ee (20) 
where 7 is the distance from the pole, and m the strength of the 
pole. 
The repulsion at any point on a unit pole of the same kind is 
dp m1 
—=— =. ; : re 
oe (21) 


In the standard medium w~=1 ; so that the repulsion is simply 

= -> in that medium, as has been shown by Coulomb. 
In a medium having a greater value of w (such as oxygen, 
solutions of salts of iron, &c.) the attraction, on our theory, ought 
to be ess than in air, and in diamagnetic media (such as water, 
melted bismuth, &c.) the attraction between the same magnetic 
poles ought to be greater than im air. 

The experiments necessary to demonstrate the difference of 
attraction of two magnets according to the magnetic or dia- 
magnetic character of the medium in which they are placed, 
would require great precision, on account of the limited range 
of magnetic capacity in the fluid media known to us, and the 
small amount of the difference sought for as compared with the 
whole attraction. 

Let us next take the case of an electric current whose quan- 
tity is C, flowing through a cylindrical conductor whose radius 
is R, and whose length is infinite as compared with the size of 
the field of force considered. 

Let the axis of the cylinder be that of z, and the direction of 
the current positive, then within the conductor the quantity of 
current per unit of area is 


iy al dB wi), ; 
nae we dy ae 


L* 


applied to Magnetic Phenomena. 175 
so that within the conductor 


C C 
a= —2 py; B=2p02, cee RE yh 0 een 5) 


Beyond the conductor, in the space round it, 


$=2Ctan-1%, . cele ae eR green ae et 


eae y __o¢__# OP 5 
If p=/x? + y? is the perpendicular distance of any point from 
the axis of the conductor, a unit north pole will experience a 


2C : 
force = ——, tending to move it round the conductor in the 


direction of the hands of a watch, if the observer view it in the 
direction of the current. 

Let us now consider a current running parallel to the axis of 
z in the plane of xz at a distance p. Let the quantity of the 
current be c’, and let the length of the part considered be /, and 


its section s, so that = is its strength per unit of section. Put- 


ting this quantity for p in equations (12, 18, 14), we find 
F 
X= —pp F 


per unit of volume; and multiplying by Js, the volume of the 
conductor considered, we find 


X= —pBell 
— —2u—, Whee ial h gy ate as ° > (26) 


showing that the second conductor will be attracted towards the 
first with a force inversely as the distance. 

We find in this case also that the amount of attraction depends 
on the value of w, but that it varies directly instead of inversely 
as 2; so that the attraction between two conducting wires will be 
greater in oxygen than in air, and greater in air than in water. 

We shall next consider the nature of electric currents and 
electromotive forces in connexion with the theory of molecular 
vortices. 


ae. 


XXVI. On the Benzole Series. 
By Artuur H. Caurcu, B.A. Oxon., F.C.S.* 


Part III. Note on the Oxidation of Nitrobenzole and its 
Homologues. 
| experiments by Hofmann, Berthelot, and others 
have shown, with reference to many important organic 
substances, how incorrect is any theory which does not permit 
them to be viewed in more than one aspect. Is nitrobenzole 
simply a hydrocarbon in which one equivalent of hydrogen is 
replaced by the group NO*? or is it the hydride of nitro- 


phenyle, Ob (sos) H? or, again, is it the nitrite of phenyle, 


C!2H®, NO*? Some of the metamorphoses to which this inter- 
esting body is subject suggest one of these views, and some 
another. The ready production from nitrobenzole of phenyl- 
amine, in which the group phenyle may be reasonably supposed 
to exist, might induce us to regard nitrobenzole as a compound 
of phenyle, possibly the nitrite ; while a reaction which I pointed 
out some time agoy, in which, by the action of sulphuric acid 
upon nitrobenzole, a compound acid was formed to which the 
empirical name of nitrosulphobenzolic acid was assigned, and 
which can hardly be regarded in any other Way. except as the 
GR H, 280°, 
almost obliges us to view nitrobenzole as containing nitrophenyle. 
I propose in the present note to cite a few experiments which 
present some of the nitro-derivatives of the benzole series in a 
new light. I feel, however, that though an apology is due for 
the imperfections of the present account, yet a preliminary 
notice of my results (results which will require much time and 
labour to bring to a satisfactory conclusion) might not be unac- 
ceptable. But I should have deferred publishing any account of 
my inquiries for some time longer, tad not an acid been lately 
discovered homologous with benzoic acid, and isomeric, but not, 
I think, identical with an acid mentioned in this paper: I refer 
to collinic acid, C!? H* 04, obtained by the oxidation of gelatine. 
Then, too, several of the speculations and anticipations of Ber- 
thelot in his work on Organic Synthesis, trench somewhat closely 
upon one of the inquiries in which I have been lately engaged. 
I intend, when my inquiries are more advanced, to make the 
two new acids (phenoie and nitrophenoic) mentioned in the pre- 
sent notice the subject of another communication. 

The oxidation of toluole, xylole, and cumole by means of bi- 


sulphite of nztrophenyle and hydrogen, CO” 


* Communicated by the Author. 
t+ Phil. Mag. April and June 1855. 


On the Oxidation of Nitrobenzole and its Homologues. 177 


chromate of potassium and sulphuric acid, has been found in 
each case to yield benzoic acid. Cymole, on the other hand, the 
last member of the series, when treated in the same way, yields 
the insolinic acid discovered by Dr. Hofmann, and not the toluic 
acid which Mr. Noad obtained by acting upon this hydrocarbon 
with dilute nitric acid. Benzole remains wholly unacted upon 
when boiled for a very long period with bichromate of potassium 
and sulphuric acid. Not so, however, with nitrobenzole, which 
is slowly converted by this powerful oxidizing mixture into a 
soft, white, crystalline mass of intensely acid reaction. In the 
first experiment, I made use of a very excellent sample of com- 
mercial nitrobenzole, a portion of which seemed to be acted on 
with greater facility than the rest. An analysis of the acid 
thus formed gave numbers which indicated a mixture of nitro- 
benzoic and nitrophenoic acids: I propose the latter name for 
the new acid, which I believe to be the next lower homologue 
of the benzoic. The view that the acid burnt was a mixture, is 
confirmed by another experiment, to be related further on. In 
order to secure the absence of nitrotoluole from the nitrobenzole 
operated upon, I converted some benzole from benzoic acid into 
nitrobenzole, and repeated my experiments with this. The action 
of a most concentrated oxidizing solution was now found to be 
very much slower than in the former case; but after long diges- 
tion the nitrobenzole solidified in great measure on cooling the 
mixture, while from the solution itself numerous white crystalline 
~spangles separated. The liquid and solid parts were together 
poured into a funnel plugged with asbestos. To separate the 
unchanged nitrobenzole, the solid stopped by the filter was 
exhausted with boiling water, and the solution filtered twice 
through paper. When cold, the filtrate was full of large nacreous 
plates of a very pale straw colour, which by recrystallization 
became perfectly white. Having had but a few grains of this 
substance at my disposal, I have not yet made an accurate ex- 
amination of its physical properties. I found, however, that its 
reaction is strongly acid, that it is fusible without decomposi- 
tion, tolerably soluble in boiling water, and that it yields cry- 
stallizable salts. Not only does its origin and the method of 
its formation preclude the existence of more than twelve atoms 
of carbon in the new acid, but the following determination of 
silver in a carefully prepared specimen of its silver-salt points 
to the formula C!? H? Ag (NO*)O# for this compound, and to 
C!? H3 (NO‘) O# for the acid itself :— 
‘971 germ. of silver-salt gave ‘537 grm. of chloride of silver = 
"4041 grm. of silver, 


Phil. Mag. 8. 4. Vol. 21. No. 139. March 1861. = N 


178 Mr. H. Church on the Oxidation of 


corresponding to a per-centage of— 


Theory, 
Experiment. CH? Ag (NO*) O4, 
Silvers) .4 0d SOG] A154: 


So far as they have been yet examined, the properties of nitro- 
phenoie acid confirm the idea that it is a true homologue of 
nitrobenzoic acid. 

I have made an attempt to prepare the original acid, the 
phenoic, of which I have supposed the above-noticed acid to be 
the nitro-derivative. Although a mixture of bichromate of po- 
tassium and sulphuric acid is without action on benzole, it acts 
most energetically on sulphobenzolic acid formed by dissolving 
benzole in Nordhausen sulphuric acid. If to a slightly diluted 
solution of sulphobenzolic acid at about 70° C. minute frag- 
ments of bichromate of potassium be added, one at a time, and 
the action which ensues at each addition be moderated by cooling 
the apparatus, an acid distillate will be obtained, on the surface 
of which small brilliant crystals, gencrally accompanied by a few 
oily globules, will be found floating. It would seem that the 
oily and solid portions of the distillate are alike in composition, 
since the analysis of the silver-salts of the two bodies, separated 
mechanically as far as possible, gave almost the same numbers. 
Of the annexed determinations, I. was made with a silver-salt 
prepared from the oily part, and II. with one prepared from the 
crystalline part of the distillate. 

I. -739 grm. gave ‘37 grm. of silver, 

II. +3822 grm. gave ‘163 grm. of silver ; 

corresponding to the following per-centages of silver :— 


Experiment. Theory, 
: II. CH Ae D4 
50:06 50:06 50°23 


Sulphotoluolic and sulphocumolic acids, when oxidized as de- 
scribed above, yield benzoic acid inabundance. I have identified 
the product by all the usual tests. I have not yet experimented 
with the xylole series. Sulphocymolic acid yields a white powder, 
apparently identical with insolinic acid. 

Nitrotoluole, when oxidized, yielded nitrobenzoie acid, which 
agreed in every respect with a pure specimen in my possession 
prepared from benzoic acid. I have before mentioned the diffi- 
culty with which nitrobenzole is acted on by the oxidizing mix- 
ture; and if this latter be somewhat diluted, it affords a means 
of separating the nitro-derivatives of toluole, &c. from nitro- 
benzole, which, when the action is complete, is siphoned off and 


Nitrobenzole and its Homologues. 179 


washed with en alkaline solution to remove the nitrobenzoic acid 
formed. 

Since sulphobenzolate of ammonium, when submitted to dry 
distillation, yields some quantity of benzole*, I imagined that 
the nitrosulphobenzolate would yield nitrobenzole: experiment, 
however, has not corroborated this view. 

In 1859 I showed+ that nascent chlorine acts powerfully on 
toluole, xylole, and other homologues of benzole, yielding the 
chlorides of toluenyle, xylenyle, &c., from which the cyanides, 
and subsequently the acids (toluic and xyloic), are producible. 
I am pursuing some inquiries in this direction with benzole, 
upon which unfortunately nascent chlorine acts with more diffi- 
culty, and at the same time does not appear to yield such definite 
results. 

There is a point of view from which some of the experiments 
which I have made acquire a fresh interest. If 1 vol. of light 
coal-naphtha containing, say 50 per cent. of benzole, be sub- 
mitted to the action of 6 vols. of oil of vitriol previously diluted 
with 1 vol. of water, and the mixture heated for some time in 
a suitable condensing apparatus, the benzole will remain nearly, 
if not quite, unacted upon, while the other hydrocarbons will be 
dissolved by the sulphuric acid. If the acid be absorbed by 
small fragments of pumice and thus used, it exerts a much more 
rapid and effectual action on the naphtha. The benzole, after 
having been washed with water, is nearly pure. The other hy- 
drocarbons which have been dissolved are now contained as sul- 
photoluolic and similar acids in the liquid, which is to be collected, 
diluted with half its bulk of water, and poured into a retort pro- 
vided with a Liebig’s condenser. Buichromate of potassium, 
about one-sixth part in weight of the acid present, is added gra- 
dually to the solution, and the mixture cautiously distilled. In 
this way a considerable proportion of benzoic acid may be ob- 
tained. 


Postscript, February 8, 1861. 


Since writing the above remarks, my attention has been 
directed to a short notice of some experiments by MM. Cloetz 
and Guignet, who also seem to have obtained a new acid by the 
oxidation of nitrobenzole. I think it mght to say that I sue- 
ceeded in producing the acid which I have termed nitrophenoic 
in June 1860. 


* Phil. Mag. December 1859. 
+ Chemical News, December 10, 1859. 


N2 


[ 180 ] 


XXVIII. Note on the Theory of Determinants. 
By A. Cayiny, Esq.* ’ 


f dasa following mode of arrangement of the developed expres- 
sion of a determinant had presented itself to me as a con- 
venient one for the calculation of a rather complicated determi- 
nant of the fifth order; but I have since found that it is in 
effect given, although in a much less compendious form, in a 
paper by J. N. Stockwell, “On the Resolution of a System of 
Symmetrical Equations with Indeterminate Coefficients,” Gould’s 
‘Ast. Journal, No. 189 (Cambridge, U. 8., Sept. 10, 1860). 
Suppose tnat the determinant 


1t tae. ie 
21. 80 438 
S12 e824 BS 


is represented by {123}, and so for a determinant of any order 
4123 .-.n}. 


Let 11], ]2], [12], [123], &c. denote as follows: viz. 


fl] = 11, [2] = 22, &c. 
Pie 12 ek, 
} 123] = 12.23.31, 

&e., 


where it is to be noticed that, with the same two symbols, e. g. 
1 and 2, there is but one distinct expression |12] (an fact 
}21 | = 21.12 ={12]); with the same three symbols 1, 2, 3, 
there are two distinct expressions, |123]}(=12.23.381) and 
, 182 | (=13.32.21); and generally with the same m symbols 
1, 2, 3...m, there are 1.2.3...m—1 distinct expressions 
}123...mj, which are obtained by permuting in every possible 
manner all but one of the m symbols. 

This beg so, and writing for greater simplicity }1}2] to 
denote the product |1 | x { 2], and so in general, the values of 
the determinants {12}, {123}, {1234}, {12345}, &e. are as 
follows: viz. 


* Communicated by the Author. 


Mr. A. Cayley on the Theory of Determinanis, 181 


No. of terms. 


spe 
eps ya eli. .e kD 
=e ge! 2 | | E | 
. 1+1=2 
{123}=+4+ ]1[2]3] . at 1 
—|l ae ee 3 
tt & Bh so sin 2 
o+3=6 


{1234,=4+ ]1)2]3}41.- | 1 
—J1l 2|3]4|. . 6 

eb ss, ot4 | a 
+[1L 2]3.4]}.. . 

—|i 2 3-4}. 6 
124+12= 24 


Oo 


(12345}=+ ]112]314]5]. | 1 
cg SASL A | ot 10 
Sly 2.31 4 [oP sty 20 
eb Sd Pere ee 


Bb l 2 3 4 Salis 30 

aid 2 814-5) % 20 

el 23.4. 5. | 04 
-60+60= 120 


where, as regards the signs, it is to be observed that there is a 
sign — for each compartment] | contaming an even number 
of symbols; thus in the expression for {1234}, the terms 
J 12] 34] have thesign — — = +, and the terms| 123 4} 
the sign —. Or, what comes to the same thing; when 7 is even, 
the sign is + or — according as the number of compartments 
is even or odd; and contrariwise when 7 is odd. As regards 
the remaining part of the expression, this merely exhibits the 
partitions of a set of n things; and the formule for the several 
determinants up to the determinant of a given order are all of 
them obtained by means of the form 


182 Mr. A. Cayley on the Theory of Determinants. 


which is carried up to the order 7, but which can be further ex- 
tended without any difficulty whatever. 

It is perhaps hardly necessary; but I give at full length the 
expressions of the determinant of the third order: this is 


{128} = 11/213] 

—|[1 213] 

—|}2 3{1| I 

—|8 142] 

+]1 2 3] 

+]1 3 2]5° 
And by writing down in like manner the expression for the 
twenty-four terms of the determinant of the fourth order, the 
notation will become perfectly clear. 


The formula hardly requires a demonstration. The terms of a 
determinant {123...n}, for example the determinant {1234} | 


are obtained by permuting in every possible manner the symbols 
in either column, say the second column, of the arrangement 


hI 
22 
3.3 
A 4 


Mr, A. Cayley on the Theory of Determinants. 183 


and prefixing the sign (+ or —) of the arrangement; and the 
resulting arrangements, for instance 


ol hy seks, .. eh s, 
2 2 al 23 
33 3.3 3 4 
4. 4, 44 4] 


are interpreted either into +11.22.83.44, —12.21.33.44, 
—12.23.34.41, or in the notation of the formula, into 


Pii2isi4i, —|12(814b -— t12341. 


And so in general. 

Suppose that any partition of n contains « compartments each 
of a symbols, 6 compartments each of 6 symbols... (a, b,... 
being all of them different and greater than unity), and p com- 
partments each of a single symbol, we have 


n=aa+PBb+ ...+ . 


And writing, as usual, [Ia=1.2.3...a, &c., the number of 
ways in which the symbols 1, 2,.8,...n, can be so arranged in 
compartments is 


IIn 
(IIa)*(I1d)*...TeII8...1p’ 


but each such arrangeraent gives (II (a—1) )* ; (1I(6—1) )é 
terms of the determinant, and the corresponding number of terms 
therefore is 
IIn 
ob, Alas ..idip: 


The whole number of terms of the determinant is IIn, and we 
have thus the theorem 
1 

Wreriesitis clin Weesekl a 
in which the summation corresponds to all the different partitions 
n=aa+8b...+p, where a, b,... are all of them different and 
ereater than unity ; a theorem given in Cauchy’s Mémoire sur les 
Arrangements, &c., 1844. But it is to be noticed also that, the 
number of the positive and negative terms being equal, we have 
besides 
ye soe hic 


Wea | aipales SO EOL EE Berea 5 Oe, Sree 
Mem ta lde te 


184 Mr, A. Cayley on the Theory of Determinants. 


or, what is the same thing, 


eee amie 
a*b? .. ged G: . Tp 


eat ale 


and thence also ~ 


j 
t= 


a* bP... ilall@... 1p’ 


where, as before, n=aa+ Pb...+p (a, b,... bemg all different 
and greater than unity); but the summation is restricted either 
to the partitions for which n—a—6...—p is even, or else to 
those for which n—a—f6...—p is odd. 

The formula affords a proof of the fundamental property of 
skew symmetrical determmants. In such a determimant we 
have not only 12=—21, &c., but also 11=0, &c. Suppose 
that n, the order of the determinant, is odd; then in each line of 
the expression 


{123...nk=|1]2]...12] 
+ &e, 


of the determinant, there is at least one compartment | 1 ] or 
| 123] &c. containing an odd number of symbols: let | 128 | 
be such a compartment, then the determinant contains the terms 
| 123] P and {182|P (where P represents the remaining 
compartments), that is, 12.238.31.Pand18.82.21.P. But 
in virtue of the relations 12=—21, &c., we have 


19 O83 a Wao ae as 


and so in all similar cases, that is, the terms destroy each other, 
or the skew symmetrical determimant of an odd order is equal 
to zero. 

The like considerations show that a skew symmetrical deter- 
minant of an even order is a perfect square. In fact, consider- 
ing for greater simplicity the case n=4, any line in the foregoing 
expression of 11234! for which a compartment contains an 
odd number of symbols, gives rise to terms which destroy each 
other, and may be omitted. The expression thus reduces itself to 


{1234} = +112] 384] 3 terms 
—| 12 34] 6 terms, 
which is in fact the square of 
12.84413.424 14.28. 
For the square of aterm, say 12.54, is 12”. 342 or 12.21 .34.43, 


that is, ] 12 ]34], and the double of the product of two terms, 
say 12.34 and 13, 42, is 2.12.34.18.42, or —12.24.43.31 


On the Chemical Analysis of the Solar Atmosphere. 185 


—13.34.42.21, that is —| 1243 | —]1342 |, and so for the 
other similar terms, and we have 

41234) = (12 .34413.42-4+14.23)?,) 
And so in general, n being any even number, the skew symme- 
trical determinant $123... is equal to the square of the 
Pfaffian 12..., where the law of these Pfaffian functions is 


12384 =12.84 418.42 414.28 
123456 = 12.3456 + 13.4562 + 14,5623 + 15.6284 + 16.2345 


where, in the second equation, 3456, &c. are Pfaflians, viz. 
3456 =34.564385.644+86.45; and so on. 


2 Stone Buildings, W.C., 
December 28, 1860. 


XXVIII. Letter from Prof. Kirncunorr on the Chemical Analysis 
of the Solar Atmosphere. 


To the Editors of the Philosophical Magazine and Journal. 


GENTLEMEN, Owens College, Manchester, 
February 1, 1860. 

{ RECEIVED a short time ago from Heidelberg the enclosed 

portion of a letter from Prof. Kirchhoff to Prof. Erdmann. 

As it gives a later account of Kirchhoff and Bunsen’s most im- 

portant researches than has yet appeared in the Nnglish journals, 
I think it may be of interest to your readers. 

I am, yours sincerely, 
Henry HE. Roscoz. 


“Since I sent in my last report to the Berlin Academy, I 
have been almost uninterruptedly engaged in following out the 
investigation in the direction I there indicated. I will not now 
speak either of the theoretical proof I have given* of the facts I 
there announced, or of the experiments by help of which Bunsen 
and I+ have shown that the bright bands in the spectrum of a 
flame serve as the surest indications of the metals present therein ; 
I will take the liberty, in this communication, of informing you 
of the progress I have made in the chemical analysis of the solar 
atmosphere. 

“The sun possesses an incandescent, gaseous atmosphere, 
which surrounds a solid nucleus having a still higher tempera- 
ture. If we could see the spectrum of the solar atmosphere, we 
should see in it the bright bands characteristic of the metals 


* Phil, Mag. July 1860. t+ Ibid. August 1860. 


186 Prof. Kirchhoff on the Chemical Analysis 


contained in the atmosphere, and from the presence of these 
lines should infer that of these various metals. The more intense 
luminosity of the sun’s solid body, however, does not permit the 
spectrum of its atmosphere to appear; it reverses it, according 
to the proposition I have announced; so that instead of the 
bright lines which the spectrum of the atmosphere by itself 
would show, dark lines are produced. Thus we do not see the 
spectrum of the solar atmosphere, but we see a negative image 
of it. This, however, serves equally well to determine with cer- 
tainty the presence of those metals which occur in the sun’s 
atmosphere. For this purpose we only require to possess an 
accurate knowledge of the solar spectrum, and of the spectra of 
the various metals. 

“T have been fortunate enough to obtain possession of an appa- 
ratus from the optical and astronomical manufactory of Steinheil 
in Munich, which enables me to examine these spectra with a 
degree of accuracy and purity which has certainly never before 
been reached. The main part of the instrument consists of four 
large flint-glass prisms, and two telescopes of the most consum- 
mate workmanship. Jy their aid the solar spectrum is seen to 
contain thousands of lines; but they differ so remarkably in 
breadth and tone, and the variety of their grouping is so great, 
that no difficulty is experienced in recognizing and remembering 
the various details. I intend to make a map of the sun’s spec- 
trum as I see it in my instrument, and I have already accom- 
plished this for the brightest portion of the spectrum—that por- 
tion, namely, included between Fraunhofer’s limes Fand D. By 
painting the lines of various degrees of shade and of breadth, I 
have succeeded in producing a drawing which represents the 
solar spectrum so closely, that, on comparison, one glance suffices 
to show the corresponding lines. 

“The apparatus shows the spectrum of an artificial source of 
light, provided it possess sufficient intensity, with as great a 
degree of accuracy as the solar spectrum. A common colourless 
gas-flame in which a metallic salt volatilizes, is m general not 
sufficiently luminous; but the electric spark gives with great 
splendour the spectrum of the metal of which the electrodes are 
composed. <A large Ruhmkorff’s mduction apparatus produces 
such a rapid succession of sparks, that the spectra of the metals 
may be thus examined with as great facility as the solar spectrum. 

“‘ By means of a very simple arrangement, the spectra of two 
sources of light may be compared. The rays from one source of 
light can be led through one half of the vertical slit, whilst those 
from another source are led through the other half. If this is 
done, the two spectra are seen directly under one another, sepa- 
rated only by an almost invisible dark line. By this arrange- 


of the Solar Atmosphere. 187 


ment it is extremely easy to see whether any coincident lines 
occur in the two spectra. 

“T have in this way assured myself that all the ios lines 
characteristic of iron correspond to dark lines in the solar spec- 
trum. In that portion of the solar spectrum which I have ex- 
amined (between the lines D and F), I have had occasion to 
remark about seventy particularly brillant lines as caused by the 
presence of iron in the solar atmosphere. Angstrém only ob- 
served three bright lines in this part of the spectrum of the 
electric spark ; Masson noticed only a few more; Van der Wil- 
ligen says that iron produces only a very few feeble lines in the 
spectrum of the electric spark. From the number of these lines 
which I have been able to observe with ease, and map with abso- 
lute certainty, some idea may be formed of the capabilities of the 
instrument which I am fortunate enough to possess. 

“ Tron is remarkable on account of the number of the lines 
which it causes in the solar spectrum; magnesium is interesting - 
because it produces the group of Fraunhofer’s lines which are 
most readily seen in the sun’s spectrum, namely, the group in 
the green, consisting of three very intense lines to which Fraun- 
hofer gave the name 6. Less striking, but still quite distinctly 
visible, are the dark solar lines coincident with the bright lines 
of chromium and nickel. The occurrence of these substances in 
the sun may therefore be regarded as certain. Many metals, 
however, appear to be absent; for although silver, copper, zinc, 
aluminium, cobalt, and antimony possess very characteristic 
spectra, still these do not coincide with any (or at least with any 
distinct) dark lines of the solar spectrum. I hope before long 
to be in a position to publish more extended information on this 

oint. 
Me The combination of Ruhmkorff’s induction coil with the spec- 
trum apparatus will doubtless also be of importance for the che- 
mistry of terrestrial matter. Very many metallic compounds do 
not give the spectrum peculiar to the metal when placed in a 
flame, because they are not sufficiently volatile, but they give it 
at once when placed on the electrodes of an electric spark. 
These lines are then indeed seen, together with those of the 
metal of the electrode, and those of the air through which the 
spark passes; and owing to the great number of bright lines 
which compose the spectrum of every electric spark, it would be 
almost impossible, without a special arrangement, to distinguish 
the lines caused by the metal of the electrodes from those pro- 
duced by the metallic salt added. The special arrangement 
which in this case removes all difficulty, consists in allowing the 
spark to pass at the same instant between two pairs of electrodes, 
in such a manner that the light of one spark passes through the 


188 T. A. Hirst on Ripples, - 


upper half of the sht, whilst the light of the other spark passes 
through the lower half of the slit, so that the two spectra are 
seen one directly above the other. If both pair of electrodes are 
pure, both the spectra are alike; if a metallic salt is brought on 
to one of the electrodes, the lines peculiar to that metal appear 
in the one spectrum in addition to those present before. These 
are recognized at the first moment, because they are absent in the 
other spectrum. The lines which are common to the two spectra 
may serve, when they are once for all drawn, as the simplest 
mode by which to represent the position of the lines of the other 
metals employed. 

“1 have proved that in this way the metals of the rare earths, 
yttrium, erbium, terbium, &c., may be detected in the most cer- 
tain and expeditious manner. Hence we may expect that, by 
help of Ruhmkorff’s coil, the spectrum-analytical method may 
be extended to the detection of the presence of all the metals. 
I trust that this expectation may be borne out in the continuation 
of the research which Bunsen and J are jointly carrying on with 
the object of rendering this method practically applicable.” 


XXIX. On Ripples, and their relation to the Velocities of Currents. 
By T. Arcuer Hirst, Mathematical Master at University 
College School, London. 


[Concluded from p. 20.] 
[With a Plate. ] 


al. 4 he art. 20 it was shown that when a jet or partially im- 

mersed solid cylinder is made to describe a circle of 
radius a in still water, the ripple it produces has a cusp C (fig. 7, 
Plate I.), which describes another circle whose radius r has to 
a the same ratio that the velocity X, with which the waves causing 
the ripple are propagated, has to the velocity u of the jet; and 
further, that the angle @ between the radii to the jet and to the 
cusp varies with 7, in accordance with the relation 


tan ($,—6)=¢,= eel oils os ela 
Hence if the axis of polar coordinates pass through, and rotate 
with the jet, this is the equation of a curve upon which the cusp 
of the ripple must le, no matter with what velocity the jet may 
be rotating. The curve itself, as may be easily shown (Plate LV. 
fig. 2), lies entirely within the cir cle (a); it commences at the jet A, 
r=a, 6=0, where it touches the axis O A, and proceeds inwards, 
turning its ‘convexity towards the centre 0, until on arriving at 


and their relation to the Velocities of Currents. 189 


a point of inflexion 2, whose coordinates are r= We G=1 —7 
(equivalent to 12° 17! 44” nearly), it commences and continues 
ever after to turn its concavity towards the centre O, which 
point it approaches asymptotically. In comparing the fore- 
eoing results with those of experiment, the above curve was found 
to be of service. 


Experiments. 

22. I proceed to describe a few experiments which will serve 
to verify the general principles upon which the foregoing results 
are based, though they are by no means sufficiently complete 
and accurate to decide, fully, the interesting question as to the 
velocities of differently shaped waves. 

23. The experiments on the ripples produced by a jet or solid 
cylinder rotating in still water were made with the modification 
of Barker’s mill represented in section by fig. 1, PL IV. DCC’D! 
is a tin tube 17 inches long and 2 inches in diameter, whose 
lower extremity, contracted to a diameter of 1 inch, is soldered 
into a hollow brass cap DD'E'E. Into this cap three brass 
tubes are fitted; one vertical, projecting 6 inches into the inte- 
rior of the tin tube, and closed at its upper extremity by a plate 
F of hard steel; and two, D B and D! B’, horizontal, in the same 
straight line, about 44 inches long, —5ths of an inch in diameter, 
and terminated by two brass caps A B and A’ B’, which slide 
over the tubes and can be removed at pleasure. In each cap 
a lateral aperture is made, into which can be fitted either a smaller 
brass tube suitable for the issue of a jet 7th of an inch in 
diameter, or a solid brass cylinder of the same diameter, which 
completely prevents the efflux of water. The whole weight of 
the portion of the instrument thus far described, and of the 
water it may contain, is supported by a steel pin OF about 
8 inches long, whose hardened and pointed upper extremity enters 
a small cavity in the centre of the steel plate i, whilst its lower 
extremity is screwed firmly into a lead weight. MN, placed 
at the bottom of a bath PQRS. By this arrangement, the 
water in the tin tube issuing at one or both of the orifices A, A! 
causes a rotation unaccompanied by sensible cscillations, and the 
issuing jets of water, by falling into the water in the bath, pro- 
duce the ripples whose forms are to be examined. When a con- 
stant velocity of rotation is required, it is merely necessary to 
retain the same depth of water in the tin tube; and this can be 
done either by regulating, with a cock, the supply of water enter- 
ing at H, or by carrying a siphon through H to a reservoir kept 
at a constant level. When necessary, too, the water in the bath 
can be kept at a constant level by similar means. 


190 T. A. Hirst on Ripples, 


24. The moment the instrument rotates with sufficient velo- 
city the ripples make their appearance, and the general resem- 
blance between their forms and that of the one drawn according 
to theory in fig. 7, Plate I., is very striking. The external branch 
A X, and the portion of the internal one between the jet A and 
the cusp C are quite distinct and well defined ; the return branch 
CBD is far less distinct, the height of this part of the ripple 
being small, and its breadth great; its existence, however, may 
be established by a closer inspection, or by a glance at the dis- 
torted image at the bottom of the bath caused by the irregular 
refraction of the light incident upon the rippled surface. Besides 
the principal ripple there are anumber of secondary ones, similar 
in form but less in extent, which precede the former, and of 
course tend to diminish its prominence. 

25. In order to compare the actual with the theoretical ripple 
more precisely, the following simple expedient was adopted :— 
A circular plate of glass K La foot in diameter, and having a cir- 
cular aperture at its centre to admit the screw O, was attached 
by means of this screw to the top of the lead weight. Its lower 
surface was silvered, and the silvering afterwards coated with 
shell-lac to protect it from the action of the water. The image 
of the ripple in this plane mirror was not only more distinct than 
the ripple itself, but the arrangement had the additional advan- 
tage of obviating errors due to parallax, since the image of the 
observer’s eye could always be made to coincide with that of any 
part of the ripple under examination. Lastly, a second and 
transparent glass plate A A’, 10 inches in diameter, was attached 
by means of a screw E E! to the cap at the bottom of the mill. This 
plate turned of course with the mill, and could be graduated in 
any required manner; it had a small indentation at a poimt in 
its circumference, in order that the axis of one, A, of the vertical 
jets (or cylinders) might be made to describe, precisely, the 
circumference of a circle 5 inches in radius. 

26. By means of the equations (32) and (40), one or two rip- 
ples AaC and Aa,C, (fig. 2), and the locus A C C, of their cusps, 
were carefully plotted on a sheet of paper; they corresponded to a 
value of a=5 inches, and in the case of the ripples, to arbitrarily 
assumed values of the ratio a between the velocities X and w of 
the wave and jet. These curves were next transferred, in white 
paint, to the glass plate A A’, and one of the jets A made to 
coincide with their origin. The instrument being now filled 
with water, the jet at A’ was made to issue horizontally in order 
to turn the mill, whilst the jet at A descended vertically into 
the bath and produced the ripple to be examined. As the velocity 
of rotation diminished, the cusp of the actual ripple described very 
accurately the curve C,C A traced on the glass plate AA’; and 


and their relation to the Velocities of Currents. 19] 


with equal accuracy the portion of this ripple between the jet 
and cusp coincided successively with the corresponding portions 
Aa,C, AaC of the theoretical ripples. To test the coincidence 
of the portion of the ripple outside the circle described by the 
jet (A X Ein fig. 7, Plate I.), a hole was drilled through the glass 
plate A A! at a distance of 24 inches from its centre, and a solid 
cylinder thrust through the same so as to be partially immersed 
in the water of the bath. The mill was turned as before by the 
jet A’ alone, the aperture at A being closed; and when the velo- 
city of rotation was properly regulated, it was found that the 
complete actual ripple produced by the immersed cylinder coin- 
cided very well with as much of the theoretical one as could be 
traced upon the glass plate. 

27. The slight divergence from perfect coincidence between 
the theoretical and actual ripples being sufficiently accounted for 
by the conditions under which the experiments were made—the 
limited extent of the bath, the disturbing effect of the portion of 
the axis O F immersed in the water, and the magnitude of the 
jet (which in theory was disregarded),—the accuracy of the prin- 
ciples upon which the foregoing theory is based may be consi- 
dered as sufficiently established, and we may proceed at once to 
give an account of the measurements from which an approximate 
value of the velocity \ with which the waves, producing the rip- 
ples in question, are propagated may be deduced. 

For this purpose the curves on the glass plate A A’ were obli- 
terated, and replaced by concentric circles whose radu increased 
by half inches from 1 to 5 inches. A constant rotation was 
secured in the manner described in art. 23, and its velocity de- 
termined in each case by counting the number n of rotations 
made in a given time ¢, the latter being measured by an accu- 
rate timepiece, the motion of whose index could be instantaneously 
arrested or renewed by simply pressing or releasing a spring. 

Since each jet issues at right angles to the horizontal arm B B’, 
it is clear that its effect, as far as the rotation of the mill is con- 
cerned, depends not only upon the height of the column of water 
in the tin tube, but also upon the inclination of the jet to the 
horizon ; for upon the former depends the velocity of efflux, and 
the uncompensated pressure against the part of the horizontal 
tube opposite to the orifice through which the jet issues, whilst 
upon the latter depends the magnitude of the horizontal compo- 
nent of this pressure, which component is alone effective in pro- 
ducing rotation. But every change in the velocity of efflux and 
in the inclination of the jet to the horizon produces a corre- 
sponding change in the distance, from the axis, of the point at 
which the jet falls into the water in the bath, and consequently 
in the radius @ of the circle described by the jet. This radius, 


192 T. A. Hirst on Ripples, 


too, also depends upon the height of the water in the bath; 
so that at first sight it would appear, not only that the latter 
ought to be kept constant throughout one and the same experi- 
ment, but that a separate determination of a should be made in 
each case. 

On setting both jets in action, however, at different. inclina- 
tions, and comparing the two ripples which they produced, it 
was soon found that, however much the radii a and a’ of the 
circles described by the jets might differ in magnitude, the radii 
x and » of the circles described by the cusps of their ripples were 
in all cases nearly equal. This result is confirmed by theory, 
which also shows that the slight difference between the radii 7 
and 7’ is due, solely, to the slight difference between the values 
of the velocities X and X/ with which the waves, produced under 
these different circumstances, are propagated. In fact it fol- 
- lows at once from equation (35) of art. 20, that 
AM or ol 
uw aa? 
and the angular velocity of rotation being the same for each jet, 
their actual velocities u and w’ will clearly be proportional to the 
radii a and a’ of the circles they describe; the above proportion, 
therefore, reduces itself to the simpler one, 


A cD mer te ps) es) alo WA 


and thus verifies the above remark. When one jet descended 
vertically and the other issued horizontally, the difference between 
rand 7’, although still very small, was at a maximum, and the 
cusp of the ripple produced by the vertical jet was always fur- 
thest distant from the axis; from which we may conclude that 
the velocity X is greater when the jet descends vertically into the 
water of the bath, than when it strikes the surface of the latter 
obliquely. When the vertical jet was replaced by a solid cylinder, 
the difference between the positions of the cusps remained about 
the same as before, thus indicating that the velocity X was ap- 
preciably the same for a jet and for a solid cylinder. 

It is also worth noting here, that when the distance, from the 
axis, of the cusp of the ripple produced by the oblique jet ex- 
ceeded the radius (5 inches) of the circle described by the vertical 
jet, the latter produced no ripple whatever. ‘The reason of this 
has already been given in art. 13; and in accordance with the 
statement there made, it was found that in all such cases the velo- 
city of the vertical jet was less than 74 inches per second, which, 
as we shall see, is the mean value of the velocity % with which 
the waves produced by each jet are propagated. Attempts were 
made to regulate the velocity of rotation so that the cusp of the 


and their relation to the Velocities of Currents. 193 


ripple produced by the oblique jet should be exactly 5 inches 
distant from the axis. Theoretically, the ripple corresponding 
to the vertical jet should then have been the znvolute of a circle 
(art. 13); in reality, however, the ripple was scarcely distin- 
guishable in such cases, the disturbance which the vertical jet 
produced upon the surface of the water‘in the bath being still 
so small. 

28. Although the apparatus was sufficiently delicate to esta- 
blish the fact of slight variations in the velocity X due to differ- 
ences in the obliquity of the jet and the velocity of efflux, it did 
not appear suitable for the full investigation of the magnitude and 
conditions of these variations; I contented myself therefore with 
a few determinations of X from a series of observations made 
under all possible conditions. From them the limits of the varia- 
tion of X may be to some extent ascertained and its mean value 
estimated. In order to calculate X from the data supplied by 
experiment, the formula 

Ai 


fon 
given in art. 20, requires a slight transformation. The circum- 
ference of the circle described by the jet being 27ra, and n rota- 
tions being made in ¢ seconds, the velocity u has the value 


Qcran 
— r 3 


so that the above equation giving the velocity X per second 
becomes 
27r 


A= 2. ° pi Matias Woe Yk tates (4:2) 


According to this, and as already hinted in the last article, the 
velocity X depends, solely, upon the number of rotations in a 
given time, and upon the distance r of the cusp of the ripple 
from the axis of the instrument; in other words, it is not de- 
pendent upon the radius of the circle described by the jet; so 
that it was not necessary to determine the distance, from the 
axis, of the point of impact between the jet and the water in the 
bath, and therefore not necessary to ascertain the height of the 
water in the bath, or to render the latter constant. 

29. Some of the results of a great many accordant observa- 
tions are shown in the following Table, wherein 2 represents the 
number of rotations per minute, 7 the distance (in inches) from 
the axis of the cusp of the ripple, and X the velocity in inches 
per second with which the corresponding waves are propagated, 
calculated according to (42) :— 


Phil. Mag. 8. 4. Vol. 21. No. 189, March 186}. O 


194 T. A. Hirst on Ripples, 


= 
3 


POVWANWSBDOUIADEAUMMHSOHA 
SRBBBVVPVNVSTSSTTSe | 
HANVQWVAOSOWA ABR WOOARDMAIOD oe 


ho 
oo 
He He C9 09 CO bO BO LODO LD LO Rt et et tt OS D> 


Of these results the first five or six are less trustworthy than 
the rest,—and this for several reasons, amongst which the follow- 
ing may be cited :—The rapidity of the rotation renders the de- 
termination of the position of the cusp more difficult ; the proxi- 
mity of the immersed axis interferes with the clear definition of 
the cusp ; and lastly, the consequences of a small error in esti- 
mating the distance of this cusp from the axis increase as this 
distance diminishes, since the cusp approaches the axis asympto- 
tically (art. 21). On the other hand, the rapid diminution of X 
shown in the Table, can in some measure be accounted for by 
the fact that, in order to avoid disturbing too much the surface 
of the water in the bath, it was found necessary, with rapid rota- 
tions, to use only one jet, and it of course issued at a small angle 
towards the horizon, so that the impact between the jet and the 
water in the bath was necessarily a very oblique one. But, as 
already mentioned in art. 20, the tendency of this obliquity is to 
diminish the velocity }. There can be no doubt that the rapid 
diminution of » in the Table is to be ascribed chiefly to these 
causes ; though it is also worth mentioning that the property of 
the wave insisted upon by Weber, 2. e. that its velocity diminishes 
as its radius increases (see art. 2), would also tend to produce 
the effect observed. 

In the last twelve observations recorded in the Table, two jets 
(or a jet and a cylinder) were used, and the ripple of the vertical 
one was chiefly examined. As a consequence, the values of A 
vary far less, and 7°5 inches per second may be taken as a mean 
value of the velocity with which waves thus produced are pro- 
pagated. 


and their relation to the Velocities of Currents. 195 


30. As an interesting coincidence, it may be mentioned that 
Poisson, in his memoir before referred to*, gives the results of 
four experiments on the velocity of waves made by Biot. In 
this case the waves were produced by suddenly withdrawing from 
the water a partially immersed solid of revolution. The velocity 
of the wave was found to vary with the form of the body, and 
with the radius of its section at the water’s level. In one case, the 
body being an ellipsoid, and the radius in question equal to 2 of 
an inch, the velocity was about 54 inches per second ; in another 
case, where the body was a sphere and the radius of the section 
1+ inch, the velocity was 7:87 inches per second. The waves 
experimented upon by Weber had a far greater velocity: they 
were produced by allowing a column of liquid suspended in a 
tube to descend suddenly into the general mass ; and their velo- 
cities varied from 17 to 34: inches per second. 

31. In the foregoing experiments, the velocity > was deter- 
mined by causing an immersed cylinder to move with a given 
velocity in still water. A few experiments were next made with 
a view of ascertaining the value of X when a cylinder is simply 
immersed in a current of known velocity. According to art. 10, 
the sine of half the angle 20 between the branches of the ripple 
caused by immersing a cylinder in a current is inversely propor- 
tional to the velocity v of the current, and directly proportional 
to the velocity >) in question. In fact it was there shown that 


tan 6 
\/ ete ge ree (48) 

To determine the velocity v at any point of the surface of a 
current, a Wollaston’s current-meter was used. As is known, 
this instrument consists of a screw which is made to rotate by 
the force of the current. The mstrument must be immersed to 
the depth of two inches at least, in order that the screw may be 
completely covered by the water; and when so immersed, the 
rotation of the screw can be communicated at any instant to a 
divided wheel, and the communication as suddenly broken. The 
space described by the current during the interval between 
making and breaking this communication—an interval which 
can be measured by means of an ordinary watch with a seconds’ 
hand—is at once read off on the wheel, the instrument having 
been. previously carefully graduated. 

The angle 0 was determined by means of a simple instrument, 
to which we may Sive the name of ripple-meter. It consisted of a 
glass plate (BCD E, PI. IV. fig. 3) 5 inches square, through which, 
at a point A, a hole ;4,th of an inch in diameter was drilled in 

* Mémoires de l’Acad. Roy. des Sciences de VInstitut. Année 1816, 
vol, i, p. 173, a 


A=v sin 0=v 


196 T. A. Hirst on Ripoles, 


order to insert a solid cylinder of ivory about 1 inch long. Pass- 

ing through the centre of A and parallel to the sides of the glass, 
a fine line Aa, an inch long, was scratched on its surface with a 
diamond point ; and through the extremity a of this lme another, 
mn, was drawn perpendicular to the former, and graduated on 

each side from a into tenths of an inch. In using this ripple- 

meter, the plate of glass was held close and parallel to the sur- 

face of the current, so that the ivory pin, by becoming partially 

immersed, might cause a well-defined ripple, Ac, visible through 

the glass; the plate was then turned until A a bisected the angle 
between the branches of this ripple, when of course the ratio ~ 
gave at once the tangent of the required angle @. In this case, 
as in that of the rotating jet, a number of secondary ripples are 
also visible: after a little practice, however, and when the cur- 
rent was not too slow (the angle b A c too obtuse), it was not dif- 

ficult to estimate, approximately, the value of tan @ corresponding 
to the principal ripple. 

The following Table contains a few of the best results of many 
experiments made on streams. In it the first column gives the 
values of tan @ as read off on the ripple-meter ; the second column 
shows the corresponding values of the velocity v as indicated in 
feet per minute by the current-meter; and the third column 
contains the respective values of A, calculated according to the 
formula (43), in inches per second. 


tan @. Ve r. 

"993 44 6:2 
774 554 6:8 
705 59 6°8 
577 67 67 
*545 71 6-8 
*392 96 70 
388 105 76 


The observations, of which the above are some of the most 
trustworthy results, were made at different periods on streams 
in Hampshire and Gloucestershire. When we take into consi- 
deration the fact that a stream could rarely be found where the 
velocity at any one point remained constant, that in all @ases 
this velocity was determined with the curreng-meter at a point 
2 or 3 inches below the surface, and lastly, that the method of 
estimating the angle formed by the branches of the ripple can 
only lead to approximate results, the general agreement of the 
values of X with those obtained from the rotatory experiments is 
as close as could be expected. The results appear to indicate 


and their relation to the Velocities of Currents. 197 


that, with one and the same immersed body, the value of X varies 
somewhat with the veloclty of the current; but there can be 
little doubt that, under more favourable circumstances, this 
variation would be found to be far less than that indicated by 
the Table. 

In many cases no ripple whatever was produced by the immer- 
sion of the cylinder of ivory attached to the ripple-meter; and in 
all such cases the current-meter indicated a velocity less than 7 
inches per second; the quickest of such currents in fact had 
only a velocity of 25 feet per minute, or 5 inches per second. 
This corroborates the explanation given in art. 11, where it was 
foreseen that a body immersed in a current whose velocity was 
less than that of the wave, would allow the water to flow past 
it without visibly rippling its surface. 

The phenomenon represented by the second figure of art. 10, 
where the branches of the ripple turn their concavities towards 
each other, and which was shown to be a necessary consequence 
of Weber’s statement, that the velocity of the wave diminishes as 
its radius increases, was never observed. A slight concavity, 
however, might easily have escaped detection. 

32. The velocity \ being once determined for any ripple-meter, 
we can of course by its means determine, conversely, the velocity 
of a current, provided the latter exceeds the limit A. For this 
purpose I made use of a more convenient, though perhaps less 
accurate ripple-meter, with a description of which I will conclude 
the present paper. AB and A Cn fig. 4 represent two strips of 
brass, each 3 inches long, and made toturn round A. Theends 
B and C of these strips also turn on axes at the extremities of 
two brass stirrups B F and C G, through which passes a wooden 
scale D EK divided into twentieths of an inch. The cylinder, of 
the same dimensions as before, by whose immersion in the cur- 
rent ripples are produced, is pushed through an aperture in the 
joint A. The stirrup BF being fixed at the zero of the scale, is 
held there by a clamping screw F, and the stirrup C G is made 
to slide along the scale until the strips AB, AC are parallel 
to the branches of the ripple. This adjustment once made, the 
distance BC, as read off from the scale, being directly. propor- 
tional to 2 sin @, is clearly inversely proportional to the velocity 
of the current (arts. 10 and 31). 

The decrease in velocity from the centre to the banks of a 
stream is clearly indicated by this little instrument. As an illus- 
tration, I give the results of a few observations made on a mill 
stream at Brimscombe near Stroud. A wocden plank was thrown 
across the stream, which was about 7 feet 6 inches wide, and 
upon it, commencing at one bank, marks were made 9 inches 
apart. By kneeling on the plank, the ripple-meter was im- 


198 M.G. R. Dahlander on the Equilibrium of a Fluid Mass 


mersed in the current exactly under each mark. In explanation 
of the following Table, it is only necessary to add that the first 
column N shows the number of the mark on the plank; the 
second column D the distance, in inches, of that mark from the 
bank; the third column d the depth, in inches, of the stream 
at each mark; the fourth column the values proportional to 
2 sin 6 as read off on the ripple-meter ; and the last column v the 
velocities in feet per minute, of the current as calculated, on the 
hypothesis of \=7°5 inches per second, by formula (43) : 


2 sin 0. 


A 


0 
1 
2 
3 
a 
5 
6 
7 
8 
9 
0 


ft 


In conclusion it may be added that, if desired, more accurate 
ripple-meters might easily be devised, and by means of such the 
velocities of currents might be determined from the forms of their 
ripples with a degree of precision little, if at all, inferior to that 
possessed by the methods now in use. It is from a theoretical 
point of view, however, that the relation between waves and rip- 
ples, which we have endeavoured to establish, promises the great- 
est interest. For there can be little doubt that a skilful experi- 
menter, pursuing the subject in this direction, would greatly 
extend our present knowledge with respect to the changes in the 
velocity of a current at different points of its surface, and espe- 
cially with respect to the velocities with which different kinds of 
waves are propagated on the surface of still water, and to the 
variation of this velocity during the propagation of one and the 
same wave. 

January 15, 1861. 


XXX. On the Equilibrium of a Flud Mass revolving freely 
within a Hollow Spheroid about an Axis which is not its Axis 
of symmetry. By G. R. DAHLANDER*, 

+ we suppose a fluid ellipsoid to revolve alone about an axis 

which is not an axis of symmetry, we easily perceive that 
it cannot assume a position of equilibrium. It is, however, dif- 


* Communicated by the Author. 


revolving freely within a Hollow Spheroid. 199 


ferent if we suppose the fluid mass surrounded by a hollow sphe- 
roid, the two bounding surfaces of which are not concentric. 
The “fluid mass can then, under certain circumstances, actually 
assume a position of equilibrium, even when its axis of rotation 
is entirely external to the mass itself, and when it thus plays the 
part of an inner satellite to the hollow spheroid, with which it 
has a common motion of rotation. The existence of such sin- 
gular states of equilibrium we will now demonstrate. 

Suppose the hollow spheroid, together with the internal fluid 
mass, to revolve about the axis of the outer bounding surface of 
the spheroid, the axis of the inner bounding surface being parallel 
to the axis ofrotation. The fluid mass can then assume a position 
of equilibrium in which its figure is that of an ellipsoid of rota- 
tion, whose axis is parallel to the above-mentioned axes. 

Let the centre of the outer bounding surface be the origin of 
a system of rectangular coordinates, the axis of z comeiding with 
the axis of rotation. Let m, n, and p be the coordinates of the 
centre of the inner bounding surface, and a, 8, y those of the 
centre of the fluid mass. The equation of the surface of the fluid 
will then be | 

poe ae Sa A\2 z— 2 

al al mY 
If the component parts of the attraction parallel to the axes be 
denoted by X, Y, Z, we have 


= —Mz-+ M'(e¢—m)—M"(z—2), 
Y=—My+M'(y—n) —M"y—8), 
Z=—Nz+N!(z—p)—N"(¢—4). 


If therefore the angular velocity be denoted by w, we get for the 
differential equation of the surfaces de niveau, 


(—Mz+M'(2—m)— —M"(¢@—«) ) dae + (— My +M/(y—n) 
—M"(y—f) )dy+ (—Nz+N'(z a on )dze 
peoecda yey 0, . wes si apc sc atuarerge ea Recs) 

where M, M’, M”, N, N’, and N” are pee Ue Me or Bae 
Consequently by integration we get 
(—M+ M'—M"+w?)(a? + y?) +(—N+ N’—N")z? 
+ 2(—M'm + M"a)a + 2(—M'n+ M"B)y 
eI yee O.. ies ye oy te ep ee) 

As equations (1) and (3) are to be identical, we have the fol- 

lowing equations of condition :— 


200 M.G. BR. Dahlander on the Equilibrium of a Fluid Mass 


—Mm+M"a 7 
—2= ME Mp | 
—Mn+M"6 

cer —M+M!—M! 4 w?’ | (4) 
—Np+N'y 2? f 
= ae M! + yw? am | 
a —N+N!—N! | 
2 —M+M RM yur | 


From which we obtain 


—M'm 7 
*=M—M—u? | 
—M!n 5 
cow Te 
1 EN och | 
Y= N—N! J 


From the first two of equations (5) it follows that 
2.2 Batti 


The geometrical signification of this proportion is, that the 
centre of the fluid mass be in the plane which passes through 
the axis of rotation and the centre of the imner bounding surface 
of the spheroid. We find, moreover, that the position of this 
centre in a state of equilibrium with a fixed angular velocity is 
independent of the density of the fluid, supposing the form and 
density of the outer spheroid to be the same. Further, we find 
that if a fluid ellipsoid satisfy the conditions of equilibrium, all 
other similar ellipsoids of the same density will also satisfy these 
conditions. Generally, from equations (5), real finite positive or 
negative values of a, 6, y can be obtained if M, M’, N, N!, m, n, 
p, and ware given. But one or more of these values may become 
infinite under certain circumstances. This is the case when the 
two bounding surfaces of the solid spheroid are similar. Then 
M=WM! and fp N’, whence the value fcr y would be infinite, 
unless at the same time p=O0, m which case y can have any 
value whatever. 

The last of equations (4) constitutes the real equation of con- 
dition, which determines the relation which must subsist between 
the density, form, and angular velocity of the fluid mass, in order 
that equilibrium may be possible for the given values of M, M’, 
N, and N’. We shall separately consider the particular case when 


es 


revolving freely within a Hollow Spheroid. 201 


both the bounding surfaces of the surrounding spheroid are 
similar. 

From what has before been stated, itisevident that pbecomes=0. 

We can take for the axis of y a line which lies in the plane 
passing through the centre of the fluid mass and the centres of 
the bounding surfaces. In this case n=O and 6=0, and also 
M=M! and N=N!. We shall now examine if an oblate ellip- 
soid of rotation can satisfy the conditions of equilibrium. Sup- 


2 
posing zal +A?, and the density of the fluid = p, then the 


last of equations (4) will become 


“es 


~ $n wpt (~— arc tan dQ) 
2 


Say ae 
— 3 pf 13 (are tan rA— sa + wy? 


2 
If Soap b° taken =H, the equation of condition becomes 


arc tan X 


B= BOG? 43)—5 wee ramets) 


But this equation is just the same as that we obtained in de- 
termining the conditions of equilibrium of a freely revolving fluid 
mass whose particles attract each other. Thus we find that pre- 
cisely the same conditions of equilibrium are involved when the 
fluid is revolving in a hollow ellipsoid with similar but eccentric 
bounding surfaces, and when it is perfectly free. Toa given 
value for > there is therefore always a corresponding angular 
velocity; and to a given angular velocity there corresponds 
either no ellipsoid, or one ellipsoid, or two different ellipsoids, 


according as E is = 0:2246. 


Between the rotation of a fluid mass confined in a hollow sphe- 
roid and a mass which revolves freely, there is, however, this 
important difference, that in the former case the rotation does 
not take place about the axis of symmetry of the fluid unless 
both the bounding surfaces of the spheroid are concentric, but 
about a parallel axis which is the axis of symmetry of the outer 
bounding surface of the spheroid,—the distance between the 
two axes being 


CC ve ° . ° ° ° e ° (7) 
whence 


202 Dr. Woods’s Remarks on 


But M’m is the attraction which the hollow spheroid exerts on 

any point within it, and aw? is the centrifugal force at the axis of 

symmetry of the fluid mass. Whence we find that at the centre of 

the fluid mass the acting forces counterbalance each other, which 

might have been anticipated from a known theorem in mechanics. 
Gothenburgh, January 7, 1861. 


XXXI. Remarks on Sainte-Claire Deville’s Theory of Dissocia- 
tion. By Tuomas Woops, M.D. 


To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, Parsonstown, February 1861. 
N an interesting paper by Sainte-Claire Deville published in 
this Magazine last December, that author gives his views on 
the decomposition of bodies by heat. His idea of the relation 
and behaviour of the constituents forming a compound, towards 
each other, is, physically considered, the same as that which I 
published in this Journal so long ago as January 1852; that is, 
that they act merely as the molecules of a simple body, differing 
in nothing from the latter, except that, beimg diverse, they 
are capable of attaining a greater proximity among themselves, 
and so of causing a greater opposite movement in the particles 
of other bodies. A reference to my paper will show a diagram 
I gave in order to explain this similarity of constitution. The 
paper was therefore the more interesting to me as it brings for- 
ward fresh ideas on a thought-of subject. As Ido not, how- 
ever, yet agree with what is new in it, I beg to offer a few 
remarks on some of its contents; and first with respect to his 
theory of dissociation. 

Sainte-Claire Deville thinks that compound gases and vapours, 
when heated to a certain temperature, as steam at 1000°, undergo 
some such change as a solid body does when it liquefies; that 
the constituent particles being removed from each other, as well 
as the compound particles, the gas loses stability, and that heat 
is rendered latent thereby. This condition he calls the disso- 
ciated state. I do not find he offers any demonstration of this 
state, but that he only ascribes to its influence the production 
of some phenomena previously otherwise explained. For instance, 
to account for the heat of chemical combination, he takes for 
granted, as an example, that the molecules of chlorine and 
hydrogen are double, and, even at low temperatures, in the disso- 
ciated state; and then ascribes the heat produced by their union 
to the latent heat of this particular condition, which he imagines 
is given out when the gases by their combination get ito a state 
of stability. 

Now, if the heat produced in this instance is due to the change 


Sainte-Claire Deville’s Theory of Dissociation. 203 


of state of the chlorine, how does it happen that the same amount 
is produced when the chlorine combines, not being in the gaseous 
state at all ? If hydrochloric acid and zinc are placed together, the 
chlorine unites with the zinc, and the same quantity of heat is 
evolved as when the zinc burns in the gas ; and the same amount is 
absorbed by the decomposition as if both the constituents again 
attained the gaseous state; or if (to take an instance where no 
gas is present, either in combination or decomposition) zine 
causes a deposition of copper from chloride of copper, exactly the 
same heat is produced by the combination of the chlorine and 
copper, and exactly the same quantity is absorbed by the decom- 
position, as if the chlorine and copper acted as gases, changing 
their state as they combined or decomposed. Unless, therefore, 
it is imagined that when the chlorine leaves the copper or hy- 
drogen it becomes for a time a gas and enters into the disso- 
ciated state, absorbing heat, and again becomes solid, giving it 
up, I cannot see how the temperature is raised. But even 
granting that it does so the phenomenon could not be accounted 
for, because when zinc decomposes chloride of hydrogen or 
chloride of copper, more heat is produced by the combination 
than is lost by the decomposition: and such could not occur if it 
were due to the latent heat of dissociation ; for the heat would be 
taken in the first instance from the materials afterwards heated, 
and so an exchange only, and not an increase, would be effected. 
It might be said that the zinc influences the result ; that is, that 
metals have a certain amount of heat connected with them which 
is given out in combining, and that this being greater in some 
instances than in others, might account for the increase of tem- 
perature when the zinc displaces the hydrogen. But if all bodies 
have definite quantities of heat, as Sainte-Claire Deville seems to 
think, the same order ought to be observed in the amounts evolved 
by their combination with the gases. For instance, if an equi- 
valent of chlorine, by uniting with zine, copper, silver, &c., pro- 
duces heat, the quantity of which varies in the order in which 
the metals are named, oxygen ought to do the same, if the 
heat evolved in combination was previously connected with the 
combining bodies: but it is known that such is not the case. 
Chlorine produces more heat with silver than it does with copper, 
and oxygen the reverse. Instances of this kind might, of course, 
be multiplied ; and they prove, I think, that no fixed amount of 
heat, resulting either from change of condition, or from latent 
heat becoming evolved as it does in the condensation of vapour, 
can be connected with matter as part of its constitution, inde- 
pendent of alteration of the relation of particles. 

Deville, in fine, thinks that every body possesses a certain 
amount of heat, or condition in itself whereby heat can be pro- 


204 Dr. Woods’s Remarks on 


duced; and therefore one of the combining bodies might evolve 
from itself the heat of combination ; whereas the theory I pub- 
lished in 1852 divests particles of any influence except that of les- 
sening the distance between themselves, or of destroying volume, 
as they come together, and so that at least two particles of matter 
are essential to its production. In his theory each body en- 
gaged in chemical action is said to give out heat by change of 
condition; in mine the volume only, or distance between the 
constituent particles, is supposed to bealtered. I still think the 
latter theory is the more reasonable, and more in accordance with 
our present scientific knowledge. 

M. Deville seems to reject this latter theory, because the 
contraction arising in chemical combination is not equivalent to 
the expansion or heat produced; and he calculates the contrac- 
tion when oxygen and hydrogen unite, to show that it is not of 
the same value or extent as the increase of volume given to other 
bodies as the accompanying or opposite movement. He also 
shows how chlorine and hydrogen unite without contraction at all; 
yet that expansion in other bodies or rise of temperature is the 
result. This apparent argument against the theory, however, dis- 
appears when it is considered that the particles whose combination 
evolves the heat are not the same as those which determine the 
volume. When oxygen and hydrogen unite, these elemental 
gases themselves, by coming together, cause other bodies to 
expand, and so are said to give rise to heat; but the volume 
attained by the compound they produce is determined by the 
distance between, not the oxygen and hydrogen, but between 
the particles of the water that results. In order, therefore, to 
calculate the contraction which causes the heat, we should know 
what takes place between the constituents of the compound: 
the bulk or volume of the compound itself tells nothing. 

An argument, therefore, for some necessary change of state 
in combining bodies as the cause of heat, drawn from the appa- 
rent want of coincidence between the contraction on the one 
hand and the heat or expansion on the other, is valueless. 
Besides, I have shown (Phil. Mag., January 1852) that the co- 
efficient of expansion increasing with the dilatation, the nearer 
particles are to each other, the greater 1s the effect they produce 
by a given contraction in causing expansion in other bodies; so 
that it is not only necessary to know the amount of contraction 
amongst the constituents of a compound at the time they com- 
bine, but also the distance they ultimately arrive at with respect 
to each other, before we can calculate the amount of heat they 
ought to produce *. 


* In the last edition of Grove’s ‘Correlation of the Physical Forces,’ 
when speaking of the theory I brought forward in 1852, to account for the 


Sainte-Claire Deville’s Theory of Dissociation. 205 


But this state of dissociation is altogether founded on gra- 
tuitous assumptions. The ground from which it springs is this : 
that as compound bodies when heated expand, the constituents 
must recede from each other as well as the compound particles. 
But this proposition has yet to be proved. I believe many facts 
favour an opposite conclusion: for instance, not to speak of the 
manner in which solids and fluids, when szmple bodies, expand, 
being somewhat similar to the same process in compounds, Gay- 
Lussac’s law with respect to the equal expansion of all gases and 
vapours for equal increments of heat, would surely show that 
the constituents of a compound do not recede from each other 
in expanding. Hydrogen, or any other simple gas, and vapour 
of ether, or other compound gas, expand exactly according to 
the same law. Could this occur with the simple particles of 
hydrogen to the same extent precisely as with compound mole- 
cules of ether, where, instead of two, we have ten elementary 
atoms to divide the distance and moving force between them? 
The resistance to expansion of a gas by heat seems to be the 
weight of the atmosphere; and consequently in all gases, the 
same resistance being present, the same expansion is attained by 
a certain increase of temperature. Now in a simple gas the 
weight is the only resistance ; whereas, if Deville’s theory is cor- 
rect, there is in compound gases not only the weight, but the 
affinity of the constituents to be partly overcome; and yet the 
same expansion is noticed for the same increase of temperature 
in both. But this would be impossible, except we imagine that 
the separation of these constituents does not absorb heat, which 
we know it does. 

It seems to me that this fact alone, of the similar and equal 
expansion of simple and compound gases by heat, shows that 
no motion takes place in one which does not occur in the other ; 
therefore that no expansion of the particles themselves, that is, 
that no separation of the simple constituents of the compound 
molecule is produced by raising its temperature, and con- 
sequently that this state of dissociation does not exist. 

A consideration of other portions of the paper would lead me 
too far for the present, but I may recur to it if you think the 
subject sufficiently teresting for your Magazine. 

Your obedient Servant, 


THOMAS Woops, M. D. 


heat of chemical combination, he seems to think it an objection (page 177) 
that the whole expansion which would bean equivalent to the contraction 
of the combining particles is not seen in the compound produced; but 
surely, as this volume would be the temperature evolved by the combina- 
tion, it cannot remain longer than a moment in the compound; it must 
be dispersed to surrounding bodies. 


[ 206 ] 


XXXII. On the Temperature Correction of Siphon Barometers. By 
Wixi1am Swan, Professor of Natural Philosophy in the United 
College of St. Salvator and St. Leonard, St. Andrews*. 


‘a the ‘ Atheneum?’ of the 5th of January, Admiral FitzRoy, 

writing on the subject of the temperature correction of 
siphon barometers, invites attention to an experiment recently 
made by Mr. Negretti. A siphon barometer was heated to 
about 110° from some lower temperature, when it was found 
that, although the mercury rose in the long or vacuum leg of the 
siphon, it did not rise, but seemed to be depressed, in the short, 
or open leg. The late Mr. Robert Bryson of Edinburgh invented 
a self-registering barometer, which is described in the Transac- 
tions of the Royal Society of Edinburgh for 1844+. In that 
instrument, variations in the pressure of the atmosphere were 
indicated by means of a float resting on the surface of the mer- 
cury in the open leg of a siphon tube, precisely as in the ordi- 
nary wheel barometer. Mr. Bryson was anxious to ascertain 
whether his instrument required any notable correction for tem- 
perature; and to settle that point experimentally, a Bunten’s 
barometer was heated to a high temperature. In Bunten’s baro- 
meter the effective height of the mercurial column is ascertained 
by reading two verniers; one indicating the level of the upper, 
and the other that of the lower surface of the mercury in a siphon 
tube. Mr. Alexander Bryson, who made the experiment, found 
that the reading of the upper vernier rapidly changed with increase 
of temperature, while the reading of the lower vernier remained ~ 
sensibly constant,—proving that the level of the mercury in the 
open leg of the siphon was very little affected by change of tem- 
perature. Mr. Bryson having communicated to me the result 
of his experiment, I immediately gave him an investigation of 
the temperature corrections of the two surfaces of the mercury 
in the siphon barometer, of which the following is substantially 
a reproduction. As Admiral FitzRoy has expressed some doubts 
regarding the results of observations of siphon barometers “as 
hitherto obtained,” I have deemed it desirable to make the fol- 
lowing investigation perfectly general, so as to include every form 
of tube; and in the first instance I have avoided employing any 
formula which is only approximately true. 

Let h,, ho be the vertical distances of the upper and lower sur- 
faces of the mercury in a siphon barometer, reckoned from any 


* Communicated by the Author; the results of the investigation having 
been communicated, on the 2nd of February, to the Literary and Philo- 
sophical Society of St. Andrews. 

T Vol. xv. p. 503. 


On the Temperature Correction of Siphon Barometers. 207 


horizontal plane below the instrument, and / the barometric 
pressure, all at a temperature of ¢ degrees Centigrade. When 
the temperature rises to ¢+ A¢ degrees, let the above quantities 


become 
h,+Ah,, hotAh,, h+Ah; 


then, if m=cubic expansion of mercury for one degree Centigrade, 


Ah=mhAt. 

And since 
h=h,—h, 
and 
h+ Miz (fy + Ady) — (hp + Als), 
we have 
Ah, —Ah,=Ah=mhAt. 

Now if 


e = volume of mercury in the barometer; 

a = area of the bore of the tube at upper surface of mercury; 

6 = area of the bore of the tube at lower surface; all at ¢ 
degrees ; 

9,= the superficial, and g, = the cubic dilatation of glass ; 


it will be easily seen that, at the temperature ¢+ A? degrees, the 
capacity of that part of the tube which was occupied by the 
mercury at ¢ degrees will become c(1-+9,At); while the capacities 
*of the portions of the tube at the ends of the former mercurial 
column, which are now filled by the expanded mercury, and 
whose lengths are Ah,, Ah,, will be 


a(l+g,Az)Ah,, 65(1+9,Az)Ah,. 
The whole volume of the mercury will therefore be 
(aAh, + bAA,)(1+9, At) +¢e(1+9,Az). 
But the volume of the expanded mercury must also be 
e(1+mAz) ;sx 
whence 
(aAh, + bAA,) (1 +9,At) =c(m—g_) At. 
This equation, along with 
Ah, —Ah,=mhAt, 
Ane 4e(m—go) +bmh(1 +9,Az)t = 
(a+ 6)(1 + 9,42) 
Difige {e(m—g.) —amh(1 +9,A?) pAt 
(a+6)(1-+ 9,42) 


gives 


208 Prof. Swan on the Temperature Correction 


Now since m is greater than g,, the coefficient of c in the above 
values of Ah,, Ah, is positive; and the coefficient of h is also 
positive for all possible values of At—g, being a very small quan- 
tity. It is therefore obvious that Af, can never vanish, but 
that Ah, may be positive, negative, or zero, according to the 
values which may be assigned to a, c,andh. The depression, 
by heat, of the mercury in the open leg of the siphon, or in 
other words, the negative value of AA,, observed by Mr. Negretti, 
and the value zero of the same quantity, observed by Mr. Alex- 
ander Bryson, are therefore both perfectly accounted for. 

It also appears, and this seems to be of practical importance, 
that we can altogether get rid of the temperature correction for 
the lower surface of the mercury, for any one given atmospheric 
pressure, by properly adjusting the value of c, and that thus we 
shall be able to make the temperature corrections for all other 
pressures exceedingly small. 

For this purpose it will be convenient to simplify the expres- 
sions for Ah,, Ah, by rejecting small terms. We then obtain 


c(m—go) +bmh 


Ah,= oat 


At, 
Ai nga) One od 5 
and Ah, will yanish when 
__ amh 
Jo 
A particular case will best illustrate this. Suppose that the 


siphon consists of two tubes of a uniform bore a, connected at 


the bottom by a narrow channel whose capacity may be neglected. 
We have then 


e=a(h+2l) ; 
Ah, = }(m—go)l + (m— 59o)h} At; 
Ahy= }(m—go)l—FGqh} At ; 
and when Ah,=0, 
[ifs Sens 
2(m—Jo) 


We must now select some particular value of h for which the 
temperature correction is to vanish; and we shall have, upon the 
whole, the smallest temperature corrections for extreme values of 
h if we make the temperature correction disappear for its mean 
value. Assuming then A=29°5 inches as sufliciently near the 


of Siphon Barometers. 209 


mean atmospheric pressure, and adopting for the coefficients of 
cubic expansion of mercury and glass for one degree Centigrade 
the values 
m='0001803, g,='0000258, 
we obtain 
[= 2°463 inches. 


This indicates a perfectly practicable arrangement. To ren- 
der the temperature correction insensible at mean atmospheric 
pressures when the siphon tube has a uniform bore, we must 
put so much mercury into the tube, that, when the pressure is 
29°5 inches, there shall be a column of about 2°5 inches of mer- 
cury in the open leg. The temperature corrections throughout 
all ordinary fluctuations of atmospheric pressure for the lower 
surface of the mercury will then be extremely small, as will be 
seen by the following Table :— 


Column of mercury Displacement of | Displacement of 


Atmospheric in open leg of ~ | Upper surface for a| lower surface of 
pressure siphon difference of tempe-| mercury for differ- 
(h). rature Az in Centi-| enceof temp. Aé 
grade degrees. in Cent. degrees. 
31 inches. 1-713 inch. -+'00545 Az —°00014Aé 
295 ,, 2-463 ,, +-00531 At -00000A¢ 
Per ser, 3-213 ,, -L-00518A¢ +-00014A¢ 


It may be well to observe that the numbers in the last column 
of the Table show that if the barometer to which they refer 
were heated, as in the experiments already described, and if the 
atmospheric pressure were much greater than 29°5 inches, we 
should have the result obtained by M. Negretti—a depression 
of the mercury in the short leg of the siphon; while if the pres- 
sure were nearly 29:5, there would be no sensible change of 
level, as observed by Mr. Bryson. 

I need scarcely remind the reader, in conclusion, that the for- 
mule I have investigated are intended to be employed when only 
the upper or only the lower surface of the mercury is observed. 
When Joth surfaces are observed, as in the Bunten barometer, 
we have simply to apply the ordinary and well-understood cor- 
rection, due to the expansion of mercury by heat. 


United College, St. Andrews, 
February 16, 1861. 


Phil. Mag, S. 4. Vol. 21, No, 189. March 1861 P 


[A2TO.:3 


XXXIII. Note on Mr. Jerrard’s Researches on the Equation of 
the Fifth Order. By A. Cayuny, Esq.* 


» | elena of the same set of quantities which are, by 

any substitution whatever, simultaneously altered or si- 
multaneously unaltered, may be called homotypical. Thus all 
symmetric functions of the same set of quantities are homo- 
typical: (v7+y—z—w)? and wy+zw are homotypical, &e. 

It is one of the most beautiful of Lagrange’s discoveries 
the theory of equations, that, given the value of any function of 
the roots, the value of any homotypical function may be rationally 
determined +; in other words, that any homotypical function what- 
ever is a rational function of the coefficients of the equation and 
of the given function of the roots. 

The researches of Mr. Jerrard are contained in his work, ‘‘ An 
Essay on the Resolution of Equations,’ London, Taylor and 
Francis, 1859. The solution of an equation of the fifth order is 
made to depend on an equation of the sixth orderin W; and he 
conceives that he has shown that one of the roots of this equa- 
tion is a rational function of another root: “The equation for 
W will therefore belong to a class of equations of the sixth 
degree, the resolution of which can, as Abel has shown, be 
effected by means of equations of the second and third degrees ; 
whence I infer the possibility of solving any proposed equation 
of the fifth degree by a finite combination of radicals and rational 
functions.” 

The above property of rational expressibility, if true for W, 
will be true for any function homotypicalwith W ; and conversely. 
I proceed. to inquire into the form of the function W. 

The function W is derived from the function P, which denotes 
any one of the quantities p,, po, p3. And if x, Xo, Ly, L4, Lz are 
the roots of the given equation of the fifth order, andif a, 8, y, 6, € 
represent in an undetermined or arbitrary order of succession 
the five indices 1, 2, 3, 4, 5, and if e denote an imaginary fifth 
root of unity (I conform myself to Mr. Jerrard’s notation), then 
Pv Pa Ps; and the other auxiliary quantities ¢, u, are obtained from 
the system of equations— 


* Communicated by the Author. 

t+ The @ priori demonstration shows the eases of failure. Suppose that 
the roots of a biquadratic equation are 1, 3, 5,9; then, givena+6=8, we 
know that either a=3, b=5, or else a=5, b=3, and in either case ad=15; 
hence in the present case (which represents the general case), a+b being 
known, the homotypical function ad is rationally determined. But if the roots 
are 1, 3, 5, 7 (where 1+7=3+5), then, given a+)=8, this is satisfied by 


3 aes 
G =). or by G = i and the conclusion is ad=15 or 7; so that here 
ab is determined, not as before, rationally, but by a quadratic equation. 


On the Equation of the Fifth Order. 211 
Vet P\LatPo@atps= t+ uy, 
apt peat pote t+ps= b+eu, 
@y + Pt, + poly + py=Ct+ Pu, 
25 + py X5 + po%s+pz= 3¢+ vu, 
Het p Let pote tpg t+ w. 


If from these equations we seek for the values of p,, Po Ps t, Uy 
we have 


By: Jo? 75:—t:—u=ll,: 4:1: T,: Wy: ly 
where IJ,, II,,.. denote the determinants formed out of the 
matrix 


cc mec ame Aiea ee 
v Bp x ee LBs Des Dy 
ae a Bo hr akgco ees 3 
& 3 ? U5, cS Wea Re uP 
& 2 Cpe Bagi bcd Gea 


2.e., denoting the columns of this matrix by 1, 2, 3, 4, 5, 6, we 
have 11,=23456, T,= —34561, H,=45612, &e. In par- 
ticular, the value of II, is 


— eer @udae bs 2, Loge 
aT tine OE a 
PISA NG 
x 33 a; 1, e 2 


Ue Ras ie AA 
And developing, and putting for shortness {a8} =x,49(%.—4p); 
&c., we have 
Tl, =( {a8} + {By} + fyot + {det + feat )\(—26+-—8 +204) 
+ (faryh + {yet + feBt + 180} + {Sat )(+e4+22—23—204), 

And this is also the form of the other determinants, the only 
difference being as to the meaning of the symbol {a6}, which, 
however, in each case denotes a function suchthat {apt =— ; Ba} : 
Writing for greater shortness, 

{oBryde} = faB} + {Bry} + {y8} + {oe} + feat, 
and in like manner : 

ee dens ca taeies Wict mune is mat lane Bas cs 
I], is an unsymmetric linear function (without constant term) of 

| P2 


212 Mr. A.Cayley’s Note on Mr. Jerrard’s Researches 


{aPryde}, Sauye8o' ; or, what is all that is material, it is an un- 
symmetric function, containing only odd powers, of {aByéde}, 
fayeBo', 
If for aByde 
we substitute any one of the five arrangements 
aBy de, 
Bydea, 
y dea, 
o ea 6 y, 
ea By 6, 
then {aByde} and {aye8o} will in each case remain unaltered. 
But if we substitute any one of the five arrangements 


aedy B, 

E4098 we, 

oy fae, 

yBae o, 

Baedy, 
then in each case {aPrydet and {ayeB8o} will be changed into 
— SaBydel and — }ayeBo} respectively. Hence I, remains un- 
altered by any one of the first five substitutions ; and it is changed 


into —II, by any one of the second five substitutions. And the 
like being the case as regards II,, &c., 1t follows that the quotient 


a or say P, remains unaltered by any one of the ten substitu- 


tions. Now the 120 permutations of «, 8, y, 6, « can be ob- 
tained as follows, viz. by forming the 12 different pentagons 
which can be formed with @, 8, y, 6, € (treated as five points), 
and reading each of them off in either direction from any angle. 
To each of the 12 pentagons there corresponds a distinct value 
of P, but such value is not altered by the different modes of 
reading off the pentagon ; P is consequently a 12-valued function. 

But there is a more simple form of the analytical expression 
of such a 12-valued function ; in fact, if [a@@yde] be any func- 
tion which is not altered by any one of the above ten substitu- 
tions—if, for instance, [#8] is a symmetrical function of x, @g, 


and 
[«Byde] = [a8] + [By] + [8] + [Se] + [ex], 
[eye8d] = [ay] + [ye] + [8] + [80] + [de], 


then any unsymmetrical function of [aSyde] and [ayeBd] will 
be a 12-valued function homotypical with P. 


an 


on the Equation of the Fifth Order. 213 


Mr. Jerrard’s function W is the sum of two values of his 
function P ; the substitution by which the second is derived from 
the first can only be that which interchanges the two functions 
[«Byde] and [aye8o] ; and hence any symmetrical function of 
[«Pyde] and [wyeGd] is afunction homotypical with Mr. Jerrard’s 
W; such symmetric function is in fact a 6-valued function only. 
Indeed it is easy to see that the twelve pentagons correspond 
together in pairs, either pentagon of a pair being derived from 
the other one by séed/ation, and the six values of the function in 
question corresponding to the six pairs of pentagons respectively. 

Writing with Mr. Cockle and Mr. Harley, 

T = LyXgt Lply + XX3 t+ XjX,+L Ag 
= 2,@y + LyTe+ LM gt Lets tUploy 
then (r+7' is a symmetrical function of all the roots, and it 
must be excluded ; but) (tT—7')? or 77’ are each of them 6-valued 
functions of the form in question, and either of these functions 


is linearly connected with the Resolvent Product. In Lagrange’s 
general theory of the solution of equations, if 

ft=2, +l, 4+ Cr+ Px, + 25, 
then the ee of the equation the roots whereof are 
( ft), (fe?)®, (fe*)?, (fr), and in particular the last coefficient 
(fifi? Joan )5, are peta by an equation of the sixth degree ; 
and this last coefficient is a perfect fifth power, and its fifth root, 
or fi fi*fi* fr’, is the function just referred to as the Resolvent 
Product. 

The conclusion from the foregoing remarks is that 2f the equa- 
tion for W has the above property of the rational expressibility of 
its roots, the equation of the sixth order resulting from Lagrange’s 
general theory has the same property. 


T 


I take the opportunity of adding a simple remark on cubic equa- 
tions. The principle which fur nishes what in a foregoing foot- 
note is called the @ priort demonstration of Lagrange’s theorem is 
that an equation need never contain extrancous roots ; a quantity 
which has only one value will, if the investigation is properly 
conducted, be determined in the first instance “by a linear equa- 
tion ; one ‘which has two values by a quadratic equation, and so 
on ; Pie is always enough, and not more than enough, to 
determine what is required. 

Take Cardan’s solution of the cubic equation #?+qgxe—r=0, 
we have az=a+0, and thence 3ab=—gq, a?+0°=r; and to 
obtain the solution we write 


. a= — 5, a+b=r, 


214 Prof. Davy on some further applications of 


But these two equations are not enough to precisely determine a, 
they lead to the 9-valued function 


Py 2 3 A os. 
? 7 g 7 af eo a 
2 — 4.4.4 his hating § 
VJ; +a/ 4. OF ate ae 4 * 97 
in order to precisely determine x, it is (as everybody knows) 


necessary to use the original equation ad= — * But seek for 


the solution as follows; viz. write e=ab(a+5), which gives 
8a°b?=—g, a®b?(a?+b*) =r, 

or what is the same thing, 
As ae ~3, Plat | ee hs sual 


these equations give v=ab(a+b), where 


3 a hoe ere 
a= ene Orie d = pan) — n/a son ee or f 
ay‘ ate ? 4g? * 3’ 
which is a 3-valued function only, ad in this case a not given. 


2 Stone Buildings, W.C., 
January 28, 186]. 


XXXIV. Onsome further applications of the Ferrocyande of Po- 
tassium in Chemical Analysis. By KymMunpd W. Davy, A.B., 
M.B., M.RILA., Professor of Agriculture and Agricultural 
Chemistry to the Royal Dublin Society*. 


| HAVE recently been engaged in making some experiments 

on the ferrocyanide of potassium or yellow prussiate of 
potash, with a view to extend its applications in chemical ana- 
lysis ; for though this important salt has already been applied to 
a number of useful purposes in analytical research, still my ex- 
periments have shown me that its use might be advantageously 
extended, particularly as a reagent in volumetric analysis, a form 
of analysis which has of late come into very general adoption, 
especially for technical purposes, on account of the great quick- 
ness and at the same time accuracy with which different sub- 
stances may by its means be determined. The principles upon 
which volumetric analysis depend are so well known, that I 
need not refer to them; and though it possesses so many ad- 
vantages over the older gravimetrical method, in which the dif- 
ferent substances are determined by weight instead of by volume, 
it yet has this drawback, that the preparation of the necessary 
standard solutions often takes considerable time, first, in order 


* Part of a paper read before the Royal Dublin Society, December 17, 
1860 ; and communicated by the Author, 


the Ferrocyanide of Potassium in Chemical Analysis. 215° 


to obtain the substance to be used for this purpose in a suf- 
ficiently pure and dry state, and secondly, to form a solution 
of it the exact strength of which may be known: for though 
it may appear avery simple operation to dissolve a known weight 
of a certain substance in a given bulk of water or other solvent, 
yet, when this has to be done with such great precision as is 
necessary in these cases, it is a tedious and troublesome opera- 
tion, and any inaccuracy in the graduation ofthe standard solu- 
tion will render all determinations made with it more or less 
inaccurate. It is obvious, therefore, that it would be most de- 
sirable that the substances which are intended to be used as re- 
agents in volumetric analysis should be easily obtained in a pure 
state, and that where considerable time and trouble have been 
expended in graduating solutions of those substances, they should 
not be liable to undergo changes whereby their strength would 
be more or less altered, but that when standard solutions have 
once been made, they might be kept and used for a great num- 
ber of determinations. 

The ferrocyanide of potassium fulfils both those conditions ; 
for it is in general met with in commerce almost chemically 
pure, and in a state in which it can at once be employed asa 
volumetric reagent ; andif at any time it should happen to occur 
not quite so pure, it can readily be purified by recrystallization ; 
and in addition to these important considerations, its solution is 
not prone to change, especially if it be not left exposed to the 
action of the light. In this latter respect it has a decided 
advantage over several of our most useful volumetric reagents, 
viz. the permanganate of potash, the protosalts of iron, sul- 
phurous acid, &c., which, from their bemg so prone to undergo 
spontaneous decomposition, must be either freshly prepared, 
or the strength of their solutions accurately ascertained every 
time they are used, if a day or so has elapsed between each de- 
termination. 

The employment of the ferrocyanide of potassium as a volu- 
metric reagent depends on the following circumstances : viz., that 
it is readily converted into the ferrideyanide of potassium (red 
prussiate of potash) under different circumstances, and that the 
point where the whole of the former salt has been changed into 
the latter may easily be known, either by the use of a diluted 
solution of a persalt of iron (which gives with a drop of the mix- 
ture a blue or green coloration as long as any of the ferrocyanide 
remains unchanged) or by some other simple indication. Thus, 
for example, when chlorine is brought in contact with the ferro- 
cyanide of potassium, this change, as is well known, takes place, 
which is expressed by the following symbols :— 


2 (K2, Fe Cy’) + Cl=(K? Fe? Cy®) +K Cl. 


216 _ Prof. Davy on some further applications of 


The same occurs, as far as the conversion of the ferrocyanide 
into ferrideyanide, when an acidified solution of the former salt 
is brought in contact with a solution of the permanganate of 
potash, which is instantly decolorized by the reducing action of 
the ferrocyanide of potassium, which is thereby converted into 
the ferridcyanide, and this decoloration of the permanganate 
continues as long as any of the ferrocyanide remains in the mix- 
ture. 

Again, if a solution of the ferrocyanide of potassium, acidified 
strongly with either hydrochloric or suiphuric acid, be brought 
in contact with a solution of the bichromate of potash, the same 
change of the ferrocyanide into the ferridcyanide immediately 
takes place. 

The first reaction has been long known, and 1s the means em- 
ployed at present for obtaining the ferridcyanide or red prussiate 
of potash for manufacturing and other purposes; the second re- 
action has been more recently discovered; but I am not aware 
that the third, in the case of the bichromate, is generally known, 
or that the changes which occur in the reaction have been pre- 
viously studied. 

From experiments which I made, it would appear that when a 
solution of ferrocyanide of potassium, acidified with hydrochloric 
acid, was mixed with one of the bichromate of potash, the follow- 
ing reaction was produced, viz. 6(K? Fe Cy?) + KO, 2 Cr O® 
+7HC]=3(K? Fe? Cy®) + 4 KC1+ Cr? C+ 7HO; for, amongst 
other facts, I may observe that when I mixed together solutions 
of the two salts in the proportions corresponding to 6 equiva- 
lents of the ferrocyanide of potassium to 1 of the bichromate 
of potash (as indicated in the above formula), acidifying the 
mixture with hydrochloric acid, I found that the whole of the 
ferrocyanide was converted into the ferrideyanide, and that any 
quantity less than that proportion of the bichromate of potash 
left more or less of the ferrocyanide unchanged. The same 
results followed the use of sulphuric acid; and it appears that a 
similar reaction occurs with this acid as with hydrochloric acid, 
with the exception that in this case the 4 equivalents of chloride 
of potassium and the 1 equivalent of sesquichloride of chromium 
are replaced by 4 equivalents of sulphate of potash and 1 of the 
sesquisulphate of chromium. 

The proportion of either acid used, provided there is enough 
to strongly acidify the mixture, does not appear to affect the re- 
action; for I obtaimed precisely the same results where a very 
large amount of acid was employed as where the quantity neces- 
sary Only to strongly acidify the mixture had been added. 

On these three reactions which I have noticed, may be based 
the means of employing the ferrocyanide of potassium in several 


the Ferrocyanide of Potassium in Chemical Analysis. 217 


useful determinations, the first, and one of the most important, 
of which is the ascertaining the amount of available chlorine in the 
chloride of lime or bleaching powder, which is a matter of much 
importance in many of the chemical arts, but particularly in 
bleaching ; for not only does the commercial value of this sub- 
stance depend on the quantity of available chlorine that it con- 
tains, which is subject to great variation from exposure to the 
air and other causes, but likewise it is of the greatest importance 
that the bleacher should readily be able to determine from time 
to time the strength of the bleaching liquor which he employs: 
for if it be too strong, he knows that the fabric which he bleaches 
will be injured; and if too weak, it will not be sufficiently bleached, 
and the process must be repeated, which mcurs much additional 
expenditure of time. 

Various methods have from time to time been proposed for the 
determination of the value of chloride of lime; but the greater 
number of them, from the trouble required to make the test-so- 
lutions, and their not keeping when made, as well as the skill re- 
quired in their use, render them inapplicable for general purposes. 

I shall therefore merely refer to the two methods which are 
chiefly used at present to determine the value of this important 
substance. The first is Gay-Lussac’s, in which the amount of 
chlorine is ascertained by seeing how much chloride of lime is 
necessary to convert a given quantity of arsenious into arsenic 
acid ; the second is Otto’s, in which protosulphate of iron is sub- 
stituted for arsenious acid, and the determination of chlorine is 
made by seeing how much of the bleaching powder is required 
to change a given weight of the protosulphate of iron into a per- 
salt of that metal: these processes are so well known that I need 
not describe them. 

In both these methods I find that more or less chlorine is 
always lost, which, however, may be reduced toa minute quantity 
by very carefully adding the solution of chloride of lime either 
to that of arsenious acid, or of protosalt of iron ; but in ordinary 
hands they (especially the latter process) will yield results in 
which too small a proportion of chlorine will be indicated, from 
the loss of that substance which will invariably take place. 

The ferrocyanide of potassium answers admirably for the 
estimation of available chlorine in the chloride of lime, when used 
in the manner I shall presently explain, and according to my 
experiments will give in ordinary hands far more accurate results 
than either Gay-Lussac’s or Otto’s method. I am aware, in- 
deed, that this salt was proposed by Mr. Mercer some years ago 
for this purpose; but the way which he recommended it to be 
used (which consisted in dissolving a certain weight of the ferro- 
cyanide in water, acidifying it, and then adding the solution of 


218 Prof. Davy on some further applications of 


bleaching powder from a burette till all the ferrocyanide was con- 
verted into ferridcyanide) 1s, I find, not a good manner of employ- 
ing the ferrocyanide in this estimation, and, like the other 
methods, will lead to aloss of chlorine; for when the solution of 
chloride of lime is added to the acidified ferrocyanide, a portion 
of the chlorine is. separated, especially if the bleaching liquor be 
added too quickly, or is not greatly diluted. But the way I pro- 
pose of using the ferrocyanide of potassium in this important 
valuation, is to mix together a certain quantity of a standard solu- 
tion of ferrocyanide with a given amount of a graduated solution 
of the chloride of lime, using more of the former salt than the 
latter can convert into ferridcyanide ; then adding hydrochloric 
acid to dissolve the precipitate formed and render the mixture 
strongly acid, and finally ascertain, by means of a standard solu- 
tion of bichromate of potash, how much of the ferrocyanide_re- 
mained unconverted into the ferridcyanide by the action of the 
chlorine of the chloride of lime,—which is effected by adding 
slowly from a graduated burette the standard solution of bichro- 
mate till a minute drop taken from the well-stirred mixture by 
means of a glass rod, ceases to give, with a small drop of a very 
dilute solution of perchloride of iron placed on a white plate, a 
blue or greenish colour, but produces instead a yellowish brown*. 
When this latter effect is observed, it indicates that all the ferro- 
cyanide has been converted into ferridcyanide; and as 147-59 
(one equivalent) of bichromate of potash is capable of converting 
1267°32 (six equivalents) of crystallized ferrocyanide of potassium 
into ferridcyanide, and as 422°44 (two equivalents) of the ferro- 
cyanide are converted into the same substance by 35°5 (one 
equivalent) of chlorine, as is seen by the formule already given, 
knowing the amount of chloride of lime employed, we have all 
the data necessary to calculate the per-centage of chlorine. 
Having made two standard solutions, the first contaiming 
21:122 grammes of ferrocyanide of potassium in a litre of the 
solution, and the second 14°759 grammes of bichromate of pot- 
ash in the same quantity of solution (weights which are to each 
other as their atomic equivalents), | made several estimations of 
chloride of lime with them, adopting the method I have just 
described, and found that it gave the most consistent results, and 
which agreed very closely with those obtained by Gay-Lussac’s 
and Otto’s methods when the latter were performed with the great- 
est care,—the only difference being that the results obtained by 
* The yellowish-brown coloration which is at first produced when 
enough of the bichromate has been added, quickly changes to a greenish 
colour by some secondary reactions which take place when the persalt of 
iron is left in contact with the mixture. but this does not interfere with 
the test ; for it is the first effect which is produced which indicates the com- 
pletion of the reaction, and not the after changes which may result. 


the Ferrocyanide of Potassium in Chemical Analysis. 219 


my method indicated a few hundredths of a part more of chlorine 
than either of those methods did, which may be accounted for 
by the unavoidable loss of a minute quantity of chlorine which 
takes place in those processes. 

In order to simplify the process, and render the calculation 
as short as possible, | would recommend for commercial valua- 
tions the following way of carrying out this principle :— 
Haying obtained a flat-bottom flask or bottle which will con- 
tain 10,000 grains of distilled water when filled up to a certain 
mark in the neck, make two standard solutions, the first by 
placing in the flask or bottle 1190 (or exactly 1189°97*) grains 
of the purest crystallized ferrocyanide of potassium (yellow 
prussiate of potash) reduced to powder, adding distilled water 
to dissolve the salt, and when this is effected, fillmg up with 
water to the mark; and having mixed the solution thoroughly, 
place it in a well-stoppered bottle. The second standard solution 
is made in the same manner, substituting for the ferrocyanide 
138°6 (or exactly 138°58) grains of bichromate of potash which 
has been purified by recrystallization and fused in a crucible at 
as low a heat as possible. Both these solutions will keep un- 
changed, and will answer for a number of determinations if they 
are preserved in well-stoppered bottles, and the ferrocyanide 
solution be kept, when not in use, excluded from. the light. 
Get a burette or alkalimeter capable of holding or delivermg 
1000 grains of distilled water, and divided into 100 equal 
divisions ; also two small bottles, one capable of delivering 1000 
grains, and the other 500 grains of distilled water when filled 
up to a certain mark on the neck of eacht, which may both be 
readily made by fillmg them with water, emptying them, and 
after they have drained for a minute or two, weighing into each 
the above weights of distilled water ; or, what will be sufficiently 
accurate for most purposes, pour from the burette into one 100 
divisions of distilled water, and into the other 50, and mark 
with a file where the fluid stands im the neck of each bottle. 
Having these all ready, take an average specimen of chloride of 
lime, and weigh out 100 grains of it, and make in the usual 
way a solution of it by trituration in a mortar with some 


* The above numbers are obtained as follows :—35'5 parts of chlorine 
are capable, as before stated, of converting 422°44 parts of the crystallized 
ferrocyanide of potassium into ferridcyanide; therefore 100 parts of the 
former will convert 1189°97 parts of the latter into the same compound. 
Again, as before observed, 1267°32 parts of the crystallized ferrocyanide 
require 147°59 parts of the bichromate of potash to convert them into the 
ferridcyanide; 1189-97 parts, therefore, will take 138°58 parts of that salt 
to produce the same cifect. 

+ Two small pipettes capable of delivering the above quantities would 
be found still more convenient, 


220 Prof. Davy on some further Applications of 


water; pour it into the flask which was used in preparing the 
two standard solutions, and having filled up with water to the 
mark in the neck, mix the solution thoroughly; and before each 
time that any of the chloride of lime is taken out, shake well 
the contents of the flask. 

Measure out into a beaker-glass, by means of the two little 
bottles, 100 divisions of the chloride of lime solution, and 50 of 
the standard solution of ferrocyanide; and having mixed them 
well together, add some hydrochloric acid to dissolve the preci- 
pitate formed and acidify the mixture strongly ; and having 
mixed the whole well, pour from the burette slowly the standard 
solution of bichromate (stirring well all the while) till a drop 
taken from the mixture and brought in contact with a drop of a 
very weak solution of perchloride of iron produces a yellowish- 
brown colour, as already noticed. Then read off the number of 
divisions of the standard solution of bichromate which was 
necessary to produce this effect; and this being deducted from 
50, gives the per-centage by weight of chlorine. 

For the standard solution of ferrocyanide having been made 
so that the 10000-grain measures should be equivalent to 100 
grains of chlorine, and as every division of the burette equals 10 
grains, each of these divisions of the ferrocyanide solution con- 
verted into ferrideyanide will indicate O°1 grain of chlorine. 
Again, the 100 divisions of the solution of chloride of lime 
represent lO grains of that substance, and we want to know 
how many divisions of the ferrocyanide solution its chlorine has 
converted into ferridcyanide. This is readily ascertained by 
the bichromate solution, which has been so graduated that 
each division represents a division of the ferrocyanide solution. 
So that to determine the per-centage of chlorine we have only 
to deduct, as before stated, the number of divisions of the 
bichromate solution employed from the 50 of the ferrocyanide 
solution, and the difference gives us the per-centage of chlorine 
by weight in the sample; thus in four experiments 50 divisions 
of the ferrocyanide solution, mixed with 100 divisions of the 
solution of chloride of lime, required 18:5 divisions of the bi- 
chromate solution to convert the whole of the ferrocyanide em- 
ployed into ferrideyanide; this number, taken from 50, leaves 
31°5 divisions of ferrocyanide, which were-converted into ferrid- 
cyanide by the chlorine of the chloride of lime; and as each 
division represents 0-1 grain of chlorme, 31°5 will be equivalent 
to 3°15 grains of chlorine, which is the amount contaimed in 10 
grains of the sample ; consequently 100 grains will contain 
31°5 grains of chlorine, which is the same amount as is obtained 
by simply deducting the number of divisions of bichromate solu- 
tion employed from 50 of ferrocyanide used in the estimation. 


the Ferrocyanide of Potassium in Chemical Analysis. 221 


Though this process appears a long one, from the details which 
are necessary to explain its principle, yet in practice it is very ex- 
peditious, and requires only a very few minutes for its performance, 
and is much quicker than either Gay-Lussac’s or Otto’s method. 

Though I have as yet chiefly confined my attention to the 
use of the ferrocyanide of potassium in the estimation of 
chlorme in bleaching powder, I have no doubt that it may 
be advantageously employed in many other useful determinations 
by carrying out the principles already explained: thus, for 
example, it may be used as a means of determining the amount 
of bichromate of potash present in a sample of that salt, or 
the quantity of chromic acid that exists under different circum- 
stances. Again, the same salt may be used in different deter- 
minations where a certain amount of chlerine is liberated, which 
represents a proportional quantity of some other substance: thus, 
for example, in the estimation of manganese ores for commercial 
purposes, where they are heated with hydrochloric acid, the 
quantity of chlorine disengaged will indicate a certain amount 
of peroxide of manganese in the ore, on the presence of which 
its commercial value almost entirely depends ; and the chlorine 
evolved may be estimated by absorbing the gas in a dilute 
solution of caustic potash, and then determining the amount of 
chlorine in it by precisely the same process as that I have re- 
commended in the valuation of chloride of lime. To test the 
accuracy of this method, I heated in a small flask a given 
quantity of pure bichromate of potash with an excess of strong 
hydrochloric acid, and collected the evolved chlorine by means 
of a dilute solution of caustic potash, employing the bulbed 
retort and curved dropping tube as recommended by Bunsen in 
the “‘Analysis of the Chromates” (see the last editionof Fresenius’s 
‘Quantitative Analysis,’ page 234), and ascertained afterwards, by 
the use of the ferrocyanide of potassium, the amount of chlozine 
evolved, which corresponded almost exactly with the calculated 
amount of that substance which should have been obtained by 
the action of the quantity of bichromate used on the hydrochloric 
acid. Again, a standard solution of ferrocyanide of potassium 
may be used, as i. de Haen has shown, to determine the strength 
of the permanganate of potash in the analyses of the ferrocyanide 
and ferrideyanide of potassium, as an acidified solution of the 
ferrocyanide, as before stated, rapidly decolorizes a solution of 
permanganate of potash, whereas the ferrideyanide has no 
action on that salt; and this reaction might be taken advantage 
of, in the valuation of chloride of lime, to determine the excess 
of ferrocyanide used in my process: but from my experiments 
I found that more precise and accurate results were obtained by 
the use of the bichromate of potash. 


222 Prof. Davy on some further applications of 


The reaction of the bichromate of potash on the ferrocyanide 
might be employed in the valuation of the ferrocyanide of 
potassium and other ferrocyanides—having previously,in the case 
of those which were insoluble, converted them into the ferro- 
cyanide of potassium by boiling them with caustic potash, and 
separating the insoluble oxides by filtration. 

It might also be employed for the valuation of the commercial 
red prussiate of potash, which is now to some extent employed 
as a bleaching agent in calico-printing, and which consists of 
varying quantities of ferro- and ferrid-cyanide of potassium 
together with chloride of potassium. By ascertaining first how 
much a given quantity of the sample requires of a standard solu- 
tion of bichromate of potash to convert the ferrocyanide present 
into ferridcyanide, the per-centage of that substance would be 
known ; and then by taking another portion of the sample and 
converting the ferridcyanide it contained, by reducing agents, 
such as the sulphites of soda and potash, &c., into the ferrocyanide, 
and finally determining the amount of bichromate necessary to 
bring the whole of the ferrocyanide then present into the state 
of ferridcyanide, the difference in the two results would indicate 
the proportion of ferridcyanide originally present in the sample. 

The last application of ferrocyanide of potassium which I shall 
notice in the present communication, is its employment as a 
reducing agent. It has long been known that the cyanide of 
potassium possesses most powerful reducing properties, and has 
been very usefully employed for that purpose in the reduction of 
different metallic salts under various circumstances; but I am 
not aware that the ferrocyanide of potassium has been proposed 
or used for similar purposes: at least, I have referred to a great 
number of analytical and general chemical works, and in none 
of them is this salt recommended as a reducing agent, though 
the cyanide is so much extolled for that purpose. According 
to my experiments, the ferrocyanide is a far more convenient 
reducing agent than the cyanide, and may be substituted for it 
in many cases of reduction with the best results, as it possesses 
many unquestionable advantages over that salt for this purpose. 
Thus the ferrocyanide does not deliquesce and decompose when 
exposed to the air, whereas the cyanide rapidly absorbs moisture, 
and, unless kept in very well-stoppered bottles, becomes quite wet, 
and in this state quickly decomposes; and this deliquescence on the 
part of the cyanide is often a source of much inconvenience in its 
use as a reducing agent, owing to the almost unavoidable absorp- 
tion of more or less moisture which takes place in mixing it with 
the substance to be reduced, and during the introduction of the 
mixture into the reducing tube. The ferrocyanide, on the other 
hand, in a thoroughly dried and finely powdered state, can be 


the Ferrocyanide of Potasstum in Chemical Analysis. 223 


intimately mixed with the substance without any appreciable 
absorption of moisture. I made the following comparative ex- 
periment to ascertain the relative absorptive properties for mois- 
ture of the two salts under the same circumstances. Having 
thoroughly dried in a water oven, till it ceased to vary in weight, 
some finely powdered ferrocyanide, I placed 50 grains of it in a 
counterpoised watch-glass, and powdering in a warm mortar 
some fresh cyanide of potassium, I placed the same quantity of 
itn a similar counterpoised watch-glass, and left them both 
exposed to the air. On examining them after four hours’ expo- 
sure, I found that the former had only gained ;8>th parts of a 
grain of moisture, whereas the latter had taken up 3°6 grains, 
or sixty times as much moisture under the same circumstances. 
After two days’ exposure I found that nearly all the cyanide had 
passed into the liquid condition, having taken up 46 grains of 
water ; whereas the ferrocyanide appeared perfectly dry, and 
had only absorbed 1°4 grain. 

The great fusibility of the cyanide is sometimes rather a dis- 
advantage, which has to be lessened by mixing it with a certain 
proportion of dried carbonate of soda; but the ferrocyanide not 
fusing at so low a temperature, does not require in most cases 
this admixture to lessen its fusibility. Again, the ferrocyanide is 
not a poisonous salt, whereas the cyanide is highly so, and must 
be used with great caution; and lastly, the former salt is little 
more than half the price of the latter. Combined with the above 
advantages, I find that the ferrocyanide is equally effective in re- 
ducing metallic oxides and sulphurets, and is especially con- 
venient for the reduction of different combinations of arsenic and 
mercury, which are reduced by it with the greatest ease. 

I made several comparative experiments with the dried ferro- 
cyanide and with the cyanide as reducing agents for the sulphuret 
of arsenic and arsenious acid, employing the same quantity of 
arsenical compound with each salt under similar circumstances ; 
and in almost every case, particularly where the quantities 
operated on were minute, I obtained more satisfactory results 
with the dried ferrocyanide than with the cyanide. 

The followmg were amongst my experinents :—I mixed the 
zath of a grain of sulphuret of arsenic with 3 grains of the dried 
ferrocyanide, and made a similar experiment, substituting the 
same quantity of cyanide; and on heating the mixtures in similar 
glass tubes, obtained almost identically fine and characteristic 
rings of metallic arsenic. 

I then intimately mixed the same quantity of sulphuret of 
arsenic with 49-9 grains of very finely powdered glass, and taking 
5 grains of this mixture, containmg the ygoth part of a grain 
of the sulphuret, mixed it with 5 grains of the dried ferrocyanide, 
and made a comparative experiment with another 5 grains of the 


224 Royal Society :— 


mixture, substituting the same quantity of cyanide; on heating 
both these mixtures in small reduction tubes, I got the charac- 
teristic metallic rigs in both, but better defined in the case of 
the ferrocyanide. | 

I finally took 2°5 grains of the mixture of sulphuret and glass, 
containing about z;%oth parts ofa grain of sulphuret of arsenic, 
and treated them in the same manner, using in one case 2°5 grains 
of ferrocyanide, and in the other 2°5 grains of cyanide, and 
obtained in each case a minute metallic ring, which, however, 
was much more distinct and satisfactory where the ferrocyanide 
had been used as the reducing agent. 

The same comparative experiments were made with arsenious 
acid, when results similar to those in the case of the sulphuret of 
arsenic were obtained. 

The ferrocyanide, therefore, is a most delicate reducing agent 
in the case of arsenical compounds, and where very minute quan- 
tities have to be detected, appears from my experiments to give 
more satisfactory results than the cyanide. 

Whether the addition of dried carbonate of soda would improve 
the ferrocyanide for some cases of reduction, I am not at present 
able to say; but in one experiment which I made with the sul- 
phuret of arsenic, I obtained as good results, using the fer- 
rocyanide alone, as where it was mixed previously with its own 
weight of dried carbonate of soda. In many cases the ferro- 
cyanide may be used as a reducing agent in a state of powder 
without separating its water of crystallization ; but, in most cases, 
it will be rendered a far better reducing agent by being previously 
dried at 212° in a water-bath or oven; and in this dried condition 
it may be kept for any length of time in a good-stoppered or 
well-corked bottle. 

Though as yet my experiments have been chiefly confined to 
the reduction of different compounds of arsenic and mercury, I 
entertain no doubt that the ferrocyanide of potassium will be 
found an equally effective reducing agent im the case of the 
combinations of other metals, and that it may with great advan- 
tage be substituted for the cyanide of potassium in many cases 
where the latter salt is used as a reducing agent. 


XXXV. Proceedings of Learned Societies. 
ROYAL SOCIETY. 
(Continued from p. 153.] 
April 26, 1860.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 
NHE following communication was read :— 
“On the Effect of the Presence of Metals and Metalloids upon 


the Electric Conductivity of Pure Copper.’ By A. Matthiessen, Esq., 
and M. Holzmann, Esq. 


After studying the effect of suboxide of copper, phosphorus, 


Dr. Chowne on the Elastic Force of Aqueous Vapour. 225 


arsenic, sulphur, carbon, tin, zine, iron, lead, silver, gold, &c., on 
the conducting power of pure copper, we have come to the conclusion 
that there is no alloy of copper which conducts electricity better than 
the pure metal. 


May 3.—Sir Benjamin C. Brodie, Bart., President, in the Chair. 


The following communications were read :— 

**On the relations between the Elastic Force of Aqueous Vapour, 
at ordinary temperatures, and its Motive Force in producing Currents 
of Air in Vertical Tubes.” By W. D. Chowne, M.D., F.R.C.P. 

In 1853 the author of this communication made a considerable 
number of experiments which demonstrated that when a tube, open 
at both ends, was placed vertically in the undisturbed atmosphere of 
a closed room, there was an upward movement of the air within the 
tube of sutticient foree to keep an anemometer of light weight in a 
state of constant revolution, though with a variable velocity. An 
abstract of the results of these experiments was printed in the Phi- 
losophical Magazine, vol. xi. p. 227. 

In order to further investigate the immediate cause or nature of 
the force which set the machine in motion, the author instituted a 
series of fresh experiments. 

These experiments were made in the room described in the former 
communication, guarded in the same manner against disturbing 
causes, and with such extra precautions as will be hereafter explained. 
The apparatus used was a tube 96 inches long and 6°75 inches 
uniform diameter, the material zinc. The upper extremity was open 
to its full extent; at the lower, the aperture was a lateral one 
only, into which a piece of zine tube 3 inches in diameter, and bent 
once at right angles, was accurately fitted with the outer orifice 
upward, Within this orifice, which was about 5 inches above the 
level of the floor, an anemometer, described in the former paper, and 
weighing 7 grains, was placed in the horizontal position. About 
midway between the upper and, the lower extremity of the tube, a 
very delicate differential thermometer was firmly and permanently 
fixed, with one bulb outside and the other inside, and the aperture 
through which the latter was inserted completely closed. The scale 
was on the stem of the outer bulb. 

The results of a long series of observations were recorded. The 
state of the dry and the wet bulb of the hygrometer, as well as the 
indications of the differential thermometer, was noted, in connexion 
with the number of revolutions performed per minute by the ane- 
mometer. While the differential thermometer indicated the same 
relative differences between the heat of the atmosphere within and 
without the tube, the velocity of the revolutions was found to vary 
considerably. This variation was discovered to be chiefly, if not 
wholly, dependent on the elasticity of vapour, due to the hygro- 
- metrical state of the atmosphere, as estimated from the dry- and the 
wet-bulb thermometers, and calculated from the tables of Regnault. 

240 observations were recorded and afterwards separated into 
groups, each group comprising those in which the differential ther- 
mometer gave the same indication. 


Phil. Mag. 8. 4, Vol. 21, No. 139, March 1861. Q 


226 Royal Society :— 


If in either of these groups we separate into two classes the cases 
in which the elasticity was highest, from the cases in which it was 
lowest, and multiply the mean of each with the corresponding mean 
of the number of the revolutions of the anemometer, their product 
is nearly a constant, thus showing that the velocity of ascent of the 
atmospheric vapour is inversely as its elasticity ; and hence it follows 
that the velocity of the ascending current in the tube varies inversely 
as the density or elastic force of the vapour suspended in the atmo- 
sphere. ‘This was rendered evident by the aid of Tables appended 
to the paper. 

When the mean elastic force of vapour calculated from the dry 
and the wet bulbs is multiplied by the constant, 13°83, the result 
gives the whole amount of water in a vertical column of the atmo- 
sphere in inches; it follows therefore that when the difference of 
temperature between the external air and that in the tube, as shown 
by the differential thermometer, is constant, the velocity of the 
current in the tube varies inversely as the weight of the vapour 
suspended in the atmosphere. 

In an Appendix the author describes some additional experiments, 
made with the view of ascertaining whether the readings of the 
differential thermometer were mainly due to actual changes of tem- 
perature within the tube, or to extraneous causes acting on the 
external bulb. He found that when the external bulb was covered. 
with woollen cloth or protected by a zine tube of about 4 inches 
diameter and 6 inches long, the temperature of the bulb was 
increased about 2° on the scale of the instrument, and that when 
they were removed the prior reading was restored, while the number 
of revolutions of the anemometer per minute was not appreciably 
affected by the change. This explains why the readings of the dif- 
ferential thermometer varied from 33°:0 to 33°°5 as described in the 
paper, without producing a corresponding change in the velocity of 
the anemometer. 

For the purpose of obtaining a. more correct estimate of the 
influence of a given increase of heat within the tube, the author 
introduced into the tube at its lowest extremity, a phial containing 
eight ounces of water at the temperature of 100° Fahr., corked so 
that no vapour could escape. The result showed that in thirteen 
observations a quantity of heat equal to an increase of one-tenth of 
a degree on the scale of the differential thermometer, was equivalent 
to a mean velocity of the anemometer of 3°6 revolutions per minute, 
the greatest number being 3°8, the least 3°3 per minute. 

These observations render it still more evident, that if a higher 
temperature within the tube had been the main cause of the revolu- 
tions of the anemometer, the variations in their velocity would not 
have been in such exact relation to the elastic force of the atmo- 
spheric vapour, as has been shown to be the case. They also lead 
to the inference, that the apparent excess of heat within the tube 
alluded to by the author in his Paper read before the Society in 
1855 did not really exist, and to the conclusion that, if such excess 
had been present, the anemometer would not have been brought to a 
state of rest by depriving the air of the room of a portion of the 
moisture ordinarily suspended in it. 


On the. Relation between Boiling-point and Composition, 227 


“On the Relation between Boiling-point and Composition in 
Organic Compounds.” By Hermann Kopp. — . 

The author was the first to observe(in 1841) that, on comparing pairs 
of analogous organic compounds, the same difference in boiling-point 
corresponds frequently to the same difference in composition. This 
relation between boiling-point and composition, when first pointed 
out, was repeatedly denied, but is now generally admitted. The con- 
tinued experiments of the author, as well as of numerous other 
inquirers, have since fixed many boiling-points which had hitherto 
remained undetermined, and corrected such as had been inaccu- 
rately observed. In the present paper the author has collected his 
experimental determinations, and has given a survey of all the facts 
satisfactorily established up to the present moment regarding the 
relations between boiling-point and composition. 

The several propositions previously announced by the author 
were :-— 

1. An alcohol, Cx H,,+20., differmg in composition from ethylic 
alcohol (C,H,O,, boiling at 78° C.) by « C,H,, more or less, boils 
2X 19° higher or lower than ethylic alcohol. 

2. The boiling-point of an acid, C,H,0O,, is 40° higher than that 
of the corresponding alcohol, C,,H,+20s. 

3. The boiling-point of a compound ether is 82° higher than th 
boiling-point of the isomeric acid, C,H,Ou.. 

These propositions supply the means of calculating the boiling- 
points of all alcohols, C, Hn+20z ; of all acids, C,H,,O.4; of all com- 
pound ethers, C,H,Ox. The author contrasts the values thus cal- 
culated for these substances with the available results of direct obser- 
vation. The Table embraces eight alcohols, Cx Hn+2Q., nine acids,- 
C,H, O04, and twenty-three compound ethers, C,,H,O.; the calculated 
boiling-points agree, as a general rule, with those obtained by experi- 
ment, as well as two boiling-points of one and the same substance 
determined by different observers. We are thus justified in assuming 
that the calculated boiling-point of other alcohols, acids, and ethers 
belonging to this series will also be found to coincide with the results 
of observation. 

The boiling-points of other monatomic alcohols, Cp H»O2, other 
monatomic acids, C,,H,,O,, and other compound ethers, Cp HmOus 
are closely allied with the series previously discussed. A substance 
containing xC more or less than the analogous term of the previous 
class, in which the same number of oxygen and of hydrogen equiva- 
lents is present, boils x x 14°°5 higher or lower ; or, what amounts to 
the same thing, a difference of #H more or less of hydrogen lowers 
or raises the boiling-pointt by «x5°. Thus benzoic acid, C,,H,O,; 
boils 8 x 14°-5 higher than propionic acid, C,H,O,, or 8 x 5° higher 
than cenanthylic acid, C,,H,,O,; cinnamate of ethyl, C,,H,,O,, boils 
10 x 14°5 higher than butyrate of ethyl, C,,H,,O,, or 10 x 5° higher 
than pelargonate of ethyl, C,,H,,O,. 

The author compares the boiling-points thus calculated for five 
alcohols, C,, HO; for six acids, C, H»O.; and for sixteen compound 
ethers, C,, H,,.O4, with the results of observation. In almost all cases 
the concordance is sufficient. 

Qe 


228 Royal Society :— 


The author demonstrates in the next place that in many series of 
compounds other than those hitherto considered, the elementary 
difference, eC, H,, likewise involves a difference of x x 19° in the boil- 
ing-point. He further shows that on comparing the boiling-points 
of the corresponding terms in the several series of homologous sub- 
stances hitherto considered, many other constant differences in boiling- 
point are found to correspond to certain differences in composition. 
Thus a monobasic acid is found to boil 44° higher than its ethyl 
compound, and 63° higher than its methyl compound ; and this con- 
stant relation holds eood even for acids other than those previously 
examined, e. g. for the substitution-products of acetic acid. Also in 
eabitanecs sat are not acids, the substitution of C,H, or C,H, 
for H, occasionally involves a depression of the boiling-points re- 
spectively of 44° and 63°; the relation, however, is by no means 
generally observed. 

The author, in addition to the examples previously quoted, shows 
that compounds containing benzoyl (C,,H,O,) and benzyl (C,, H.) 
boil 78° (=4 x 14°°5+4 x “50) higher than the corresponding terms 
containing valeryl (C,,H,O,) and amyl (C,,H,,), a relation, however, 
which is ieee ise not generally met with. He discusses, moreover, 
other coincidences and differences of boiling-points of compounds 
differing in a like manner in composition. Not in all homologous 
series does the elementary difference «C,H, involve a difference of 
2xX19° in boiling-point. The author shows that this difference is 
greater for the hydrocarbons, C, H»-6 and CxHn+2; for the acetones 
and aldehydes, C,H, Oz; for the so-called simple and mixed ethers, 
C,H»+202; for the chlorides, bromides, and iodides of the alcohol 
radicals, Cy, H»+1, and for several other groups; that it is, on the con- 
trary, smaller for the anhydrides of monobasic acids, Cp Hn—20¢; for 
the ethers, C, H»-2Og (which may be formed either by the action of 
one molecule of a dibasic acid, C, H,-20s, upon two molecules of a 
monatomic alcohol, C,,H,+4202, or by the action of two molecules of 
a monobasic acid, C,,H,,0,, upon one molecule of a diatomic alcohol, 
C,,Hn+204), and several other series. 

The author thinks that the unequal differences in boiling-points 
corresponding in different homplogaug series to the elementary differ- 
ence wC, H,, are probably regulated by a more general law, which will 
be found when the boiling-points of many substances shall have been 
determined under pressures differing from those of the atmosphere. 

“From the observations at present at our disposal it may be 
affirmed as a general rule, that in homologous compounds belonging 
to the same series, the differences in boiling-points are proportional 
to the differences in the formule. Exceptions obtain only in cases 
when terms of a particular group are rather difficult to prepare, or 
when the substances boil at a very high temperature, at which the 
observations now at our command are for the most part uncertain. 
Again, it may be affirmed that the difference in boiling-points, 
corresponding to the elementary difference C,H,, is in a great many 
series =19° ; in some series greater, in some series less.” 

The author proceeds to discuss the boiling-points of isomeric com- 
pounds. Ie shows that in a great many cases isomeric compounds 


On the Relation between Boiling-point andComposition. 229 


belonging to the same type, and exhibiting the same chemical cha- 
racter, boil at the same temperature, and that there is no reason why, 
for the class of bodies mentioned, this coincidence should not obtain 
generally. On the other hand, different boiling-points are observed 
in isomeric compounds possessing a different chemical character, 
although belonging to the same type (e. g. acids and compound ethers, 
C,,H,O,; alcohols and ethers, C,,H,,,:02), and im isomeric com- 
pounds belonging to different types (e. g. allylic alcohol and acetone). 

The author shows that the determination of the boiling-point of a 
substance, together with an inquiry into the compounds serially 
allied with it by their boiling-points, constitutes a valuable means of 
fixmg the character of the substance, the type to which it belongs, 
and the series of homologous bodies of which it is a term. He 
quotes as an illustration eugenic acid. The boiling-point of this 
acid, C,,H,,0,,is 150°; and on comparing this boiling-point with the 
boiling-points of benzoic acid, C,,H,O, (boiling-point 253°), and of 
hydride of salicyl, C,,H,O, (boilmg-point 196°), it is obvious that 
eugenic acid cannot be homologous to benzoic acid, whilst, on the 
other hand, it becomes extremely probable that it is homologous to 
hydride of salicyl, and consequently that it belongs rather to the 
aldehydes than to the acids proper. 

The author, in conclusion, calls attention to the importance of 
considering the chemical character in comparing the boiling-points 
of the volatile organic bases, and shows the necessity of distinguish- 
ing between the primary, secondary, and tertiary monamines in order 
to exhibit constant differences of boiling-point for this class of sub- 
stances. He discusses the boiling-points of the several bases, 
C,Hn»_sN and CrHn+3N, and points out how in many cases the 
particular class to which a base belongs may be ascertained by the 
determination of the boiling-point. 

The comprehensive recognition of definite relations between com- 
position and boiling-point is for the present chiefly limited to organic 
compounds. But for the majority of these compounds, and indeed 
for the most important ones, this relation assumes the form of a 
simple law, which, more especially for the monatomic alcohols, 
C,,H,,O2, for the monobasic acids, C,,H,,O4, and for the compound 
ethers generated by the union of the two previous classes, is proved 
in the most general manner ; so much so, indeed, that in many cases 
the determination of the boiling-poiat furnishes most material assist- 
ance in fixing the true position and character of a compound. 

The author points out more especially that the simplest and most 
comprehensive relations have been recognized for those classes of 
organic compounds which have been longest known and most accu- 
rately investigated, and that even for those classes the generality and 
simplicity of the relation, on account of numerous boiling-poits in- 
correctly observed at an earlier date, appeared in the commencement 
doubtful, and could be more fully acknowledged only after a consi- 
derable number of new determinations. Thus he considers himself 
justified in hoping that also in other classes of compounds, in which 
simple and comprehensive relations have not hitherto been traced, 
these relations will become perceptible as soon as the verification of 


230 Royal Society :— 


the boiling-points of terms already known, and the examination of 
new terms, shall have laid a broader foundation for our conclusions. 


May 10.—Sir Benjamin C. Brodie, Bart., President, in the Chair. 


The Bakerian Lecture was delivered by Mr. Fairbairn, F.R.S. 
The Lecturer gave a condensed exposition of the experiments and 
results detailed in the following Paper. He also exhibited the appa- 
ratus employed, and explained the methods followed. 

«Experimental Researches to determine the Density of Steam at 
all Temperatures, and to determine the Law of Expansion of Super- 
heated Steam.” By William Fairbairn, Esq., F.R.S., and Thomas 
Tate, Esq. 

The object of these researches is to determine by direct experiment 
the law of the density and expansion of steam at all temperatures. 
Dumas determined the density of steam at 212° Fahr., but at this ~ 
temperature only. Gay-Lussac and other physicists have deduced 
the density at other temperatures by a theoretical formula true for a 
perfect gas: 


VP _459+T (1.) 

VP. 45040... 1. 
On the expansion of superheated steam, the only experiments are 
those of Mr. Siemens, which give a rate of expansion extremely high, 
and physicists have in this case also generally assumed the rate of 
expansion of a perfect gas. Experimentalists have for some time 
questioned the truth of these gaseous formule in the case of conden- 
sable vapours, and have proposed new formulee derived from the 
dynamic theory of heat ; but up to the present time no reliable direct 
experiments have been made to determine either of the pomts at 
issue. The authors have sought to supply the want of data on these 
questions by researches on the density of steam upon a new and ori- 
ginal method. 

The general features of this method consist in vaporizing a known 
weight of water in a globe of about 70 cubic inches capacity, and 
devoid of air, and observing by means of a ‘‘ saturation gauge’”’ the 
exact temperature at which the whole of the water is converted into 
steam. ‘The saturation gauge, in which the novelty of the experi- 
ment consists, is essentially a double mercury column balanced upon 
one side by the pressure of the steam produced from the weighed 
portion of water, and on the other by constantly saturated steam of 
the same temperature. Hence when heat is applied the mercury 
columns remain at the same level up to the point at which the 
weighed portion of water is wholly vaporized; from this point the 
columns indicate, by a difference of level, that the steam in the globe 
is superheating ; for superheated steam increases in pressure at a far 
lower rate than saturated steam for equal increments of temperature. 
By continuing the process, and carefully measuring the difference of 
level of the columns, data are obtained for estimating the rate of 
expansion of superheated steam. 

The apparatus for experiments at pressures of from 15 to 70 lbs. 
per square inch, consisted chiefly of a glass globe for the reception of 
the weighed portion of water, drawn out into a tube about 32 inches 


On the Density of Steam at all Temperatures. 201 


long. The globe was enclosed in a copper boiler, forming a steam- 
bath by which it could be uniformly heated. The copper steam- 
bath was prolonged downwards by a glass tube enclosing the globe 
stem. To heat this tube uniformly with the steam-bath, an outer 
oil-bath of blown glass was employed, heated like the copper bath by 
gas jets. ‘The temperatures were observed by thermometers exposed 
naked in the steam, but corrected for pressure. The two mercury 
columns forming the saturation gauge were formed in the globe stem, 
and between this and the outer glass tube; so long as the steam in 
the glass globe continued in a state of saturation, the inner column 
in the globe stem remained stationary, at nearly the same level as 
that in the outer tube. But when, in raising the temperature, the 
whole of the water in the globe had been evaporated and the steam 
had become superheated, the pressure no longer balanced that in 
the outer steam-bath, and, in consequence, the column in the globe 
stem rose, and that in the outer tube fell, the difference of level 
forming a measure of the expansion of the steam. Observations of 
the levels of the columns were made by means of a cathetometer at 
different temperatures, up to 10° or 20° above the saturation point ; 
and the maximum temperature of saturation was, for reasons deve- 
loped by the experiments, deduced from a point at which the steam 
was decidedly superheated. 

The results of the experiments, which in the paper are given in 
detail, show that the density of saturated steam at all temperatures, 
above as well as below 212°, is invariably greater than that derived 
from the gaseous laws. 

The apparatus for the experiments at pressures below that of the 
atmosphere was considerably modified ; and the condition of the steam 
was determined by comparing the column which it supported with 
that of a barometer. The results of these experiments, reduced in 
the same way, are extremely consistent. 7 

As the authors propose to extend their experiments to steam of a 
very high pressure, and to institute a distinct series on the law of 
expansion of superheated steam, they have not at present given any 
elaborate generalizations of their results. The following formule, 
however, represent the relations of specific volume and pressure of 
saturated steam, as determined in their experiments, with much 
exactness. 

Let V be the specific volume of saturated steam, at the pressure P, 
measured by a column of mercury in inches ; then 


49513 
V=25°62 eRe ead e e e e e 2. 
wu ee p- me 
49513 : 
— el 4 e.  8 ° e e e e Se 
wn at SUN ses 


In regard to the rate of expansion of superheated steam, the ex- 
periments distinctly show that, for temperatures within about ten 
degrees of the saturation point, the rate of expansion greatly exceeds 
that of air, whereas at higher temperatures the rate of expansion 
approaches very near that of air. Thus in experiment 6, in which 
the maximum temperature of saturation is 174°°92, the coefficient of 


2o2 Royal Society. 


expansion between 174°'92 and 180° is ;4,, or three times that of 
air; whereas between 180° and 200° the coefficient is very nearly the 
same as that of air (steam= 4, air=;4,), and so on in other cases. 
The mean coefficient of expansion at zero of temperature from seven 
experiments below the pressure of the atmosphere, and calculated 
from a point several degrees above that of saturation, is -}_, whereas 
for air it is ;15. Hence it would appear that for some degrees 
above the saturation point the steam is not decidedly in an aériform 
state, or, in other words, that it is watery, containing floating vesicles 
of unvaporized water. 


Table of Results, showing the relation of density, pressure, and 
temperature of saturated steam. 


Pressure ~ Specific Volume. Pronarienc 
ee if in Ibs.per,in inches of of saturation From enor > 
; sq. in. | mercury. Fahr. experiment, Hy formula @)) ona 
(e} 
1 2°6 5°35 | 136-77 8266 8183 Sing 
2 4°3 8°62 1ao°3a 5326 5326 0 
3 4°7 945 | 159:36 4914 4900 ae 
4 6°2 12°47 170°92 3717 3766 + 7k 
5 6°3 12°61 171°48 3710 3740 es 
6 6'8 13°62 174°92 3433 3478 + 7s 
7 8-0 16°01 182:30 3046 2985 — sy 
8 i 18°36 188°30 2620 2620 0 
9 13 22°88 198°78 2146 2124 — 37 
EY 26°5 53°61 242-90 941 937 —saE 
ae 27°4 55°52 244°82 906 906 0 
3’ | 276 | 55°89 | 245-22 891 900 rete 
4' 30° 1 66°84 255°50 758 798 0 
5' | 87:8 | 76°20 | 263-14 648 669 ote 
6' 40°3 81°53 267°21 634 628 —st0 
e 41°7 84°20 269°20 604 608 ++t5 
8' 45°7 92°23 274°76 583 562 — sy 
9' 49-4 99°60 279°42 514 519 +343 
11’ 51°7 104°54 282°58 496 496 0 
12’ 55°9 112°78 287°25 457 461 ++ 
13' | 60°6 | 122°25 | 292-53 432 428 uke 
14' 56°7 114°25 288°25 448 456 + sg 


Adopting the notation previously employed, and putting 7 for the 
rate or coefficient of expansion of an elastic fluid at ¢, temperature, 
we find Vv 

- as pals 
ee Se HY 9 . ° e . . (4.) 
Fe obey see 


1 , 
where — = the rate of expansion at zero of temperature. In the case 
2) 


1 
of air e,= 459. 
The following Table gives the value of the coefficient of expansion 
of superheated steam taken at different intervals of temperature from 
the maximum temperature of saturation. 


Geological Society. 233 


Coefficient of 


Bee | mahon, | mmORBSputoniS han, | Semel | of emt 
1 136°77 140 170 — ett 
2 155-33 160 190 ii ere 
S| soso) sie | | 
5 was { been’ 180 a ay 
6 17492 | ed pe = te 
8 188-30 191 211 Sig ae 
ees 8) aug? gag (op eae 
v | 2602 1] 353 b79 es ue 
9" 279-42 | a aes — = 
13" Roeee boson? RG op a TE 


Hence it appears, that as the steam becomes more and more super- 
heated, the coefficient of expansion approaches that of a perfect gas. 
The authors hope that these experiments may be continued, and that 
the results obtained at greatly increased pressures will prove as 
important as those already arrived at. 


GEOLOGICAL SOCIETY. 


[Continued from p. 157.] 
December 5, 1860.—L. Horner, Esq., President, in the Chair. 


The following communication was read :— 

‘‘On the Structure of the North-west Highlands, and the Rela- 
tions of the Gneiss, Red Sandstone, and Quartzite of Sutherland and 
Ross-shire.”’ By Professor James Nicol, F.R.S.E., F.G.S. 

The author first referred to his paper in the Quart. Journ. Geol. 
Soc., vol. xii. pp. 17, &c., in which the order of the red sandstone 
on gneiss, and of quartzite and limestone on the sandstone, was 
established, and in which the relation of the eastern gneiss or mica- 
schist to the quartzite was stated to be somewhat obscure on account 
of the presence of intrusive rocks and other marks of disturbance. 
Having examined the country four times, with the view of settling 
some of the doubtful points in the sections, the author now offered 
the matured result of his observations. He agrees with Sir R. 
Murchison as far as the succession of the western gneiss, red sand- 
stone, quartzites (quartzite and fucoid-bed), and limestone is con- 


234 Geological Soctety.:— 


cerned; but differs from him in maintaining that there is no upper 
series of quartzite and limestone, and that there is no evidence of an 
‘* upward conformable succession’’ from the quartzite and limestone 
into the eastern mica-slate or gneiss—the o-called “ upper gneiss.”’ 
The ‘‘ upper quartzite” and “ upper limestone ” the author believes - 
to be portions of the quartzite of the country, in some cases separated 
by anticlines and faults and cropping out in the higher ground, and 
in other instances inverted beds with the gneiss brought up by a 
contiguous fault and overhanging them. ‘his latter condition of 
the strata, as well as other cases where the eastern gneiss is brought 
up against the quartzite series, have, according to the author, given 
rise to the supposed ‘‘ upward conformable succession” above referred 
to. Im some cases where “‘ gneiss ”’ is said to have been observed 
overlying the quartzite, Professor Nicol has determined that the 
overlying rock is granulite or other eruptive rock, not gneiss. 

The sections described by the author in support of his views of 
the eastern gneiss not overlying the quartzite and limestone, but 
being the same as the gneiss of the west coast, and brought up by a 
powerful fault along a nearly north and south line passing from 
Whiten Head (Loch Erriboll) to Loch Carron and the Sound of Sleat, 
are chiefly those which had been brought forward as affording the 
proofs on which the opposite hypothesis is founded; and in all, the 
author finds irruptions of igneous rocks, and other indications of 
faults and disturbance, depriving them, in his opinion, of all weight 
as evidence of a regular order of ‘ upward conformable succession.” 

Prof. Nicol further argues that the mode of the distribution of the 
rocks shows that there is through Sutherland and Ross-shire a real 
fault, and no overlap of eastern gneiss of more than a few feet or 
yards at most, and that the fact of different strata of the quartzite 
series being brought against the gneiss at different places supports 
this view, and points toa great denudation having taken place along 
the line of fault. ‘Though the quartzite is here and there altered by 
the igneous rocks, yet it is truly a sedimentary rock, and so is the 
limestone ; but the eastern gneiss or mica-schist is a crystalline rock 
throughout: this fact, according to the author, is inimical to the 
hypothesis of the eastern gneiss overlying the limestone and quartzite. 
It has been insisted upon, that the strike of the western gneiss is dif- 
ferent from that of the east; but the author remarks that the strike 
is not persistent in either area, and that great movements subse- 
quent to the deposition of the quartzite series have irregularly affected 
the whole region. With regard to mineralogical characters, Prof. 
Nicol insists that both the eastern and the western gneiss are essen- 
tially the same. Both are locally modified with granitic and horn- 
blendic matter near igneous foci ; but no proof of a difference of age 
in the two can be obtained therefrom. The alteration in bulk of the 
gneiss in the western area, by the intrusion of the vast quantities of 
granite now observable in it, may perhaps have caused the great 
amount of crumpling and faulting along the N. and S. line of fault, 
dividing the western from the eastern gneiss,—a fault comparable 
with and parallel to that running from the Moray Firth to the Linnhe 
Loch, and to the one passing along the south side of the Grampians. 


Geological Structure of the South-west Highlands of Scotland. 235 


December 19, 1860.—L. Horner, Esq., President, in the Chair. 
The following communications were read :— 


1. “ On the Geological Structure of the South-west Highlands of 
Scotland.” By T. F. Jamieson, Esq. Communicated by Sir R. I. 
Murchison, V.P.G.S. 

In this paper the author attempts to throw light on the relations 
of those rocks which figure in geological maps as the mica-schist, 
clay-slate, the chlorite-slates, and the quartz-rock of the South-west- 
ern Highlands, which range N.E. through the middle of Scotland, 
forming an important feature in the geology of that country. An 
examination of these rocks, as displayed in Bute and Argyleshire, 
has led Mr. Jamieson to believe that, from the quartz-rock of Jura 
to the border of the Old Red Sandstone, there is a conformable series 
of strata, which, although closely linked together, may be classed 
into three distinct groups, namely, Ist, a set of lower grits (or 
quartz-rock), many thousand feet thick; 2ndly, a great mass of 
thin-bedded slates, 2000 feet or more thick; and 3rdly, a set of 
upper grits, with intercalated seams of slate of equal thickness. 
Beds of limestone occur here and there sparingly in all the three 
divisions ; the thickest being deep down in the lower grits. All the 
limestones are thiclfest towards the west. The siliceous grits also 
appear to be freer from an admixture of green materials towards the 
west. All the members of the series (namely, the upper grits, slates, 
and lower grits) have a persistent S.W.—N.E. strike, sometimes in 
Bute approaching to due N. and 8. They are conformable, and 
graduate one into another in such a way as to show that they belong 
to one continuous succession of deposits. The materials of which they 
have been formed seem to have been derived from very similar sources. 
The upper and the lower grits are very similar in composition, being 
made up of water-worn grains of quartz, many of which are of a 
peculiar semitransparent bluish tint. 

The rocks of the district have been thrown into a great undula- 
tion, with an anticlinal axis extending from the north of Cantyre 
through Cowal by the head of Loch Ridun on to Loch Eck (and: 
probably by the head of Loch Lomond on to the valley of the Tay, 
at Aberfeldy), and with a synclinal trough lying near the parallel 
of Loch Swen. The anticlinal fold is well seen in the hill called 
Ben-y-happel, near the Tighnabruich quay in the Kyles of Bute. 
Southward of this ridge, which is composed of the lower grits or 
quartzite, the thin-bedded greenish slates and the upper grits suc- 
ceed conformably ; and the latter are separated by a trap-dyke from 
the Old Red Sandstone of Rothsay. ‘This section the author de- 
scribed in detail; also the corresponding section to the north of the 
anticlinal axis, towards Loch Fyne, and along the west shore of Loch 
Fyne. ‘The lower grits extend as far as Loch Gilp, and are then 
succeeded by the green slates and the upper grits, which falling in the 
synclinal trough are repeated through Knapdale towards Jura Sound, 
where the green slates again form the surface along the eastern coast 
of Jura, lying on the quartzite or grits of that island. Throughout 
the synclinal trough and the neighbouring district (that is, from 


236 Geological Society :— 


Loch Fyne to Jura Sound) the grits and slates are intimately mixed, 
with numerous intercalated beds of greenstone, some being of great 
thickness. Mr. Jamieson pointed out that this feature of the di- 
strict has hitherto in great part been misunderstood, and that Mac- 
culloch was in error when he denominated these rocks ‘ chlorite- 
schist.” 

The probable relationship of the rocks of the Islands of Shuna, 
Luing, and Scarba to those of Jura and Bute were then dwelt upon; 
the greenstones of Knapdale, &c., and their relation to the sedi- 
mentary rocks, were described in detail; and the limestones of 
the district briefly noticed. As no fossils have hitherto been found, 
paleontological evidence of the age of these rocks is wanting; but 
the author, regarding their general resemblance to the quartz-rocks, 
limestones, and mica-schists of Sutherlandshire, thinks them to be of 
the same date as those rocks of the North-west Highlands. 


2. “On the position of the beds of the Old Red Sandstone in 
the Counties of Forfar and Kincardine, Scotland.” By the Rev. 
Hugh Mitchell. Communicated by the Secretary. ; 

In Forfar- and Kincardine-shire, south of the Grampians, the Old 
Red Sandstone is developed in the following series, with local modi- 
fications :—I1st (at top), Conglomerate; 2nd, grey flagstone with 
intercalated sandstone (about 40 feet thick at Cauterland Den, 
120 feet at Carmylie) ; 3rd, gritty ferruginous sandstone, with 
occasional thin layers of purplish flagstone. Of the last, 120 feet 
are seen at Cauterland Den; it occurs also at Ferry Den, &c. The 
flagstone of this third or lowest member of the group yields Ripple- 
marks, Rain-prints, Worm-markings, and Crustacean tracks (of 
several kinds, large and small). Parka decipiens has been found in 
the lowest grits; and Cephalaspis in the sandstone at Brechin, im- 
mediately under the grey flagstones. 

In the second member, namely the grey flags, Fish-remains have 
of late been found more or less abundantly throughout the district, 
together with Crustacean fossils. Cephalaspis Lyellit, Ichthyodoru- 
lites, Acanthodian fishes, Pterygotus, Eurypterus, Kampecaris For- 
fariensis, Stylonurus Powriensis, Parka decipiens, and vegetable re- 
mains are the most characteristic fossils. 

The author pointed out that some few genera of Fish and Crus- 
taceans were present both in this zone and in the Upper Silurian 
formation, and that still fewer links existed to connect the fauna of 
the Forfarshire flags with the Old Red Sandstone north of the Gram- 
pians, with which it appears to have, in this respect, almost as little 
relation as with the Carboniferous system. With the Old Red of | 
Herefordshire these flags appear to have some few fossils in common ; 
but of about twenty species found in Forfarshire, only about four 
could be quoted from Herefordshire. 

In conclusion, the author noticed the vast vertical development of 
the whole series, and its great geographical extent ; and particularly 
dwelt upon the distinctness of the fauna of the flagstones of Forfar- 
shire, as giving good grounds for the treatment of the Old Red 
Fauna as peculiar to a separate geological period, both as distinct 


P. B. Brodie on the Distribution of the Corals in the Lias. 237 


from the Silurian System, and in some degree as divisible into two 
or more members of one group :—three members, if the upper or 
Holoptychius-beds of Moray, Perth, and Fife, the middle or Fish- 
beds of Cromarty and Caithness, and the lowest or Forfarshire 
beds be counted separately ; but two, if we regard some of the Old 
Red beds north of the Grampians as equivalent in time to those on 
the south. 


January 9, 1861.—L. Horner, Esq., President, in the Chair. 


The following communications were read :— 

1. “On the Distribution of the Corals in the Lias.” By the Rev, 
P. B. Brodie, M.A., F.G.S. 

From observations made by himself and others, the author was 
enabled to give the following notes. In the Upper Lias some Corals 
of the genera Thecocyathus and Trochocyathus occur. The Middle 
Lias of Northamptonshire and Somersetshire has yielded a few Corals. 
The uppermost band of the Lower Lias, namely the zone with Am- 
monites raricostatus and Hippopodium ponderosum, contains an unde- 
scribed Coral at Cheltenham and Honeybourn in Gloucestershire ; 
and a Montlivaltia in considerable abundance at Down Hatherly in 
Gloucestershire, at Fenny Compton and Aston Magna in Worcester- 
shire, and at Kilsby Tunnelin Northamptonshire. The middle mem- 
bers of the Lower Lias appear to be destitute of Corals. In the zone 
with Ammonites Bucklandi, called also the Lima-beds, Jsastrea occurs 
in Warwickshire and Somersetshire. Dr. Wright states that Isastrea 
Murchisoni occurs in the next lowest bed of the Lower Lias, namely 
- the White Lias with Ammonites Planorbis, at Street in Somerset ; 
and another Coral has been found in the same zone in Warwick- 
shire. Lastly, in the ‘‘ Guinea-bed” at Binton in Warwickshire 
another Coral has been met with. 

The Montlivaltie of the Hippopodium-bed and the Jsastrea of the 
Lima-beds appear to have grown over much larger areas in the 
Liassic Sea than the other Corals here referred to. 


2. ‘On the Sections of the Malvern and Ledbury Tunnels, on the 
Worcester and Hereford Railway, and the intervening Line of Rail- 
road.” Bythe Rev. W.S. Symonds, A.M., F.G.S., and A. Lambert, 
Esq. 

In this paper the authors gave an account of the different strata 
exposed by the cuttings of the Worcester and Hereford Railway 
(illustrated by a carefully constructed section), including the dif- 
ferent members of the New Red Sandstone (on the east of the Mal- 
vern Hills), the syenite and greenstone (forming the nucleus of the 
Malverns), and the Upper Llandovery beds, the Woolhope shales, 
the Woolhope limestone, Wenlock shales, Wenlock limestone, and 
Lower Ludlow rock on the west side of the syenite, followed by some 
beds of the Old Red series, violently faulted against the Ludlow rock 
at the west end of the Malvern Tunnel. ‘Then the open railway 
passes over Upper Ludlow rocks and some lower beds of the Old Red 
series, here and there covered by drift, until the Lower Ludlow rock 
is again traversed at the east end of the Ledbury Tunnel, and is 


238 Intelligence and Miscellaneous Articles. 


shown to be much faulted and brought up against Upper Ludlow 
shales and Aymestry rocks. The Wenlock shales and the Wenlock 
limestone are then traversed; these are much faulted, the Lower 
Ludlow beds again coming in, followed by Aymestry rock, Upper 
Ludlow shales, Downton sandstone, and, at the east end of the 
tunnel, by red and mottled marls, grey shales and grits, purple 
shales and sandstones, with the Auchenaspis-beds, forming the pas- 
sage-beds into the Old Red Sandstone, as described in a former 
paper (Quart. Journ. Geol. Soc. vol. xvi. p. 193). 

In a note, Mr. J. W. Salter, F.G.S., described the great abun- 
dance of Upper Silurian fossils found in these cuttings, and now 
chiefly in the collection of Dr. Grindrod and other geologists at 
Malvern and the neighbourhood. 


XXXVI. Intelligence and Miscellaneous Articles. 


ON THE FIBROUS ARRANGEMENT OF IRON AND GLASS TUBES, 


[Extract from a Letter from Dr. Debus to Professor Tyndall. ] 


Queenwood College, Feb. 17, 1861. 


FEW weeksago Mr. E. brought me a piece of iron tube which 

had been exposed for several years to the action of moist air. 

Nearly the whole of the tube was converted into oxide ofiron. This 

suggested certain thoughts, the results of which were new and in- 
teresting to me. 

You know, when a piece of glass tube, sealed and filled with water, 
is heated, the tube is cracked, and cracked in a longitudinal direc- 
tion. Why is this? Glass tubes are made by taking a piece of hol- 
low glass in a viscous state and pulling it at both ends. Now, the 
particles of the glass do not adhere to each other on all sides 
with a force of the same strength, but in some directions this force 
is stronger, in others weaker. Under the strain produced by the 
pulling, they arrange themselves so as to offer to the pulling force 
the greatest resistance. Therefore the greatest cohesion of the par- 
ticles is found, in the formed tube, parallel to the length of the tube, 
and the weakest cohesion in a direction perpendicular to this. This 
explains the cracking of the tube as mentioned above. 

Mr. E. could not give me exact information as to how iron tubes 
are made, but he said they were passed through rollers. Now, if 
this is correct, the particles of iron ought to arrange themselves in 
a similar way to the particles in a glass tube. If such a tube oxi- 
dizes, the oxygen naturally would overcome the cohesion of the iron 
first in those places where this cohesion is weakest, that is, in lines 
parallel with the tube. Such is actually the case. The tube men- 
tioned had deep furrows, so to say, hollowed out by the oxygen along 
its length, just in the same way as u glass tube would crack under 
pressure. 

I need not mention to you other examples; but one case more, 
and then I have done. You gave some years ago an explanation of 


Intelligence and Miscellaneous Articles. 239 


cleavage*. The paper wherein this explanation was given never came 
to my hands; and I do not remember that you explained the thing 
to me when we had personal intercourse, The principle alluded to 
appears to me to be the true cause of the phenomenon. , 
If a plastic mass is exposed to pressure, the particles turn until 
they are in such a position as to offer the greatest resistance to the 
pressure brought to bear upon them. But that direction wherein 
they offer the greatest resistance to pressure is also that where the 
cohesion is least. Consequently cleavage ought to take place ina 
direction perpendicular to the pressure exerted. 
Am I right or wrong? Of course I could say more; but why 
should I carry water to the well? 
H. Desvus. 


ON THE CALCIUM SPECTRUM. 
To the Editors of the Philosophical Magazine and Journal. 


GENTLEMEN, 


In acommunication published in the last Number of the Philoso- 
phical Magazine, we pointed out the appearance of a well-defined blue 
line in the spectrum produced by igniting the evaporated residue of 
a deep-well water. From the circumstance of this line, which is situ- 
ated somewhat more towards the violet end of the spectrum than the 
line Sr 6, not being referred to in the paper of Profs. Kirchhoff and 
Bunsen, nor indicated in their beautiful representations of the spectra 
of the alkaligenous metals, we were induced to attribute its pro- 
duction to the probable existence of a previously unrecognized mem- 
ber of the calctum group of metals. Further experiments, however, 
have satisfied us that the blue line in question really belongs to the 
calcium spectrum. On finding this to be the case, we communicated 
with Professor Bunsen, who in return informed us that Professor 
Kirchhoff and himself had observed this line, but, not thinking it 
sufficiently bright to be suitable for the recognition of calcium, had 
not made reference to it in their paper. It can, however, be seen 
with a degree of brilliancy at least equal to that of many of the lines 
represented, when perfectly pure chloride of calcium is ignited in a 
somewhat darkened room. 

We remain, Gentlemen, 
Your obedient Servants, 
F, W. and A. Dupr&. 


ON THE LUNAR TABLES AND THE INEQUALITIES OF LONG PERIOD 
DUE TO THE ACTION OF VENUS. BY M. DE PONTECOULANT. 
In the Number of the Comptes Rendus of the labours of the Aca- 

demy of the 12th of November last, M. Delaunay has inserted a 

memoir in which he gives an account of the researches in which he 

has been engaged, concerning the two lunar disturbances of long 


* Fibrous iron was one of my illustrations.—J, T. 


240 Intelligence and Miscellaneous Articles. 


period depending on the action of the planet Venus, which Professor 
Hansen has proposed to introduce into the expressions for the 
moon’s motions. According to M. Delaunay’s calculations (the accu- - 
racy of which I have at present no intention of disputing) the value of 
the coefficient of the first of these disturbances—that, namely, whose 
period is about 273 years—is nearly the same as that attributed to it 
by the astronomer of Gotha; but the coefficient of the second, whose 
period is about 240 years (and which is the most important of the 
two, since its coefficient, calculated at first by Professor Hansen at 
23''-2, is according to his account at least 21'47), ought to be con- 
sidered, according to the researches of M. Delaunay, as altogether 
insensible, if not absolutely nothing. 

This conclusion, which is moreover perfectly in accordance with 
the announcement of the illustrious geometrician Poisson, published 
more than twenty-seven years ago in his memoir of 1833, gives rise 
to several questions of extreme importance, not only, as it seems to 
me, with respect to the perfection of the lunar tables, but also on the 
subject of scientific priority, and even of national honour. In order 
that the members of the Academy may be able to judge of this for 
themselves, it will be sufficient to mention that the principal cor- 
rections which the astronomers of the Greenwich Observatory have 
thought it necessary to make in the precious tables of our fellow- 
countryman Damoiseau—iables which are so remarkable from the 
fact that they are the first that were constructed from theory alone, 
without recourse to observation,—and the preference which they have 
accorded to the new lunar tables of Professor Hansen, are principally 
founded on the existence (considered by them to he conclusively 
demonstrated) of the two inequalities arising from the action of 
Venus, which M. Delaunay has just calculated. To this it will be 
sufficient to add that it was on these grounds that the extraordinary 
prize of £1000 was allotted to the same Professor by the Lords of 
the Admiralty, at the suggestion of the learned director of the Green- 
wich Observatory, for the really marvellous addition, as Mr. Airy 
calls it, which he has made to the lunar theory. This assertion, if 
suffered to pass without refutation, might lead us to undervalue the 
labours of those astronomers, French and foreign, who have 
brought about the rapid progress of this difficult theory, and have 
advanced it to its present state of perfection. 

I shall not now dwell further on these observations, which from their 
length would extend beyond the limits prescribed by the Academy 
to its own members, and still more to strangers whose claims it admits 
to the honour of an insertion in the Comptes Rendus ; but I thought 
it advisable to lose no time in announcing that Iam busily occupied 
in drawing up a memoir, in which all the observations called for by 
a question of gravity so great that the history of science has rarely 
furnished one similar to it will be detailed at length, so that it may 
not be supposed, either in France or abroad, that a memoir so im- 
portant as that of M: Delaunay has escaped unnoticed or remained 
unanswered.—Comptes Rendus, December 1860. 


ad 


PRiL Mag. Ser. 4. Vol. 21.PL. 1V- 


LFBASIPC, SEs 


THE 
LONDON, EDINBURGH ayn DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENGE. 


[FOURTH SERIES.] 


APRIL 1861. 


XXXVII. On a New Proposition in the Theory of Heat. 
By Professor KirncuHore*. 


— few months ago I communicated to the Society cer- 

tain observations, which appeared of interest because they 
give some information respecting the chemical composition of the 
solar atmosphere, and point the way to further knowledge on 
this subject. These observations led to the conclusion that a 
flame whose spectrum consists of bright lines is partially opake 
for rays of light of the colour of these lines, whilst it 1s perfectly 
transparent for all other light. Iu this statement we find the 
explanation of Fraunhofer’s dark lines in the solar spectrum, and 
the justification of the conclusions regarding the composition of 
‘the sun’s atmosphere; for we find that a substance which, when 
brought into a flame, produces bright limes coincident with. the 
dark lines of the solar spectrum, must be present in the sun’s 
atmosphere. ‘The fact that a flame is partially opake solely for 
those rays which it emits, was, as I stated at the time, a matter 
of some surprise to me. Since that time I have arrived, by very 
simple theoretical considerations, at a proposition from which 
the above conclusion is immediately derived. As this proposition 
appears to me to be of considerable importance on other accounts, 
I beg to lay it before the Society. A hot body emits rays of heat. 
We feel this very perceptibly near a heated stove. The intensity of 
the rays of heat which a hot body emits, depends on the nature 
and on the temperature of the body, but is quite independent of 
the nature of the bodies on which the rays fall. We feel the 
rays of heat only in the case of very hot bodies; but they are 


* Abstract of a Lecture delivered before the Natural History Society of 
Heidelberg. Communicated by Professor Roscoe. 


Phil, Mag. 8. 4, Vol. 21. No. 140, April 1861. R 


242 Prof. Kirchhoff on a New Proposition 


emitted from a body, whatever be its temperature, although the 
amount diminishes with the temperature. In proportion as a 
body radiates, it loses heat, and its temperature must sink unless 
this loss is made up. A body surrounded by substances of the 
same temperature undergoes no change of temperature. In this 
case the loss of heat caused by its own radiation is exactly com- 
pensated by the rays which surrounding substances give out, a 
part of which the body absorbs. The quantity of heat which 
this body absorbs in a given time must be equal to that which in 
the same time it emits. This holds good whatever the nature 
of the body may be; the more rays a body emits, the more of 
the incident rays must it absorb. The intensity of the rays which 
a body emits has been called its power of radiation or emission ; 
and the nuniber denoting the fraction of the incident rays which 
is absorbed has been called the power of absorption. The larger 
the power of emission a body possesses, the larger must its power 
of absorption be. 

A somewhat closer consideration shows that the relation be- 
tween the powers of emission and absorption for one temperature 
is the same fer all bodies. This conclusion has been verified in 
many special cases, both in the last ten years and in former 
times. The foregoing proposition requires, however, that all the 
rays of heat under consideration are of one and the same kind; so 
that these rays are not qualitatively so far different that one part 
of them are absorbed by the bodies more than another part ; for, 
were this the case, we could not speak of the power of absorption 
of a body, simply because it would be different for different rays. 
Now we have long known that there really are different kinds of 
heating rays, and that in general they are unequally absorbed by 
bodies. There are both dark- and luminous-heating rays; the 
former are almost all absorbed by white bodies, whilst the latter 
rays are thus scarcely absorbed at all. Indeed the variety of the 

rays of heat is even greater than the variety of the coloured rays 
of light. The rays of heat, the dark as well as the lumimous, 
are influenced in the same manner as the rays of light, by trans- 
mission, reflexion, refraction, double refraction, polarization, in- 
terference, and diffraction. In the case of the lummous rays of 
heat, it is not possible to separate the light from the heat; when 
one is diminished in a given relation, the other is diminished in 
the same ratio. This has led to the conclusion that rays of light 
and heat are essentially of the same nature ; that rays of light are 
simply a particular class of the heat-giving rays. The dark rays of 
heat are distinguished from the rays of light , Just as the differently 
coloured rays are distinguished from each other, by their period 
of vibration, wave- length, and refractive index. They are not 
visible because the media of our eyes are not transparent to them. 


in the Theory of Heat. 243 


A difference of quality is noticed amongst the rays of light, not 
only in respect to the colour, but also in respect to the state of 
polarization. Hence not only have we to distinguish the heating 
rays according to the wave-lengths, but we have also to divide 
rays of one wave-length into those variously polarized. If we 
take into consideration these various kinds of rays of heat, the 
conclusions which we had drawn concernimg the relation between 
the powers of absorption and emission cease to be binding. 
Whether this relation is still found to exist when these variations 
are taken into consideration, is a question which has, as yet, not 
been decided either by theoretical considerations or by an appeal 

to experiment. I have succeeded in fillmg up this gap; and I 
have found that the proposition concerning the ratio between the 
power of emission and the power of absorption remains true, 
however different the rays which the bodies emit may be, as long 
as the notions of emissive and absorptive powers be confined to 
one kind of ray. 

_ The proposition which I have discovered may be thus more 
precisely defined :—Let a body C be placed behind two screens 
S, and S,, in which two small openings are made. Through these 
openings a pencil of rays proceeds from the body C. Of these 
rays we consider that portion which corresponds to a given wave- 
length A, and we divide this into two polarized components, 
whose planes of polarization are two planes a and 0 at right 
angles to each other, passing through the axis of the pencil of 
rays. Let the intensity of the polarized component a be HE 
(emissive power). Now suppose that a pencil of rays, having a 
wave-length =), and polarized in the plane a, falls through the 
openings 2 and J upon the body C. ‘The fraction of this pencil 
which is absorbed by the body C is called A (absorptive power). 
Then the relation 5 
nature of the body C, and is alone determined by the size of the 
openings 1 and 2, by the wave-length >, and by the tempera- 
ture. I will point out the way in which I have proved this pro- 

position. I began by considering that bodies are conceivable 
which, although very thin, absorb all the rays which fall upon 

them, or which have the capacity of absorption =1. I call such 
bodies perfectly black, or simply black. I first mvestigated the 
radiation of such black bodies. Let C be a black body. The 
body C is supposed to be enclosed in a black envelope, of which 
the screens 8, and S, are a part, and the two screens are sup- 
posed to be connected by a black surface surrounding all. 

Lastly, let the opening 2 be closed by a black surface, which I 
will call “surface 2.” The whole system is to be considered to 
possess the same temperature, and to be protected against loss 

R2 


is independent of the position, size, and 


244. Prof. Kirchhoff on a New Proposition 


of heat from without by an absolutely non-conducting medium. 
Under these circumstances the temperature of the body C cannot 
alter; the sum of the intensities of the rays which it emits must 
therefore be equal to the sum of the intensities of the rays which 
it absorbs ; and because it absorbs all those that fall upon it, the 
sum of the intensities of the rays it emits must be equal to the 
sum of the intensities of the rays which fall upon it. If, now, 
we suppose the followmg change: The “ surface 2” is removed 
and replaced by a circular mirror which reflects all the rays fall- 
ing upon it, and whose centre is in the middle of opening 1. 
The equilibrium of the heat must still be kept up; the sum of 
the rays which fall on the body C must still remain equal to the 
sum of the rays which it emits. But, as it emits just as much 
as before, the quantity of rays which the mirror reflects upon 
the body C must be equal to that which the surface 2 emitted. 
The mirror produces an image of opening 1, which is coincident 
with opening 1. For this reason, just those rays come back to 
the body C, after one reflexion from the mirror, as the body C 
would have emitted through the openings | and 2 if this last one 
had been open; and the intensity of these rays is equal to the 
intensity of the rays which the surface 2 sent back through the 
opening 1. This last intensity however, is, evidently indepen- 
dent of the nature of the body C; and hence it follows that the 
intensity of the pencil of rays which the body C radiates through 
the openings 1 and 2, is independent of the form, position, and 
constitution of the body C; supposing of course that this body 
is black, and that its temperature is a given one. According to 
this, however, the qualitative composition of the pencil of rays 
might become different if the body C were replaced by another 
black body of the same temperature. This is, however, not the 
ease. If I call e the power of emission of this black body com- 
pared with a certain wave-length and a given plane of polariza- 
tion—that, therefore, which I have called E under the suppo- 
sition that C is a body of any kind—then e is independent of 
the nature of the body C, if it only be black. In order to render 
this evident, a further arrangement is necessary. Into the pencil 
of rays which passes from the opening 1 towards the surface 2, 
Jet us suppose a sinall plate placed, which is of so: slight a thick- 
ness that it shows in the visible rays the colours of thin plates ; 
let it be so placed that the pencil of rays is incident at the polar- 
izing angle; let the material of the plate be so chosen that it 
neither absorbs nor emits a sensible amount of rays; let the 
envelope joining the screens 8, and S, be so shaped that the 
image which the plate reflects of the surface 2 lies in the envelope. 
At the position, and of the size of this image, let an opening in the 
cuvelope be made; tuis I will call “opening 3.” Let a screen 


in the Theory of Heat. | 245 


be so placed that no straight line can be drawn from any point 
of opening 1 to any point of opening 8 without passing through 
the screen. Let the opening 3 be now closed with a black sur- 
face, which I will call “surface 3.” The whole system is then 
supposed to possess the same temperature; there is therefore im 
this case equilibrium as regards the heat. This equilibrium is 
supported by rays which, proceeding from surface 3, suffer 
reflexion on the plate, pass through opening 1, and fall on the 
body C. ‘These rays are polarized in the plane of incidence of 
the plate, and contain, according to the thickness of the plate, 
sometimes more of one, sometimes more of another kind of ray. 
Let the surface 3 be removed and replaced by a circular mirror 
whose centre is situated at the spot where the plate reflects an 
image of the centre of the opening 1; then the rays emitted by 
surface 3 will no longer fall on body C, but instead of them 
those reflected from the mirror will fall upon it, and the equili- 
brium of the temperature remains unchanged. If we reflect that 
it does not matter what thickness the plate possesses, or in what 
position we turn it round the axis of the pencil determined by 
passing through openings | and 2, we arrive, by means of similar 
considerations, at the conclusion that the power of emission of the 
black body C, considered with respect to a given wave-length 
and a given plane of polarization, is quite independent of the 
constitution of this body. A conclusion which naturally arises 
from this proposition is, that a// rays which a black body emits 
are completely unpolarized. | 

If we imagine that in the foregoing arrangement the body 
C is not black, but of any other colour, the following equation is 
found by similar reasoning :— 


senate OA nua ae a 


This equation indicates that the relation between emission and 
absorption remains constant for all bodies. The equation may 
obviously be written 

B= App Pet Get Oo Say ae) 
or 


I will now notice some remarkable conclusions derived from 
my proposition. If we heat any body, a platinum wire for ex- 
ample, gradually more and more, it first emits only dark rays ; 
at the temperature at which it begs to glow, red rays begin to 
appear; at a certain higher temperature yellow rays are seen ; 
then green rays, until at last it becomes white-hot, 2, e. emits all 


246 On a New Proposition in the Theory of Heat. 


the rays present in solar ight. The power of emission (E) of the 
platinum wire is therefore equal to 0 for the red rays at all tem- 
peratures lower than that at which the wire begins to glow; for 
yellow rays it ceases to be equal to O at a rather higher tempera- 
ture; for green at a still higher temperature, and soon. Accord- 
ing to equation (1), the emission-power (e) of a completely black 
body must cease to be equal to 0 for red, yellow, green, &c. rays at 
the same temperatures at which the platinum wire began to emit 
red, yellow, green, &c. rays. Let us now consider the case of 
any other body which is gradually heated. According to equa- 
tion (2), this body must begin to give off red, yellow, and green 
rays at the same temperatures as the platinum wire. All bodies 
must therefore begin to glow at the same temperature, or at the 
same tempcrature begin to give off red, and at the same tempera- 
ture yellow rays, &c. This is the theoretical explanation of an ex- 
perimental conclusion obtained by Draper thirteen years ago. The 
intensity of the rays of given colour which a body radiates at a 
given temperature may, however, be very different,—according 
to equation (2) it is proportional to the power of absorption (A). 
The more transparent a body is, the less luminous it appears. 
This is the reason why gases, in order to glow visibly, need a tem- 
perature so much higher than solid or liquid bodies. 

A second deduction which I will mention brings me back to 
my special subject. The spectra of all opake glowing bodies are 
continuous; they contain neither bright nor dark lines. Hence 
we can conclude that the spectrum of a glowing black body (the 
term being used in the sense already defined) must also be a con- 
tinuous one. ‘The spectrum of an incandescent gas consists, at 
any rate most frequently, of a series of bright lmes separated 
from each other by perfectly dark spaces. If the power of emis- 


: > Sa 
sion of such a gas be represented by H, the relation = has an 


appreciable value for those rays which correspond to the bright 
lines of the spectrum of the gas, but it has an inappreciable value 
for all other rays. According to equation (3), however, this 
relation is equal to the absorptive power of the incandescent gas.. 
Hence it follows that the spectrum of an incandescent gas will be 
the converse of this, as I express it, when it is placed before a 
source of light of sufficient intensity, which gives a continuous 
spectrum ; 2. e. the lines of the gas-spectrum, which before were 
bright, will be seen as dark lines on a bright ground. A remark- 
able deduction from my proposition which I will nfention is, 
that, if the more remote source of light is an incandescent solid 
body, the temperature of this body must be higher than that of 
the mcandescent gas in order that such a conversion of the spec- 
trum may occur. 


On the Repulsion of an Electrical Current on ttself. 247 


The sun consists of a luminous nucleus, which would by itself 
produce a continuous spectrum, and of an incandescent gaseous 
atmosphere, which by itself would produce a spectrum consisting 
of an immense number of bright lines characteristic of the nu- 
merous substances which it contains. The actual solar spectrum 
is the converse of this. Were it possible to observe the spectrum 
belonging to the solar atmosphere with all its attendant bright 
- lines, vo one would be surprised to hear that, from the existence 
of the characteristic bright lines of sodium, potassium, and iron 
in the solar spectrum, the presence of these bodies in the sun’s 
atmosphere has been ascertained. According to the proposition 
which I have just laid down, there can, however, be just as little 
doubt concerning the truth of this assertion, as if we saw the 
real spectrum of the solar atmosphere. 

I will, Jastly, mention a phenomenon which, although appa- 
rently trivial, was of peculiar interest to me, because I foresaw it 
theoretically, and afterwards verified it by experiment. Accord- 
ing to theory, a body which absorbs more rays polarized in one 
direction than in another, must also emit those rays in the same 
proportion. A plate of tourmaline cut parailel to the optical 
axis absorbs, at common temperatures, more of those rays falling 
perpendicularly, whose plane of polarization is parallel to the axis 
of the crystal, than of those whose plane is at mght angles to the 
axis. At temperatures above a red heat, tourmaline also pos- 
sesses this same property, although in a less marked degree. 
Hence the rays of light which the plate of tourmaline emits per- 
pendicular to its surface must be partially polarized ; and, more- 
over, they must be polarized in a plane perpendicular to the plane 
of polarization of the rays which have been transmitted by the 
tourmalme. This theoretical conclusion is borne out by ex- 
periment. 


XXXVITI. Remarks on Ampére’s Experiment on the Repulsion 
of a Rectilinear Electrical Current on itself. By Mr. Jamus 
CroLu, Glasgow*. 


q* reference to Dr. Forbes’s “ Notes on Ampére’s Experiment 
on the Repulsion of a Rectilinear Electrical Current on 

itself,’ which appeared in the Philosophical Magazine for Fe- 

bruary, the followmg remarks may perhaps be acceptable. 

I have long been under the impression that Ampére’s experi- 
ment, although successful, does not prove the thing intended, 
namely, that the different parts of a rectilinear electrical current 
are mutually repulsive; for the motion of the wire is evidently 


* Communicated by the Author. 


248 Mr. J. Croll’s Remarks on Ampére’s Eaperiment on 


due to the action of angular currents, and not to a repulsion ex- 
isting between the current in the mercury and the current in the 
branch of the wire in the same straight line. 

Let abcd be the wire floating 
on the mercury, P the point where 
the current enters the mercury, and 
N the point where it leaves it, after 
passing through the wire in the di- 
rection indicated by the arrows. 
The common explanation is, that 
the movement of the wire is due to 
there being in each of the branches 
ab and ed, separately, a repulsion between the current which tra- 
verses them, and the current that is transmitted into the mercury 
before penetrating into the wire or after going out from it; and 
as the current of the mercury and that of the wire are only the 
prolongation of cach other im a right Ime, this 1s considered 
sufficient proof that the one part of the rectilinear current repels 
the other part. 

The following is, however, I think, the true explanation. The 
current Pa in the mercury ts at right angics to the current bc 
in the cross part of the wire. The former current is directed 
towards, and the latter current from the summit of the angle 
abe formed by them. Now, according to Ampére’s well-known 
law of angular currents, the two currents will repel each other. 
In this case the current bc being the moveable one, it will of 
course recede, maintaining a position parallel to itself. This 
eross current be is also at right angles to the current Nd 
on the other side of the glass partition; the former moving 
towards, and the latter from the summit of the angle dcd 
formed by them. These two currents for the same reason will 
repel cach other. The combined influence of the currents P a 
and N d in the mercury will be to cause the cross section of the 
wire which is at right angles to them to recede, maintaining a 
position parallel to itself. It follows, therefore, according to the 
law of angular currents, that Ampére’s experiment must be suc- 
cessful; but then its success does not prove that the parts of a 
rectilinear electrical current are repulsive of each other, but 
simply that a moveable current at right angles to a fixed one is 
repelled when the one current is directed towards, and the other 
from the summit of the angle formed by these two currents. 

It would appear from Dr. Forbes’s experiments, that the dif- 
ferent sections of a rectilinear current are mutually attractive ; 
not repulsive, as is generally supposed. To remoye as much as 
possible all resistance to the motion of the wire, and also to sim- 
plify the conditions of the experiment, imstead of floating the 


the Repulsion of a Reetilinear Electrical Current on itself. 249 


moveable wire upon mercury, he placed it upon one of the arms of 
a delicate torsion balance. ‘The ends of the moveable wire were 
made to bear slightly against the extremes of the two wires in 
connexion with the poles of the pile. When the current was 
established, the moveable wire placed upon the balance was 
attracted by the wires proceeding from the pile, and not repelled 
as in the case of Ampére’s experiment; and the stronger the 
current, and the more complete the contact of the ends of the 
wires, the greater the attraction was found to be. 

There is one objection which may be urged against the con- 
clusiveness of the experiment. It is well known that the ends 
of two wires connecting the poles of a voltaic pile before they 
are brought into contact, are statically charged, the one with 
positive, and the other with negative electricity, the intensity of 
the charge depending upon the force of the pile. Now it is evi- 
dent that these two wires being charged with different electri- 
cities, must attract each other. It is evident also that, however 
close the two ends of the wires may be brought together, unless 
they are in absolute contact in every part, a thing impossible 
without soldering the ends together, the current will not pass 
from the extremity of the one wire to that of the other through the 
intermediate space, which is almost non-conducting, unless there 
is an excess of positive electricity on the one wire and of negative 
on the other; and the more.so, considering the low tension of 
voltaic electricity. This being the case, the ends of the conduct- 
ing wire and those of the moveable branch will always be charged 
with different quantities of electricity, and hence attraction will 
be the consequence; yet one would suppose that, unless the 
current is in reality self-attractive, the attraction arising from 
this cause would not be able to overcome the repulsion which 
must ensue from the action of angular currents just considered. 

There is one objection to the common notion that the parts of 
a rectilinear current are mutually repulsive, that I have never 
seen adduced, which isasfoliows: It results from a law of Ohm, 
which has been confirmed experimentally by Kohlrausch, that in 
the conductor connecting the poles of a voltaic pile, while the 
current is circulating, different sections of the conductor are dif- 
ferently charged. In any part of the conductor whatever, a 
section taken towards the positive pole is always positive in rela- 
tion to a section taken towards the negative pole; and vice 
versa, a section towards the negative pole is negative in relation 
to any section taken towards the positive pole. It follows from 
this that the different sections of the current must attract each 
other. 

The difference of the tension of any two sections depends upon 
the resistance to conduction ; that is to say, the force by which 


250 Prof. Challis on Theories of Magnetism 


any two sections of the current attract each other when the current 
is passing, is always as the amount of the resistance which opposes 
this attraction. The attraction must always exceed the resist- 
ance, or else there can be no current. What does all this mean 
if we do not admit that the sections of the current mutually 
attract each other ? 

The same difference of electric state exists in the various see- 
tions of the pile itself; for we know that there is always an ex- 
cess of positive electricity at the one pole, and of negative at the 
other, and these electricities must tend to unite through the pile 
itself. But there is opposed to the attractive force of the elec- 
tricities for uniting, not only the resistance in the pile itself, but 
also the electromotive force which decomposes the electricity. 
This electromotive force must always exceed the attraction of the 
electricities: this must be admitted; for unless the foree which 
separates the electricities is greater than the attraetive force 
which tends to unite them, there could be no decomposition of 
the electricity, aud of course no current. 

In the pile itself there are two forces—one tending to unite 
the various sections of the current, and the other tending to 
separate them; the latter force being the strongest, the sections 
of the current in the pile will mutually repeleach other. In the 
external conductor which unites the poles of the pile, the latter 
force has no existence; hence the various sections of the current 
in the conductor are mutually attractive. By virtue of the 
repulsion in the pile and the attraction in the conductor, the 
electricity decomposes in the former and unites in the latter; and 
this constitutes what we call an electric current. 


XXXIX. On Theories of Magnetism and other Forces, in reply to 
Remarks by Professor Maxwell. By J. Cuarus, F.R.S., 
F.R.A.S., Plumian Professor of Astronomy and Experimental 
Philosophy in the University of Cambridge *. 


N an article on “ Molecular Vortices applied to Magnetic 
Phenomena,” contained in the March Number of the Phi- 
losophical Magazine, Professor Maxwell has made, respecting 
certain points of the general physical theory which I have lately 
proposed, some remarks which call fora reply. I refer chiefly 
to two paragraphs in p. 163, the first of which is as follows :— 
“ Currents, issuing from the north pole and entering the south 
pole of a magnet, or circulating round an electric current, have 
the advantage of representing correctly the geometrical arrange- 
ment of the lines of force, if we could account for the pheno- 


* Communicated by the Author. 


and other Forces. 251 


mena of attraction, or for the currents themselves, or explain 
their continued existence.” The generation of such currents I 
have explained on hydrodynamical principles in my theories of 
galvanism and magnetism, as also in that of electricity. They 
are shown to be secondary currents, which are always produced 
when a uniform primary current traverses a medium, in which 
there is a gradation of density, such as that which must exist 
from the top to the bottom of a heavy mass resting on a hori- 
zontal plane, in order that the force of gravity on the individual 
particles may be counteracted. The primary currents are ascribed 
exclusively to motions of the ether caused by the rotations of 
the earth and of the other bodies of the solar system about their 
axes. As this is a constant cause, the streams are constant. 
The retention of an induced state of gradation of density from 
end to end, is considered to be the distinctive property of a 
magnetized bar. The observed attractions and repulsions are 
satisfactorily accounted for by the variation of the fluid pressure 
from point to point of space in the secondary currents considered 
as instances of steady motion, such variation, together with the 
dynamical effect of the currents, producing differences of pres- 
sure at different points of the surfaces of the atoms of which 
the substances attracted or repelled are supposed to consist. 
Thus the three explanations which Professor Maxwell considers 
to be requisite respecting currents to which the phenomena of 
galvanism and magnetism are attributed, are in fact given by 
my general theory quite consistently with its original hypotheses. 

The other paragraph commences thus :—‘ Undulations issuing 
from a centre would, according to the calculations of Professor 
Challis, produce an effect similar to attraction in the direction 
of a centre.” I consider that both central attraction and central 
repulsion are accounted for by my calculations. Professor Max- 
well then adduces the following objection :—“ Admitting this to 
be true, we know that two series of undulations traversing the 
same space do not combine into one resultant as two attractions 
do, but produce an effect depending on relations of phase as 
well as intensity.” This point I have considered in articles 2 
and 5 of the Theory of Gravity contained in the Philosophical 
Magazine for December 1859. There is no limitation as to 
the function W, which expresses the velocity or condensation of 
the ztherial waves, excepting that it must either be a single 
circular function, or consist of the sum of several such functions. 
Let it in general be represented by }.msin (b¢+c). Then, ac- 
cording to the theoretical calculation, the motion of translation 
given to an atom in the direction of the propagation of the 
waves, that is, the repulsive action, depends on the non-periodic 
part of the square of this function, the quantity which I have 


252 Prof. Challis on Theories of Magnetism 


called g being in this case insignificant. Now, whatever be the 
phases of the several component functions, the non-periodie part 
of the square of their sum is equal to the sum of the non-periodic 
parts of the squares of the separate functions. In the case of 
attractive action, according to the investigation given in the 
Mathematical Theory of Attractive Forces contained in the Phi- 
losophical Magazine for November 1859, the motion of trans- 
lation depends on the value of g, and on the product of W and 
d?W 
dt? * 
assigned, the non-periodic part of the product for the sum of 
the terms is the sum of the non-periodic parts of the products 
for the component terms taken separately, independently of 
their phases. In short, as we are only concerned with squares 
of circular functions, the mutual interferences by difference of 
phase do not come under consideration. On this account the 
dynamical effects of two series of undulations from separate 
sources, take place independently of each other, and combine 
according to the laws of the composition of accclerative forces. 
To the additional objection, that, ‘‘if the series of undulations be 
allowed to proceed, they diverge from each other without any 
mutual action,” I can make no reply, because I do not under- 
stand it. I can only conclude that it was written under some 
misapprehension. 

Professor Maxwell goes on to assert that “the mathematical 
laws of attractions are not analogous in any respect to those of 
undulations.” In making this assertion he must surely have 
overlooked the very remarkable analogies exhibited by the facts, 
that undulations, like central forces, diverge from a centre, and 
diminish in intensity according to some law of the distance. 
Each body in the universe on which a series of undulations is 
incident, becomes a centre of minor undulations, just as when 
waves on the surface of water encounter an insulated obstacle, 
the obstacle becomes a centre of subordinate waves. The con- 
tinuous generation of subordmate undulations corresponds to 
- the maintenance of the gravitating power of the body. 

Perhaps, however, the assertion, although it is not limited, 
was intended to apply only to such attractions as are observed 
in a magnetic field. If so, it is in accordance with my general 
theory, which makes a distinction between attractions and repul- 
sions by means of undulations, and attractions and repulsions due 
to currents. Electric, galvanic, and magnetic forces are of the 
latter kind. But, while it is admitted that the laws of these 
forces “have remarkable analogies with those of currents,” I 
should not say that they are analogous “to the laws of the con- 
duction of heat and electricity, and of elastic bodies,” because, 


But it is easily seen that if W have the form above 


and other Forces. 2538 


according to the views which I maintain, these are phenomena 
which ultimately may receive explanations by means of ztherial 
undulations and currents, and therefore ought not to be put in 
the same category. 

As the article I have been referring to contains a theory of 
magnetic phenomena wholly different from that which I have 
advanced, it may be worth while to point out a difference in 
principle between the fundamental hypotheses of the two theories. 
Professor Maxwell assumes the existence of a magnetic medium, 
which is not fluid, but “ mobile,” and which acts along lines of 
magnetic force by stress combined with hydrostatic pressure ; in 
other words, there is greater pressure in the equatorial, than in 
the axial, direction of the magnetic field. To account for this 
difference of pressure, it is assumed that “ molecular vortices” 
circulate about axes parallel to the lines of magnetic force. Why 
they are called ‘‘ molecular” is not expressly stated im this arti- 
cle; but it may be gathered from other of the author’s writings, 
that he conceives the matter of the vortices to consist of mole- 
ecules which by their motions may come into collision, the result- 
ing dynamic effect depending on the number and frequency of 
such collisions. It is not my intention to criticise these hypo- 
theses, which have been adduced merely for the sake of remarking 
that, as they are of a particular character, and have been framed 
apparently with special reference to observed laws of magnetic 
phenomena, the results of a mathematical investigation founded 
on them can hardly amount to more than an empirical expression 
of those laws. After all that can be done by this kind of re- 
search, an independent and @ priori theory of the same kind as 
that which I have proposed, if not the very one, is still needed. 

The hypotheses on which my investigations have been founded 
are these only. The physical forces are modes of action of the 
pzessure of the ether, which is a continuous fluid medium, having 
the property of pressing in proportion to its density, and filling 
all space not occupied by the discrete atoms of sensible bodies, 
which atoms are inert, spherical, and of different, but constant, 
magnitudes. It may be remarked that these hypotheses include 
no ideas that are not intelligible by sensation and experience, 
and therefore conform to the rule of philosophy according to 
which cur knowledge of natural operations must ultimately rest 
on such ideas. Also they are strictly related to antecedent and 
existing physical science. The prominent terms, ether and atom, 
which had their origin in ancient speculations, have obtained. re- 
markable significance in modern science,—the first, by explana- 
tions of the phenomena of light, and the other, by aiding us to 
conceive of chemical analyses. The hypotheses under the above 
form are mainly due to Newton, who gave a definition of atoms, 


254 Mr. T. Tate on certain peculiar Forms 


and suggested the dynamic action of the ether; but the state of 
mathematics in his day did not allow of investigating the conse- 
quences of the latter idea. In attempting to do this in the pre- 
sent advanced state of mathematics, I have only added, for that 
purpose, to the Newtonian hypotheses, an exact definition of the 
wether, and the supposition that the atoms are spherical. In the 
first instance I appled the hypotheses as a foundation for a 
theory of light, having long since seen that the theory which 
proposes to account for the phenomena of light by the oscillations 
of the diserete atoms of a medium having axes of elasticity, is 
contradicted by facts, and must therefore be abandoned. This 
charge [ have brought against it in an article on elliptically 
polarized light in the Philosophical Magazine for April 1859 
(p. 288); and it has found no defender. When this first appli- 
cation was made, I had no conception of any modes of applying 
the same hypotheses to explain the phenomena of gravity, elee- 
tricity, galvanism, and magnetism. If they are found to admit 
of applications so varied and extensive, the explanations are no 
longer personal, the hypotheses themselves explain, because they: 
ave true. The only advantage I pretend to possess in these re- 
searches is, the discovery of the true principles of the application 
of partial differential equations to determine the motion and 
pressure of an elastic fluid. But this kind of reasoning, though 
it is indispensable for the establishment of the truth of the 
general physical theory, may be tried on its own merits, quite 
independently of its applic: ition in that theory. For this reason 
I expressed the intention of carefully revising the proofs of the 
propositions in hydrodynamics which have been alre: ady enun- 
ciated in this Journal, and the results of which have been applied 
in the physical theory. But my occupations do not allow of 
entering on this task ant present. 
Cambridge Observatory, 


March 16, 1861, 


XL. On certain peculiar Forms of Capillary Action. 
By Tuomas Tarn, Lsg.* 


IQUIDS rise in small tubes by what is called capillary 
action, that is, by the cohesion of the particles of the 

liquid for one another, as well as by their adhesion to the sides 
of the tube. It has been ascertained ihat the height to which a 
liquid is-raised by capillary action varies inversely as the dia- 
meter of the tube. The chief object of this paper is to deter- 
mine, by direct experiment, the law of capillary resistance exerted 


* Communicated by the Author. 


of Capillary Action. 255 


by a liquid filling small orifices or perforations made in rigid 
plates of different thicknesses. 

Let AC represent a wide glass tube, closed at Fig. 1. 
the top, and having a perforated plate He, capable 
of being wetted, cemented to its lower extremity ; 
1B a glass tube, about half an inch in diameter, 
cemented to this plate, open at its lower extremity, 
and communicating with the tube AC; e asmall 
perforation made in the plate; DB a glass vessel 
containing water or any other liquid to be ex- 
amined. ‘The tube EB is graduated from the 
exterior surface of the plate into inches and 
decimal parts of an inch. ‘The tubes being filled 
with water, and the extremity B inserted in the 
water contained in the vessel DB, it will be 
found that the orifice e may be raised for some 
inches above the level FD of the water in the 
vessel before the atmospheric air will enter the 
orifice. The height C D, at which the external 
air enters the orifice, obviously gives us the measure of the ca- 
pillary resistance of the liquid in the orifice. The followmg 
results of experiments show that, the temperature being constant, 
the height of the column C D, measuring the capillary resistance 
of the liquid, varies inversely as the diameter of the orifice. 

The experiments recorded in the following Table of results, 
were made with the apparatus represented in fig. 1. The orifices 
were made in plates of gutta percha by means of fine steel wires, 
whose diameters had been previously determined, Slight oscil- 
lations and other extraneous causes having been found to affect 


the results of the experiments, each result here given is the mean 
of five experiments. 


Table of results of experiments giving the columns of capillary 
resistance corresponding to different diameters of the orifices. 


The liquid was water at the temperature of 56° F., and the 
thickness of the plate was 05 of an inch. 


Diameter of the |Corresp. column Value of h 
orifice in parts | C D of capillary} by formula 


of an inch, resist. in inches, ee 
dD. h. ‘=39 D 
es 3°35 3:32 


en 1:80 1-82 
ee 1-40 1:36 
ds 112 l-ld 


256 On certain peculiar Forms of Capillary Action. 


The near coincidence of the results of the second and third 
columns shows that, other things being the same, the height of the 
column CD, measuring the capillary resistance, varies inversely as 
the diameter of the orifice. 

The column of resistance, CD, is slightly affected by the thick- 
ness of the plate: thus with a half thickness of plate, and with 
an orifice of th of an inch, the height of this column was found 
to be 3 inches nearly. 

The number of perforations made in the plate does not affect 
the results. 

An increase of temperature sensibly reduces the height of the 
column CD: thus at the temperature of 84°, with an orifice of 
7th of an inch, this column was found to be about ;45th of an 
inch less than it was at the temperature of 56°. 

The column of capillary resistance, C D, for viscous liquids, 
such as diluted solutions of gum and sugar, was found to be 
considerably greater than the corresponding column for water. 

Let the tube EB (fig. 2), closed at the top by the perforated 
plate Ee, be depressed in the liquid, the orifice e beg wet; it 
will be found that the liquid will not rise in the tube to the same 
level as the liquid im the vessel: the column of depression C D, 
in this case measuring the capillary resistance under the same 


Fig. 2. Fig. 3; Fig. 4. 


ililitit 
HANI 


Vhs 


ili! 
ili 


reat 


circumstances, is nearly equal to the elevation of the column C D 
of fig. 1. Here the resistance is simply due to the film of liquid 
filling the orifice e. It is scarcely necessary to state that, when 
the orifice e is dry, or nearly dry, the liquid will rise in the tube 
to the same level as the liquid in the vessel EB. 

In like manner, if the tube, partially filled with liquid, be 
raised as represented in fig. 3, it will be found that the liquid 
will stand in the tube some distance higher than the level of the 
liquid in the vessel. The column of elevation, C D, in this case 
measures the capillary resistance to the pressure of the external 
air. 


On a Theorem relating to Equations of the Fifth Order. 257 


If the tube, completely filled with liquid, be raised as repre- 
sented in fig. 4, it will be found that the liquid will stand in the 
tube some distance higher than the level of the liquid in the 
vessel. The column of elevation C D, measuring the capillary 
action, was found, under the same circumstances, to be nearly the 
same as in the preceding cases. Here the capillary action is 
restricted to the orifice of the thin plate, the diameter of the 
tube EB with which the experiment was performed being about 
oneinch. This experiment strikingly shows that the height of 
the column measuring capillary action for any given liquid at a 
constant temperature depends (chiefly, if not entirely) upon the dia- 
meter of that portion of the tube immediately in contact with the 
upper surface of the liquid. 

March 18, 1861. 


XLI. On a Theorem of Abel’s relating to Equations of the 
Fifth Order. By A. Cayiuny, Esq.* 
P / SHE following is given (Abel, Giwvres, vol. x1. p. 253) as an - 
extract of a letter to M. Crelle :— 

“Si une équation du cinquiéme degré, dont les coefficients 
sont des nombres rationnels, est résoluble algébriquement, on peut 
donner aux racines la forme suivante, 

a=c-+ Aata,? do5ag> + A,a,3 dy3 458 a5 + Agaos ag 


ou 


as 


ay? + Asay a? 5 a3 ag ; 


a=m+n/1+2 4VAl te +e? 4 -V1 +e), 
a,=m—n/1+e Perv h(l +e —V1+¢ +e), 
dg=m+n/1Fe—V Al +e+ V1 +e), 
az=m—n/1LEE—V h(l+e— V1+e +), 


A =K+4+Kla +K"a.+K"aa,, A,=K+K!a,+K"a,+ Kaya, 
A,=K+K'a,+K"a + K"aa,, Az=K+Kla,+ K"a,+ K"aja,. 


Ties quantités c,h, e, m,n, K, K!, K", K'" sont des nombres 
rationnels. 

“Mais de cette maniére léquation z°+axr+b=0 n’est pas 
résoluble tant que a et 6 sont des quantités quelconques. J’ai 
trouvé de pareils théorémes pour les équations du 7*™¢, 11*™, 
13°m°, &c. degré. Fribourg, le 14 Mars, 1826.” 

The theorem is referred to by M. Kronecker (Berl. Monatsb. 
June 20, 1853), but nowhere else that I am aware of. 

It is to be noticed that in the expressions for a, a, dq, a3, the 


| * Communicated by the Author. 
Phil. Mag, 8. 4, Vol. 21. No. 140, April 1861. S 


258 Mr. A. Cayley on a Theorem of Abel’s relating 


radicals are such that 


SI FeV 1 t+e+ Vite) VA +e—V1+e)she(1 +e), 


a rational number. 

The theorem is given as belonging to numerical equations ; 
but considering it as belonging to literal equations, it will be 
convenient to change the notation; and in this point of view, 
and to avoid suffixes and accents, I write 


e=O+ Aa Bi y8 85 + BBS 258 as + Cys d5 a5 Be 4 Ddtak Biys, 
where 
a=m+mn/O+Vp+qV0, 
B=m—n/O+V p—qV@, 
y=m+n/O—Vn+qV@, 
S=m—m/O—-V p—qvO; 
the radicals being connected by 
SOV p+yVOV p—qvO=s, 
and where 
A=K+lLa+My+Ney, B=K+L6+M6-+ N68, 
C=K+Iy+Ma+Nay, D=K+L6+M6+ N68, 


in which equations 0, m, n, p, g, ©, s, K, L, M, N are rational 
functions of the elements of the given quintic equation. 

The basis of the theorem is, that the expression for 2 has only 
the five values which it acquires by giving to the quintic radicals 
contained in it their five several values, and does not acquire any 
new value by substituting for the quadratic radicals their several 
values. For, this being so, # will be the root of a rational quintic ; 
and conversely. 

Now attending to the equation 


JOVp+qVOV p—IVO=s, 
the different admissible values of the radicals are 
JO, Vpt+qv®, Vp—gv®, 
—/6, Vp—qv0, —Vp+qVv®, 
JO, —Vp+qv@, —Vp—qv®, 
-J®, —Vp=4q¥6,  VptqV® 


corresponding to the systems 


to Equations of the Fifth Order. 259 


a, B ‘? oD ) 
ends 8, @ 
Y> 6, a, B 
a, B ihe 6 


of the roots a, 8, y, 5; 7. e. the effect of the alteration of the 
values of the quadratic radicals is merely to cyclically permute 
the roots a, 8, y, 6; and observing that any such cyclical per- 
mutation gives rise to a like cyclical permutation of A, B, C, D, 
the alteration of the quadratic radicals produces no alteration in 
the expression for z. 

The quantities a, 8, y, 5 are the roots of a rational quartic. 
If, solving the quartic by Huler’s method, we write 


a=m+/F+/G+ /H, /FGH=y, a rational function, 

B=m—/F+/G—V/H, 

y=m+/F—/G—VH, 

S=m—/F —/G6+/H, 
then the expressions for F, G, H in terms of the roots are 
| (a+y—B—6)?, (a+B—y—8)*, («+6—B—y)’, 
which are the roots of a cubic equation 

u?—)u? + pu—v?=0, 


where A, “4, v are given rational functions of the coefficients of 
the quartic. We have 


JG4+V/H=V(VE+ caer erat om 


a OER Ree ~ VF. 


So that, takmg O=F, the last-mentioned expressions for «, 8,,6 
will be of the assumed form 


a=m+/O0+Vn+qV0, &e. 
The equation | 

/ OV p+qV OV p—qV O=s 
thus becomes 


Re /G Hi se or F(G—H)?=s?; 


that is, 
—F° + F(R’ + G?+ H*) —2EGH Ss? ; 


S2 


260 Mr. A. Cayley on a Theorem of Abel’s relating 
or, what is the same thing, and putting O for F, 
—X0?+ (A?— p)O—3/?=s?. 
Hence in order that the roots of the quartic may be of the 
assumed form, 
a=m+t+/O4Vn+9V0, &e., 


where m, p, g, © are rational, and where also 
/O Jp +qVO /n—qY V@=s, a rational function, 
the necessary and sufficient conditions are that the quartic should 
be such that the reducing cubic 
u>?—)u? + pu—v? =0 
(whoseroots are (2+ 8 —y—86)?, (« +y—B—5S)?, (« +8—B—y)?) 
“may have one rational root @, and moreover that the function 
—r0?+ (A?— pp)O—3y? 
shall be the square of a rational function s. This being so, the 
roots of the quartic will be of the assumed form, 
a=m+/O+Vn+qV0, &e. 


And from what precedes, it is clear that any function of the roots 
of the quartic which remains unaltered by the cyclical substitu- 
tion «Syd, or what is the same thing, any function of the form 


h(a, B, Y 6) + (8, Y> 6, c) +(y; 5, a, B) oh f(S, a, B, Y) 


will be a rational function of m, ©, p, g, s, and consequently of 
the coefficients of the quartic. The above are the conditions in 
order that a quartic equation may be of the Abelian form. 

It may be as well to remark that, assuming only the system 
of equations 


a=m+/O+/T, 

B=m—/O4VT, 

y=m+/0-VT, 

S=m—/O—1/ 1’, 
then any rational function of a, 8, y, 5 which remains unaltered 
by the cyclical substitution «Sy5 will be a rational function of 
6, T+, TY, /TT(T—-T), /O(T—-T), /O/TT.. In 
fact, suppose such a function contains the term 

(SOS T/T)" 


then it will contain the four terms 


(/6)*{0 + (— PY T/T)" + (—)"U(— 


to Equations of the Fifth Order. 261 
( /o)( VT) V0), 

(-V6)"( VP)"(-VT)’, 

( Ye)(-V/T)*(-V TY, 
(—/6)"(-/T)"( 1)”, 


which together are 


an expression which vanishes unless (—)*, (—)” are both posi- 
tive or both negative. The forms to be considered are therefore 


a A Wa aed eae So 


+ + + 
~ + + 
a — — 


The first form is 
(V/O)* (STP T+ (TPT), 
which, «, 8, y bemg each of them even, is a rational function 
of ©, T+T', TY’. 
The second form is 
(VOUT TY WS TPS TY» 
which, « being odd and £ and y each of them even, is the pro- 
duct of such a function into \/O(T—T’). 
The third form is 
(VOUS TPS TY —(S TS T)*5, 
which, « being even and @ and y each of them odd, is the pro- 
duct of such a function into »/ TT’ (T—T’). 
And the fourth form is 
(VO) US TPS TY + / TS T)*S, 
which, a, 8, y being each of them odd, is the product of such a 
function into »/@(T— 1’). 
Hence if T=p+ q/ 0, T’=p—q/9, and 
/OrV/ptqV/@ /p—q/ O=s, 
®, T+T'(=2p), TY (=p?—¢?20), /TY(T—T' )(= = 


/O(T—T’)(=2¢8), and /O/TT(=s) 


are respectively rational functions. Thisis the @ posteriori veri- 


PL +(-PI (VT) TY} > 


262. Ona Theorem relating to Equations of the Fifth Order. 
fication, that with the system of equations 
a=m+/O + Vp+qv@, &e., /OV p+qV OV p—qVvO=s, 
any function , 
f(a, B, ¥, 6) + (8, y, 9; a)+ oly, 6, a, B) + (6, a, B, Y) 
is a rational function. } 
The coefficients of the quintic equation for # must of course 
be of the form just mentioned; that is, they must be functions 
of a, B, y, 6, which remain unaltered by the cyclic substitution 
a8yd. To form the quintic equation, I write 
0—x=a, 
Aa? BF y5 8? = b, DS*a? BFy?= C, BR*y28? a? =d, Cry? 83 a5 8? =e; 
then we have 
O=a+b+c+d-+e, 
and the quintic equation is 
fl fo fo? fo® fo*=0, 
where is an imaginary fifth root of unity, and 
fo=a-+ bo + cw? + dw? + ew*. 
We have 
fo fot= 0? + (o +.04)>!ab + (@? + o°) Zac, 
fo? fo® = Ya? + (w* + w*)2ab + (w? + w*)2/a0, 
where &! is Mr. Harley’s cyclical symbol, viz. 
Dlab=ab+be+cd+de+ea; 
and so in other cases, the order of the cycle being always abcde. 
This gives 7 
fo fo*fo* fot = Lat + Ya?b? — Lab + 2Za*bhe— Labed 
—52z/a?(be+ cd) ; 
and multiplying by f1, = =a, and equating to zero, the result is 
found to be wh 
+a°— 5abede—5>'a3(be + cd) + 5>/a(b7e? + c7d*) =0. 
Or arranging in powers of a, this is 
od ee 7 
+a?. —5(be+cd) | 
+a’. 5 (bc? + ce? + ed? -+ db*) 
Ce ere 3 
ry : 5 (bc + c8e + e8d+d°b) 20: 
+5 (be? + c?d*?—becd) 


6+c+e+4d° 
ae { —5(b%de + c®bd + e?ch + dec) 


+5 bd2e? + cbh2d? + ec? b? + de*ec? 


On the Stability of Satellites in small Orbits. 263 
the several coefficients bemg, it will be observed, cyclical func- 
tions to the cycle 4, c, e, d. 

Putting for a its value —(x—6), and for 4, c, d, e their values, 
the quintic equation in z is 
| (x—0)° 7 
+ (z—9)°. —5(AC+BD)28y6 | 
+(z—@)?. —5(A*Byd+ B*Cde2+C*D28 + D*ASy)a8ys 
74 5(A®D 0776 + BeAyé*2 + C#Bda28 + D5C28*y)a8yd = 
+5(A?C?+ B*D?—ABCD)2*6*°e . ae. 
J 


(A588? + Beyé8x2 + 058238? + Dea S52) 288 
—5(ASBCyS + B°CDaz + C3D Az + DSABBy)a262y°S2 
4.5(AB°C228 + BC*D2@2 + CD2A2y8-+ DE2A%S2) e262 


where, as before, 
A=K-+La+My+Nay, 
B=K+L8+Mé6+N86, 
C=K+ly+Ma+Nye, 
D=K+L6+MS8+N68; 


and the coefficients of the quintic equation are, as they should 
be, cyclical functions to the cycle z8y6. 


2 Stone Buildings, W.C.., 
February 10, 186]. 


XLII. On the Stability of Satellites in small Orbits, and the 
Theory of Saturn’s Rings. By Dantet VauGHAn *. 


is dee mysterious revolutions of planets and comets were not 

rendered intelligible to astronomers until mathematical 
investigations revealed the peculiar curves which moving bodies 
must describe when left to the exclusive control of solar gravity. 
The process of deductive inquiry, which proved so beneficial in this 
and other departments of celestial mechanics, may be successfully 
applied to another problem which the results of telescopic obser- 
vation have forced on the attention of mathematicians. The 
physical constitution of Saturn’s rings, the circumstances on 
which their stability depends, and the causes which prevent their 
conversion into satellites, have already been made the subject of 
many able essays; but, though regarding these productions as 
valuable contributions to science, I think it advisable to select a 


* Communicated by the Author. 


264 Mr. 1). Vaughan on the Stability of Satellites in small Orbits, 


less difficult road to the solution of the curious problem, and to 
seek a clue to the stability of the annular appendage of Saturn 
by investigating the form which matter must necessarily assume 
in very great proximity to a central body. 

In my communication published in the Philosophical Maga- 
zine for last December (1860), I treated on the equilibrium of 
satellites revolving extremely near to their primaries; and I 
endeavoured to give an estimate of the smallest orbits which they 
could describe in safety. In the cases I considered, the satellite 
was supposed to have its movements adjusted for keeping the 
same point of its surface always directed towards the primary, 
not merely because the hypothesis facilitated the investigation, 
but because observation lends it every support, and the principles 
of natural philosophy furnish most cogent reasons for its adop- 
tion. In describing a very small orbit without such an adjust- 
ment, a satellite must experience, not only excessive tides in its 
seas, but even incessant commotions in its solid matter; and the 
destruction of power by friction necessarily involves a continual 
change in the rotatory movement of the subordinate world, after 
a manner analogous to that which I described in a paper pre- 
sented to the British Association for the Advancement of Science 
in 1857. This must have the ultimate effect of establishing a 
synchronism of the orbital and diurnal movements, together with 
a coincidence of the planes in which they are performed ; so that 
the disturbimg force may give the secondary planet a permanent 
elongation, without rendering it a prey to the effects of violent 
dynamic action. From late researches, however, | am convinced 
that a want of these peculiar conditions would not seriously 
affect the fate of a large satellite when brought into dangerous 
proximity to its primary; and would not change, to any great 
extent, the magnitude of the orbit in which its dismemberment 
must be inevitable. ; 

A homogeneous fluid satellite, having its motions adapted for 
keeping one part of its surface in perpetual conjunction with the 
primary, must find repose in a form differing little from an ellip- 
soid. This proposition, which in my last article was assumed as 
true, may be proved by showing that the relation between the 
forces exerted on every part of the fluid mass is almost precisely 
such as is necessary for equilibrium when the figure is an ellip- 
soid, the dimensions being small compared with the diameter of 
its orbit. For this purpose put A, B, and C for the major, mean, 
and minor semiaxes of the ellipsoid, while P, Q, and R express 
the forces of attraction at their extremities in the absence of all 
disturbances. Now at any point in the surface, the coordinates 
of which referred to the centre are represented by a, ), and ¢, 
the components of the attraction in the direction of each axis 


and the Theory of Saturn’s Rings. 265 


will be expressed by 
aP bQ) cR e 1 
“A? B? "0% e e . e e oy e ( ) 
If N denote the centrifugal force at the extremities of the major 


axis, the intensity at the proposed pomt will be nies , and 


the components in the direction of the three semiaxes will be 
aN bN 

eas, 

To find the components of the disturbing force of the primary 
when the major axis ranges with its centre, we may use methods 
analogous to those pursued in the lunar theory for estimating the 
amount of solar disturbance. Thus, putting # for the radius of 
the circular orbit which the satellite describes, and M for the 
attractive force of the primary at the distance z, the attraction 


which it exerts on the satellite at the point under consideration 
will be 


Oe rc ce 


Mz? 
Pad gt ee ee (3) 


This is equivalent to two forces—one acting in the direction of 
the major axis and expressed by 


M23 
(a®—2aw +02 +b? +42)? 
the other directed to the centre of the satellite and expressed by 
Ma? Va? +02 + c? ; (5) 
(x? —2ax +a? +b? +02)? a eee 
From the first, (4), arises a disturbance operating exclusively 

in the direction of the major axis, and represented by 
pea es gn 8 pn 

(a? —2ax + a? + b?+c?)2 & 


eet 


the squares and higher powers of “» °, and - being rejected as 


too small to affect the result to any appreciable degree. Under 
the same conditions, the radial force (5) resolved with reference 
to the three axes gives the components 

Ma Md Me . 

Ae 3 aaa . e e 4 ) e (7) 


x & 2 
Accordingly, if X represent the sum of the components acting in 


* A demonstration of this theorem may be found in the article on 
“ Attraction ” in the eighth edition of the Encyclopedia Britannica. 


266 Mr. D. Vaughan on the Stability of Satellites in small Orbits, 


the direction of A, Y the sum of those in the direction of B, 
and Z the sum of those in the direction of C, it appears from 
(1), (2), (6), and (7) that 

aP aN 2aM 


le 


bQ bN 6M 
15 = ay B = + epi? a eh 6. cs ee (9) 


Tres oh eg 


Now it is well known that, to satisfy the conditions of equili- 
brium, or to make gravity perpendicular to the surface in all 
parts of the satellite, it is necessary that 


Xda+Vdbt7de=0.. ws oe te pe 
Substituting their values for X, Y, and Z, there results 
P—N 2M Ree M R.M 
(Sa - S )aaat (AR M54 (B 4% o \cde re 
Q 
But the equation of an ellipsoid is a3 -- ap + = 1, and its 
differential, multiplied by the constant quantity 8S, becomes 
Sada _ Shdb , Sede 
=r tape + ce =0. 0" 
A comparison of the corresponding terms of equations (12) and 


(13) will enable us to fix the necessary relations of the constants 
for satisfying the former. It thus appears that 


See at ME oe 


rye + oy — BY ay tat Ieee (15) 
R ti bade, 


These relations being independent of the values of the coordi- 
nates a, b, and c, they will be the same for every part of the sur- 
face of the body; and it follows that an equilibrium established 
at any one locality must extend to every part of the entire mass. 
Accordingly the relative magnitudes which the axes A, B, and C » 
must possess, to make gravity perpendicular to the sur face at any 
intermediate pot, must give gravity a like vertical direction in 
all places, and secure the same stability to every portion of the 
satellite which has an ellipsoidal form. This, however, would 
not appear to be rigorously correct if, in the expressions for the 


_and the Theory of Saturn’s Rings. 267 


disturbances by the primary, the squares and higher powers of 
= and - were retained; and accordingly the very close ap- 
proximation to a true ellipsoid can be exhibited only when the 
size of the satellite is very small compared with that of its orbit. 
If the disproportion between both were not very great, the form 
of the satellite would resemble that of an egg slightly flattened 
by lateral pressure; yet even in such extreme cases the hypo- 
thesis in regard to the ellipsoidal form can lead to no material 
error in estimating the intensity of gravity on its surface, and 
the dimensions of the smallest orbit in which its parts can be 
held together by their mutual attraction. 

From equations (8) and (14), (9) and (15), and (10) and (16), 
the following are readily deduced :— 


P—N 2M aS 
X=a( A, Tora » or =e e - ° (17) 
2—N M bS 
R M cS 
Z=o( G +=), or = G2 ee (19) 


But calling the force of gravity at the given locality F, it is evi- 
dent that F is equal to “X?+ Y?+Z?. On substituting for X, 
Y, and Z their values given by the last equation, there results 


as? 6282 22 Cre RS 
pe — or =* Ta + abt + (20) 
The quantity under the radical in the last expression is the value 
of the normal of the ellipsoid; and hence the force of gravity 
everywhere on the surface is proportional to the length of the 
normal corresponding to the locality. At the extremity of each 
axis this gravitative power, like the normal, is inversely propor- 
tional to the lengths of the axes themselves—a result which might 
be more readily deduced from equations (17), (18), and (19). In 
the first, for instance, if the point be situated at the end of the 
major axis, a becomes equal to A and X, which then expresses 


that the entire gravity at the point is equal to B. ; while the two 
other equations, (18) and (19), treated in a similar manner, would 


give © and C for the values of the intensity of gravity at the 
terminations of the mean and minor axes. 

The cases in which equilibrium is impossible will be indicated 
by the occurrence of imaginary radicals, when we determine the 
relation between the constant quantities in formule (14), (15), 


268 Mr. D. Vaughan on the Stability of Satellites in small Orbits, 


and (16); and as this may be found by simple equations for all 
except the semiaxes A, B, and C, it is to their values alone that 
we must look for imaginary expressions. The formule referred 
to give 
ee ee 


in (P—N)+ oar V «?(P—N)?—8SMa, } 


x 1 ) 


Re , 1 
~ 2M 2M 

Now it is evident that none of the above radicals can become 
imaginary except the first ; and the stability of the body ceases 
to be possible when a?(P—N)?—8MSz, in passing from a posi- 
tive to a negative value, becomes equal tonothing. In this case 

x 

A= AM (P—N). e ° ° ® ry (22) 
But by comparing the expressions given in my last article for 
centrifugal force and the disturbance of the primary at the extre- 
mity of the major axis of the satellite, it appears that the latter 


C= V/ AMSz + R22?. 


is double the former, or that N equals aa We may deduce 


the same result by considering that the orbital velocity of the 
satellite’s centre is equal to “Mz; and from this the rotatory 


velocity of the extremity of the greater axis 1s equal to 7 Ma, 
or Ay/ M Calling this », 
x 
v MA 
N= RX? or N= Sie ; : 2 Y : (28) 
This value being substituted for N in the last equation, gives 


A= ea li whence Pela » 2 (24) 
z w 


The diminished force of gravity which, at the extremity of A, 


is represented by P—N— a thus becomes 


a . ap thease 


the satellite were a homogeneous fluid, the stability must become 
impossible when more than three-fifths of the attraction along 
the major axis is neutralized by centrifugal force and the disturb- 
ing influence of the central sphere. 

The cause of the unstable equilibrium in such cases will be 
rendered more intelligible by a further examination of equa- 


and the Theory of Saturn’s Rings. 269 
tion (14), which, on multiplying its members by A, becomes 


2MA § 

P—N as Tee — A’ e e ° ° . 
The terms of the first member constitute the expression for the 
force of gravity at the extremity of A; and the impossible root 
merely shows that gravity at this point, after having lost over 
three-fifths of its intensity by the disturbances, cannot amount 


(25) 


S brits : 
to —, and consequently can no longer maintain the inverse ratio 


A 
to the length of the axis. This peculiar relation between the 
length of each axis and the gravity at its extremity has already 
been deduced from formula (20), and is indispensable to the 
equilibrium of similar columns of fluid extending from these 
points, either to the centre of the body, or through shells of 
matter equally dense, and bounded by the surfaces of concentric 
ellipsoids similar in position and dimensions. ‘This leads to the 
conclusion maintained on different grounds in my last commu- 
nication, in which I regarded the rupture of the satellite as n- 
evitable, when an increase of elongation would fail to give any 
preponderance to the pressure along the greater axis, or when 
the ellipticity required to be increased to an infinite extent to 
counteract a very slight augmentation of the disturbing forces. 
My former estimates, indeed, do not agree very closely with the 
present investigation in determining the amount of disturbance 
necessary to bring stabiiity to an end; but in these estimates 
the eccentricity of the elliptical section containing the mean and. 
minor axes of the satellite was neglected ; and from more exact 
calculations, which are not yet in a condition to be published, it 
appears that some reduction must be made in the value I first 
assigned to the smallest orbit in which a homogeneous satellite 
could be preserved. 

To furnish another proof that the central and the superficial 
conditions of equilibrium necessarily lead to the same results in 
every respect, let us suppose a portion of the fluid to be enclosed 
in three tubes; two of which are connected at the centre and 
extend to the nearest and most distant part of the surface, while 
the third stretches along the surface to mect their extremities, 
while it coincides with the plane in which they are situated. 


Now the force of gravity being (PN oe at the extre- 
mity of the major axis, it must be reduced to — _ oe a 


along this line at a distance from the centre denoted by a, and 
the element of the pressure in the tube (taking the transverse 


270 Mr. D. Vaughan on the Stability of Satellites in small Orbits, 


section and density of the fluid as unity) will be 


Se ie 


The integral of this expression, taken within the limits of a=0 
and a=A, gives for the central pressure of the fluid in the 


longer tube 


4(p-n—=4). 4 Ly ii 


A similar process applied to the fluid in the tube coinciding with 
the minor axis, will give for the differential of pressure, 


R M 
G+) ede rae meee 


and a similar integration will give for its pressure at the centre, 
C MC 
B (BSS). obey <i walecrneaanl 


For stability it is necessary that the contents of both tubes should 
press to the centre with the same amount of force, or that ~ 


4(p—n—“4)_E(r+*2)=0. . (80) 


Now from the peculiar position which the third tube is sup- 
posed to occupy on the surface, the general equation for the 
equilibrium of its contents will become Xda+Zdc=0, or by 


substitution, 
(<> - oe )ada+ (e+ =) ele=0. sucked 


Integrating within the limits of a=A, c=0, and a=0, c=C, 


this becomes 
(p-n—2*)_S(R+%2)=0. . (82) 


The identity of equations (80) and (82), and the relation 
between (26), (28), and (31), show that the equilibrium of the 
internal and external parts of the mass depend on precisely the 
‘same conditions, and that the fluid should rush to the most pro- 
‘minent parts of the satellite from the surface, as well as from its 
internal regions, whenever gravity along the major axis was dimi- 
nished more than 60 per cent. by the disturbing forces. Brevity 
compels me to omit the more lengthy investigation which would 
be required to show that such consequences are not peculiar to 
special localities, but are the same on all parts of the surface of 
the body. 


and the Theory of Saturn’s Rings. a 


These results might lead us to infer that a satellite which had 
been introduced into the region of instability by the action of a 
resisting medium, must undergo a sudden and not a gradual 
dismemberment. Before embracing this opinion, however, a few 
modifying circumstances should be considered. The change in 
the figure of the body must increase the time of rotation, while 
the diminished size of the orbit calls for a shorter period of re- 
volution ; and the synchronism of the diurnal and progressive 
movements will be destroyed. But we may safely assert that 
the effects of the resisting medium in producing this change are 
exceedingly small compared with the influence of tidal action in 
keeping the same side of the satellite always turned to its pri- 
mary, especially when the distance from the latter became very 
small. The result in such cases must be a little different for a 
solid satellite, which accommodates its form to the new conditions 
of equilibrium by a limited number of paroxysmal changes sepa- 
rated by intervals of many millions of years. On such occur- 
rences, the reduction of the velocity of rotation, together with 
the tendency of the major axis to range with the primary*, 
would lead to a series of librations, which, in a dangerous proxi- 
mity to the latter body, would tend more to promote than to 
prevent the final dismemberment. 

It must be also recollected that our formule have been deduced 
on the supposition that all parts of the satellite are equally dense ; 
and some modifications are therefore required in applying them 
to the cases likely to occur in the realms of Nature. If the den- 
sity increased very rapidly from the surface to the centre, gravity 
might be entirely suppressed at the ends of the greater axis 
before it became incapable of maintaining the stability of the 
internal matter; and it would seem that im such a case the 
satellite might part successively with many layers of the fluid of 
which it is composed, before the increased disturbance called for 
a general disunion of the internal mass. If, however, the in- 
creasing density towards the centre merely results from the great 
pressure in these localities, the separation of matter from the 
surface must weaken the tie which holds the remainder of the 
satellite together; and the dismembering action, when once 
begun, will proceed without interruption until a dissolution of 
the entire mass is completed. Butit is in cases where the satel- 
lite is solid that the mighty change im its condition assumes the 
most awful character, as the cohesion of its parts must prevent 
the gradual loss of matter from its surface, and keep the dis- 
turbing forces under restraint until they become capable of 


* There is some inaccuracy.in my last article in the incidental statement 
respecting the intensity of this directive force at different distances, 


272 Mr. D. Vaughan on the Stability of Satellites in small Orbits, 


effecting a simultaneous dilapidation of the entire planetary 
structure. 

I have regarded it as important to trace the precise manner in 
which these sublime catastrophes must take place; not so much 
on account of their connexion with the existence of planetary 
rings, as for the light which they throw on the nature of 
temporary stars. In an article published in the Supplemental 
Number of the Philosophical Magazine for December 1858, I 
maintained that these singular displays of stellar brilliancy were 
great meteoric displays in the atmospheres, or rather the dormant 
photospheres, of dark central bodies of space, as they were tra- 
versed by the wrecks of dilapidated worlds. The same theory 
has been set forth in my paper presented to the British Associa- 
tion in 1857; and I have endeavoured in other publications to 
support it with satisfactory proof. But the most conclusive evi- 
dence on which it depends, is to be derived from the instanta- 
neous manner in which the attendant of a dark central body 
must undergo a total dismemberment, as it explains the sudden 
manner in which these celestial curiosities are ushered into exist- 
ence with all the splendour of distant suns. Humboldt, in the 
third volume of his ‘Cosmos,’ calls special attention to the fact 
of the extreme brilliancy of the temporary stars in their incipient 
stages, regarding it as a remarkable peculiarity, and one well 
deserving of consideration. 

Without adducing any further evidence on this subject, I shall 
now proceed to trace the condition which matter must assume in 
the region where such disturbing forces render it imcapable of 
forming a single mass, held together by the power of gravity. 
On the dismemberment of a satellite on this dangerous ground, 
the resulting host of fragments would scatter into numberless 
orbits; and the wide range over which they must extend may 
be estimated from the greatest and least size of the elliptical 
paths which their velocities and positions should assign to them. 
For these, however, we can only give at present approximate 
values, taking no cognizance of the mutual disturbances of the 
fragmentary host. And in this case the matter from the most 
distant part of the satellite would describe an ellipse, the dia- 
meter of which is equal to 


23 (a + A) 
2u°—(v+A)* 


The fragments from the nearest point of the dismembering mass 
would describe an elliptical orbit the diameter of which is 


2a°(u—A) | 
22° —(e2—A)§ 


and the Theory of Saturn’s Rings. 273 


But the size of the smallest orbits might fall considerably below 
this limit, in consequence of the rupture of many of the frag- 
ments at their least distances from the primary, either by the 
attraction of that body, or by the heat evolved when they are 
transformed into blazing meteoric masses. 

The condition which matter must ultimately assume in the 
central zone, where it can no longer exist as one great satellite 
or in a limited number of smaller ones, must depend in some 
degree on the form of the primary planet. If this body be an 
oblate spheroid, considerably flattened by rapid rotation, as is 
the case with Saturn, the orbits of the several fragments must 
be subject to apsidal motion, to an extent depending on their 
transverse axes and excentricities. Accordingly those fragments 
describing the same track will be equally affected by it, and will 
form a line which remains unbroken during many revolutions. 
As one ring of fragments is thus made to roll within another, it 
is evident that both must ultimately become circular; and the 
fragmentary host will at length exhibit the nearest approxima- 
tion to a state of repose, by moving in exact circles around the 
central planet. 

There are even more cogent provisions for equalizing the dis- 
tribution of the great ocean of disconnected matter over the vast 
zone in which it circulates. The attraction of the central body 
which led to the great dismemberment, must be adequate not 
only to forbid the reconstruction of a satellite, but even to pre- 
vent the parts of the mighty wreck from congregating to any 
point in an undue proportion. Whenever a preponderance of 
matter occurred at any locality, the impediments of friction 
would tend to equalize the angular velocity of the nearest and 
most distant fragments in the group ; and the new relations be- 
tween gravity and centrifugal force would immediately lead to 
their dispersion by the disturbing action of the primary. If the 
latter body were a very flattened spheroid, it would serve to con- 
fine the great annular ocean of fragments to the same plane, in 
opposition to small effects arising from the disturbances of di- 
stant spheres; and Laplace has shown that, supposing Saturn’s 
ring to consist of numerous independent satellites, they will be 
prevented from departing from a common plane, in consequence 
of the action of his equatorial matter. 

In addition to the foregoing agencies for securing the peculiar 
characters of the annular appendage, I must notice another which 
is inseparable from the movements of such collections of fluid or 
solid matter circulating in independent orbits. A vast amount 
of heat must be developed by their friction and their mutual 
collisions; while the calorific influence of such a mechanical 
action will be augmented by the slight excentricity impressed on. 

Phil. Mag. 8. 4, Vol, 21, No. 140. April 1861. T 


274, Mr. J. S. Stuart Glennie on the 


their orbits by the disturbances of the external satellites. The 
increased temperature originating from this cause, must not only 
permit the existence of fluids im the extensive fields of floating 
matter, but also maintain an atmospheric covering of vapour, to 
give more continuity and symmetry to the annular appendage. 
If the physical characters of Saturn’s rmgs be such as matter, 
not having an improbably great density, must necessarily assume 
in the region which they occupy, the independent movements of 
its parts may be regarded as a continual source of heat, which 
may perhaps in some degree mitigate the sway of intolerable 
cold in the frigid zone of the solar system. 


Cincinnati, Feb. 19, 1861. 


XLIII. On the Principles of Energetics.—Part I. Ordinary Me- 
chanics. By J. 8. Stuart Guenniz, M.A., F.R.AS* 


his | fee the introductory paper, “On the Principles of the 
Science of Motion,” I suggested that this name might 

be given to a new general science, rankmg with the similar 
science of Growth, and not be used merely as a general name for 
the sciences of Ordinary + Mechanics (Stereatics and Hydraties) 
and Molecular Mechanics (Physics and Chemics{). The science 
of Motion would, as a distinct science, or as a philosophy of the 
Mechanical Sciences, consider, first, the relations of motions, as 
motion, and without reference to their originating or determi- 
ning causes or forces; and secondly, the conditions, and corre- 
lations of the conditions, of Pressure, bodily, or molecular, to 
which modern experiment and analysis give us the hope of being 
able to refer all the forces of motion. ‘To the former section of 
General Mechanics I would give the name, coined or made cur- 
rent by Ampére, Kinematics§; for the latter section I would 
adopt the term Energetics ||,already introduced by Rankine witha 
similar meaning to that given by the above statement of its object. 

2. It is proposed in the following papers partially to develope 
the conceptions of the introductory paper, by stating the funda- 
mental principles of the proposed Science of Energetics, with 
their applications to the mechanical interpretation of phenomena. 
The justification and development of these principles is the work 
of the sciences of Mechanics, Physics, and Chemics respectively. 

3. The science of Energetics may be defined as the theory of 

* Communicated by the Author. 

+ Would there not be a more definite distinction between the two 
branches of Mechanics by means of the adjectives Corporal and Molecular? 

{ Phil. Mag. January 1861, p. 54. 

§ Essai sur la Philosophie des Sciences. 


|| “A science whose subjects are material bodies, and physical pheno- 
mena in general,” Edinb. Phil. Journ. N. S. ii, 1855, p. 125. 


Principles of Energetics. 275 


Mechanical, as distinguished from Biological Forces. And 
without such a theory it is evident that no general and concur- 
rent laws or relations can be established between phenomena of 
Motion, as distinguished from phenomena of Growth. Attrac- 
tions (gravic, electric, and magnetic) and Waves (acoustic, optic, 
and thermotic) are the motions offered by Physics for explana- 
tion by mechanical forces, or conditions of pressure. The con- 
stitution and combination of bodies are the phenomena of which 
Chemics require a similar mechanical interpretation. These 
sciences may be distinguished from Mechanics, with its ordinary 
limitation of meaning, as forming together the science of Mole- 
cular Mechanics. But in Ordinary Mechanies also there are 
phenomena, the causal relations of which have been hitherto as 
little established as those of the phenomena of Attraction or of 
Affinity. Such unexplained mechanical phenomena are the uni- 
form motion of the planets, and their velocities of rotation, as yet 
unconnected even by an empirical law. 

The principles of Energetics more particularly belonging to 
Ordinary Mechanics will therefore be in this paper applied to 
the explanation of these mechanical facts. 

4, (I.) A Force is the condition of difference between two pres- 
sures in relation to a third. 

5. To establish the principles of Energetics applicable to the 
first part of Mechanics, it seems unnecessary to use the term pres- 
surewith other than its usual limited meaning as Statical pressure. 
Such a meaning would at least be wide enough for this first prin- 
ciple. For it might be otherwise expressed :—the general cause of 
the movement of a body is a difference between two (previously) 
equilibratmg pressures upon it. But in order that it may be 
seen, at least generally, how I propose to bring the idea of Pres- 
sure into Physics and Chemies, and hence to make this principle 
the foundation of Molecular as well as of Ordinary Mechanics, 
it may be well to state at once that “ under the term Pressure I 
shall include every kind of force which acts between elastic 
- bodies, or the parts of an elastic body, as the cause (condition) 
or effect of a state of strain, whether that force is tensile, com- 
pressive, or distorting* ;” and that I consider elasticity to be 
“une des propriétés générales de la matiére. lle est en effet 
Porigine réelle, ou ’intermédiaire indispensable des phénoménes 
physiques les plus importans de l’univers..... La gravitation et 
Pelasticité doivent étre considérées comme les effets d’une méme 
cause qui rend dépendantes ou solidaires toutes les parties maté- 
rielles de l’univers +.” 


* Rankine, Camb. and Dub. Math. Journ. 1851, vol. 11. p. 49. 
+ Lamé, Théorie Mathématique de ?’ Elasticité des Corps Solides, pp. 1 
2 


and 2, 
T2 


276 Mr. J. S. Sttiart Glennie on the 


6. The special application of this principle is less to pheno- 
mena than to physical hypotheses. For as Force is thus 
conceived, not as an absolute entity acting upon matter, but 
as a condition of the parts of matter itself, “and as a condition 
determined by the relative masses and distances of these parts, 
any valid hypothesis of a force or of a motion to account 
for any set of phenomena is thus seen to imply an assertion 
as to relative masses and distances which can be more or less 
readily submitted to experiment or observation and analysis. 
And hypotheses of Forces which, like electric and magnetic 
fluids, or “‘ uniform elastic ethers, the sole source of physical 
power*,” exist absolutely, and are not merely expressions of facts 
of mass- and distance-difference, are by this principle rejected as 
unscientific. ‘ Lorsq’une branche de la Physique mathématique 
est ainsi parvenue a écarter tout principe douteux, toute hypo- 
thése restrictive, elle entre réellement dans une phase nouvelle. 
Kt cette phase parait définitive, car la série historique, et en 
méme temps rationnelle, des progrés accomplis, signale une ten- 
dance constante vers l’indépendance de toute loi préconguet.” 

How the mutually pressing or repelling parts of matter are to 
be conceived in order that from facts of difference in relative 
masses and distances alone, the forces of Molecular may be 
referred to similar conditions with those of Ordinary Mechanics, 
has been in the introductory paper indicated, and will in the 
second part of this paper be more fully developed. 

7. (II.) Motion, the effect of Force, whether mechanical, phy- 
sical, or chemical, may be distinguished as beginning or conti- 
nuous; and continuous motion as uniform or accelerated. The 
condition of the beginning of motion is a difference of pressure 
on the body that begins to move; the condition of a uniform 
continuous motion is a neutralization of the resisting pressure ; 
the condition of an accelerated continuous motion is a uniform 
or varying resisting pressure. 

8. This principle evidently embodies those of the Inertia of 
Matter, of the Composition of Motions, and of Accelerating 
Force. 

The principle of Inertia is the fundamental scientific principle 
of Non-spontaneity, or the impossibility of a motion undetermined 
by a change in the previously existing relations of the body. 
The inertia of a body or molecule is simply the relation between 
its pressure and that of the bodies acting upon it. All the 
meaning of this principle is in the relativity of the conception it 
gives of the phenomena of matter; it appears, therefore, to betray 


* Challis, “Ona Theory of Magnetic Force,” Phil. Mag. February 1861, 
p. 107. 
t Lamé, Théorie Analytique de la Chaleur, Discours préliminaire, p. Vi. 


Principles of Energetics. 277 
some obscurity of thought to speak of “intrinsic or absolute 
inertia,” 

The law of the Composition of Motions is but an extension of 
that of Inertia*. For the compounding of a motion is but the 
beginning of another motion; and the change in velocity and 
line of motion of the particle due to each force (difference of 
pressure) is the same as if the others did not act. 

There seems to be a clearer conception afforded of uniform 
and accelerated motion by referring these phenomena, as by this 
principle, to their actual physical conditions. 

9. The application of this principle leads to the following 
theorem suggestive of an explanation of the apparent effect and 
non-effect of the resisting medium on the comets and planets 
respectively. 

According as the resultant of a resisting medium passes or 
not through the centre of gravity of a revolving body is it an 
accelerating force of revolution, or a partially neutralized accele- 
rating force of rotation. 

If the medium is uniform, or if—though it varies in density, 
according to some such law as that with so great probability 
assumed for the solar medium, viz. inversely as the square of the 
distance from the central body t—the face of the revolving body 
is so small that the resultant of the resisting pressures thereon 
passes infinitesimally near the centre of gravity of the whole 
body, it may be easily proved that such a resultant of resistance 
will act as an accelerating force, which, did the body move on a 
solid surface, would retard its revolution, but which, as it moves 
through'a fluid medium, will, by the progressive decrease of its 
major axis and excentricicy, cause its orbit to approach more and 
more to the circular form ; and there will hence result, as in the 
case of Encke’s comet, a secular inequality in the expression of 
the mean longitude, and consequently in the period. 

But if, with the above law of decreasing density, the re- 
sultant of resistance to revolution falls at a finite distance below 
the centre of gravity of the body, it is clear that an unbalanced 
pressure thus applied will affect, not the revolution, but the rota- 
tion of the body ; and that the tendency either to cause or acce- 
lerate rotation will be partly at least neutralized by the resistance 
of the medium to this new motion. 

For let a be the direction of revolution, @’ the resultant of the 
resistance thereto of a medium varying in density. It is evi- 


* Price, ‘ Treatise on Infinitesimal Calculus,’ vol. ii. p. 370. 

Tt See Encke, Ueber die Existenz eines widerstehenden Mittels im 
Weltraume; and Pontécoulant, Théorie Analytique du Systeme du Monde, 
vol. tii. book 4, chap. 5, 


278 Mr. J. S. Stuart Glennie on the 


dent that «! will act as an 
accelerating force of rota- 
tion in the direction £; 
and that this rotation will 
be retarded, and e’ partly 
neutralized by the resist~ 
ance in the direction #9’. 

10. In the actual case 
of theplanets, their masses 
and velocities of rotation 
are such that the solar medium can be of course conceived, not 
as causing, but only as tending slightly to accelerate their 
rotations. And a problem is by this theorem suggested of ex- 
treme interest, but also, in the present state of hydrodynamics, 
of extreme difficulty, as to how far this accelerating force of rota- 
tion is neutralized. The earth’s rotation has been hitherto 
considered and proved to be invariable, only in respect of the 
action of the sun and moon; and it is to be remembered that 
doubts have been thrown on its actual invariability even during 
the short period of 4000 years; that one-tenth of a second in 
10,000 years would be a large astronomical quantity; and that 
their actual times are all that, at best, we know of the rotations 
of the other planets. I shall not at present offer any further 
remarks on this problem, considered either as a purely hydro- 
dynamical one, or with the data afforded by the planetary system, 
except to note that nothing seems as yet to have been done towards 
determining the relative effect of a resisting medium on (what 
may at any moment be called) the back of a revolving and rota- 
ting body. And it should seem that little further* can be done 
towards the solution of this problem without experimental data on 
this point especially. The determination of the secular inequality, 
the result of the variously directed and most improbably equili- 
brating forces of the medium, becomes still more complicated 
when such a triple motion as that of a satellite is considered. 

Such, then, is the theorem I would venture to offer as, if not 
giving as yet the demonstrable explanation of the effect of the 
resisting medium on the bodies of the solar systemy, at least sug- 
gesting new and very interesting experimental and analytical 
problems m hydrodynamics. 

11. (III.) The condition of Translation is a difference of 
polar pressures on a point; the condition of Rotation is equal 


* Stokes, ‘On Fluid Friction.’ 

+ I may refer to, though I cannot here discuss, the remarks on this sub- 
ject of Sir John Herschel, ‘ Outlines of Astronomy,’ 5th edit. p. 389 note ; 
and of Prof. Challis in his paper “ On the Resistance of the Luminiferous 
Medium,” Phil. Mag. May 1859. ; 


Principles of Energetics. 279 


and opposite differences of polar pressures on two rigidly con- 
nected points; the condition of compound Translation and Ro- 
tation is unequal and opposite differences of polar pressures on 
two rigidly connected points; and the relation between the 
former and the latter depends on the distance between the centre 
of gravity of the body and the point of application of the result- 
ant of such unequal opposite forces. 

12. In explanation of this principle, it will be sufficient to 
remark that it is merely an expression of the ideas of a single 
force at the centre of gravity, a couple, and a single force not at 
the centre of gravity, in terms of the above general physical con- 
ception of a Force. 

13. The latter paragraph suggests the following general pro- 
blem :—Given a force which, acting instantaneously at the centre 
of gravity of a body of a given mass in a vacuum, gives it a cer- 
tain velocity: what are the different relations between the velo- 
city of revolution and that of rotation when the same body is 
struck at certain different distances from the centre of gravity, 
and on any axis, by the same force ? 

The interest of this abstract problem is in the generality of 
its application to bodies which, while trans- 


lated along 2, rotate about y from a resultant z 

of unequal pressures and resistances, having 

its point of application in or parallel to z (a oe 
wheel) ; and to bodies which, while trans- f 


tive impulse” applied at some point in y (a 
planet). For “le double mouvement de y, 
translation et de rotation des planétes, qui 
parait au premier abord si compliqué, a pu résulter d’une seule 
impulsion primitive qui ne passait pas par leur centre de 
gravité*.” From what previously existing conditions such a 
primitive impulse originated, whether from the rotation of a 
genetic ring, as in the Nebular Theory of Laplace, or other- 
wise, we have not here to inquire. But towards a mechanical 
explanation of the planetary elements, or a hydrodynamical 
theory of the formation of the solar system, the experimental + 
and analytical investigation of the above general problem seems 
to open the way. 

14. In reference to the application of general or particular 
solutions of such a problem to the planets, it may be remarked 
that, as we are not of course here given the primitive impulse, 


lated along 2, rotate about z from “a primi- at 


* Pontécoulant, Théorie Analytique du Systéme du Monde, vol. i. p. 144. 
f~ Extend Plicker’s experiments, for stance. See Taylor’s ‘ Scientific 
Memoirs,’ vol. iv. p. 16, and vol. v. pp. 584 and 621. : 


280 On the Principles of Energetics. 


the first step towards a rational is the discovery of an empirical 
law of the rotations, in which such an element as the inclination 
of the rotation axis to the plane of revolution (easily calculable 
except for the two innermost and two outermost planets) would 
evidently be involved. 

Such a law seems pointed to by the regularity of the decrease 
of the rotations, when the angular, ins stead of the linear velocities 
or times are considered, The respeetive angular velocities of 
rotation of the inner family are "29811, 26902, 26181, and 
25879; and of Jupiter and Saturn, 63313 and ‘59907 re- 
spectively. 

15, The attempts I have made to discover the law of the pla- 
netary rotations have had as yet no complete result*, But the 
following incidental observation with regard to the angular velo- 
cities of revolution and the distances may perhaps be worth noting 
towards such a theory of the formation of the system as above 
alluded to. 

By Kepler’s third law, 


r 


y 
P=cD*; whence = or w=cl —: 
D Dp: 


But under this law there might, in comparing successive velo- 
cities and distances, be found relations of inequality ad infinitum. 
The actual relations may, however, be thus expressed :—The 
angular velocities of revolution and the distances are in inverse 
gcometrical progressions with inverse differenees, except the in- 
nermost planet of each family. 

To say that the distances are in geometrical progression, each 
nearer planet being half the distance of the next more remote, 
or that the angular velocities of revolution are in geometrical 
progression, cach nearer planet revolving with twice the velocity 
of the next more remote, would be very far from accurate ; but 
it seems interesting to ‘observe, as by this law, that when the 
distance of a planet is more than twice that of the next inner, 
its angular velocity of rotation is /ess than half that of the next 
inner, and vice versd, And that the only exceptions to this rule 
should be the innermost planet of each family, viz. Mereury and 
Jupiter, appears significant, 


* The results of an approximative formula were given in a paper “On a 
general Law of Rotation applied to the Planets,” read by me at the Oxford 
Meeting of the British Association, June 1860, 

t See Tumboldt’s remarks on the Law of Bode, or rather of Titius. 
Cosmos, vol, 1. pp. 319, 820, 


Theory of Molecular Vortices applied to Electric Currents. 281 


Mercury and Venus. 


= 36,298051 =} x 68,631843 + 1,982129, 
= (00029760 =2 x 0:0011651 + 0-:0006468. 


ei< 5 


Venus and Earth. 
D=68,631843 =+4 x 94,885000 + 21,189343, 


=0:00116510=2 x 0:00071676 — 0:00026842. 


Earth and Mars. 
D=94,885000 = x 144,575333 + 22,587334, 


‘ = 0:00071676=2 x 0:00038108 — 0:00004540. 


cl< 


Jupiter and Saturn. 


D=493,654546 = x 905,087708 +41,110692, 

n=0 000060411 = 2 x 0:000024332 + 0:0000117470, 
Saturn and Uranus. 

D=905,087708 =4 x 1820,020075 —4,922829, 

is = 0°000024382 = 2 x 0:0000085318 + 0:0000072598. 


Uranus and Neptune. 
D=1820,020075 =4 x 2849,991384 +395,024383, 
r=0 0000085313 =2 x 0:0000043542 — 0:0000001871*. 


6 Stone Buildings, Lincoln’s Inn, 
March 1861. 


XIV. On Phy silt vac of F Foree ce. By y ule C. Meera Pro- 
fessor of Natural Philosophy in King’s College, Londont. 


[With a Plate. ] 
Part I1.—The Theory of Molecular Vortices applied to Electric 


Currents. 
WE have already shown that all the forces acting between 
magnets, substances capable of magnetic induction, and 
electric currents, may be mechanically accounted for on the sup- 


* This fifteenth paragraph may be taken as an abstract of my paper 
“On the Revolutional Velocities and Distances of the Planets,” read before 
the Royal Astronomical Society,glan. 11, 1861. 

+ Communicated by the Author. 


282 Prof. Maxwell on the Theory of Molecular Vortices 


position that the surrounding medium is put into such a state 
that at every point the pressures are different in different direc- 
tions, the direction of least pressure being that of the observed 
lines of force, and the difference of greatest and least pressures 
being proportional to the square of the intensity of the force at 
that point. 

Such a state of stress, if assumed to exist in the medium, and 
to be arranged according to the known laws regulating lines of 
force, will act upon the magnets, currents, &c. im the field with 
precisely the same resultant forces as those calculated on the 
ordinary hypothesis of direct action at a distance. This is true 
independently of any particular theory as to the cause of this 
state of stress, or the mode in which it can be sustained in the 
medium. We have therefore a satisfactory answer to the ques- 
tion, “Is there any mechanical hypothesis as to the condition of 
the medium indicated by lines of force, by which the observed 
resultant forces may be accounted for?” The answer is, the 
lines of force indicate the direction of minimum pressure at every 
point of the medium. 

The second question must be, ‘“ What is the mechanical cause 
of this difference of pressure in different directions?” We have 
supposed, in the first part of this paper, that this difference of 
pressures is caused by molecular vortices, having their axes 
parallel to the lines of force. 

We also assumed, perfectly arbitrarily, that the direction of 
these vortices is such that, on looking along a line of force from 
south to north, we should see the vortices revolving in the direc- 
tion of the hands of a watch. 

We found that the velocity of the circumference of each vortex 
must be proportional to the intensity of the magnetic force, and 
that the density of the substance of the vortex must be propor- 
tional to the capacity of the medium for magnetic induction. 

We have as yet given no answers to the questions, ‘‘ How are 
these vortices set in rotation?” and “ Why are they arranged 
according to the known laws of lines of force about magnets and 
currents?” These questions are certainly of a higher order of 
difficulty than either of the former; and I wish to separate the 
suggestions I may offer by way of provisional answer to them, 
from the mechanical deductions which resolved the first question, 
and the hypothesis of vortices which gave a probable answer to 
the second. 

We have, in fact, now come to inquire into the physical con- 
nexion of these vortices with electric currents, while we are still 
in doubt as to the nature of electricity, whether it is one sub- 
stance, two substances, or not a substance at all, or in what way 
it differs from matter, and how it is connected with it, 


applied to Electric Currents. 283 


We know that the lines of force are affected by electric cur- 
rents, and we know the distribution of those lines about a cur- 
rent; so that from the force we can determine the amount of the 
current. Assuming that our explanation of the lines of force 
by molecular vortices is correct, why does a particular distribu- 
tion of vortices indicate an electric current? A satisfactory 
answer to this question would lead us a long way towards that 
of a very important one, ‘‘ What is an electric current ?” 

I have found great difficulty in conceiving of the existence of 
vortices in a medium, side by side, revolving in the same direc- 
tion about parallel axes. The contiguous portions of consecu- 
tive vortices must be moving in opposite directions; and it is 
difficult to understand how the motion of one part of the medium 
can coexist with, and even produce, an opposite motion of a part 
in contact with it. 

The only conception which has at all aided me in conceiving 
of this kind of motion is that of the vortices being separated by 
a layer of particles, revolving each on its own axis in the oppo- 
site direction to that of the vortices, so that the contiguous sur- 
faces of the particles and of the vortices have the same motion. 

In mechanism, when two wheels are intended to revolve in 
the same direction, a wheel is placed between them so as to be 
in gear with both, and this wheel is called an “idle wheel.” 
The hypothesis about the vortices which I have to suggest is 
that a layer of particles, acting as idle wheels, is interposed be- 
tween each vortex and the next, so that each vortex has a ten- 
dency to make the neighbouring vortices revolve in the same 
direction with itself. 

In mechanism, the idle wheel is generally made to rotate 
about a fixed axle; but in epicyclic trains and other contrivances, 
as, for instance, in Siemens’s governor for steam-engines*, we 
find idle wheels whose centres are capable of motion. In all 
these cases the motion of the centre is the half sum of the motions 
of the circumferences of the wheels between which it is placed. 
Let us examine the relations which must subsist between the 
motions of our vortices and those of the layer of particles inter- 
posed as idle wheels between them. 

Prop. 1V.—To determine the motion of a layer of particles 
separating two vortices. 

Let the circumferential velocity of a vortex, multiplied by the 
three direction-cosines of its axis respectively, be a, 6, y, as in 
Prop. II. Let J, m, n be the direction-cosines of the normal to 
any part of the surface of this vortex, the outside of the surface 
being regarded positive. Then the components of the velocity 
of the particles of the vortex at this part of its surface will be 

* See Goodeve’s ‘ Elements of Mechanism,’ p. 118. 


284 Prof. Maxwell on the Theory of Molecular Vortices 


nB—my parallel to 2, 
ly—na_ parallel to y, 
ma—lB parallel to z. 


If this portion of the surface be in contact with another vortex 
whose velocities are «', 6’, y', then a layer of very small particles 
placed between them will have a velocity which will be the mean 
of the superficial velocities of the vortices which they separate, so 
that if w is the velocity of the particles in the direction of a, 


u= tm(y!—y)—4n(8'-8), «ss (27) 


since the normal to the second vortex is in the opposite direction 
to that of the first. 

Prop. V.—To determine the whole amount of particles 
transferred across unit of area in the direction of 2 in unit of 
time. 

Let 2), yj, 2; be the coordinates of the centre of the first vor- 
teX, Xo) Yo) Zo those of the second, and so on. Let V,, Vo, &e. 
be the volumes of the first, second, &c. vortices, and V the sum 
of their volumes. Let dS be an element of the surface separa- 
ting the first and second vortices, and z, y, z its coordinates. 
Let p be the quantity of particles on every unit of surface. 
Then if p be the whole quantity of particles transferred across 
unit of area in unit of time in the direction of a, the whole mo- 
mentum parallel to « of the particles within the space whose 


volume is V will be Vp, and we shall have 
Vor Spd S ei nude - wake een 


the summation being extended to every surface separating any 
two vortices within the volume V. 

Let us consider the surface separating the first and second 
vortices. Let an element of this surface be dS, and let its 
direction-cosines be /,,m,,n, with respect to the first vortex, and 
1,, Mg, 2. With respect to the second; then we know that 


1+1,=0, m+m,=0, m+7,=0. . . (29) 


The values of a, 8, y vary with the position of the centre of 
the vortex; so that we may write 
da da de 
Oy = ty F dé (%—2) + dy (%a—41) + de (2g—%,), + (80) 


with similar equations for 8 and y. 
The value of wu may be written :— 


applied to Electric Currents. 285 
ld 
7 3 ou (m,(e—2) re ms(2—2,) ) 


ld ld i 
+592 (miymm) +melv—v) +592 (mlemai) mle 29) 


ar i eta) t na(a—2) ) ic = (n,(y—y,) +ns(y—ys) ) 


—3 oF (m(e—2,) +m (2—2,)). = oie gg Md es dice s+ 


In effecting the summation of SupdS, we must remember that 
round any closed surface =/dS and all similar terms vanish ; also 
that terms of the form S/ydS, where / and y are measured in 
different directions, also vanish; but that terms of the form 
SledS8, where / and z refer to the same axis of coordinates, do 
not vanish, but are equal to the volume enclosed by the surface. 
The result is 

—- 1 (/{dy 
eee a, 


d 
=) (V,+V,+&.); » . (82) 
or dividing by V=V,+ V.+ &c., 


1 (dy d8 
P =e Pp (3 — re Py . . . ° e . e e (33) 
If we make 


1 
p= a7’ ° : e > ° e e e ) e * (34) 


then equation (33) will be identical with the first of equations (9), 
which give the relation between the quantity of an electric cur- 
rent and the intensity of the lines of force surrounding it. 

It appears therefore that, according to our hypothesis, an 
electric current is represented by the transference of the move- 
able particles interposed between the neighbouring vortices. We 
may conceive that these particles are very small compared with 
the size of a vortex, and that the mass of all the particles 
together is inappreciable compared with that of the vortices, and 
that a great many vortices, with their surrounding particles, are 
contained in a single complete molecule of the medium. The 
particles must be conceived to roll without sliding between the 
vortices which they separate, and not to touch each other, so 
that, as long as they remain within the same complete molecule, 
there is no loss of energy by resistance. When, however, there 
is a general transference of>particles in one direction, they must 
pass from one molecule to another, and in doimg so, may ex- 


286 Prof. Maxwell on the Theory of Molecular Vortices 


perience resistance, so as to waste electrical energy and generate 
heat. 

Now let us suppose the vortices arranged in a medium in any 
arbitrary manner. The quantities i 4 , &e. will then in 
general have values, so that there will at first be electrical cur- 
rents in the medium. These will be opposed by the electrical 
resistance of the medium ; so that, unless they are kept up by a 
continuous supply of force, they will quickly disappear, and we 
shall then have — = =0, &e.; that is, adx+ Bdy+rydz will 
be a complete differential (see equations (15) and (16)) ; so that 
our hypothesis accounts for the distribution of the lines of force. 

In Plate V. fig. 1, let the vertical circle E E represent an elec- 
tric current flowing from copper C to zinc Z through the con- 
ductor E EH’, as shown by the arrows. 

Let the horizontal circle M M' represent a line of magnetic 
force embracing the electric circuit, the north and south direc- 
tions bemg indicated by the ines 8 N and NS. 

Let the vertical circles V and V’ represent the molecular vor- 
tices of which the lme of magnetic force is the axis. V revolves 
as the hands of a watch, and V’ the opposite way. 

It will appear from this diagram, that if V and V! were conti- 
guous vortices, particles placed between them would move down- 
wards; and that if the particles were forced downwards by any 
cause, they would make the vortices revolve as in the figure. 
We have thus obtained a point of view from which we may regard 
the relation of an electric current to its lines of force as analogous 
to the relation of a toothed wheel or rack to wheels which it 
drives. 

In the first part of the paper we investigated the relations of 
the statical forces of the system. We have now considered the 
connexion of the motions of the parts considered as a system of 
mechanism. It remains that we should investigate the dynamics 
of the system, and determine the forces necessary to produce 
viven changes in the motions of the different parts. 

Prop. V1.—To determine the actual energy of a portion of a 
medium due to the motion of the vortices within it. 

Let «, 8, y be the components of the circumferential velocity, 
as in Prop. II., then the actual energy of the vortices in unit of 
volume will be proportional to the density and to the square of 
the velocity. As we do not know the distribution of density and 
velocity in each vortex, we cannot determine the numerical value 
of the energy directly; but since y also bears a constant though 
unknown ratio to the mean density, let us assume that the energy 


applied to Electric Currents. 287 


in unit of volume is 
E=Cy(a?+ 6?+ 97), 
where C is a constant to be determined. 
Let us take the case in which 


ae pee ae 
“Tle? B= dy’ Y= ‘ge’ e ° . (35) 
Let 
b=, + do, sign aM hoy ie 
and let 


— 


“all d*h, d*, oS) =m, and —— ‘iad + (oo d*ho =i) = Mp} ; 37) 


dem \ dx? * “dy? du? * “dy? * de? 
then ¢, is the potential at any point due to A magnetic system 
m,, and ¢, that due to the distribution of magnetism represented 
by m,. The actual energy of all the vortices is 


B=SCy(e2+62+7%)dV, . . . . (88) 


the integration being performed over all space. 
This may be shown by integration by parts (see Green’s 
‘Essay on Electricity,’ p. 10) to be equal to 


= —4arCX (p,m, + Poma+ Pymat+ghym)dV. . (89) 
Or since it has been proved (Green’s ‘ Essay,’ p. 10) that 
d,m dV =Xidh.m,dV, 
E= —4rC(gym, + dgmgt+2hym,)dV. . . . (40) 


Now let the magnetic system m, remain at rest, and let m, be 
moved parallel to itself in the direction of # through a space dz ; 
then, since ¢, depends on m, only, it will remain as before, so 
that $m, will be constant; and since ¢, depends on m, only, 
the distribution of ¢, about m, will remain the same, so that 
go mz Will be the same as before the change. The only part of 
E that will be altered is that depending on 2¢,m,, because ¢, 


becomes ¢, + = dz on account of the displacement. The varia- 
tion of actual energy due to the displacement is therefore 
sE= —4rC> (2 ma) GV 02..." Nae) 


But by equation (12), the work done by the mechanical forces 
on m, during the motion is 


sw= = (Pima V)8e 5 ee ae 


and since our hypothesis is a purely mechanical one, we must 


288 Prof. Maxwell on the Theory of Molecular Vortices 


have by the conservation of force, 
sE+6W=0; . 4 2 3. 6 et 


that is, the loss of energy of the vortices must be made up by 
work done in moving magnets, so that 


— 403 (2! mdV Jb +3 (“P myaV )8x=0, 
or 


Cg cm ko yale 


~ Sar? 


so that the energy of the vortices in unit of volume is 


i 
gp Mla + B+") 5 » Mr te 


and that of a vortex whose volume is V is 


a Wet B+ yV. 0 

In order to produce or destroy this energy, work must be ex- 
pended on, or received from, the vortex, either by the tangential 
action of the layer of particles in contact with it, or by change 
of form in the vortex. We shall first investigate the tangential 
action between the vortices and the layer of particles in contact 
with them. 

Prop. VII.—To find the energy spent upon a vortex in unit of 
time by the layer of particles which surrounds it. 

Let P, Q, R be the forces acting on unity of the particles in 
the three coordinate directions, these quantities being functions 
of z, y, and z. Since each particle touches two vortices at the 
extremities of a diameter, the reaction of the particle on the vor- 
tices will be equally divided, and will be 

‘Ie ] ] 
2 ts 2 Q, 2 ; 


on each vortex for unity of the particles ; but since the superficial 


density of the particles is Bh (see equation (34)), the forces on 


Qe 
unit of surface of a vortex wili be 
eee ] ] 
nt gens mae — an 


Now let dS be an element of the surface of a vortex. Let the 
direction-cosines of the normal be /, m, x. Let the coordinates 
of the element be z, y, z. Let the component velocities of the 


applied to Electric Currents. 289 


surface be u, v, w. Then the work expended on that element 
_ of surface will be 


Te =—X (Put Qt Rw)d8. . plank Sa 


Let us begin with the first term, PudS. P may be written 


ahr ge . BP 
Pot 7 # Ty as =a dz ay . . e ° ° e (48) 
and 
u=nB—my. 
Remembering that the surface of the vortex is a closed one, so 


that 
LaxdS ==Xmed8 = nydS = XmzdS=0, 


and 
LmydS = Znzd8S =V, 
we find 
dP dP 
SPudS = (—s- aa ME ieeareasarge so 

and the whole work done on the vortex in unit of time will be 

- =— = —=(Pu-+ Qu + Rw)dS 

3 = dR ees ui ak 2) 
=e = de dz)* Ve?) 


Prop. Be oy. find the relations Sais ee ee of 
motion of the vortices, and the forces P, Q, R which they exert 
on the layer of particles between them. 

Let V be the volume of a vortex, then by (46) its energy is 


i 
K= gn Met B+ 7*)V, UP aa eS FE 
and 
oe ied. oe 72). 
WE. age! Ns = tO tT ney 
Comparing this value with that given in equation (50), we find 
dQ dR _ pi) Pee ee dg 
“\de dy at) tO Nae ae ee 
dBi dQ dy\ _ P 
+7 ae cae: ==) She ee We eee (53) 


This equation being true for all values of a, 8, and y, first let 
8 and y vanish, and divide by «. We find 
Phil. Mag. 8. 4. Vol. 21. No. 140. April 1861. U 


290 =Prof. Maxwell on the Theory of Molecular Vortices 


dQ dR_ da 

Eee | 

Similarly, 
sales dR dP_ 4B sit» ene 

dz dz" dé? 

and 


From these equations we may determine the relation between 
the alterations of motion = &c. and the forces exerted on the 
layers of particles between the vortices, or, in the language of 
our hypothesis, the relation between changes in the state of the 
magnetic field and the electromotive forces thereby brought into 
play. 

In a memoir “On the Dynamical Theory of Diffraction” 
(Cambridge Philosophical Transactions, vol. ix. part 1, section 6), 
Professor Stokes has given a method by which we may solve 
equations (54), and find P, Q, and R in terms of the quantities 
on the right-hand of those equations. I have pointed out* the 
application of this method to questions in electricity and mag- 
netism. 

Let us then find three quantities F, G, H from the equations 


dG dil | ‘) 

de dy rare | 

dH: dF 

pe das iz 55 
dx dz HB; ie 
dF dG | 


dy nant ar = MY; J 
with the conditions 


i a d 
and 
dF dG dH 
dx dy + —_ “dz =0, e e *-e@ e e e (57) 


Differentiating (55) with respect to ¢, and comparing with (54), 
we find 


dF dG dH 
P= ae? Q= — Wi? R= Fon e . © (58) 


* Cambridge Philosophical Transactions, yol. x. part 1. art. 3, “On 
Faraday’s Lines of Force.” 


applied to Electric Currents. 291 


We have thus determined three quantities, F, G, H, from which 
we can find P, Q, and R by considering these latter quantities 
as the rates at which the former ones vary. In the paper already 
referred to, I have given reasons for considering the quantities 
F, G, H as the resolved parts of that which Faraday has conjec- 
tured to exist, and has called the electrotonic state. In that 
paper I have stated the mathematical relations between this elec- 
trotonic state and the lines of magnetic force as expressed in 
equations (55), and also between the electrotonic state and elec- 
tromotive force as expressed in equations (58). We must now 
endeavour to interpret them from a mechanical point of view 
in connexion with our hypothesis. 

We shall in the first place exaraine the process by which the 
lines of force are produced by an electric current. 

Let AB, Pl. V. fig. 2, represent a current of electricity in the 
direction from A to B. Let the large spaces above and below 
AB represent the vortices, and let the small circles separating 
the vortices represent the layers of particles placed between them, 
which in our hypothesis represent electricity. 

Now let an electric current from left to right commence in 
AB. The row of vortices gh above AB will be set in motion 
in the opposite direction to that of a watch. (We shall call this 
direction +, and that of a watch —.) We shall suppose the 
row of vortices k/ stillat rest, then the layer of particles between 
these rows will be acted on by the row g/ on their lower sides, 
and will be at rest above. If they are free to move, they will 
rotate in the negative direction, and will at the same time move 
from right to left, or in the opposite direction from the current, 
and so form an imduced electric current. 

If this current is checked by the electrical resistance of the 
medium, the rotating particles will act upon the row of vortices 
Kl, and make them revolve in the positive direction till they 
arrive at such a velocity that the motion of the particles is reduced 
to that of rotation, and the induced current disappears. If, now, 
the primary current A B be stopped, the vortices in the row gh 
will be checked, while those of the row k / still continue in rapid 
motion. The momentum of the vortices beyond the layer of 
particles p g will tend to move them from left to right, that is, 
in the direction of the primary current; but if this motion is 
resisted by the medium, the motion of the vortices beyond pq 
will be gradually destroyed. 

It appears therefore that the phenomena of induced currents 
are part of the process of communicating the rotatory velocity of 
the vortices from one part of the field to another. 


[To be continued. ] 
U2 


[ 202 ] 


XLV. Chemical Notices from Foreign Journals. 
By I. Atxrnson, PA.D., F.C.S. 


(Continued from p. 126.] 


ERNOULLLI has published the result of an investigation of 
tungsten and some of its compounds*. With a view to a 
scientific investigation of the alloys of this metal, his first endea- 
vour was to obtain the metal in a melted state; the result of 
his researches proves, however, that all previous statements as to 
the fusibility of pure tungsten are inaccurate. In his experi- 
ments pure tungstic acid was used; the experiments were made 
with the furnaces of the Royal Iron Foundry in Berlin, where 
he was able to command temperatures higher than any previously 
used in such experiments. 

In one experiment a Hessian crucible was used lined with 
charcoal, in which there was a cavity to receive the tungstic acid, 
and over which there was a layer of charcoal powder. The eru- 
cible, provided with a cover, was kept at a white heat for nearly 
an hour. In this way a metallic mass was obtained free from 
carbon, but without any traces of fusion. In a subsequent ex- 
periment the Hessian crucible was completely fused, and accord- 
ingly they were replaced by the best American graphite ern- 
cibles. Even these did not resist the continuous heat of the 
furnace for 24 hours. A metallic mass was obtained, which was 
caked together and had some metallic lustre. This was heated 
again with charcoal in a crucible protected in the most complete 
manner; and the heat was greater than that ever observed in 
any puddling furnace, so much so that the slag from the coke 
dropped in a thin stream through the grates. 

Notwithstanding this great heat the tungsten had not melted, 
although it had sintered to a tolerably compact mass. The 
metal thus obtained was heated for eighteen hours in a por- 
eelain furnace without any change resulting. 

Hence the author concludes that, with our present means, 
metallic tungsten is infusible. 

Bernoulli also investigated the alloys of tungsten with metals, 
especially iron. Cast-iron turnings were intimately mixed with 
1, 2, 3, 4, 5, 10, 15, and 20 per cent. of pure tungstic acid, in 
the idea that the carbon of the iron would reduce the acid to the 
state of metal. Some experiments were also made in which a 
larger per-centage of acid was taken; but in this case some 
powdered charcoal was added. The mixtures were heated in a 
eraphite crucible to an intense white heat. With an addition of 
10 per cent. of acid, the alloy had the properties of steel; it was 
very sonorous, had a clear grey colour, a pure fracture, and was 

* Poggendorft’s Annalen, December 1860, 


Chemical Notices :—M. Bernoulli on Tungsten. 293 


malleable. The addition of 15 per cent. of acid yielded an alloy 
which might be considered as steel. It was very hard, but was 
not sufficiently malleable. With 20 per cent. the hardness was 
still greater, but the malleability much less. 

The iron in these experiments was grey iron, and contained a 
considerable quantity of graphite, and it was found that with 
white iron a different result was obtained. The experiments 
were made in the same way as the previous ones; it was found 
that an alloy was only formed when charcoal dust was added ; 
otherwise the tungstic acid sintered together, and very little tung- 
sten combined with the iron, The alloy obtained with the addi 
tion of charcoal had none of the appearance of steel; it was 
white on fracture, had the structure of the iron used, and was 
imperfectly malleable. 

With an addition of tungstic acid in the proportion of 75 per 
cent. no regulus was obtained. Analogous experiments were 
made with the minerals Wolfram and Scheelite, and similar 
results were obtained. The manganese present in Wolfram exerted 
a considerable influence on the result ; and with Scheelite the 
lime combines with the silica to form a slag, so that the alloy is 
purer. 

It follows from these experiments, that it is not the carbon 
present in the iron in a state of chemical combination which 
reduces the tungstic acid, but that which is mechanically inter- 
mingled. From white east iron no carbon is withdrawn by the 
tungstic acid, and accordingly no steel is obtained if charcoal be 
not added. 

The waste cast-iron turnings of the workshop may hence be 
used for preparing directly a cast steel, to which the tungsten 
imparts great hardness; or if the iron does not contain too 
much sulphur, phosphorus, or silica, a very useful rough cast 
steel may be obtained by fusing it directly with a quantity of 
powdered Wolfram proportionate to the per-centage of carbon 
which it contains. 

The author determined the carbon in these alloys by three 
methods. In the first, a piece of the alloy was laid upon a fused 
cake of chloride of silver, and was left for several days, covered 
with distilled water. In this way the iron gradually dissolved ; 
and when the decomposition was complete, the charcoal and 
tungsten were collected on an asbestos filter, dried and weighed, 
and then the carbon determined in the usual way by combustion 
with oxide of copper. In another case the alloy was decomposed 
by chloride of copper, and in a third case it was digested with 
iodine until the iron was dissolved. In these cases the carbon 
contained in the alloy amounted to about 1 per cent. 

Kxperiments to alloy tungsten with other metals were also 


294 M. Bernoulli on Tungsten and its Alloys. 


made. With copper, reguli were obtained, which, however, were 
not homogeneous; the individual particles could be distinctly 
seen. In general it was also found that copper, lead, zine, 
antimony, bismuth, cobalt, and nickel only became alloyed with 
tungsten when the reduction of the two metals took place simul- 
taneously. The alloys are so infusible, that, with more than 10 
per cent. of tungsten, no reguli are obtained, and at a higher 
temperature the more volatile metals escape and metallic tungsten 
is left behind. Iron differs in this respect from other metals. 
It alloys in all proportions with tungsten; with above 80 per 
cent., however, the alloys are infusible. 

In order to prepare the tungstic acid used in these experi- 
ments, powdered Wolfram was fused with excess of carbonate of 
soda in an iron crucible, the fused mass dissolved, and boiled to 
reduce manganic acid, and filtered. The solution, which con- 
sisted of tungstate and carbonate of soda, was neutralized with 
nitric acid, and the tungstate of soda crystallized out. This was 
dissolved and treated with nitric acid, and the precipitate of hy- 
drated tungstic acid was well washed. It was then dissolved in 
ammonia, which left a residue of niobic and silicic acids; the 
evaporated liquor deposited a fine crop of crystals of tungstate of 
ammonia. This was well washed with water, and then repeatedly 
treated with fresh quantities of nitric acid for some days to 
remove nitrate of ammonia. The acid was ultimately washed 
out and gently heated, by which it was obtained of a fine pure 
sulphur-yellow colour. 

The author found, in all these experiments, that it was not 
possible to obtain pure yellow acid by directly heating the tung- 
state of ammonia, even when this was done under access of air. 
It invariably became of a green colour. This has been observed 
before, and has been differently interpreted, some ascribing it to 
the formation of a suboxide, and some to an admixture of yellow 
acid and the blue oxide W? O°. 

Bernoulli has found that it is a true compound. When the 
yellow acid was heated to the highest temperature of a gas blow- 
pipe, it gradually changed to a green colour, and from being 
amorphous became crystalline. Similar results were obtained 
by using the high temperature of a stoneware furnace, which 
has an oxidizing flame. The tungstic acid was placed in suit- 
ably protected platinum crucibles, and heated for periods varying 
from eighteen to seventy-two hours. A green crystalline mass 
was obtained, while on the upper part of the crucible there were 
smaller crystals of the same colour. When the caked mass was 
divided and subjected to a further heat for eighteen hours, the 
result was confirmed; part had sublimed in fine crystalline lamin. 

Bernoulli analysed these two modifications by reduction with 


MM. Deville and Debray on the Preparation of Oxygen. 296 


hydrogen, and found that they had the same per-centage com- 
position, WO’, They must therefore be regarded as two iso- 
meric modifications of the same acid, of which the yed/ow is 
formed both in the moist and in the dry way, but in the latter 
case only at a Jow temperature ; while the green variety is only 
formed in the dry way and at a high temperature. The latter 
he proposes to call pyrotungstic acid, in antithesis to Scheibler’s 
acid*, which is metatungstic acid. Including the ordinary acid, 
there are therefore three varieties. 

Bernoulli has made a new determination of the equivalent. of 
tungsten, both by oxidizing tungsten, and by reducing tungstic 
acid. He obtained results varying within very narrow limits, 
which lead to the number 93:4 as that of the equivalent. 
Dumas had obtained the number 92+. 

Bernoulli finally discusses the formula of the natural tung- 
states, and attempts to show that the two modifications of 
tungstic acid also occur in nature. Le adduces a great many 
analyses of Wolfram. Most of them contain a certain quantity 
of lime and magnesia, which he considers accidental constituents. 
But in most cases a niobic acid is present—in the tungsten from 
Zinnwald 1:1 per cent. ; this is to be regarded as replacing part 
of the tungstic acid, with which it is therefore isomorphous. 

The author finally describes the mode of analysing the tung- 
sten minerals. 


Engaged in investigating the methods of working up the pla- 
tinum residues for the Russian Government, Deville and Debray 
had occasion to examine the different methods of preparing 
oxygen on a large scale. They find} that sulphate of zine, 
which, as a waste product, is now so plentiful, furnishes an eco- 
nomical source of this gas. When calcined in an earthen vessel, 
it is converted into light white oxide, which, when the sulphate 
is pure, may be used for painting. The temperature required 
for its decomposition does not exceed that necessary for binoxide 
of manganese. The other products of the decomposition are 
sulphurous acid and oxygen, which may be separated by means 
of the solubility of the former in alkalies; or the following 
method may be used, which is employed by the authors for pre- 
paring oxygen by the decomposition of sulphuric acid. 

This body at a red heat may be decomposed into sulphurous 
acid, water, and oxygen, by means of a very simple apparatus, 
consisting of a retort, of about 5 litres, filled with thin platinum 
foil, or, better, a serpentine tube filled with platinum sponge and 
heated to redness. A thin stream of sulphuric acid passes into 


* Phil. Mag. vol, xx. p. 374. t Ibid, vol. xvi. p. 211. 
{ Comptes Rendus, November 26, 1860, 


296 M. Carré on the Production of Low Temperatures. 


this apparatus through an S tube; the products pass first through 
a cooler which condenses the water, and then through a washer 
of a special form. In this way pure and inodorous gas is ob- 
tained, and a solution of sulphurous acid, which may be changed 
either into sulphite or hyposulphite of soda, or may be used in 
the sulphuric acid chambers. The expense ‘of oxygen prepared 
by this plan is very small; for the method consists essentially i in 
abstracting oxygen from the atmosphere. Hvenif the sulphurous 
acid were not utilized, sulphuric acid would still be the cheapest 
source of oxygen, cheaper even than binoxide of manganese. 


M. Carré has applied* the great cold produced by the evapo- 
ration of condensed ammoniacal gas to the production of low 
degrees of temperature. 

The apparatus he uses consists of two ordinary cylindrical 
metal receivers connected by a tube. One of these is four times 
the size of the other, and is filled to three-quarters its capacity 
with the strongest solution of ammonia. At the time of closing 
the vessel, care is taken to expel all air. The largest vessel is 
placed over the fire, the smaller being immersed in cold water. 
The solution is heated to 130° or 140°, the temperature being 
indicated by a thermometer fitted in the larger vessel. At this 
point nearly all the ammonia is expelled from the solution, and 
liquefies in the second retort. When the separation is complete, 
the larger vessel is cooled down: the reabsorption of the liquefied 
gas commences immediately, and its volatilization produces a 
degree of cold which readily freezes the water surrounding it. 
The temperature sinks to —40°; and M. Balard, who tried the 
experiment at the Collége de France, was able to solidify mercury. 

Besides this apparatus, M. Carré has devised another form of 
it, which is continuous in its action, but otherwise depends on 
the same principle. 


M. Leroux, of the Ecole Polytechnique, has made some deter- 
minations of the refractive indices of vapours at high tempera- 
tures, by means of an apparatus constructed for that purpose, on 
which M. Babinet+ has reported to the Academy. 

M. Dulong had found that the refractive index of oxygen 
was 1:000278 ; of hydrogen, 1:000188; of nitrogen, 1-000300 ; 
and of chlorine, 1:000772, that of air being 1:000294. M. 
Leroux has found that the refractive indices of the vapours of 
the following substances, saturated at the ordimary pressure, are 
respectively— 


* Comptes Rendus, December 24, 1860, 
+ Ibid. November 26, 1860. 


M. Leroux on Refractive Indices of Vapours. 297 


Sulphur: 6: ow, L00L629 
Phosphorus . . . 1:001864 
PASORITCH 02 ¥5, he eet tal DOT 
Merenty .)) 6 0 sie 1000896 
The apparatus by which these results were obtained consists 
of a very large furnace mounted on an axis, and provided at its 
lower part with a divided circle, by which it can be inclined at 
any angle. In the centre of the furnace there is a prism analo- 
gous to that of Borda, employed by Dulong. This prism is made 
of solid iron, and the rays enter and emerge through glass plates 
cemented by a method peculiar to M. Leroux. The exact mea- 
surement of the angle of the prism presents some ingenious 
points. As in Babinet’s goniometer, the light is concentrated 
on the prism, while filled with the vapour, by a telescope, and the 
light on its emergence is received on another telescope provided 
at its focus with a micrometric wire. With the first telescope, 
its distance from the furnace, the size of the furnace, the distance 
of the second telescope and its focal distance, which is above 2 
yards, the extent of this gigantic goniometer is about 23 feet. 
The means of verifying the results leave nothing to be desired. 


Rose*, in a paper on the separation of tin from other metals, 
and on its quantitative estimation, describes the following method 
of effecting these objects. 

The separation of tin from other metals is usually effected by 
oxidation with nitric acid, so as to convert the tin into stannic 
acid: in certain cases, however, this method gives inaccurate 
results, and can only be said to be quite successful in the case 
of the strongly basic oxides. 

Another method consists in dissolving the binoxide of tin in 
hydrochloric acid, and precipitating by sulphuric acid. Both 
modifications of binoxide are precipitated im this manner, in the 
presence of a large excess of water. The precipitates require a 
long time in order to settle completely, more especially when 
there is a large quantity of free hydrochloric acid. The precipi- 
tate must be carefully washed free from hydrochloric acid other- 
wise when it 1s ignited some tin cscapes in the form of chloride. 
The ignition is best effected with the addition of some carbonate 
of ammonia. 

In the presence of certain substances, phosphoric acid for 
example, even this method gives inaccurate results. The pre- 
sence of a large excess of hydrochloric acid does not hinder the 
precipitation of some phosphoric acid along with the binoxide 
of tin. 

When tin is to be separated from other metals, it must be 


* Poggendorfi’s Annalen, January 1861, 


298 Prof. H. Rose on the separation of Tin from other Metals. 


oxidized with nitric acid in the usual manner, and the residue 
digested with moderately strong hydrochloric acid. On the 
addition of a large quantity of water, all is dissolved, and the tin 
is then precipitated with sulphuric acid. 

In the separation of copper and tin by the ordinary method, 
the binoxide always contains a trace of copper; but by the above 
process the separation of the two metals is complete, the binoxide 
is quite free from copper. 

Tin and lead are best separated by fusing the alloy with 
sulphur and carbonate of potash. On treating the mass with 
water, the sulphide of tin dissolves. This is the best method of 
analysing the fusible alloy of tin, bismuth, and lead. Tin and 
silver are also best separated in this way. 

In an acid solution, tin and bismuth are best separated by 
sulphide of ammonium. 

The separation of iron from tin can only be completely effected 
by oxidizing the alloy with nitric acid, dissolving in hydrochloric 
acid, and saturating the hydrochloric solution with sulphuretted 
hydrogen. 

Tin is best separated from titanium by means of sulphide of 
ammonium. 

The separation of the oxides of tin from magnesia and the 
alkaline earths is best effected by igniting them with sal- 
ammoniac, by which the tin escapes as chloride. In general all 
the tin is expelled by one ignition; but two are always amply 
sufficient to remove the last traces of tin. 


In the analysis of minerals, the separation and estimation of 
tin is best effected by converting it ito the oxide. The volu- 
metric analysis, however, is very convenient for the determina- 
tion of the tin in tin-salts. The ordinary method is to convert 
the protochloride of tin in hydrochloric acid solution into the 
bichloride by means of oxidizing agents, such as permanganate 
or bichromate of potash. But protochloride of tin absorbs atmo- 
spheric oxygen, even during the determination, to such an extent 
as materially to vitiate the results of analyses. 

Stromeyer* has observed that good results are obtained by 
the addition of sesquichloride of iron im excess to the freshly 
prepared solution of tinin hydrochloric acid. The reaction is as 
follows :— 

Sn Cl-+ Fe? Cl? =Sn Cl? +2 Fe Cl. 


The protochloride of iron formed is determined by permanga- 
nate; and as it is not nearly so susceptible to atmospheric 
oxygen as protochloride of tin, much more accurate results are 
obtained. 

* Liebig’s Annalen, February 1861. 


M. Reboul on Derivatives of Glycerine. 299 


_ Tin may also be directly dissolved in sesquichloride of iron to 
which hydrochloric acid has been added, 


Sn-+ 2 Fe? Cl?= Sn Cl?+ 4 Fe Cl. 


But this method is only available with tolerably pure tin; for 
-tmany other metals reduce perchloride of iron, and consume 
solution of permanganate. 


There are several compounds which have the formula C+ H*Cl?. 
One of these is obtained by the action of pentachloride of phos- 
phorus on aldehyde, and another by the action of chlorine on 
chlorinated ethyle. Beilstein observed some time ago that these 
two bodies were identical, and he has recently proved* that the 
same is the case with two corresponding isomeric compounds of 
the .benzoic acid series: the one, chlorobenzole, C!* H® Cl?, is 
obtained by the action of pentachloride of phosphorus on oil of 
bitter almonds; and the other is the chlorinated chloride of ben- 
zyle, C'4 (H® Cl) Cl. 

The latter body is formed, as Cannizaro showed, by the action 
of chlorine on toluole; and Beilstein used this method of pre- 
paring it. He finds that it has all the physical properties of 
chlorobenzole. A careful comparison also of the chemical 
actions of the two substances, both by his own direct experi- 
ments and by those of other experimenters, leave no doubt as to 
the complete identity of the two substances. 


Reboul has published} the results of a lengthened and im- 
portant investigation on some derivatives of glycerine. The 
compounds which the author describes may be derived from an 
oxygenized body, glycide, C® H® 04, which has not been isolated, 
and which might be considered as the anhydride of glycerine, to 
which it would bear the same relation as lactide does to lactic 
acid. It would play the part of a diatomic alcohol, and would 
yield a series of ethers, the general formation of which may be 
thus expressed :— 


C® H6 044 A— H? 0?=C® 4A O02, 
C° Hé 04+ A A’—2H?0?=Co BH? A A’, 
A and A! representing the formule of monobasic acids. 

The starting-point for his research 1s hydrochloric glycide, ob- 
tained by the action of potash on bihydrochloric glycerine, 
C® H® Cl? 02, which simply removes hydrochloric acid, 

C® A Cl? O? —HCl=C® H? C10. 
Bihydrochloric glycerine itself is formed by saturating a mix- 
* Liebig’s Annalen, December 1860. 


+ Annales de Chimie, September 1860. Répertoire de Chimie, November 
1860. 


300 M. Reboul on Derivatives of Glycerine. 


ture of glycerine and acetic acid with gaseous hydrochloric acid. 
The chief product of the action is bihydrochloric glycerine, 
which may be separated by fractional distillation; or, by heat- 
ing the crude product with caustic potash, hydrochloric glycide 
is directly obtained. It isa colourless liquid, heavier than water, 
and smelling like chloroform. It boils at 118°—119°: it is 
metameric with Geuther’s hydrochlorate of acroleine, with 
Riche’s monochlorinated acetone, and with chloride of pro- 
pionyle. 

Monohydrochlorie glycide combines directly with fuming hy- 
drochloric acid to form dihydrochloric glycide, C° H4 Cl? : this body 
may also be formed by acting on hydrochloric glycide with pen- 
tachloride of phosphorus, an action which gives rise to the forma- 
tion of trihydrochloric glycerine, 

C® H® ClO?+ PCI’ = C® H® Cl + PCI 0?; 

Hydrochloric Trihydrochloric 

glycide. glycerine. 
and this, decomposed by potash, loses hydrochloric acid, and the 
new body is formed, 
C° H® C8—HCl=Cé H4 Cl?, 

This body is identical with what Berthelot has called epibrom- 
hydrine. It is metameric with bichlorinated propylene, and 
with Geuther’s chloride of acroleine. Similar compounds con- 
taining bromine and iodine were also obtained. 

By the action of ammonia on bihydrochloric glycide a base is 
formed, which the author considers identical with that obtained 
by the action of amznonia on terbromide of allyle. 

Hydrochloric glycide unites directly with the oxyacids to form 
a glyceric ether, contaiming an equivalent of oxyacid and of hy- 
dracid. Thus,— 

C® H® C10?+ C4 H4 O*=C® H® (C4 H? O?) C104. 
Hydrochloric Acetic Acetohydrochloric 
glycide. acid. glycerine. 

By the action of water, hydrochloric glycide fixes two equi- 
valents, and monohydrochloric glycerine is formed :— 

C° H® ClO? + H? O?=C® H7 C104, . 
Hydrochloric Monohydrochloric 
glycide. glycerine, 
By the action of aleohol the hydrochloric compounds of glycide 
are transformed into mixed glyceric ethers, contaimmg an equi- 
valent of acid and an equivalent of alcohol, 
C® H® ClO?-+ C+ H® O?= C® H® Cl (C4 H®) 04, 
Hydrochloric Alcohol. Hydrochloric 
glycide. ethylglycerine. 


On anew Element, probably of the Sulphur Group. 301 


When these bodies are treated with potash, hydrochloric acid is 
removed, and the resultant compound, ethylglycide, is a glycide 
containing the alcohol radical in the place of an equivalent of 
hydrogen :— 

C® Hé (C4 H5) Cl0*— HC1=C® Hi (C* H9) 04. 
Hydrochloric Ethylglycide. 
ethylglycerine. 

Ethylelycide is a mobile liquid boiling at 128°. When treated 
with hydrochloric acid, it yields the compound C® H® (C* H®) Cl0*, 
If the compound hydrochloric amylglycerine be treated with 
ethylate of soda, ethylamylglycerine is formed. Thus,— 

C® H¢ (C'° H") ClO4+ C4 H® NaO?= C H$ (C!° H") (C4 H®) O° + NaCl. 
Hydrochloric Ethylate Ethylamylglycerine. 
amylglycerine. of soda. 

The glyceric ethers containing two equivalents of the same acid 
are Only a particular case of this reaction. 

When hydrochloric glycide is acted upon by hydrosulphate of 


sulphide of potassium, a compound is obtained analogous to 


mercaptan, 
C* H® ClO?+ KS HS=KCl1+ C® H® S? 0?, 
Hydrochloric New body. 
glycide. 


A second mercaptan in this series is doubtless formed by the 
action of dihydrochloric glycide on hydrosulphate of sulphide of 
potassium, and which would have the formula C® H® $+. 


XLVI. On the existence of a new Element, probably of the 
Sulphur Group. By Witi1smM Crooxss, F.C.8S*, » 


ie the year 1850 Professor Hofmann placed at my disposal 
upwards of 10 lbs. of the seleniferous deposit from the 
sulphuric acid manufactory at Tilkerode in the Hartz Mountains, 
for the purpose of extracting from it the selenium, which was 
afterwards employed in an investigation upon the selenocyanidest. 
Some residues which were left in the purification of the crude 
selenium, and which from their reactions appeared to contain 
tellurium, were collected together and placed aside for examina- 
tion at a more convenient opportunity. They remained unnoticed 
until the beginning of the present year, when, requiring some 
tellurium for experimental purposes, I attempted its extraction 
from these residues. Knowing that the spectra of the incandescent 
vapours of both selenium and tellurium were free from any 
* Communicated by the Author. 


+ Chem. Soc. Quart. Journ. vol. iv. p. 12, and Gmelin’s Handbook 
(Cavendish Soc, Translation), vol. viii. p. 122, 


802 Mr. W. Crookes on the existence of a new Element, 


strongly-marked line which might lead to the identification of 
either of these elements, it was not until I had in vain tried 
numerous chemical methods for isolating the tellurium which I 
supposed to be present, that the method of spectrum-analysis was 
used. A portion of the residue, introduced into a blue gas-flame, 
gave abundant evidence of selenium ; but as the alternate light 
and dark bands due to this element became fainter, and I was 
expecting the appearance of the somewhat similar, but closer, 
bands of tellurium, suddenly a bright green line flashed into view 
and as quickly disappeared. An isolated green line in this por- 
tion of the spectrum was new to me. I had become intimately 
acquainted with the appearances of most of the artificial spectra 
during many years’ investigation, and had never before met with 
a similar line to this; and as from the chemical processes through 
which this residue had passed the elements which could possibly 
be present were limited to a few, it became of interest to discover 
which of them occasioned this green line. 

After numerous experiments, I have been led to the conclu- 
sion that it is caused by the presence of a new element belong- 
ing to the sulphur group; but, unfortunately, the quantity of 
material upon which I have been able to experiment has been 
so small, that I hesitate to assert this very positively. I am, how- 
ever, at work upon some of the seleniferous deposit itself, and 
hope shortly to be able to speak more confidently upon this 
point, as well as to give some account of its properties. 

In the purest state that I have as yet succeeded in obtaining 
this substance, it communicates as definite a reaction to the 
flame as soda,—the smallest trace introduced into the burner 
of the spectrum apparatus giving rise to a brilliant green Ime, 
perfectly sharp and well-defined upon a black ground, and 
almost rivalling the Na line in brilliancy. It is not, however, — 
very lasting: owing to its volatility, which is almost as great as 
selenium, a portion introduced at once into a flame merely shows 
the line as a brilliant flash, remaining only a fraction of a 
second; but if it be imtroduced into the flame gradually, the 
line continues present for a much longer time. 

The properties of the substance, both in solution and in the 
dry state, as nearly as I can make out from the small quantity 
at my disposal, are as follows :— 

1. It is completely volatile below a red heat, both in the 
elementary state and in combination (except when united with 
a heavy fixed metal). 2. From its hydrochloric solution it is 
readily precipitated by metallic zinc in the form of a heavy black 
powder, insoluble in the acid liquid. 38. Ammonia added very 
gradually until in slight excess to its acid solution, gives no pre- 
cipitate or coloration whatever, neither does the addition of car- 


probably of the Sulphur Group. 303 


bonate or oxalate of ammonia to this alkaline solution. 4. Dry 
chlorine passed over it at a dull red heat unites with it, forming 
a readily volatile chloride soluble in water. 5. Sulphuretted 
hydrogen passed through its hydrochloric solution precipitates 
it incompletely, unless only a trace of free acid is present ; but 
in an alkaline solution an immediate precipitation of a heavy 
black powder takes place. 6. Fused with carbonate of soda and 
nitre, it becomes soluble in water,—hydrochloric acid added in 
excess to this liquid producing a solution which answers to the 
above tests 2, 3, and 5. 

An examination of these reactions shows that there are very 
few elements which could by the remotest possibility be mis- 
taken for it. | 

The accompanying list includes every element, with the ex- 
ception of the gases, bromine, iodine, and carbon. Opposite the 
name of each I have placed the number of the reaction which 
eliminates it from the list of possible substances, taking great 
care, in every case, to give the benefit of any doubt which might 
arise, on account of an imperfectly known or doubtful reaction, 
in favour of the opposite opinion to that which I desire to prove, 
and, in cases where several reactions would prove the same thing, 
only making use of the most trustworthy. 


1, 5. Aluminium. 1. Iron. Selenium. 
Antimony. 1, 5. Lanthanium. 1, 5. Silicium. 
Arsenic. 1. Lead. 1. Silver. 

2, 3, 5. Barium. 2, 5. Lithium. 2, 5. Sodium. 
2, 3, 5. Beryllium. 2, 5. Magnesium. 2, 3, 5. Strontium. 
1, Bismuth. 1. Manganese. 5. Sulphur. 
1, 2, 5. Boron. 3, 6. Mercury. 1. Tantalum. 
6. Cadmium. 1. Molybdenum. Tellurium, 
2, 5. Cesium. 1. Nickel. 1, 5. Terbium. 
2, 3, 5. Calcium. 1. Niobium. 1, 5. Thorium. 
1, 5. Ceriwn. 1, Norium. A pb rei 
1, Chromium, Osmium. 1. Titanium. 
1. Cobalt. 1. Palladium. 1. Tungsten. 
1. Copper. 5. Phosphorus. 1. Uranium. 
1, 5. Didymium. 1. Platinum. 1. Vanadium, 
1, 5. Erbium. 2, 5. Potassium. 1, 5. Yttrium. 
1. Gold. 1, Rhodium. 2. Zine. 
1. Umenium. 1, Ruthenium. 1, 5. Zirconium. 
1. Indium. 


There are therefore left the following, amongst which, if already 
known, it must occur :—antimony, arsenic, osmium, selenium, 
and tellurium ; and although, to my own mind, many of the re- 
actions detailed above are sufficient proof that it cannot be one 
of the first three elements, yet I have thought it better to let 
them pass. 

Kach of the above five bodies, both in the elementary state 
and in combination, has been rigidly scrutinized in the spectrum 


304 Existence of a new Element, probably of the Sulphur Group. 


apparatus by myself and many friends. Not a trace of such a line 
is shown by either of them in the green part of the spectrum,— 
Antimony, arsenic, and osmium, in fact, giving continuous spectra, 
in which every colour is visible. The remaining elements, sele- 
nium and tellurium, might almost be dismissed unchallenged, 
inasmuch as I was first led to the examination by finding that it 
was not either of these. Nevertheless I have, as stated at the 
commencement of this paper, repeatedly examined their spectra, 
and find no trace of such a line, the alternate light and dark 
bands in the almost continuous spectra of selenium and tellurium 
forming in fact so strong a contrast to the one single green ray 
of the new substance, that the latter may readily be detected in 
the presence of an enormous excess of either of the former. 

In order to remove any remaining doubt which there might 
be as to the green line being due to any of the elements men- 
tioned in the above list, I have, moreover, specially examined the 
spectra produced by each of these bodies in detail, either in their 
elementary state, or in their most important compounds. Many 
of them give rise to spectra of great and characteristic beauty, 
but none give anything like the green line; nor, in fact, is there 
any artificial spectrum, except that of sodium, which equals it in 
simplicity. 

There still may be urged the possibility of its being a compound 
of two or more known elements, or an allotropic condition of one 
of them ; a moment’s thought, however, will show that neither of 
these hypotheses is tenable. They would in reality prove what 
they are raised to oppose; for nothing less could follow than a 
veritable transmutation of one body into another, and a conse- 
quent annilulation of all the groundwork upon which modern 
science is based. If an element can be sochanged as to have 
totally different chemical reactions, and to have the spectrum of 
its incandescent vapour (which is, par excellence, an elementary 
property) altered to an appearance totally unlike that given by 
its former self, it must have been changed into something which 
it originally was not. ‘This, in the present position of science, is 
an absurdity. 

The method of exhaustion which I have adopted to prove 
the elementary character of the body which communicates this 
green line to the spectrum of the blue gas-flame*, may seem 
unnecessary as well as unchemical in the present state of the 
science ; I was obliged, however, to rely upon what I may call 
circumstantial evidence of its not being a known element, 
owing to the very small quantity of substance at my command 


* TI need scarcely add that the line is quite distinct from either of the 
green or blue lines seen in a gas-flame which is undergoing complete com- 
bustion. It is moreover far more brilliant than these. 


Geological Soctety. 305 


(I believe I overestimate the amount which I have as yet ob- 
tained, at two grains), which precluded me from trying many 
reactions. The method of spectrum-analysis adopted to prove 
the same fact, although perfectly conclusive to my own mind, 
might not have been so to others, unsupported by chemical 
evidence. 

The following diagram will serve to show the position in the 
spectrum which the new green line occupies with respect to the 
two lithium and the sodium lines. 


Lia Li8 Naa 


j= ae 


New 
Green Line. 


For confirmatory experiments on many of the observations 
mentioned in this paper, I am indebted to my friend Mr. C. 
Greville Williams. The detailed examination of the various 
spectra are at present being joimtly pursued by us, and will be 
published as soon as completed. 


XLVII. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Contined from p. 238. ] 


January 23, 1861.—L. Horner, Esq., President, in the Chair. 
othe following communications were read :— 

1. “On the Gravel and Boulders of the Punjab.” By J. 
D. Smithe, Esq., F.G.S. 

In the Phimgota Valley (a continuation of the great Kangra or 
Palum Valley) the drift consists of sand and shingle with boulders of 
gneiss, schist, porphyry, and trap, from 6 inches to 5 feet in diameter. 
Some of the boulders, having a red vitreous glaze, occur in irregular 
beds. This moraine-like drift lies on the tertiary beds, which, here 
dipping gently towards the plains, gradually become vertical, and 
are succeeded by variegated compact sandstones, gradually inclining 
away from the plains ; next come various slates, at a high angle ; and 
gneissic rocks lie immediately over them. 


2. “On Pteraspis Dunensis (Archeoteuthis Dunensis, Roemer).” 
By Prof. T. H. Huxley, F.R.S., Sec. G.S. 

The fossil referred to in this communication is from Daun in the 
Eifel, and was described by Dr. Ferd. Roemer (in the ‘ Palzonto- 


Phil. Mag. S. 4. Vol. 21. No. 140. April 1861. X 


306 Geological Society :— 


graphica,’ vol. iv. p. 72, pl. 13) as belonging to the naked Cepha- 
lopods, under the name of Paleoteuthis Dunensis (changed to Archeo- 
teuthis in the ‘ Leth. Geogn.’); and in the Jahrb. 1858, p. 55, Dr. 
IF’. Roemer described a second specimen from Wassennach on the 
Laacher See. Prof. Huxley reproduced, with remarks, Dr. Roemer’s 
description of the specimens; and, after observing that Mr. S. P. 
Woodward had already suggested (Manual of Mollusca, p. 417) 
that Roemer’s fossil was a fish, he stated his conviction that it was 
really a Pteraspis, agreeing in all essential particulars with the 
British Pteraspides, though possibly of a different species. 


3. ‘On the ‘ Chalk-rock ’ lying between the Lower and the Upper 
Chalk in Wilts, Berks, Oxon, Bucks, and Herts.” By W. Whitaker, 
Esq., B.A., F.G.S. 

The author has more particularly examined the band which he 
terms ‘“ Chalk-rock’’ on the northern side of the western part of the 
London Basin. Here it has its greatest thickness (12 feet) to the 
west, gradually thinning eastward. It is a hard chalk, dividing into 
blocks, by joints perpendicular to the bedding; and it contains hard 
calcareo-phosphatic nodules. It contains no flints; and in the di- 
strict referred to none occur below it; but there is often a band 
of them resting on its upper surface. It seems to form an exact 
boundary between the Upper and the Lower Chalk, being probably 
the topmost bed of the latter. In this case it will often serve as an 
index of the relative thickness of these divisions, or as a datum for 
the measurement of the extent of denudation that the Upper Chalk 
has suffered. North of Marlborough, where it is thick, the Chalk- 
rock appears to have given rise to two escarpments (an upper and a 
lower) to the western portion of the Chalk Range. 

Fossils are usually rare in this bed; but Mr. J. Evans, F.G.S., 
collected several from it near Boxmoor; and amongst them the 
genera Belosepia (hitherto known only as Tertiary), Baculites, Nau- 
tilus, Turrilites, Solarium, Inoceramus, Parasmilia, and Ventriculites 
are represented; and the following species have been identified— 
Litorina monilifera and a new species, Pleurotomaria sp., Myacites 
Mandibula, Spondylus latus, Sp. spinosus, Rhynchonella Mantelliana, 
Terebratula biplicata, and T. semiglobosa. 


February 6, 1861.—L. Horner, Esq., President, in the Chair. 
The followmg communication was read :— 


“On the Altered Rocks of the Western and Central Highlands.” 
By Sir R. I. Murchison, F.R.S., V.P.G.S., and A. Geikie, Esq., 
F.G.S. 


In the introduction it was shown that the object of this paper was : 
to prove that the classification which had been previously established — 


by one of the authors in the county of Sutherland was applicable, 
as he had inferred, to the whole of the Scottish Highlands.. The 


structure of the country from the borders of Sutherland down the | 
western part of Ross-shire was detailed, and illustrated by alarge map — 


oe eee eee ee ee oe 


On the Altered Rocks of the Western and Central Highlands. 307 


of Scotland coloured according to the new classification, and by 
numerous sections. Everywhere throughout this tract it could be 
proved that an older gneiss, which the authors called ‘‘ Laurentian,” 
was overlain unconformably by red Cambrian sandstones ; these again 
unconformably by quartz-rocks, limestones, and a gneissose and 
schistose series of strata, as previously shown in the typical district of 
Assynt. From the base of these quartz-rocks a perfect conformable 
sequence was shown to exist upward into the gneissose rocks, which 
is not obliterated by granite or any similar rock. 

The tract between the Atlantic and the Great Glen consists, 
according to the authors, of a series of convoluted folds of the upper 
gneissose rocks, until, along the line of the Great Glen, the under- 
lying quartzose series is brought up on an anticlinal axis. A pro- 
longation of this axis probably exists along part of the west coast of 
Islay and Jura, two islands which exhibit a grand development of 
the lower or quartzose portion of the altered Silurian rocks of the 
Highlands. 

From the line of the Great Glen north-eastward to the Highland 
border, the country was explained as consisting of a great series of 
anticlinal and synclinal curves, whereby the same series of altered 
rocks which occurs on the north-west is repeated upon itself. One 
synclinal runs in a N.E. and S.W. direction across Loch Leven. 
The anticlinal of quartzose rocks that rises from under it to the S.E. 
spreads over the Breadalbane Forest to the Glen Lyon Mountains, 
where it sinks below the upper gneissose strata with their associated 
limestones. Ben Lawers occupies the synclinal formed by these 
upper strata; and the limestones and quartz-rock come up again in 
another anticlinal axis corresponding with the direction of Loch 
Tay. The continuity of these lines of axis was traced both to the 
N.E. and $.W. 

It thus appeared that the crystalline rocks of the Highlands are 
capable of reduction to order; that the same curves and folds could 
be traced in them asin their less altered equivalents of the South of 
Scotland; and that in what had hitherto appeared as little else than 
a hopeless chaos, there yet reigned a regular and beautiful simplicity. 

In conclusion, Sir Roderick Murchison vindicated the accuracy 
of his published sections in the N.W. of Sutherland, which had 
been approved after personal inspection by Professors Ramsay and 
Harkness ; and he gave detailed reasons for disbelieving the accu- 
racy of the sections recently put forth by Prof. Nicol, which were 
intended as corrections of his own. He concluded by affirming 
that, through the aid of Mr. Geikie, the proofs of the truthful- 
ness of his own sections, showing a conformable ascending order 
from the quartz-rocks and limestones into crystalline and micaceous 
rocks, had now been extended over such large areas that there could 
no longer be any misgivings on the subject. 


F ebruary 20, 1861.—L. Horner, Esq., President, in the Chair, 


The following communications were read :— 
1. ‘* On the Coincidence between Stratification and Foliation in 


X 2 


308 Geological Soctety :-— 


the Crystalline Rocks of the Highlands.”” By Sir R. I. Murchison, 
V.P.G.S., and A. Geikie, Esq., F.G.S. 

Allusion was, in the first place, made to the early opinions of 
Hutton and Macculloch, who regarded the gneissic and schistose 
rocks of the Highlands as stratified. Mr. Darwin’s views of the na- 
ture of the ‘‘ foliation”’ of gneiss and schist were then referred to ; 
and it was insisted that this condition was not to be found in the 
rocks of the Highlands,—the so-called ‘ foliation’”’ which the late 
Mr. D. Sharpe had described in 1846 as characterizing the crystal- 
line rocks of that country being, according to the authors, really 
mineralized stratification. It was then pointed out that, as Prof. 
Sedgwick had previously insisted on the wide difference between 
‘‘ foliated” or ‘‘ schistose’’ and ‘‘ cleaved” or ‘‘ slaty ” rocks, and as 
Prof. Ramsay had in 1840 recognized interlaminated quartz as being 
parallel to stratification in the Isle of Arran, ‘‘ foliation’’ should be 
regarded as coincident with stratification, and not with cleavage, in 
the Scottish Highlands. 

After some observations on the occurrence of cleavage in slates 
at Dunkeld, Easdale, Ballahulish, and near the Spittal of Glenshee, 
the authors stated their belief that all the ‘‘ foliation” of the ery- 
stalline rocks of the Highlands is nothing more than lamination due 
to the sedimentary origin of deposits, in which the sand, clay, lime, 
mica, &c. have subsequently been more or less altered, and that the 
‘arches of foliation” described by Mr. D. Sharpe (Phil. Trans. 
1852) correspond in a general way with the parallel anticlinal axes 
shown by the authors in a former paper to exist in the Highlands. 
They remarked that the synclinal troughs, however, are not expressed 
in Mr. Sharpe’s figures, and that he has omitted the bands of lime- 
stone which they refer to as an important evidence of the stratifica- 
tion of the district. They also pointed to the acknowledged difficulty 
which the quartzites presented to Mr. Sharpe, but which readily fall 
into the system of undulated strata that they have described. One 
of the quartzites having yielded an Orthoceratite, and pebbles being 
present in one of the schists of Ben Lomond, these facts were ad- 
duced as further evidences of the real stratal condition of the schists 
and quartzites of the Highlands. 


2. ‘On the Rocks of portions of the Highlands of Scotland South 
of the Caledonian Canal, and on their equivalents in the North of 
Ireland.”” By Professor R. Harkness, F.R.S., F.G.S. 

The author, having had an opportunity of examining the geology 
of the North-west of Scotland in the year 1859, and more especially 
the arrangement of rocks described by Sir R. Murchison as “ fun- 
damental gneiss, Cambrian grits, lower quartz-rock, limestones, 
upper quartz-rock, and overlying gneissose flags,” applied the results 
of his observations during last summer to portions of the Highlands 
lying south of the Caledonian Canal, and to the North of Ireland. 
Developed over a large portion of these districts are masses of 
gneissose rock, of varying mineral nature, and sometimes putting on 
the aspect of a simple flaggy rock. Where these gneissose masses 


Mr. Drew on the Succession of Beds in the Hastings Sand. 809 


come in contact with plutonic masses, they exhibit that highly 
erystalline aspect which induced Macculloch and others of the Scotch 
geologists to regard them as occupying an extremely low position 
among the sedimentary series, and to apply to them the Wernerian 
term “primitive.’”’ Many of Macculloch’s descriptions, however, 
show that this assumed low position is not the true place of this 
gneiss among the sedimentary rocks which make up the Highlands 
of Scotland. 

In a section from the southern flank of the Grampians to Loch 
Earn (and in other sections, from Loch Earn to Loch Tay, from 
Dunkeld to Blair Athol, in the Ben y Gloe Mountains, in Glen 
Shee, &c.), there is seen a sequence which indicates that this gneiss 
is the highest portion of the series of rocks, with underlying quartz- 
rock and limestone. 

In the county of Donegal, Ireland, a like sequence is seen. A 
section from Inishowen Head to Malin Head, along the east side of 
Loch Foyle, presents us with gneissose rocks above limestone and 
quartz-rocks, exactly as in Scotland. In no portion of Scotland 
south of the Caledonian Canal, nor in the North of Ireland, did the 
author recognize any trace of the ‘‘ fundamental gneiss.” 


March 6, 1861.—Leonard Horner, Esq., President, in the Chair. 


The following communications were read :— 

1. “On the Succession of Beds in the Hastings Sand in the 
Northern portion of the Wealden Area.” By F. Drew, Esq., F.G.S., 
of the Geological Survey of Great Britain. 

Having first referred to the division of the Wealden beds by former 
authors into the ‘‘ Weald Clay,” the ‘‘ Hastings Sand,” and the 
“Ashburnham Beds,” and the subdivision of the ‘‘ Hastings Sand” by 
Dr. Mantell into ‘‘ Horsted Sands,” ‘ Tilgate Beds,” and ‘* Worth 
Sands,” and having defined the district under notice as lying be- 
tween and in the neighbourhood of the towns of ‘Tenterden, Cran- 
brook, ‘Tunbridge, Tunbridge Wells, East Grinstead, and Horsham, 
Mr. Drew proceeded to describe, first, the several beds in the meri- 
dian and vicinity of Tunbridge Wells. ‘The Weald Clay is at least 
600 feet thick in this district, and is underlain by sands and sand- 
stones, termed by the author the ‘‘ Tunbridge Wells Sand,” on ac- 
count of its being well exposed there. ‘This subdivision is about 
180 feet thick, and was described in detail,—an important feature 
being the ‘ rock-sand,” or massive sandstone forming the picturesque 
natural rocks of the neighbourhood. ‘The shales and clays under- 
lying these sands form the ‘‘ Wadhurst Clay” of the author, and are 
at places 160 feet thick. ‘This subdivision has yielded much iron- 
stone in former times. It is underlain by other sand and sand- 
stones, more than 250 feet thick, also yielding ironstone. ‘These 
are termed ‘‘Ashdown Sand” by Mr. Drew on account of their 
forming the heights of Ashdown Forest. 

Eastward of the meridian of Tunbridge Wells Mr. Drew has found 


310 Geological Society. 


the same sequence of beds, and he believes a similar succession to 
occur around Battle and Hastings. Westward of Tunbridge Wells 
as far as East Grinstead, the same beds occur, but beyond that 
the Weald Clay and Tunbridge Wells Sand alone are exposed; and 
the latter is here divided into upper and lower beds by shale and clay 
(termed ‘“ Grinstead Clay ” by the author), which thicken westward 
to 50 feet and more. It is the ‘‘ Lower Tunbridge Wells Sand” 
that forms natural rocks near Grinstead. Near Horsham the Weald 
Clay contains, at about 120 feet from its base, bands of stone known 
as the ‘‘ Horsham Stone,’’ used for roofing and paving. . 

The author then explained at large the grounds on which he 
proposed to replace Dr. Mantell’s term ‘‘ Horsted Sands” by “ Upper 
Tunbridge Wells Sand,”’ that of ‘‘ Worth Sands” by “ Lower Tun- 
bridge Wells Sand,” and that of ‘“ Tilgate Beds” by ‘‘ Wadhurst 
Clay,”’ and his reason for proposing the name of “ Ashdown ” for 
the next lowest bed of the “‘ Hastings Sand.” 

The paper concluded with a description of some of the chief litho- 
logical characters of the clays and sandstones of the Wealden area 
under notice. 


2. “On the Permian Rocks of the South of Yorkshire; and on 
their Paleontological Relations.’ By J. W. Kirkby, Esq. Com- 
municated by T. Davidson, Esq., F.G.S. 

The author, after defining the area to be treated of, first noticed 
the results of the labours of former observers in this district; and 
then succinctly described the several strata, referring to Professor 
Sedgwick’s Memoir on the Magnesian Limestone for descriptions of. 
the physical geography and very much of the lithological characters 
of the country under notice. The strata treated of Mr. Kirkby re- 
cognizes (in descending order) as, 1. the Bunter Schiefer, about 50 feet 
thick; 2. the Brotherton Beds, 150 feet; 3. the small-grained 
Dolomite, 250 feet; 4. the Lower Limestone, 150 feet; 5. the 
Rothliegendes or Lower Red Sandstone, 100 feet. These were then 
compared and coordinated with the Permian strata of Durham, where 
the three limestone members are thus represented :—1. The Upper 
Limestone by the Yellow, Concretionary, and Crystaline Limestone 
(250 feet) ; 2. The Middle Limestone by the Shell- and Cellular 
Limestone (200 feet); and 3. The Lower Limestone by the Com- 
pact Limestone (200 feet) and the Marl-slate (10 feet),—the over- 
and under-lying sandstones being much alike as to thickness in the 
two areas. 

After some remarks on the probable geographical conditions 
existing in the Permian epoch, the author proceeded to treat of the 
Permian fossils of South Yorkshire in detail. These belong to about 
thirty species, and are nearly all from the Lower Limestone,—three 
species only occurring in the Brotherton beds. With three excep- 
tions they occur also in the several limestones of Durham; five of 
them are found in the lower part of the red marls of Lancashire ; 
and six of them are found at Cultra and ullyconnel in Ireland. 
The distribution of the species in the several beds at different loca- 


Intelligence and Miscellaneous Articles. 311 


lities having been fully treated of, the Permian fossils of South York- 
shire were compared, first, with those of Durham; next, with those 
of Lancashire; and thirdly, with those of Ireland. Remarks on the 
distribution of the Permian Fauna in time concluded the paper. 


XLVIII. Intelligence and Miscellaneous Articles. 


SOME RESULTS IN ELECTRO-MAGNETISM OBTAINED WITH THE. 
BALANCE GALVANOMETER. BY GEORGE BLAIR, M.A. 
GINCE bringing the balance galvanometer, along with some other 


apparatus, before the Society in the course of last session, the 
writer had made some experiments with this new galvanometer, which 


led to results that he did not anticipate, and which he considered to 
be of sufficient importance to justify him in presenting them to the 
Society. The object originally aimed at in its construction was to 
obtain an exact measure, by weight, of the actual amount of deflective 
force which the current exerts upon the magnetic needle. The in- 
strument constructed for this purpose is represented in fig. 1. The 


312 Intelligence and Miscellaneous Articles. 


coil consists of a total length of 1660 feet of No. 22 copper wire, 
weighing rather more than 6 lbs., and divided into four parts, the 
ends of which are brought out and connected with their respective 
terminals G G, so that they can be used separately or as one coil. 
The needle with which the first experiments were made consisted of 
a small rectangular steel bar, 14 inch in length, rather less than jth 
of an inch in breadth, and about half the thickness of a shilling. It 
weighed exactly 18 grains, and, when magnetized, its lifting power 
was 44 grains, or nearly 24 times its own weight. The index M, 
which is 9 inches in length, weighs only 2 grains. A small brass 
pulley, 4th of an inch in diameter, is fixed upon the axis between the 
index and the supporting screw L. ‘The balanced lever E H consists 
of a thin shp of hard spring-brass, placed edgewise for strength, and 
tapered, for lightness, towards the end of the long arm AH. The 
short arm A E is loaded to act as a counterpoise; and to this arma 
scale-pan C is suspended, at a distance from the fulcrum equal to 
exactly 5th of the length of the other arm. It carries also at its 
extremity a thin horizontal projection, which vibrates between two 
screw-points D, D’, and by which, with the aid of the wooden foot- 
screws of the instrument, the lever can be always Fig. 2. 
exactly levelled when balanced. ‘The fulcrum 
B is supported on a stout brass bar F, which is 
firmly held in its place by means of the screw I, 
and can be removed at pleasure. When it is 
desired that the needle shall have hberty to 
move in both directions, the extremity H of the 
long arm of the lever is connected with the 
needle by a slender wire suspended from a very 
fine thread, fixed to the upper part of the pulley 
and carried down on both sides of it, as shown 
in fig. 2. The arm AH is divided into ten 
equal parts, each of which is subdivided into 
tenths ; and, estimating the poles of the needle 
to be at a distance of about 4th of its total length 
from the extremities, the diameter of the pulley 
is so adjusted that a weight of 100 grains, sus- 
pended at the distance of one of the large divi- 
sions from the fulcrum, acts with a force of 1 
grain at the poles of the needle; suspended at 
division 2, it acts with a force of 2 grains; at 
2°5, with a force of 21 grains, and so on. 

‘The following Table exhibits the results of the first series of expe- 
riments made with a small Grove’s battery, the platinum plates of 
which expose only two inches of surface, and having the zine plates 
immersed in a saturated solution of chloride of sodium. It is a 
striking characteristic of Grove’s battery that it slightly increases in 
force after being some time in action; and it would have been pre- 
ferable, therefore, to use a Daniell’s, on account of its remarkable 
constancy ; but the writer had not a sufficient number in series. The 
fourth column indicates the weight required to bring the index of 


Intelligence and Miscellaneous Articles. 313 


the balance galvanometer back to zero; the fifth column expresses 
the same weight reduced to the force which it exerts at the poles of 
the needle, but increased in each case by half a grain, to compensate 
for the small preponderance given to the long arm of the lever 
in order to keep the needle vertical when not deflected by the 
current ;— 


Table I. 
1 . 2. a 4 . 5 . 6 . 
Angles on Angles on Weights Force at “at 
No. of tangent balance Fi ieee to bring poles of Raped 
pairs. galvya- galvanometer, the needle to needle, in nadiieedl 
nometer, without weight. zero. grains, 5 
Le] ! ° / 
1 4 30 66 100 grs. at 2°5 3°00 3°12 
2 8 30 77 30 ” ” 5°5 6:00 5°96 
6 29 30 87 1000 grs. at 2°2 22°50 22°64 


12 44 45 89 ” 5 4°9 49°50 39°64 


It will be seen that, up to six pairs, the numbers in the fifth column, 
expressing the force of the current in grains at the poles of the needle, 
vary very nearly in the same ratio as the tangents of the angles of 
deflection on the tangent galvanometer reduced to a comparable form 
in the sixth column. With twelve pairs, however, the weight re- 
quired to balance the current is 49°5, or very nearly 50 grains; 
whereas, according to the tangent galvanometer, it should not have 
exceeded 40 grains. Reflecting on this anomaly, the writer could 
only arrive at the conclusion that the needle, surrounded by a very 
powerful current in such a large coil, ceased to act as a permanent 
magnet, and was temporarily charged with a higher magnetism in- 
duced by the current itself. Subsequent experiments completely 
confirmed this conclusion; and he was led to examine the subject 
more minutely by observing that the needle, after being several times 
subjected to the action of the current from twelve pairs, appeared to 
have lost its permanent magnetism; for he afterwards found re- 
peatedly that when the index was brought back by successive 
increments of weight to 40°, the smallest possible additional weight 
sent it back to zero. Before taking out the needle to ascertain 
this, he submitted it a second time to the action of six and twelve 
pairs, with the following results :— 


Number of pairs. Current force by tang. galvan. Weights supported. 
6 22°64 7'5 grains, 
12 39°64 24°5 i, 


whereas it will be seen, by referring to the preceding Table, that 
originally it supported 22°50 and 49°50 grains respectively. The 
needle was then taken out, and was found to have almost entirely 


314 Intelligence and Miscellaneous Articles. 


lost its magnetism. It had originally lifted 44 grains; it was 

now only with the greatest precaution that it lifted 2 grains. But 
7°5 > 24°5 

and (22°64) : (39°64)? 


A ef 
bs, 3:06. 


The writer had therefore little doubt that, if not merely demagnetized, 
but formed of soft iron, the needle, when placed in a favourable 
position, would turn with a force proportional to the square of the 
current ; whereas it plainly appears from Table I., that so long as its 
permanent magnetism is sufficient to resist the inducing action of 
the current, the needle is deflected with a force simply proportional 
to the current. 

To determine this interesting question, two new needles were con- 
structed, similar in shape and size to the former, but somewhat 
lighter, each weighing only 17°25 grains. ‘The one was of steel, 
tempered to the hardness of glass; and was magnetized till it lifted 
with some difficulty 43 grains; the other was of soft hoop-iron, 
well annealed. With these needles the following results were 
obtained from experiments conducted very carefully, and using, for 
greater accuracy, a single-thread suspension :— 


Table II. 
a 2. 3. 4. 5. 6. 
Angles on a Deflective a "a . 

| No, of tangent Tangents to force at poles | Ratioof Ratio pt 

pairs. galvano- rad. 1. of needle, in | tangents. pee eee ss * 

meter. grains. craps? Bo 
With |( 3 | 17 40 0-318 115 115 | 114 
magnetized, 6 31 20 0-609 22°0 22°0 42°1 
steel 9 41 0 0°869 32°5 315 85°8 
needle. | 12 | 47 0 1-072 43°5 38°8 130°6 
| 3| 1740 | 0-318 60 | 60 | 60 
With needle | OE asi 0 0-601 20°5 Le eee 21°5 
of soft iron |) 9 40 20 0-849 400 | 161 42-9 
12 47 0 1°072 57:0 20°4 68°4 


A glance at the above Table will show that, with the permanently 
magnetized needle, the numbers in column 4, expressing the de- 
flective force of the current in grains, are very nearly proportional 
to the numbers in column 5, expressing the simple ratio of the tangents 
or quantities of current; whereas with the soft iron needle they are 
nearly proportional to the sguares of the same quantities, reduced to 
a comparable form in column 6. In both cases the only marked de- 
viation coincides with the powerful current from twelve elements of 
the battery, in which cuse the steel needle, evidently acting under 
the superadded influence of induced temporary magnetism, is deflected 


Intelligence and Miscellaneous Articles. 315 


with a force which exceeds the estimated amount by 4°7 grains, 
whereas the soft iron needle, under the same current force, falls 
short of the calculated amount by 11°4 grains. The last effect is 
probably attributable to the fact that, as the needle approaches satu- 
ration, the law of the squares gradually merges into the law of 
simple proportion. ‘The writer regrets that he had not at com- 
mand sufficient battery power to put this point to the test of decisive 
experiments, but hopes to do so shortly with a Daniell battery of 50 
or 100 elements. In the meantime the results above given, having 
been arrived at with great care, and amply confirmed by experiments 
several times repeated, appear to establish very conclusively the 
following principles :— 

1. A permanently magnetized steel needle, suspended in the 
middle of a galvanometer coil, is deflected with a force simply pro- 
portional to the quantity of current transmitted, so long as the 
current force which acts upon it is not sufficient to impart tempo- 
rarily a higher magnetism than that which it permanently possesses. 
Beyond this point, the deflective force exerted on the magnetized 
steel needle increases in a somewhat higher ratio than the current, 
and therefore the accuracy of any form of galvanometer can be 
trusted only within certain limits of current force and of length and 
proximity of coil. 

2. A pure soft iron needle, suspended at an angle of about 40° to 
the direction of the current (the angle varying according to the 
shape of the needle), is deflected with a force which, within certain 
limits of current power, is very exactly proportional to the squares 
of the quantities of current. Beyond these limits the deflective force 
exerted on the needle increases in some constantly diminishing ratio 
lower than that of the squares of the current. 

3. The action of the current in deflecting a magnetic needle is 
precisely the same action, and follows the same law, as that which 
it exerts in magnetizing a bar of soft iron. The amount of magnetism 
actually imparted to a bar or needle of soft iron is directly propor- 
tional to the quantity of current; for the force with which a soft iron 
needle is deflected under different currents is not proportional to its 
temporary magnetism in each case, but to the product of its mag- 
netism multiplied by the force of the current. By increasing the 
force of the current, two effects are produced ; in the first place, the 
magnetism of the needle is increased in the same proportion; and 
secondly, the increased current acting upon this increased magnetism 
deflects the needle with a force proportional to the product of the 
two, or in other words, proportional to the square of the actual 
quantity of current. 

1t only remains to add the results of two series of experiments, 
showing the very striking difference between the defiective forces 
exerted upon the two needles at different angles of inclination. 
Table III. shows the increasing weights required to balance the 
needles at angles successively diminished by 10°; Table LV. exhibits 
the effect produced by successive additions of weights, equivalent to 
a force of ten grains acting at the poles of the needles. In both 


316 Intelligence and Miscellaneous Articles. 


cases the battery power employed was twelve small Grove’s, but the 
current declined, in the course of the experiments, from 47° to 45° 
on the tangent galvanometer, which accounts for the fact that the 
maximum weights supported are less than in the earlier experiments 
recorded in Table II. In working out Table III., the weight em- 
ployed (1000 grains) was simply advanced along the lever, and its 
reduced amount at the poles of the needle noted when the index, in 
gradually retreating, pointed to the successive angles specified. The 
results in Table IV. were obtained by moving the weight from one 
to another of the successive divisions, marked 1, 2, 3, &c. on the 
lever; and the differences of the angles vary, as might be expected, 
in nearly the reverse order of the differences of weights in Table 
II. :— 
Table III. 


Angles on Weights reduced Differences of 
balance to force at successive 
galvanometer. |needle, in grains. | weights. 
90 6'0 Se 
80 6-5 oF 
70 15:5 75 
With magnetized steel 60 23-0 7-0 
needle. 4 50 30:0 5-0 
40 35:0 bs 
30 39-4 af 
20 41°5 0°5 
see 10 42-0 
gt 90 0-0 i 
I § 80 155 nh 
29°35 
With soft iron needle. “ he 11-0 
50 50:0 vs 
40 53°0 
Table IV. 
Weights reduced} Angles on Differences of 
to force at balance successive 
needle, ingrains.| galvanometer. angles. 
0-0 90 0 e 
10-0 75 30 rete 
With magnetized steel 20:0 63 0 
needle. 30-0 48 30 a - 
40°0 26 0 
\ 4165 
PU rh he aa Wi pea DEEL 
10-0 84 0 see 
20°0 76 30 8 10 
With soft iron needle. |< 30-0 68 20 
8 10 
40°0 59 10 12 0 
50-0 47 10 
52°0 0 0 


Intelligence and Miscellaneous Articles. 317 


It will be observed from Table III. that a very small weight was 
sufficient to throw back the steel needle to 80°, and that, on the 
contrary, it is from 90° to 70° that the soft iron needle sustains 
itself with comparatively the greatest power, requiring very nearly 
double the weight which suffices for the steel needle to balance it at 
the latter angle. When reduced to 40°, however, the smallest pos- 
sible additional weight throws back the iron needle to zero, and in 
every case it was necessary to moveit aside with the finger to nearly 
that angle, before it would exhibit the slightest action under the 
influence of the current, or, in other words, any perceptible trace of 
longitudinal magnetization. In fact, being laterally magnetized 
when hanging in a vertical position, it necessarily offered a certain 
resistance to deflection. 

On taking out the steel needle after these experiments, it was 
found to have retained its original magnetism unimpaired. 


The tangent galvanometer by which the force of the current was 
Fig. 3. 


318 Intelligence and Miscellaneous Articles. 


determined in the preceding experiments, and which the writer had 
also the honour of submitting to the Society last session, is repre- 
sented in fig. 3. It is a very convenient modification of Gaugain’s 
instrument, described in the Annales de Chimie, vol. xli. 1854. The 
circular frame A, containing a variety of coils of different lengths 
and sizes of covered wire, is 9°6 inches in external diameter ; so that 
when the instrument is in use, the divided circle must be drawn out 
till its centre is 2°4 inches in front of the coil or coils through 
which the current is to be sent. To facilitate this operation, the 
horizontal bar D, upon which the disk slides, has the proper distances 
for each coil marked upon it, and these are successively exposed to 
view at the back of the instrument, in proportion as the disk is drawn 
smoothly forward by means of the handle C. The needle is only 
one inch in length, but carries parallel to itself a fine filament of 
glass for an index*; it is suspended by a silk fibre, and is raised so 
as to hang freely within its glass shade by turning the pin E. The 
ends of the coils are carried down through the hollow pillar B, and 
by connecting the electrodes of the battery with the proper terminals, 
the current can be sent through one or more of the coils. It canbe 
sent through one convolution of No. 16, through 203 convolutions 
of No. 34, or any other of the intermediate lengths and sizes of wire; 
and in this way the resistance and the force exerted by the current 
upon the needle can be very exactly adapted to the character of the 
battery, or other rheomotor employed.—From the Proceedings of the 
Glasgow Philosophical Society for January 16, 1861. 


ON THE PRESENCE OF ARSENIC AND ANTIMONY IN THE SOURCES 
AND BEDS OF STREAMS AND RIVERS. BY DUGALD CAMPBELL, 
ANALYTICAL CHEMIST TO THE HOSPITAL FOR CONSUMPTION, 
BROMPTON. 


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


Since my communication upon the above subject, published in 
the Philosophical Magazine of October last, I have repeated my 
experiments upon several of the sands I then reported upon, and 
with the like results which I then gave. I have also made experi- 
ments upon other specimens since obtained, and in all I have hitherto 
examined I have found arsenic, and generally, if not always, accom- 
panied with antimony. The process followed was the same as I 
formerly described, only I invariably used hydrochloric acid without 
the slightest trace of arsenic in it, as some doubts had been cast 
upon my former results, in a notice of my paper in the ‘ Chemical 


* The thickness of the index is grossly exaggerated in the figure; it 
ought to be as fine as a hair, and short in one arm. 


Intelligence and Miscellaneous Articles. 319 


News’ of the 20th of October last, because in my anxiety to admit 
of any one testing the accuracy of my results, I had described how 
the process might be conducted with what is generally sold as pure 
acid, but which, if properly tested, is rarely free from arsenic. 

During these last experiments, it occurred to me to distil the sands 
with a second and a third dose of acid, and in most cases I have 
found the yield of arsenic and antimony to be much greater, say from 
two to five times, in the second distillate than in the first; and in 
some I have found the third distillate to give more than the first, 
but in others less. 

These results induce me to say that, before a sand could be pro- 
nounced not to contain any arsenic or antimony, it should be distilled 
to dryness with at least three distinct doses of acid, each distillate 
being tested carefully in the manner described in my former com- 
munication. 

I am, Gentlemen, 
Your obedient Servant, 
Ducatp CAMPBELL. 


7 Quality Court, Chancery Lane, 
March 25th, 1861. 


NOTE ON A MODIFICATION OF THE APPARATUS EMPLOYED FOR 
ONE OF AMPERE’S FUNDAMENTAL EXPERIMENTS IN ELECTRO- 
DYNAMICS. BY PROFESSOR TAIT. 


My attention was recalled by Principal Forbes’s note* (read to the 
Royal Society of Edinburgh on January 7), to his request that I should 
at leisure try to repeat Ampére’s experiment for the mutual repulsion 
of two parts of the same straight conductor, by means of an apparatus 
which he had procured for the Natural Philosophy Collection in the 
University. Some days later I tried the experiment, but found that, 
on account of the narrowness of the troughs of mercury, it was im- 
possible to prevent the capillary forces from driving the floating wire 
to the sides of the vessel. I therefore constructed an apparatus in 
which the troughs were two inches wide, the arms of the float being 
also at that distance apart. Making the experiment according to 
Ampére’s method with this arrangement, I found one small Grove’s 
cell sufficient to produce a steady motion of the float from the poles 
of the pile; in fact, the only difficulty in repeating the experiment 
lies in obtaining a perfectly clean mercurial surface. 

Two objections have been raised against Ampére’s interpretation 
of this experiment, one of which is intimately connected with the 
subject of Principal Forbes’s note. This is, the difficulty of ascer- 
taining exactly what takes place where a voltaic current passes from 
one conducting body to another of different material. It is known 


* Phil. Mag. for February 1861. 


320 Intelligence and Miscellaneous Articles. 


that thermal and thermo-electric effects generally accompany such a 
passage. To get rid of this source of uncertainty, I have repeated 
Ampére’s experiment in a form which excludes it entirely. In this 
form of the experiment the polar conductors and the float form one 
continuous metallic mass with the mercury in the troughs,—the float 
being formed of glass tube filled with mercury, with its extremities 
slightly curved downwards so as nearly to dip under the surface of 
the fluid, and the wires from the battery being plunged into the 
upturned outward extremities of two glass tubes, which are pushed 
through the ends of the troughs so as to project an inch or two in- 
wards under the surface of the mercury. A little practice is requisite 
to success in filling the float and immersing it in the troughs with- 
out admitting a bubble of air. This float, being heavier than the 
ordinary copper wire, plunges deeper in the fluid, and encounters 
more resistance to its motion; but with two small Grove’s cells only, 
Ampére’s result was easily reproduced, even when the extremities 
of the float rested in contact with those of the polar tubes before the 
circuit was completed. It is obvious that here no thermo-electric 
effects can be produced in the mercury; and I have satisfied myself 
that the motion commences before the passage of the current can 
have sensibly heated the fluid in the tubes. 

The other class of objections to Ampére’s conclusion from this 
experiment, depending on the spreading of the current in the mer- 
cury of the troughs, is of course not met by this modification. I 
have made several experiments with a view to obviate this also; but 
my time has been so much occupied that I have not been able as yet 
to put them in a form suitable for communication to this Society.— 


From the Proceedings of the Royal Society of Edinburgh, vol. iv. 


NOTE RESPECTING OZONE. 


In the Philosophical Magazine, May 1860, page 403, is a short 
account of ‘‘ the production of Ozone by means of a Platinum Wire 
made incandescent by an Electric Current,” by M. Le Roux, which 
has just recalled to my memory the following fact. 

I have frequently observed that a coil of platinum wire heated to 
whiteness in a strong jet of purified hydrogen, and then removed from 
the jet, imparted a feeble ozone-like odour to the ascending stream 
of hot air above the wire as long as the wire remained nearly white- 
hot, and ceased to impart this odour at a somewhat lower tempe- 
rature. 


G. Gorr. 


Birmingham. 


Phil. Mag. Ser.4.Vol.21.PLV. 
j Fig: 8. 


J. Basire se. 


Phil.Mag. Sev. 4.Vol.21. Pl. 


j 
i 
: : 


THE 
LONDON, EDINBURGH anno DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FOURTH SERIES.} 


MAY 1861. 


XLIX. On the Determination of the Direction of the Vibrations 
of Polarized Light by means of Diffraction. By L. Lorenz*. 


1 ae question whether the vibrations of polarized light are 
perpendicular to the plane of polarization, or in that plane, 
notwithstanding its great theoretical importance, is still unde- 
cided. On comparing the different arguments that may be ad- 
vanced in favour of either hypothesis, only two will be found 
that have an essential bearing on the subject,—the experiments, 
namely, of Jamin on the reflexion of light by transparent media, 
and the polarization of light caused by diffraction. 

The experiments of Jamin have hitherto been explained on 
the supposition that the vibrations of polarized light are perpen- 
dicular to the plane of polarization. ‘This, however, is not deci- 
sive of the question, since it has hitherto been assumed that 
there is an instantaneous change of refractive power at the 
boundary of two transparent media; whereas I shall prove, in a 
subsequent essayt ‘On the Reflexion of Light,” that Jamin’s 
experiments can only be brought into complete accordance with 
Fresnel’s formule for the reflexion and refraction of light, on the 
hypothesis that these formule hold good for infinitely small 
changes of the refractive index, that is to say, on the hypothesis 
that there is a gradual passage from one medium to the other. 

It may be asked whether Fresnel’s formule really hold good 
for an infinitely small change of refractive power, and whether 
these formule may be deduced on either hypothesis as to the 
direction of the vibrations of polarized light; two questions 
which I shall answer in a third essay. 
alee by F. Guthrie, from Poggendorff’s Anzalen, vol. exi. p. 315, 
'-> See Poggendorff’s Annalen, vol. cxi. p. 460: a translation of -this 
paper will be given in a future Number of this Magazine, 


Phil, Mag. 8. 4, Vol. 21, No. 141. May 1861, Y 


322 M. L. Lorenz on the Determination of the Direction 


The change of the plane of polarization by diffraction conducts 
us by another road to the determination of the same question. 
Several years ago Mr. Stokes furnished a mathematical proof 
that the plane of polarization must be changed by diffraction. 
Doubts have, however, justly been entertained as to the accuracy 
of his conclusions, because he only succeeded in solving the 
problem of diffraction imperfectly ; and I have therefore sought 
the complete solution of the problem by other methods, which I 
have found particularly applicable in the theory of elasticity. 

When an undulation passes through an opening in a solid 
plane, waves proceed from the opening on both sides of the 
plane. The motion in the plane is not known, except inso- 
far as it is determined by the fact that the sum of the compo- 
nents of the incident and reflected waves are equal to the com- 
ponents of those transmitted, and that the normal and tangen- 
tial pressures on both sides of the plane of the opening are the 
same at every point. Let the components of the incident rays 
be denoted by w, v, and w; those of the transmitted rays by w,, 24, 
and w,; of the reflected by w,, vo, and w.; and let the plane. of 

‘coordinates 2, y, 2 coincide with the plane of the opening. 

The first condition gives, for x=0, 


U+Ug—Uy;=0, V+V,~—1,=0, wt+wo—w,=0; « (1) 


and by the help of these equations it may easily be deduced from 
the second condition for =O, that 


dictate th) 324) d(v+,—2) aU; d(w+We—W)) _ ¢, (2) 


dx dx dx : 
If the incident waves are waves of light, then 
du dv dw 
de a dy Ai a =0; 


and equations (1) and (2) may be satisfied by the supposition 
that 


RO Ds i Pal 

dx ° dy ' dz ” (3) 
du, . dv, . dwe ian dhe 
de dy a s2.Q); 


from which it is evident that no waves of condensation can be 
formed. 
The law of the motion is expressed by the differential equation 
a + & + a = i a (4) 
te ay ew ae eo 


which must satisfy all the components, where w expresses the 


of the Vibrations of Polarized Light by Diffraction. 3828 


rate of propagation, and¢thetime. This equation will obviously 
be satistied by the expression 


valea’ obi! § 


Y 


where r=,/x* + (y—6)?-+ (z—y)?, and therefore also by 
A Se Ls p(wi—r, B,y) ‘ 
D= on a3 ay rere 


which function ®, when the limits of integration are determined 
by the boundaries of the opening, also possesses the property 
that its differential coefficient with respect to z becomes equal to 
d (w, t, y, z) when « decreases to nothing, and the point yz is 
within the opening. If 2 increases to nothing, the value of the. 
differential coefficient is —d(wt, y, 2); and if the point yz is 
without the opening, it becomes nothing when x=0; for by 
differentiating the integral with respect to 2, w=O enters asa 
factor, thus causing every element of the integral to disappear, 
except those in which r=0, that is to say, y=, z=y. Whence, 
if 2 is positive, and the point (yz) is within the limits of the 
integral, : 


ST = feelers] Ho rmters9 


and if x is negative, 


di *=0 
| =a Hels ys 2) 


_ Introduce now other functions VY, X, ©,, V,, X,, which are 
related to the respective functions yp, x, $,, Wy; X, m the same 
way as ® is to @, and put 
| d®, d(F+F 

ee ee 


Ps dv, d(F+F)) is 
y= V+ a F <a ° ° e ° ( ) 
ee ee TE) 
titres Ge ods Sd 
where the functions F, F, are so chosen that 
du, doy , dey 
dz dy. az 


ae 2 


324 M. L. Lorenz on the Determination of the Direction 


becomes equal to nothing, then 


A?F= — ss con Fh 
dz dy 


dz 


aja FO hex | 


(6) 
dx? ' dy ' dz* | 


To the components w,, V,, W of the reflected wave we give the 
same values as to w,, ¥,, w,; Only it must be observed that in 
the first 2 is always negative, in the latter positive. 

Assuming now that 


TB ae 

[F]*-°=0 and =) =0, ». 2. (7) 
the truth of which will appear from what follows, we get by 
means of (1) for z=0, 

U+U, —U, =u —29,(wt, y, z)=0,> 

V+V, —¥, =V— 2p, (wt, y, z)=0, ~ + (8) 

W+ WoW, = W—2yx, (wt, y, z)=0; 
and by means of (2) for =O, 


avg ehh _ Oe oda yaaa 


dz dz 
d(v+vu,—v d 
eS. = 5 — yp (ut, y, 2a U, » (9) 
d(w+wo—w dw 
Aut aw) _ 9 vot,y, 2)=0. | 


All the conditions are hereby fulfilled, and the functions ¢, ¢,, 
a, &e. determined. The truth of equations (7) may now also 
be easily demonstrated. 


The problem of diffraction is therefore completely solved by 
equations (5), (6), (8), and (9). If-we now pass to the parti- 
cular case in which the incident waves lie in a plane, the compo- 
nents are determined by the following equations, 

u= £6, v=o, w=, 
where 
6= cos k(wi—ax —by — cz), 


a&+bn+cf=0, a?+?+c?=1. 


Since, moreover, we only require to determine the motion at 
a point at a considerable distance behind, the opening in the 
screen must be very great; and putting p for the distance of the 


of the Vibrations of Polarized Light by Diffraction. 325 
observed point from the origin of coordinates, we have 


p= Vx? + (y—B)?+ (z—y)?=p—mB—ny, 


where 
p= Varty+2, m= 


and /, m, and v being the cosines of the angles made by the 
diffracted ray with the coordinate axes, /?+m?+n?=1. Now 
from (9) we get 


(wt, y, 2) =4ak& sin k (wi—by—cz), 
O=akéS, 


whence 


where 
nt Sa f dB {dy sin k[wt—p + (m—B)8 + (n—e)y]. 


And the values of the functions that enter into (5) being found 
in a similar manner, we get 


uy ga 1 (1E +mn +n8)]S, 
v,=$k(a+l) [n—m(lE+ mn +n8)]8, 
=ghk(a+l)[(€—n(lE+ mn +né) |S. 


These te a hold good also for the waves reflected from 
the opening, only that in this case / is negative. For a point in 
the direction opposite to that of the meident ray a+/=0, and 
therefore all the components of the motion are equal to nothing. 

Mr. Stokes has arrived at the same result, although he did 
not regard the reflected wave, and has not completely solved the 
problem. Ifa plane be supposed to pass through the refracted 
and the incident ray, and if « denote the angle which the vibra- 
tions of the incident ray make with the normal to this plane, «, 
the angle made by the vibrations of the diffracted ray with the 
same normal, and 8 the angle of diffraction, then we easily find, 
as Stokes has done, that 


tan a, = cos P tan a, 


which is independent of the form and position of the opening. 
The vibrations therefore become more nearly vertical after pass- 
ing through a vertical slit or grating. Accordingly, therefore, 
as experiment shows that the plane of polarization is rendered 
more vertical or more horizontal by diffraction, so must the vibra- 
tions of polarized light be parallel or perpendicular to the plane 
of polarization. It must, however, be renembered that, mathe- 
matically speaking, the screen is supposed to be a plane which 
does not itself vibrate, and which reflects no light from its edges. | 


326 M. L. Lorenz on the Determination of the Direction 


The experiments that have hitherto been tried leave this 
question still undecided; for while Stokes, from experiments 
made with glass gratings, found that the plane of polarization is 
rendered more horizontal, Holtzmann, from experiments made 
with a smoke-grating, came to the opposite conclusion. In order 
finally to settle this question, I have imstituted a course of expe- 
riments with gratings of various kinds. 

By means of a heliostat and collecting lens, I introduce a por- 
tion of the sun’s rays into a chamber. At some distance from 
the focus of the first lens a smaller lens receives the rays, and 
transmits them, almost parallel, through a polarizing Nicol’s 
prism, which is fastened in a tube to a vertical circular are. An 
index with a vernier gives the angle which the plane of polariza- 
tion of the transmitted light makes with the vertical lime. At 
the distance of about 7 metres the light falls on a vertical gra- 
ting, which is fastened to a small plate in the middle of a hori- 
zontal circular arc, which is provided with a moveable horizontal 
telescope. Before the object-glass is placed a doubly-refracting 
prism of rock-crystal, which divides the polarized pencil into 
two, polarized perpendicularly to each other, This prism can 
be turned about the axis of the telescope. In general, therefore, 
two horizontal bands of light of unequal brightness will be seen 
in the telescope ;, but by turning the Nicol’s prism or the doubly- 
refracting crystal about its axis, the intensity of these two 
images can be rendered equal. 

The experiments were generally conducted as follows :—The 
Nicol’s prism was turned in such a direction that the plane of 
polarization made an angle of 45° with the vertical line, and the 
telescope was so placed that its vertical thread passed through 
the two illuminating points, while the horizontal thread lay be- 
tween the two horizontal bands of diffracted hight. When the 
telescope was turned through the angle 8, both bands, owing to 
the position of the rock-crystal, were of equal intensity. The 
telescope was then put back into its original position, and the 
Nicol’s prism was turned into such a position that one of the 
images entirely disappeared. 

If the Nicol’s prism required to be turned through the angle 
5 (or 5+ 90° or 6+180°), the plane of polarization must have 
been turned through the same angle, provided that the light has 
not been elliptically polarized by diffraction ; and if 6 be positive, 
the plane of polarization has been rendered more horizontal. 

Sometimes I first determined 6, and then the angle of diffrac- 
tion 8, for which the two bands are equally bright. 

There is, however, a source of error in these experiments, of 
which I only became aware after some time. If, for example, 
the upper half of the grating produce a more brilliant diffracted 


of the Vibrations of Polarized Light by Diffraction. 327 


image than the lower, then if the grating entirely cover the 
object-glass, as was always the case in the above experiments, 
the upper diffracted image will be too bright. And if this image 
be polarized horizontally, 6 will be found too great ; if vertically, 
too small. To render the experiment perfect, it is therefere neces- 
sary to turn the rock-crystal through an angle of 180°, and take 
the mean of the two values of 6 so obtaimed. If this precaution ™ 
be neglected, very considerable errors may be introduced, espe- 
cially when smoke-gratings are employed, and I imagine it is 
this that has misled Holtzmann. He observed, in the case of a 
smoke-grating, that for a diffraction of 20° there was a very con- 
siderable difference in the brightness of the horizontal and verti- 
cally-polarized images. This is nearly always so with gratings 
of this description: the upper or the lower image appears the 
brightest, without reference to the position of the plane of polari-. 
zation. With a perfectly accurate grating, M. Holtzmann would 
not have been able to distinguish the slight difference that really 
does exist. 

_ My first experiments were made with a gold grating (1000 
bars to the Paris inch). Light polarized at an angle of 45° 
with the vertical, when diffracted with this grating, gave two 
images, of which neither could be made entirely to disappear for 
any position of the rock-crystal ; and this was still more evident 
when the grating was placed obliquely. The diffracted light must. 
therefore either have been elliptically polarized,or have been partly 
converted into ordinary light. That the former was the case, 
I inferred from the fact that elliptically-polarized light could be 
converted by diffraction into circularly and plane-polarized. If, 
for example, I passed light polarized at the angle « through a 
Fresnel’s parallelopiped, whose reflecting surfaces made the angle 
45° with the vertical, the angle a could be so chosen that one 
image in the telescope could be made entirely to disappear, or, 
on the other hand, so that the two images, on turning the rock- 
crystal, always retained the same intensity. : fire 

By- measurements made in this manner, I convinced myself. 
that the phenomenon is essentially the same as that which 
accompanies the ordinary reflexion of light from polished metal. 
surfaces, and that the effect of the diffracted light is imper- 
ceptible in comparison with that reflected from the edges. 

I now provided myself with various smoke-gratings. Polished 
glass surfaces were smoked with burning camphor, and then 
treated with a few drops of oil of turpentine to fix the smoke to 
the glass. These were then divided by means of a machine into 
bars only an inch long (2, 5, 10, and 16 to the millim.). 

With these gratings I no longer observed any elliptic polari- 
zation. I found no observable differences in the results for the 


328 MM. L. Lorenz on the Determination of the Direction 


different gratings, and content myself therefore with giving the 
mean results for them all. 

When the grating was perpendicular to the incident ray, and 
on the side of the glass towards the telescope, as was the case in 
Holtzmann’s experiments, I found the angle 6, through which 
the plane of polarization was turned, extraordinarily small, and ~ 
therefore only determined it accurately for a single angle of dif- 
fraction (65°). The plane of polarization of the incident light 
was in all the following experiments inclined at an angle of 45° 
with the vertical. 

The mean result for 8=65° was 

Sead; O2's 
The plane of polarization therefore had become very slightly 
more horizontal. For greater values of 8 I found 6 still smaller, 
which at first greatly perplexed me. 

When the grating was turned round so as to be on the side 
towards the incident ray and perpendicular to it, the plane of 


polarization was turned through a greater angle in the same 
direction, and for 8=65° I found 


6=12° 30'. 


These results agree neither with Holtzmann’s experiments, nor 
with the conclusions that seem to follow from theory. I think, 
however, they can be explained as follows. | 

When the light first passes through the glass and then through 
the grating, the circumstances are almost the same as when it 
encounters the grating in the substance of the glass, as may be 
concluded from the fact that there is no reflexion at the boundary 
between the smoke and the glass. The diffraction therefore 
takes place within the substance of the glass, and the diffracted 
light 1s afterwards refracted in passing out of the plate. If , 
be the diffraction in the glass (8 being the observed diffraction), 
and n the index of refraction of glass, then sin@=nsinf,. In 
consequence of the refraction, the plane of polarization is again 
altered and becomes more veréical. Supposing now that the 
vibrations are perpendicular to the plane of polarization, the 
change of the plane of polarization 6,, caused by the diffraction 
§,, is determined by the equation 


tan (45°—6,)=cos@. 


If therefore 6 be the angular change of the plane of polarization 
after eflexion at the first surface of the glass, we have by Fres- 
nel’s formule, 


__ tan (45—6,) _—cos8 
tan (15° 8) = cos (B= Ai) ~ eos (B— A) 


of the Vibrations of Polarized Light by Diffraction. 329 


The mean index of refraction n was determined by experiment 
as to the angle of polarization, and I found 


log n= 0°18886. 


For 8=65° we should therefore have 5=2° 11’, which agrees 
pretty well with experiment, which gave 6=1° 52’, That 6 
should decrease as 3 increased, as appeared from experiment, 
follows also from this calculation. 

If, on the contrary, the smoked side of the glass is turned 
towards the incident ray, the light is diffracted before it reaches 
the surface of the glass, and is afterwards twice refracted. We 
have therefore 


tan (45°—8) = eee ; 


from which it follows that if B=65°, 5=16° 2! 30", 

In this case experiment gave a decidedly less value for 6, which 
shows that the actual circumstances are only approximately those 
assumed, and that the diffraction of the light only takes place 
partially within the substance of the glass. This is still more 
evident when the grating is placed obliquely to the incident rays, 
so as to make equal angles with them and the axis of the tele- 
scope; since in that case for 8=90° I found 6=20° instead of 
45°, which is given by calculation. 

It is obvious, therefore, that the circumstances, though very 
complicated, are naturally accounted for in all essential particu- 
lars, on the supposition that the vibration of polarized light is 
perpendicular to the plane of polarization, whereas the other hy- 
pothesis is altogether irreconcileable with experiment. 

In order to render these results less complicated and more 
susceptible of calculation, I contrived a different arrangement ot 
the smoke-gratings. Canada balsam was melted over the sur- 
face of the glass, and a smooth glass plate was pressed down on 
it, which it was found could easily be done without injuring the 
grating. As Canada balsam has almost the same index of refrac- 
tion as glass, all the circumstances could then easily be calculated. 
The grating was so placed that it made equal angles with the 
incident rays and the axis of the telescope. In this position of 
the apparatus the vertically polarized portion of the incident 
light was found to be weakened more than that polarized hori- 
zontally ; and therefore the change of the plane of polarization 
was positive, although reflexion at the two glass surfaces tended 
to turn the plane of polarization in the opposite direction. As 
the mean of many experiments with several gratings (2, 5, 10 
bars to the millim.), I found— 


330 Onthe Direction of the Vibrations of Polarized Light. 


| 40° | 50° | 60° | 70° | so° | 90° | 100° 
3 observed ......, 2:24| 30 | 4:54] @36| 742/96 | 123 
Calculated... 230 | 354] 537] 7-37 | 9:53 119-22 | 15-0 


where 6 is given by the equations 


COS : 
tan(45°—68) are Sey or sin +2, = sin 4 B, 
48 being the angle which the incident ray makes with the nor- 
mal to the erating, 3A, that made by the refracted ray with the 
same line, while Q, is the diffraction within the substance of the 
glass itself. 

It will be seen that experiment agrees very well with calcd 
tion, only that it gives results in all cases a little too small. 
Whatever, therefore, may be the cause of this difference, experi- 
ment most decidedly favours the hypothesis that the vibrations 
of polarized light are perpendicular to the plane of polarization, 
since in the opposite case 6 would be negative and of much 
greater magnitude. 

T next investigated the effect of diffraction by smoked metal 
gratings. When, however, these were of a perfect dull black, 
the diffraction images produced by them were far too feeble; 
they were therefore rendered smoother by passing a drop of oil 
of turpentine over them. Gratings of this description must, 
moreover, be rather fine and very accurately made. Some expe- 
riments made with a grating of 400 bars to the Paris imch (the 
thickness of the wire bars was 549th of a millim.), the grating 
being equally inclined to the incident light and the axis of the 
telescope, gave approximately the following results :— 


— |) ee ee eee eee eee eee 


The change of direction is positive, but much greater than it 
should be according to calculation. The polarization of the 
diffracted light was moreover slightly elliptical, from which it 
was evident that the reflexion from the metal surfaces of the 
wires was not entirely prevented by the smoke. On endeavour- 
ing to smoke the grating more perfectly, I partly destroyed its 
accuracy, and rendered it unfit for further experiments of this 
description. I have not succeeded in obtaining reliable results 
with other gratings of this description: there are peculiar diffi- 
culties in the way of checking the reflexion from the metal edges, 
and at the same time cana obte the diffraction image suffi. 
ciently large and distinct. 


_ On the Boiling-points of different Liquids. - $831 


The results obtained are, however, not unimportant, since the 
excessive values of 6 can easily be accounted for on the ground 
of eliptie polarization. 

If it be supposed, for example, that the difference of phase of 
the vertical and horizontal components is A, and that 6, is the 
change of direction when there is no elliptic polarization, an easy 
calculation gives 
tan 26, 


cos A? 


whence 6 must always be greater than 6,, their signs, however, 
being always the same. 

As experiment gave 6 positive, it confirms the result already 
obtained, that the vibration of polarized light is perpendicular to 
the plane of polarization. sid td. 

Copenhagen, June 28, 1860. 


tan 26= 


L. On certain Laws relating to the Botling-points of different 
Liquids at the ordinary Pressure of the Atmosphere. By 
Tuomas Tate, Hsq.* 3 


T is well known that the boiling-point of water is raised by. 

the addition of a soluble salt, or by the addition of a strong 
acid, and that this augmentation of the boiling-temperature de- 
pends upon the relative amount of salt or acid added, as the case 
may be; but, as far as I know, no general formule have hitherto 
been given to express the relation between the augmentation of 
boiling-temperature and the relative weight of the substance 
added to the water. 

Different weights of anhydrous salt being dissolved in 100 
parts of pure water, and the augmentation of boiling-temperature 
being observed, we obtain data for expressing the relation of the 
per-centage of the salt to the corresponding augmentation of 
the boiling-temperature of the solution. The salts which I have 
examined in this manner are as follows :—the chlorides of sodium, 
potassium, barium, calcium, and strontium ; the nitrates of soda, 
potassa, lime, and ammonia; and the carbonates of soda and 
potassa. I have found for all these salts, that the augmentation 
of boiling-temperature may be approximately expressed in a certain 
power of the per-centage of the salt dissolved: thus, if k be put for — 
the weight of dry salt in 100 parts of water, and T the corre- 
sponding temperature of ebullition above that of boiling water 
under the same atmospheric pressure, then 


Pht A sh: ai dliw (EX aoe ee 


* Communicated by the Author. 


332 Mr. T. Tate on the Boiling-points of different Liquids 


where ais constant for each salt only, and the exponent a is con- 
stant for all the salts contained in certain special groups. The 
salts enumerated may be divided into four distinct groups, the 
salts in each possessing certain remarkable points of relationship 
with respect to their boiling-temperatures ; viz., the augmentations 
of boiling-temperature of the solutions in each group of salts have 
a constant ratio to one another for all equal weights of salt dis- 
solved. Thus if 'T and T’ be put for the augmentations of boil- 
ing-temperature corresponding to any equal portions of two salts 
dissolved, belonging to the same group, then 


= = a constant quantity. 

The constant quantity here expressed is, in some cases, nearly 
equal to the inverse ratio of the combining equivalents of the 
bases of the salts. 

Moreover, if the weights of two portions of one kind of salt, 
separately dissolved in 100 parts of water, be proportional to the 
two portions of another salt belonging to the same group and 
similarly dissolved, then the ratio of the augmented temperatures 
of ebullition of the former will be equal (approximately) to the 
ratio of the augmented temperatures of ebullition of the latter. 

I 
Thus if Z = o then . oe ie and conversely ; 
where x, and k, are the respective weights of one kind of salt 
separately dissolved in 100 parts of pure water, T, and T, the 
respective augmented temperatures of ebullition; and X’,, #,, 
T',, and T’, are the corresponding symbols for the other salt. 

For the sake of conciseness of expression, I shall sometimes 
speak of this augmentation of temperature simply as the tempe- 
rature of ebullition, which, in fact, it would be if the tempera- 
ture of boiling water were taken as zero. 

The first group of salts comprises the chlorides of sodium, po- 
tassium, and barium, together with carbonate of soda. 

The second group comprises the chlorides of calcium and 
strontium, and probably other salts. 

The third group comprises the nitrates of soda, potassa, and 
ammonia. 

The fourth group comprises the carbonates of potassa, and ni- 
trate of lime. 

If T=af(k) represent the relation between T and & of a salt in 
any group, a being constant, and f(4) a known function of f, 
then T=<a'f(k) will be the formula of relation for any other salt 
in the same group. For let T and T’ be the temperatures of 
ebullition in cach case respectively for equal values of k, then 


at the ordinary Pressure of the Atmosphere. 333 
=5= a constant for all values of T and T’ corresponding to 
ae values of fk. 

The annexed diagram represents the ap- 
paratus with which these experiments were 
made, DB an oil-bath heated on a sand- 
bath ; A B a wide tube of some length con- 
taining the solution of the salt; T a ther- 
mometer passing through a perforated cork 
C, and having its bulb immersed in the li- 
quid to within about one- -quarter of an inch 
of the bottom of the tube. A slit is made 
in the side of the cork to keep the vapour 
in the tube at the same pressure as the ex- 
ternal air. Pieces of platinum-foil were put 
in the liquid to facilitate the discharge of 
vapour; and the oil in the bath was time 
after time agitated to keep all the parts of 
the liquid at a uniform temperature. The 
boiling-temperature of pure water corre- 
sponding to the atmospheric pressure was 
first determined; known weights of anhy- 
drous salt, corresponding to 100 parts by te oe 
weight of water, were time after time introduced into the tube, 
and the corresponding temperatures of ebullition were noted: 
the elevations of these temperatures above that of boiling water 
were entered in the following Tables of results. The process 
was continued, in some cases, until the solution of maximum salt 
was nearly attained. A correction for the observed temperatures 
was made on account of the column of mercury in the stem of 
the thermometer not in contact with the liquid. 


2" 


Augmentations of boiling-temperatures, in degrees Centigrade, of 
different solutions of the salts contained in Group 1. 


Corresponding boiling-temperatures of the different solutions of salt above that 


Weight of pure water. 


of salt i in 


Chloride} Chloride 


100 parts Chloride| Carbon-| Value of T |Value of T’ ‘Value of T"| Value of" 
of water,! of so- |of potas-| of ba- | ateof| by formula |by formula |by formula |by pte 
dium, sium, rium, soda, 1 = oe no lay | pee 3, 
4 5 ak rgerer’ T= — 12° 57 * Uy 32 T = at 
0 0 0 0 0 0 0 0 0 
8 1-1 8 ee 4 1:07 yh ae 47 
16 25 1°86 8 i 2-54 1-70 93 1:07 
24 4:2 | 2-93 | 1:4 18 4:22 2:80 1-46 1:80 
32 6:0 4:10 | 2:0 2°5 6°05 4:00 2-05 2°57 
40 8:0 |. 5-34 f 2°6 33 8-00 5°33 2-67 3°14 
48 tae 660 | 33 AO eitheeasii eta Goats 3°30 
= yh eens We come a ie ee eee 3-93 


334 Mr. T. Tate on the Boiling-points of different Liquids 


Here the near coincidence of the results in the second and 
sixth columns shows that the experimental values of & and T 
may be approximately represented by the formula 

, | phesaae 
T= top h: - : a a0 sar ae 

Again, the near coincidence of the results in the third and 
seventh, fourth and eighth, fifth and ninth columns shows that 
in this group of salts the temperatures of ebullition have a con- 
stant ratio to each other for all equal weights of salt. 

The errors of these formule are probably within the limits of 
the errors of observation. Owing to the oscillations of the mer- 
cury column at the boiling-points of the liquids, the errors of the 
readings of the thermometer might amount to about one-fourth 
of a degree. 

These experimental results for the most part agree with those 
given by Legrand (see Dr. Miller’s ‘Chemistry,’ second edition, 
p. 247). 


Augmentations of boiling-temperatures, in degrees Centigrade, of 
different solutions of the salts contained in Group 2. 


If T and T’ be put for the augmentations of the boilmg-tempe- 
ratures of the solutions of the chlorides of calcium and strontium 
respectively for any equal portions of the salts dissolved, then it 
will be found that T’=-34T very nearly, as shown in the follow- 
ing examples :— 
(1) For k=16, T=2; then by the formula, ‘T’=1-08. 
By experiment, T’=1. 

(2) For s=64, T=16°8; then by the formula, T’/=9-07. 
By experiment, T’=9. 

(3) For £=96, T=27:2; then by the formula, T’=14°68. 
By experiment, T’ = 147, . 

(4) For £=112, T=82:3; then by the formula, T’=17+44, 
By experiment, T’=17°2. 


Augmentations of boiling-temperatures, in degrees Centigrade, of 
different solutions of the salts contained in Group 3. 


If T, T’, T” be put for the augmentations of the boiling- 
temperatures of the solutions of the nitrates of soda, potassa, 
and ammonia respectively, and 4, k', kK" the corresponding per- 
centage of salts respectively dissolved, then the following for- 
mule will be found to represent the results of experiments very 
nearly :— . 


T= gy k™; sf doe? | 


and for all equal weights of salt, 


at the ordinary Pressure of the Atmosphere. 335 
| We eipe ie RRA 


and 
a TU ie VR eee ce ow BD 
Applications of formula (8). 
(1.) For k=24; then by the formula, T=2-57. 
A ort By experiment, Te26. 
(2.) For k=48; then by the formula, T=4°97. 
By experiment, T=. 
(3.) For 4=96; then by the formula, T=9°65. 
By experiment, P=9:72. 
_ (4.) For k=120; then by the formula, T=11-93. 
| By experiment, T=12. 
(5.) For k=168; then by the formula, T=16°47. 
By experiment, T=16:5. 
(6.) For k=216; then by the formula, T=20: 93. 
By experiment, T=20°3. 


Applications of formula (4). 
(1) For T= 2:6, T’= 2:23. By experiment, T’= 2:3. 
Py eer T= 7° 45, T’= 6:38. By experiment, T’= 6:5. 
(3) For T=16:3, T"=13-97. By experiment, T’=13° 8. 
(4) For T= 20°3, T"=17:4. By experiment, T’=17°0. 


Applications of formula (5). 


(1) For T’=2:3, ‘T’= 1:61. By experiment, T’= 1:8. 

(2) For T’=6- 5, T= 4°55. By experiment, T’= 4°6. 

(3) For T’=8-5, T'= 5-95. . By experiment, T'’= 5:9... 
y, Xp 

(4) For T=17, = Polh9, - By. experiment, T=11's. 


Augmeniations of boiling-temperatures, in degrees Centigrade, of 
different solutions of the salts in Group 4. | 


Corresponding boiling-temperatures of the different solutions of 
salt above that of pure water. 


Weight of salt 
in 100 parts 
of water, 5 ; Carbonate of Value of T Value of T 
ke sisi of lime, | ~ potassa, by formula by formula 


we Weks 1305. may a 
gros* | T=gt- 


0 0 0 0 0 
16 1 133 1°12 1-16 
32 27 3°12 2:76 273 
48 47 5:30 4:70 4°63 
64 7-0 78 6:97 6°82 
80 9:2 10°5 9°15 9-18 
96 11°63 13°5 11°62 11°81 
112 14-2 17-0 14:20 14°87 


176 25°0 29°5 25°61. 25°81 


336 Mr. T. Tate on the Boiling-points of different Liquids 


Here the near coincidence of the results in the second and 
fourth columns shows that the relation of k and T may be very 
nearly represented by the formula 


1 
= 1°305 
ih — 33:25 k o . ° e e o e (6) 
Moreover, the near coincidence of the results in the second and 


fifth columns shows that T= iy very nearly, or that in this 


group of salts the temperatures of ebullition, T and T’, have a 
constant ratio to each other for all equal weights of salt. 


On a certain law connecting (approximately) the bovling-tempera- 
tures of particular salts in the same group with the chemical equi- 
valents of their bases, and in one instance with the equivalents 
of the entire salts. 


For the chlorides of sodium and barium we have found 


ee 
= for all equal weights of the salts ; 
but Equiv. of sodium 23°31 1 
= Aon = 5 Very nearly. 


Hquiv. of barium 68°66 3 

Hence it follows that, for all equal weights of salt, the boiling- 
temperatures, T" and T, of these two chlorides are (approximately) 
in the inverse ratio of the equivalents of their bases. 

Again, for the chlorides of sodium and potassium we have 

a 1:5, for all equal weights of the salts; 
but Equiv. of potassium _ 39:26 
Equiv. of sodium ~ 23°31 

Hence it appears that the same law holds (approximately) true 
for these two salts. 

In like manner, for the chlorides of calcium and strontium we 
have 


= 168, 


> 
7 1°85, for all equal weights of the salts ; 
but Equiv. of strontium — 43°75 —9.18 
Equiv. of calcium ~~ 20 ° ~~ 


In this case the approximation is not so close. 
For the nitrates of soda and potassa we have 


7 = "60, for all equal weights of the salts ; 
but Equiv. of soda 31°31 _ 


Equiv. of potassa 47:26 — o 


at the ordinary Pressure of the Atmosphere. 337 


Hence it appears that the same law holds (approximately) true 
for these two salts. 

For the nitrate of lime and the carbonate of potassa included 
in the fourth group, we have 


a = - =°87, for all equal weights of the salts ; 
but 
Equiy. carb. of potassa _ 69 
Equiv. nitrate of lime ~ 82 — 
In this case, for all equal weights of the salts, the boiling-tem- 
peratures, T and 'T’, are (approximately) zn the inverse ratio of the 
equivalents of the entire salts. 

How far these laws may be extended to other substances 
future researches will determine; at the same time it must be 
observed that it is quite consistent with analogy to suppose that 
the chemical composition of a substance should affect the boil- 
ing-temperature of its solution. Although the law here indi- 
cated is not strictly true, yet it is sufficiently exact to warrant 
further inquiry, and the cases to which it is found to apply are 
too numerous to be referred to accidental coincidence. 


— ‘84, 


On the boiling-point of diluted sulphuric acid. 
With the exception of the sixth, seventh, and ninth experi- 
ments, the following experimental results were given by Dalton. 
The per-centages of concentrated acid in the liquids were calcu- 
lated from the observed specific gravities of the liquids by means 
of Ure’s Table, given at p. 801, fourth edition, of his work on 
the Arts and Manufactures. 


Augmentations of the boiling-temperatures, in degrees Fahrenheit, of 
diluted sulphuric acid at mean atmospheric pressure, containing 
different proportions of concentrated acid in 100 parts, the 
specific gravity of the concentrated acid being 1:846. 


Weight of con- | Corresponding Value of k | 


a ee 
the liquid, above 212°, k=14:15 TS, 
k. T. 

100 353 100-30 
96:21 Bits) $8.08 
93°66 289 93°59 
90°53 261 90-43 

| 86°82 223 85°81 
76°88 190 73:18 
48-00 40 48-39 
: 41-00 28 42°S6 
34:00 16 35°66 

0 0 0 


Phil, Mag. S. 4. Vol. 21. No. 141. May 1861. Z 


8388 Prof. Maxwell on the Theory of Molecular Vortices 


Here the near coincidence of the results in the first and third 
columns shows that the relation between & and T may be ap- 
proximately expressed by the formula 


’ le 1 1B) . . . e y ) 


LI. On Physical Lines of Force. By J.C. Maxwetu, Professor 
of Natural Philosophy in King’s College, London. 


[With a Plate. ] 
Part Il.—The Theory of Molecular Vertices applied to Electric 


Currents. 
[Concluded from p. 291.] 


Ae an example of the action of the vortices in producing in- 
duced currents, let us take the following case:—Let B, 
Pl. V. fig. 3, be a circular rg, of uniform section, lapped uni- 
formly with covered wire. It may be shown that if an electric 
current is passed through this wire, a magnet placed within the 
coil of wire will be strongly affected, but no magnetic effect will 
be produced on any external point. The effect will be that of 
a magnet bent round till its two poles are in contact. 

If the coil is properly made, no effect on a magnet placed out- 
side it can be discovered, whether the current is kept constant or 
made to vary in strength; but if a conducting wire C be made 
to embrace the rmg any number of times, an electromotive force 
will act on that wire whenever the current in the coil is made to 
vary; and if the circuit be closed, there will be an actual current 
in the wire C. 

This experiment shows that, in order to produce the electro- 
motive force, it is not necessary that the conducting wire should 
be placed in a field of magnetic force, or that lines of magnetic 
force should pass through the substance of the wire or near it. 
All that is required is that lines of force should pass through the 
circuit of the conductor, and that these lines of force should vary 
in quantity during the experiment. 

In this case the vortices, of which we suppose the lines of 
magnetic force to consist, are all within the hollow of the rig, 
and outside the ring all is at rest. If there is no conducting 
circuit embracing the ring, then, when the primary current is 
made or broken, there is no action outside the ring, except an in- 
stantaneous pressure between the particles and the vortices which 
they separate. If there is a continuous conducting circuit em- 
bracing the ring, then, when the primary current is made, there 
will be a current*in the opposite direction through C; and when 


applied to Hlectric Currents. 339 


it is broken, there will be a current through C in the same direc- 
tion as the primary current. 

We may now perceive that induced currents are produced 
when the electricity yields to the electromotive force,—this force, 
however, still existing when the formation of a sensible current 
is prevented by the resistance of the circuit. 

The electromotive force, of which the components are P, Q, R, 
arises from the action between the vortices and the interposed 
particles, when the velocity of rotation is altered in any part of 
the field. It corresponds to the pressure on the axle of a 
wheel in a machine when the velocity of the driving wheel 1s in- 
creased or diminished. 

The electrotonic state, whose components are F, G, H, is 
what the electromotive force would be if the currents, &c. to 
which the lines of force are due, instead of arriving at their actual 
state by degrees, had started instantaneously from rest with their 
actual values. It corresponds to the impulse which would act on 
the axle of a wheel in a machine if the actual velocity were sud- 
denly given to the driving wheel, the machine being previously 
at rest. 

If the machine were suddenly stopped by stopping the driving 
wheel, each wheel would receive an impulse equal and opposite 
to that which it received when the machine was set in motion. 

This impulse. may be calculated for any part of a system of 
mechanism, and may be called the reduced momentum of the 
machine for that point. In the varied motion of the machine, 
the actual force on any part arising from the variation of motion 
may be found by differentiating the reduced momentum with 
respect to the time, just as we have found that the electromotive 
force may be deduced from the electrotonic state by the same 
process. 

Having found the relation between the velocities of the vor- 
tices and the electromotive forces when the centres of the vortices 
are at rest, we must extend our theory to the case of a fluid 
medium containing vortices, and subject to all the varieties of 
fluid motion. If we fix our attention on any one elementary 
portion of a fluid, we shall find that it not only travels from one 
place to another, but also changes its form and position, so as to 
be elongated in certain directions and compressed in others, and 
at the same time (in the most general case) turned round by a 
displacement of rotation. 

These changes of form and position produce changes in the 
velocity of the molecular vortices, which we must now examine. 

The alteration of form and position may always be reduced to 
three simple extensions or compressions in the direction of three 
rectangular axes, together with three angular rotations about 

Z 2 


3840 Prof. Maxwell on the Theory of Molecular Vortices 


any set of three axes. We shall first consider the effect of three 
simple extensions or compressions. . 
Prop. 1X.—To find the variations of «, 8, y in the parallelo- 
piped z, y, z when w becomes v+ 6x; y, y+6y; and z, 2+6z; 
the volume of the figure remaining the same. 
By Prop. II. we find for the work done by the vortices against 
pressure, 


SW =p,o(ayz) — — — (atyzda + B?zxdy+y*%axydz); (59) 
and by Prop. VI. we find td the variation of energy, 
oh = —— fo («Bat BoB+ydy)ayz. . « . « « (60) 


The sum a4 BE must be zero by the conservation of energy, 
and o(vyz) =0, since xyz 1s constant ; so that 


a(3a—a~)+-8(88-8 4) +(8y—-7=)=0. (61) 
In order that this should be true independently of any relations 
between a, 8, and y, we must have 


daa, SB= =p, Sy = ay. pie ae 


Pie op. X.—To find the aan of a, 8, y due toa rotation 0, 
about the axis of # from y to z, a rotation 6, about the axis of y 
from z to 2, and a rotation @, about the axis of z from 2 to y. 

The axis of 8 will move away from the axis of « by an angle 
6,; so that 8 resolved in the direction of x changes from 0 to 

The axis of y approaches that of 2 by an angle @, ; so that the 
resolved part of y in direction z changes from 0 to y@. 

The resolved part of « in the direction of « changes by a quan- 
tity depending on the second power of the rotations, ¥ which may 
be neglected. The variations of a, 8, y from this cause are 
therefore 

du=y0,—PBO,, SB=a0,—y0,, Sy=R0,—aO,. (63) 

The most general expressions for the distortion of an element 
produced by the displacement of its different parts depend on the 
nine quantities 


Ae Ch ee d qd. dy. 
ip Oe? hs 783 Fp By, dy sag = y3 £ 82, Pa 3 


and these may always be pane rand in terms of nine other quan- 
tities, namely, three simple extensions or compressions, 


da! dy! ba! 


gee OT 3 
« 


a “ 


applied to Electric Currents. 341 


along three axes properly chosen, a, 7’, 2', the nine direction- 
cosines of these axes with their six connecting equations, which 
are equivalent to three independent quantities, and the three 
rotations @,, 0, @, about the axes of 2, y, 2. 

Let the direction-cosines of 2! with respect to 2; y, 2 be 
J}, m,,,, those of y’, 7,, m,n, and those of 2’, U5, mg, ng 3 then 


we find ) 
aS Phd ar the + ie 
dx 
# seam ston sim tte: (64) 


d Sx! Sy! Sx! 
Gq, ot =i =r 3; Pie y! + dstts yp — + gy | 


with similar equ uations for quantities involving dy and dz. 


, Let a', B', y' be the values of a, 6, y referred to the axes of 
2’, y'; a; aa 
a’ =latmB+ny, 
falatmetnn | eRe ee OO 
y! =lsa + ms8 + ngy. 
We shall then have 
da=/ da! + / 08! + [359 + 78, — 88s, ie on (66) 


= hel +18 + hy +10,—80. (67) 


By substituting the values of a’, 6’, y', and comparing with equa. 
tions (64), we find 
d 


d 
ba= a Be BT Baty 7 Be a PL ee (68) 


as the variation of « due to the change of form and position of 
the element. The variations of 8 andy have similar expressions, 
Prop. XI.—To find the electromotive forces ina moving body, 
The variation of the velocity of the vortices in a moving ele- 
ment is due to two causes—the action of the electromotive forces, 
and the change of form and position of theelement. The whole 
variation of @ is therefore 


dQ dR d d 
See (2-5 7, Jt a oe WHOS B04 9-7 8e. « (69) 
But since @ is a function of a, y, 2 and ¢, the variation of # may 
be also written 


Sax Ada 4 o = by 4 moult oat. 
dx 


dz dk be 6 . . e (70) 


342 Prof. Maxwell on the Theory of Molecular Vortices 


Equating the two values of 6a and dividing by d¢, and remem- 
bering that in the motion of an incompressible medium 


ddxe daddy. dd 
da dt Gy dk de Be =); e e ° e e e (71) 


and that in the absence of free magnetism 


de dB. dy 
a dy een eT ne ae 
we find 
1/dQ dR d dx d dz YY d dx 
a a, ee re ee + B— 
b\ds dy dz dt dz dt “dy dt dy dt 
dydx dadz dady dBdx da 


Putting 
an (SF di (74) 
and 
de). Mf erG = la ee 
ha ro et . 


where F', G, and H are the values of theelectrotonic components 
for a fixed point of space, our equation becomes 


dx dz dG d dy ao) = 
(Oto G — 1a EG) ~ lB eg HOG ay. 


The expressions for the variations of @ and y give us two other 
equations which may be written down from symmetry. The 
complete solution of i three equations is 


dz = dv | 
P=pyt He, they rs 


Qk : dx ‘ ay 
sal iid: eid oe oe3 dt dy? f 
da Fiat di dV 
Mott ge Oe dsct ager anit 
The first and second terms of each equation indicate the effect 
of the motion of any body in the magnetic field, the third term 
refers to changes in the electrotonic state produced by alterations 
of position or intensity of magnets or currents in the field, and 
Y is a function of 2, y, z, and ¢, which is indeterminate as far 
as regards the solution of the original equations, but which may 
always be determined in any given case from the circumstances 
of the problem. The physical interpretation of V is, that it is 
the electric tension at each point of space. 


applied to Electric Currents. 343 


The physical meaning of the terms in the expression for the 
electromotive force depending on the motion of the body, may 
be made simpler by supposing the field of magnetic force uni- 
formly magnetized with intensity « in the direction of the axis 
of z. Then if /, m, n be the direction-cosines of any portion of 
a linear hidaathe, and § its length, the electromotive force 
resolved in the direction of the conductor will be 


=S(P/+Qm+Rn), 5 2... (78) 


dz _ nit), 
e=Sya(m Foti) bs ales Vicars @ 


that is, the product of we, the quantity of magnetic induction 


or 


== ; nl ; ), the area swept 
out by the conductor 8 in unit of time, resolved perpendicular 
to the direction of the magnetic force. 

The electromotive force in any part of a conductor due to its 
motion is therefore measured by the number of lines of magnetic 
force which it crosses in unit of time; and the total electromo- 
tive force in a closed conductor is measured by the change of the 
number of lines of force which pass through it ; and this is true 
whether the change be produced by the motion of the conductor 
or by any external cause. 

In order to understand the mechanism by which the motion 
of a conductor across lines of magnetic force generates an elec- 
tromotive force in that conductor, we must remember that in 
Prop. X. we have proved that the change of form of a portion of 
the medium containing vortices produces a change of the velocity 
of those vortices; and in particular that an extension of the 
medium in the direction of the axes of the vortices, combined 
with a contraction in all directions perpendicular to this, pro- 
duces an increase of velocity of the vortices ; while a shortening 
of the axis and bulging of the sides produces a diminution of the 
velocity of the vortices. 

This change of the velocity of the vortices arises from the in- 
ternal effects of change of form, and is independent of that pro- 
duced by external electromotive forces. If, therefore, the change 
of velocity be prevented or checked, electromotive forces will 
arise, because each vortex will press on the surrounding particles 
in the direction in which it tends to alter its motion. 

Let A, fig. 4, represent the section of a vertical wire moving 
in the direction of the arrow from west to east, across a system 
of lines of magnetic force running north and south, The curved 
lines in fig. 4: represent the lines of fluid motion about the wire, 
the wire being regarded as stationary, and the fluid as having a 


over unit of area multiplied by (m 


344 Prof. Maxwell on the Theory of Molecular Vortices 


motion relative toit. It is evident that, from this figure, we can 
trace the variations of form of an element of the fluid, as the 
form of the element depends, not on the absolute motion of the 
whole system, but on the relative motion of its parts. 

In front of the wire, that is, on its east side, it will be seen that 
as the wire approaches each portion of the medium, that portion 
is more and more compressed in the direction from east to west, 
and extended in the direction from north to south; and since 
the axes of the vortices lie in the north and south direction, their 
velocity will continually tend to increase by Prop. X., unless 
prevented. or checked by electromotive forces acting on the cir- 
cumference of each vortex. 

We shall consider an electromotive force as positive when the 
vortices tend to move the interjacent particles upwards perpendi- 
eularly to the plane of the paper. 

The vortices appear to revolve as the hands of a watch when 
we look at them from south to north; so that each vortex moves 
upwards on its west side, and downwards on its east side. In 
front of the wire, therefore, where each vortex is striving to in- 
crease its velocity, the electromotive force upwards must be 
greater on its west than on its east side. There will therefore 
be a continual increase of upward electromotive force from the 
remote east, where it is zero, to the front of the moving wire, 
where the upward force will be strongest. 

Behind the wire a different action takes place. As the wire 
moves away from each successive portion of the medium, that 
portion is extended from east to west, and compressed from north 
to south, so as to tend to diminish the velocity of the vortices, 
and therefore to make the upward electromotive force greater 
on the east than on the west side of each vortex. The upward 
electromotive force will therefore increase continually from the 
remote west, where it is zero, to the back of the moving wire, 
where it will be strongest. 

It appears, therefore, that a vertical wire moving eastwards 
will experience an electromotive force tending to produce in it 
an upward current. If there. is.no conducting cireuit m_ con- 
nexion with the ends of the wire,:no.current will be formed, and 
the magnetic forces will not be altered; but if such a circuit 
exists, there will be a current, and the lines of magnetic force 
and the velocity of the vortices will be altered from their state 
previous to the motion of the wire. The change in the lines of 
force is shown in fig. 5. The vortices in front of the wire, instead 
of merely producing pressures, actually increase in velocity, while 
those behind have their velocity diminished, and those at the sices 
of the wire have the direction of their axes altered ; so that the 
final effect is to produce a force acting on the wire as a resist- 


applied to Electric Currents. 345 


ance to its motion. We may now recapitulate the assumptions 
we have made, and the results we have obtained. 

(1) Magneto-electric phenomena are due to the existence of 
matter under certain conditions of motion or of pressure in every 
part of the magnetic field, and not to direct action at a distance 
between the magnets or currents. The substance producing 
these effects may be a certain part of ordinary matter, or it may 
be an ether associated with matter. Its density is greatest in 
iron, and least in diamagnetic substances; but it must be in all 
cases, except that of iron, very rare, since no other substance has 
a large ratio of magnetic capacity to what we call a vacuum. 

(2): The condition of any part of the field, through which limes 
of magnetic force pass, is one of unequal pressure in different 
directions, the direction of the lines of force being that of least 
pressure, so that the lines of force may be considered lines of 
tension. 

(3) This inequality of pressure is produced by the existence 
in the medium of vortices or eddies, having thei axes in the 
direction of the lines of force, and having their direction of rota- 
tion determined by that of the lines of force. 

We have supposed that the direction was that of a watch to a 
spectator looking from south to north. We might with equal 
_ propriety have chosen the reverse direction, as far as known facts 
are concerned, by supposing resinous electricityinstead of vitreous 
to be positive. The effect of these vortices depends on their 
density, and on their velocity at the circumference, and is inde- 
pendent of their diameter. The density must be proportional to 
the capacity of the substance for magnetic induction, that of the 
vortices in air beg 1. The velocity must be very great, in 
order to produce so powerful effects in so rare a medium. 

The size of the vortices 1s indeterminate, but is probably very 
small as compared with that of a complete molecule of ordinary 
matter*. ’ 

(4) The vortices are separated: from each other by a single 
layer of round particles, so that a system of cells 1s formed, the 
partitions being these layers of particles, and the substance of 
each cell being capable of rotating as a vortex. 

(5) The particles forming the layer are in rolling contact with 
both the vortices which they separate, but do not rub against 
each other. They are perfectly free to roll between the vortices 


* The angular momentum of the system, of vortices depends on their 
average diameter; so that if the diameter were sensible, we might expect 
that a magnet would behave as if it contamed a revolving body within it, 
and that the existence of this rotation might be detected by experiments on 
the free rotation of a magnet. I have made experiments to investigate this 
question, but have not yet fully tried the apparatus. 


846 Prof. Maxwell on the Theory of Molecular Vortices 


and so to change their place, provided they keep within one 
complete molecule of the substance ; but in passing from one 
molecule to another they experience resistance, and generate 
irregular motions, which constitute heat. These particles, 3 in our 
theory, play the part of electricity. Their motion of translation 
constitutes an electric current, their rotation serves to transmit 
the motion of the vortices from one part of the field to another, 
and the tangential pressures thus called into play constitute elec- 
tromotive force. ‘The conception of a particle having its motion 
connected with that of a vortex by perfect rolling contact may 
appear somewhat awkward, I do not bring it forward as a mode 
of connexion existing in nature, or even as that which IT would 
willingly assent to as an electrical hypothesis, It is, however, a 
mode of connexion which is mechanically conce ivable, and easily 
investigated, and it serves to bring out the actual mechanical 
connexions between the known electro-magnetic phenomena; so 
that I venture to say that any one who understands the provisional 
and temporary character of this hypothesis, will find himself 
rather helped than hindered by it im his search after the true 
interpretation of the phenomena. 

The action between the vortices and the layers of particles is 
in part tangential; so that if there were any slipping or differen- 
tial motion between the parts in contact, there would be a loss of 
the energy belonging to the lines of force, and a gradual trans- 
formation of that energy into heat. Now we know that the 
lines of foree about a magnet are maintained for an indefinite 
time without any expenditure of energy ; so that we must con- 
clude that wherever there is tangential action between different 
parts of the medium, there is no motion of shpping between 
those parts. We must therefore conceive that the vortices and 
particles roll together without shpping; and that the interior 
strata of each vortex receive their proper velocities from the ex- 
terior stratum without slipping, that is, the angular velocity 
must be the same throughout e ach vortex 

The only process in whic th electro-mi enetic energy is lost and 
transformed into heat, is in the passage of electricity from one 
moleeule to another, In all other cases the energy of the vor- 
tices ean only be diminished when an equivalent quantity of me- 
chanical work is done by magnetic action. 

(6) The effect of an electric current upon the surrounding 
medium is to make the vortices in contact with the current 
revolve so that the parts next to the current move in the same 
direction as the current. The parts furthest from the current 
will move in the opposite direction ; and if the medium is a con- 
ductor of electricity, so that the particles are free to move in an 
direction, the particles touching the outside of these vorticeswil 


applied to Electric Currents. 347 


be moved in a direction contrary to that of the current, so that 
there will be an induced current in the opposite direction to the 
primary one. 

If there were no resistance to the motion of the particles, the 
induced current would be equal and opposite to the primary one, 
and would continue as long as the primary current lasted, so that 
it would prevent all action “of the primary current at a distance. 
If there is a resistance to the induced current, its particles act 
upon the vortices beyond them, and transmit the motion of rota- 
tion to them, till at last all the vortices in the medium are set in 
motion with such velocities of rotation that the particles between 
them have no motion except that of rotation, and do not produce 
currents. 

In the transmission of the motion from one vortex to another, 
there arises a force between the particles and the vortices, by 
which the particles are pressed in one direction and the vortices 
in the opposite direction, We call the force acting on the par- 
ticles the electromotive force. The reaction on the vortices is 
equal and opposite, so that the electromotive force cannot move 
any part of the medium as a whole, it can only produce currents. 
When the primary current is stopped, the electromotive forces 
all act in the opposite direction, 

(7) When an electric current or a magnet is moved in pre- 
sence of a conductor, the velocity of rotation of the vortices in 
any part of the field is altered by that motion. ‘The force by 
which the proper amount of rotation is transmitted to each vor- 
tex, constitutes in this case also an electromotive force, and, if 
permitted, will produce currents. 

(8) When a conductor is moved in a field of magnetic force, 
the vortices in it and in its neighbourhood are moved out of 
their places, and are changed in form, The force arising from 
these changes constitutes the electromotive force on a moving 
conductor, and is found by calculation to correspond with that 
determined by experiment. 

We have now shown in what way electro-magnetic phenomena 
may be imitated by an imaginary system of molecular vortices, 
Those who have been already inclined to adopt an hypothesis of 
this kind, will find here the conditions which must be fulfilled in 
order to give it mathematical coherence, and a comparison, so 
far satisfactory, between its necessary results and known facts, 
Those who look in a different direction for the explanation of the 
facts, may be able to compare this theory with that of the exist- 
ence of currents flowing freely through bodies, and with that 
which supposes electricity to act at a distance with a foree de- 
pending on its velocity, and therefore not subject to the law of 
conservation of energy. 


348 Mr. G. B. Jerrard’s Remarks on Mr, Cayley’s Note. 


The facts of electro-magnctism are so complicated and various, 
that the explanation of any number of them by several different 
hypotheses must be interesting, not only to physicists, but to ali 
who desire to understand how much evidence the explanation of 
phenomena lends to the credibility of a theory, or how far we 
ought to regard a comeidence in the mathematical expression of 
two sets of phenomena as an indication that these phenomena 
are of the same kind. We know that partial coincidences of this 
kind have been discovered; and the fact that they are only 
partial is proved by the divergence of the laws of the two sets of 
phenomena in other respects. We may chance to find, in the 
higher parts of physics, instances of more complete coincidence, 
which may require much investigation to detect their ultimate 
divergence. 


Note.—Since the first part of this paper was written, I have 
~ seen in Crelle’s Journal for 1859, a paper by Prof. Helmholtz on 
Fluid Motion, in which he has pointed out that the lines of fluid 
motion are arranged according to the same laws as the lines of 
magnetic force, the path of an electric current corresponding to 
a line of axes of those particles of the fluid which are in a state 
of rotation. This is an additional instance of a physical analogy, 
the investigation of which may illustrate both electro-magnetism 
and hydrodynamics. 


LII. Remarks on My. Cayley’s Note. By G. B. Jerranp*. 
Lye by wu, v two rational x-valued homogeneous 
functions of the roots of the equation 
a + Ava™—14 Aga? ,.-+-A,=0, 
we find by Lagrange’s theory that 


V=Mn—1 t+ Mn—2U+ fra U +e. ss : 
U= Van FV V+ Va_s¥?e +. ty, otf? (e) 


in which fyi, Mn—2) ++ Mor Vn—1) Yn—2)++Vq are symmetrical fune- 
tions of the roots of the original equation in z; and u, v depend 
separately on two equations of the nth degree 


UP a, UP ont At. eee O, ln) Se 
v+B, y®—14. Bo yn-2 4 Ae +B,=0, oar (V) 


Gh}, tg) + «Any By, Bos,»+ Bn being, as well as y»_1,..¥g, symmetrical 
functions of the roots of the equation in 2. 
I ought to observe that any coefficient, u,_,, in the equation 


* Communicated by the Author. 


Mr. G. B. Jerrard on the Equations of the Fifth Order. 349 


(e,) may take the form 
Mn_s 
D >] 
M,_., D being expressive of whole functions, and D, which re- 
mains constant while M,,_, successively becomes M,_1, M,_»,..Mo, 
being such as not to vanish except when (U) has equal roots. 
We find in fact from the researches of Lagrange that 


HD Ply) E(u,).s Kah ‘ 


where F(u) =nu"-! + (n—1)a, u®-2 + (n— —2)agu"3+ aie 4c 
U), Uo)». Up denoting the n roots of the equation (U). 
Of the meaning of the analogous expression 


Naas 
Dp! 


which obtains in (e,) for v,_,, 1t is needless to speak. Indeed, 
having found one of the two equations (e), say (e), we may in 
general deduce the other, (e,), from it by the method of the 
highest common divisor. 

“Let us now examine the following extract from Mr. Cayley’s 
paper in the last Number (that for March) of the Philosophical 
Magazine. 


& Writing,” he says, “ with Mr. Cockle and Mr. Harley, 


TH Uylgt Uyly + Lyle + Lsle TL Ly, 
T= y2y +2, L Ag+ UUs t Leas 


then (7+7' is a symmetrical function of all the roots, and it : 
must be excluded; but) (r—7')? or r7' are each of them 6-valued 
functions of the form in question, and either of these functions 
is linearly connected with the Resolvent Product. In Lagrange’s 
general theory of the solution of equations, if 


fr=2,+tt,+ F034 82,4445, 


then ‘the coefficients of the equation the roots whereof are ( ft)®, 
(fu?)°?, (fe®)?, (fe*)®, and in particular the last coefficient 
(ft fe fe fe), are determimed by an equation of the sixth 
degree ; and this last coefficient is a perfect fifth power, and its 
fifth root, or fu fi? fr? fu*, is the function just referred to as the 
Resolvent Product. 

“The conclusion from the foregoing remarks 1s, that if the 
equation for W has the above property of the rational expresst- 
bility of its roots, the equation of the sixth order resulting from 
Lagrange’s general theory has the same property.” 

Here the question arises, Is it certain that fi fi? fi? fi4 can, by 


850 Mr. J. S. Stuart Glennie on the 


means of Lagrange’s theory, be expressed generally in rational 
terms of (ft fi? fv3 fv4)° ?* 

Denoting those functions by u, v respectively, we have in this 
case vu"), 


A=30, w=, 
Now on substituting w”—! or w° for v in the equation (e,), we 
see that (e,) will merge into 


. Ms Mg Ut Mgt? + 66+ (Mo—])w?=0, . « (e) 
wherein, since (U) is in general irreducible+, we must have 
Hs=0, f4=0,..Ho—1=0. 
Accordingly, on combining the equations (e,), (U), that is to 
say, (e,), (U), we find 
—— 0 . 
u= 953 
the equation (e,) being, as we see, illusory. 

We are therefore not permitted to assume that the resolvent 
product can in general—that is, when (U) has no equal roots— 
be expressed rationally in terms of its fifth power. 

Again, it is generally possible to establish a rational commu- - 
nication between that fifth power and the function W, as is 
evidenced in this latter case from the non-existence of any illusory 
equation corresponding to (e,). 

We are thus furnished, as will be seen, with a new confirmation 
of the validity of my method of solving equations of the fifth 
degree. 


April 1861. 
[To be continued. | 


Mechanics. By J. 8. Stuart Gurnniz, M.A., F.R.AS.T 
Srcrion I. Physics. 
16. | PROCEED to consider the Principles of Energetics, or 


the science of Mechanical Forces, which seem to afford 
the bases of an explanation of physical motions. There is at 
present no attempt at a systematic elaboration of these principles, 
or mathematical application of them to the expression and expla- 


* Tt will be understood that owr present inquiry relates to the possibility 
of expressing either of the two quantities w, » as a rational function of the 
other and of the elements, Aj, Ag,..Am. Thus R(v,..) is supposed to mean 
the same thing as R(v, Aj, Ag,..Am); R indicating a rational function. 

+ As defined by Abel. 

t+ Communicated by the Author. In reference to the first part of this 
paper, note that the word “rotation” in the fourth line from the bottom 
of p. 280 of the last Number for “ revolution.” 


Principles of Energetics. 351 


nation of phenomena. Previous to such an attempt, it is thought 
advisable to enunciate these principles in their most general form, 
and give them merely experimental illustration. 

The principles to be set forth in this paper will lead me to 
remark on the physical theories recently published in this Journal 
by Prof. Challis and Prof. Maxwell. It will be found that as my 
theory refers attractions to differential conditions of stress and 
strain, of pressure and tension, among elastic bodies, it agrees 
rather with the molecular theory of the latter, than with the hy- 
drodynamical theory of the former; that the point of funda- 
mental difference from both is in the conception offered of 
Matter; and that on this point my theory is a development of 
the views to which experiment has led Mr, Faraday. 

17. (I.) Atoms are mutually determining centres of pressure. 

18. If this idea of an atom, as a body of any size, acting and 
reacting on another similar body by the pressure of the con- 
tinued, infinitesimal, but similar particles of which each centre 
is an aggregate, be clearly conceived, it may be expressed in 
many different forms. I have, for instance, in the introductory 
paper spoken of a body thus conceived as a Centre of Lines of 
Pressure, or an Elastic System with a centre of resistance. But 
here, more clearly to express the idea in contrast with the fun- 
damental hypotheses of Prof. Challis, an atom may be defined 
as a centre of an emanating elastic ether, the pressure of which 
is directly as the mass of its centre, and the form of which de- 
pends on the relative pressures of surrounding atoms. Thus, if 
you will, matter may be said to be made up of particles in an 
elastic ether. But that ether is not a uniform circumambient 
fluid, but made up of the mutually determining ethers (if you 
wish to give the outer part of the atom a special name) emana- 
ting from the central particles. And these central particles are 
nothing but what (endeavouring to make my theory clear by 
expressing it in the language of the theories it opposes) I may 
call zetherial nuclei. 

“ Hence,” according to the conception of Faraday, “ matter 
will be continuous throughout, and in considering a mass of it 
we have not to suppose a distinction between its atoms and any 
intervening space....... The atoms may be conceived of as 
highly elastic, instead of being supposed excessively hard and 
unalterable in form..... With regard also to the shape of the 
SLOMS . 6. ee That which is ordinarily referred to under the 
term shape would now be referred to the disposition and relative 
intensity of the forces *.” 


* Phil. Mag. 1844. vol. xxiv. p. 142; or Experimental Researches, 
vol. ii. p. 284, See also Phil. Mag. 1846, vol. xxviii. No, 188; or Expe- 
rimental Researches, vol. iii. p. 447. 


852 Mr. J. S. Stuart Glennie on the 


19. I venture to offer this conception of atoms, not as a mere 
hypothesis, but as a fundamental scientific principle. For there 
is this involved in it—that as a phenomenon is scientifically ex- 
plained only when, and so far as, it is shown to be determined 
by other phenomena, the conception of Matter itself must be 
relative, and its parts be conceived as mutually determined. 

Now Pressure is not only an ultimate idea, including all those 
qualities of Matter classed by the metaphysicians as the Seeundo- 
primary, but is, unlike those, for instance, of Trinal extension, 
Ultimate ineompressibility, Mobility, and Situation (the primary 
qualities), not an absolute, but a relative conception, and, as 
such, that on which alone. can be founded a strictly scientific 
theory of material phenomena. For in the foundation of a 
theory based on the conception of the parts of matter as centres 
of pressure, there is nothing, properly speaking, hypothetical, 
as no absolute, intrinsic, or independent qualities of form, hard- 
ness, motion, &c. are postulated for atoms; and in their defini- 
tion nothing more is done than an expression given to our ulti- 
mate and necessarily relative conception of matter. 

In defining Atoms as Centres of Pressure, they are thus no less 
disting uished on the one hand from Centres of Force, than from 
the little hard bodies of the ordinary theories ; for such Centres 
of Force are just as absolute and self-existent in the ordinary 
conception of them as are those little bodies. And in a scientific 
theory there can, except as temporary conveniences, be no abso- 
lute existences,—entities. Ilence (Mechanical) Force, or the 
cause of motion, is conceived, not as an entity, but as a condi- 
tion—the condition, namely, of a difference of Pressure*; and 
the figure, size, and hardness of all bodies are conceived as rela- 
tive, dependent, and therefore changeable. There are thus no 
absolutely ultimate bodies. 

20. But the full justification of advancing this conception of 
Atoms as a fundamental scientific principle, is found in the prin- 
ciples of the modern critical school of philosophy—in that espe- 
cially of the relativity of knowledge. From such a point of view 
this principle cannot here be considered. I must limit myself, 
therefore, to a criticism of the opposed conception of atoms in a 
uniform ether, as developed by Prof. Challis, and to the attempt 
to show that, with the conception of atoms here offered, Prof. 
Maxwell’s somewhat arbitrary hypothesis of vortices becomes un- 
necessary. For I agree with the former in thinking that, “after 
all that can be done by this kind of research, an independent 
and @ priort theory ..... 1s stillneeded t ;” and I observe that 


* See the first part of this paper, Phil. Mag. April, p. 275. 
+ “On Theories of Magnetism and other ‘Forees, 1 in reply to Remarks 
by Professor Maxwell,” Phil. Mag. April, p. 253, 


Principles of Energetics. 353 


the object of the latter “is to clear the way for speculation *,” 
rather than to advance a complete general theory. 

In examining Professor Challis’s ‘ fundamental hypothetical 
facts,” I hope to show that they are opposed (1) by Newton’s 
Rules of Philosophizing; (2) by the principles of Metaphysics, 
as the modern Science of the Conditions of Thought; and (3) by 
the conceptions of matter, of the interaction of its different parts, 
and of motion and force, to which modern experimental researches 
have led. 

21. “The fundamental hypothetical facts on which the [Prof. 
Challis’s| theory rests are, that all substances consist of minute 
spherical atoms, of different, but constant, magnitudes, and of the 
same intrinsic inertia, and that the dynamical relations and 
movements of different substances are determined by the mo- 
tions and pressures of a uniform elastic medium pervading: all 
space not occupied by atoms, and varying in pressure in propor- 
tion to variations of its density+.” Prof. Challis further says 
that he has “been guided by Newton’s views on the ultimate 
properties of matter, especially as embodied in the Regula Tertia 
Philosophandi in the Third Book of the ‘ Principia’; ” and that 
he has merely “‘ added to the Newtonian hypotheses two others, 
viz. that the ultimate atoms of bodies are spherical, and that they 
are acted upon by the pressure of a highly elastic medium ft.” 
But on reference to the cited rule, no “ Newtonian hypotheses” 
will be found, only a statement of the.actual general qualities of 
matter. And, setting aside the “additional hypothesis” of 
sphericity, so far are the hypotheses of ultimate indivisible 
atoms, and these of an indeterminate number of different sizes, 
though of the same intrinsic inertia, Newtonian, that Newton 
says, ‘At si vel unico constaret experimento quod particula 
aliqua indivisa, frangendo corpus durum et solidum, divisionem 
pateretur; concluderemus vi hujus regule, quod non solum 
partes divisee separabiles essent, sed etiam quod indivise in infi- 
nitum dividi possent.”” And Le Seur and Jacquier add in their 
note: “Hine patet differentia Newtonianismi et hypotheseos 
Atomorum; Atomiste necessario et metaphysicé atomos esse 
indivisibiles volunt, ut sint corporum unitates ; Metaphysicam 
hane queestionem missam facit Newtonus . . . . omnem hace de re 
Theoriam Metaphysicam experimentis facile postponens.” So 
that not only are Professor Challis’s hypotheses as to “ ulti- 
mate” bodies unwarranted by the rule he vouches, but he 
appears as of that very metaphysical school of Atomists, New- 


* «The Theory of Molecular Vortices applied to Magnetic Phenomena,” 
Phil. Mag. March, p. 162. 

+ Phil. Mag. Feb. 1861, p. 106. t Ibid. Dec. 1859, pp, 443 and 444, 
Phil. Mag, 8. 4. Vol. 21. No. 141, May 1861. 2A 


854. Mr. J. S. Stuart Glennie on tne 


ton’s opposition to which is implied in his Regula Tertia Philo- 
sophands. 

No less clear is it that the postulate of two different kinds of 
matter, one with the qualities of inertia and elasticity, the other 
without the second of these qualities, is opposed by the very 
terms, not only of the third rule, “ Qualitates corporum que 
intendi et remitti nequeunt, queeque corporibus omnibus compe- 
tunt in quibus experimenta instituere licet, pro qualitatibus cor- 
porum universorum habendz sunt,” but by the terms of the 
first rule also, “causas rerum naturalium non plures admitti 
debere, quam que et vere sint et earum phenomenis expli- 
candis sufficiant.” 

22. Consider, secondly, how such hypotheses are judged by 
the modern principles of Metaphysics. For it is evident that 
the theories of every science must ultimately be judged by the 
results of a science, Téyvn Texvov Kal eTLoTHUN ETLOTNLOV, 
which, defining the conditions of knowledge, gives canons for 
the criticism of hypotheses. As this is no place for a metaphy- 
sical discussion, let it suffice to say that the theory of the rela- 
tivity of cognition seems to justify the enouncement of this canon 
as a test of theories put forward as scientific. A scientific (phy- 
sical) theory is founded on postulates of Relations, not on postu- 
lates of absolutely existing Entities. According to this rule it is 
evident that if, for instance, a theory requires an atom of a cer- 
tain size or hardness, it can only be granted where it will stand 
as an expression of the relation between the forces distinguished 
at that point as internal and external; so if a certain elasticity, 
rotatory, or other motion of a body is required, the theory must 
take that elasticity or rotatory motion, not as an absolute pro- 
perty, but along with those relative conditions of other bodies 
which determine such elasticity or motion. 

23. Without advancing any other defence, this canon may be 
justified by the consequence of its neglect. For a theory founded 
on postulates of absolute qualities—entities—must necessarily 
reason in a circle, accounting for phenomena by the same phe- 
nomena already assumed as ultimate. 

Thus, though Professor Challis says that it would be contrary 
to principle “to ascribe to an atom the property of elasticity, 
because, from what we know of this property by experience, it is 
quantitative, and being most probably dependent on an aggrega- 
tion of atoms, may admit of explanation by a complete theory of 
molecular forces*,” he has no hesitation in ascribing elasticity 
to the particles of the ether, which, if anything, are as much 
atoms of matter as the “hard” atoms. But further, as to hard- 
ness, 1s it not the case that, “from what we know of this pro- 

* Phil, Mag, February 1860, p. 89. 


Principles of Energetics. 355 


perty by experience,” it also “may admit of explanation by a 
complete theory of molecular forces?” Is it not therefore self- 
contradictory to attribute elasticity to one sort of matter, and 
justify its denial to another, on grounds which would equally 
apply to the quality by which this other sort of matter is distin- 
guished from the former? And is not a theory fallacious which, 
if it attempts to explain relative elasticity or relative hardness, 
must do so by means of hypothetical and inconceivable, abso- 
lutely elastic, and absolutely hard entities ? 

24. But further, examining these fundamental facts by the 
results of the analysis of the qualities of matter, it will be seen 
that it is attempted to found a physical theory on the hypothesis 
of a physical matter acting on a mathematical matter. An elastic 
matter may be physically conceivable ; but the interaction of such 
a matter and bodies without any physical quality, but mere 
abstractions of the metaphysical qualities deduceable from the 
respective conditions of occupying and being contained in space, 
cannot but be experimentally inconceivable. 

25. Consider therefore, thirdly, the experimental conceptions 
to which these “hypothetical facts” are opposed; and (1) the 
conception of matter. 

The conception of an absolute, or uniform, and universal elastic 
sether is opposed to the conception now formed of such similar 
entities as the old electric fluids, &c.; namely, that electricity is 
not an entity, but the expression of a certain physical relation 
between bodies, the electric state being kept up by, and entirely 
dependent upon, the bodies among which the electric body at 
any time is, or may be brought. Hence it should seem that if a 
theory requires an elastic ether, its elasticity must be conceived 
as relative or determined by the masses and distances of bodies, 
and hence evidently elasticity be conceived as “une des propriétés 
générales de la matiére* ”’ 

And the notion of absolutely existing spherical atoms of dif- 
ferent magnitudes not only begs as many separate creations of 
atoms as our fancy may suggest differences in their size, but is 
opposed to the conception of the transmutation of matter, general- 
ized from the fact that we have in physics at least no creations, 
but perpetual changes dependent upon the ever-varying relations 
of bodies. 

_ 26. But (2) the idea of motions arising from the action of an 
elastic fluid on an inelastic absolutely hard and smooth body is 
opposed to all experimental conceptions of the interaction of the 
parts of matter. For not only do we seem to be led by experi- 
ment to a conception of the continuity of every part of matter by 
the cohesion of other bodies, so that it should seem to be impos- 

* Lamé, quoted in Part I. of a ams Phil. Mag. April, p. 275. 
2 


» 


356 Mr. J. S. Stuart Glennié on the 


sible for a fluid to act on a solid except through a mediate or 
immediate cohesion, but we are led by the Mechanical Theory of 
Heat to conceive every impulse communicated to a body to be 
productive of internal as well as external motion. It is of course 
necessary to make abstraction, out of the infinite number of 
effects, of the particular effect we may desire to consider. But 
an hypothesis of infinitely hard atoms not merely requires, in the 
consideration of the motion of such an atom, abstraction to be 
made of the interior relative motions also consequent on that 
difference of pressures which causes its external relative motion, 
but explicitly denies any internal motion. 

It may be here noted that the Mechanical Theory of Heat 
would lead us to consider as “ ultimate’? no special class of 
bodies or molecules, except simply those, of the internal motions 
of which we do not in any particular theoretical, or cannot in an 
experimental, investigation take account. So any hardness may 
be called “infinite ”’ if we do not consider the internal motions, 
or change of form, consequent on the application of a force which 
causes the translation of the body. But Professor Challis re- 
quires us to concede as physical facts what are properly but con- 
venient mathematical abstractions. 

27. Again (3), the conception of the origination of motion 
under such conditions as a uniform ether and discrete atoms 
therein, all of the same mass, is opposed to the experimental con- 
ception ‘of motion as or iginating in difference in the mutual pres- 
sures of bodies. For these hypotheses give us the conditions of 
an eternal equilibrium. In the theory I propose, it is evident 
that anything short of an absolute equality in the masses and 
distances of the parts of matter implies infinite mutually deter- 
mining motions. 

And Professor Challis speaks of “the existence of the wether 
as the sole source of physical power*.” But in a mechanical 
theory, as 1 have in the introductory, and in the first part of 
this, paper shown, nothing can be accurately spoken of as, of 
itself, ‘a source of power.” ‘A source of power,” a cause of 
motion, or a force, is simply the difference in relation to a third 
body of two resultant pressures upon it. And there can thus be 
no conceivable mechanical power in a fluid of which the elasticity 
is uniform, and on whick the reaction of different solids withm 
it should seem, by this theory, to be either nothing or the same. 

28. Professor Challis further conceives the physical forces to 
be correlated as ‘ modes of action of a single elastic medium.” 
But I shall endeavour in the sequel to distinguish these cor- 
relations, and to show that they are either coexisting, mutually 


* Phil. Mag. February 1861, p. 106; and December 1859, p. 444. 


Principles of Energetics. 357 


causative, or sequential molecular motions. For the true applica- 
tion of Hydrodynamics would seem to be rather to actual solids 
and fluids, than to such “ hypothetical facts” as form the bases 
of Professor Challis’s Theory of Physics. How much work re- 
mains to be done in that true direction is well known; and the 
greatness of the results in the knowledge that might thereby be 
given of the formation of the solar and other sidereal systems, 
makes every contribution to Hydrodynamics, whatever the 
immediate particular application of the theorems, of peculiar | 
value. 

29. If, therefore, the true application of Hydrodynamics has 
been mistaken, and if a Hydrodynamical Theory of Physics must 
be founded on entities, hypothetical solids and fluids, to which 
such objections as the foregoing can be urged, there remains for 
us only a Molecular Theory of Physics. It is because to such a 
Theory all the most important modern physical researches seem 
to poimt, that I have thought it necessary to examine at such 
length the “fundamental facts” of Professor Challis. For the 
great result of modern science may be said to be the relative con- 
ception it gives of every phenomenon, and hence the demand 
that the fundamental facts of any theory be conceived, not as 
absolute and independent existences, but as expressions of rela- 
tions. Now a Molecular is distinguished from a Hydrodyna- 
mical Theory of Physics in this,—that while in the latter the 
states and motions of bodies are explained by the action on them 
of some hypothetical, uniform, absolute, and all-pervading entity, 
in the former theory, physical states and motions are referred to 
differential conditions of stress and strain among the actual con- 
stituent molecules of bodies. Hence the evident experimental 
advantage of a Molecular Theory is, that its hypotheses being 
as to relative conditions of Molecular pressure and tension, trans- 
mission of motion, &c., they are more or less capable of experi- 
mental proof or disproof; and such a theory will be at least pro- 
lific in the suggestion of experiment. But where one deals with 
the waves or currents of an absolute ether acting on absolute 
atoms, a plausible theory may indeed be made out, but it is 
because its conceptions are fundamentally opposed to, so that 
its minor hypotheses cannot be checked by, experiment. 

30. It is as the new fundamental principle of a Molecular 
Theory of Physics that I venture to suggest the above conception 
of Atoms. It is because, however convinced of the soundness of 
this principle, I am very diffident of my own powers of applying 
it, that I have gone at such length into its illustration, and the 
criticism of the opposed conception, as developed by Professor 
Challis. For should the mechanical explanation which, by 


358 Chemical Notices :—M. Sawitsch on Acetylene. 


means of this principle, I propose to give of physical and che- 
mical phenomena be found liable to serious objection, I hope 
the above remarks will have made this conception of Atoms 
sufficiently clear to be applied with greater success by others. 

6 Stone Buildings, Lincoln’s Inn, 


April 11, 1861. 
[To be continued. | 


LIV. Chemical Notices from Foreign Journals. 
By H. Atxinson, PA.D., F.CS. 


[Continued from p. 301.] 


AWITSCH* found that, under certain circumstances, mono- 

brominated ethylene, €? H® Br (bromide of vinyle), parted with 
hydrobromic acid and became converted into acetylene, €* H?, the 
gas discovered by Edmund Davy and investigated by Berthelot. 
He was led to investigate this deportment more minutely, and 
having tried the action of monobrominated ethylene on amylate 
of sodium, has found in it a mode of preparing this gas. 

About 45 grammes of brominated ethylene were heated in a 
closed vessel with amylate of sodium. An abundant precipitate 
of bromide of sodium was formed, and the mass became liquid 
from the regenerated amylic alcohol. The vessel was then care- 
fully cooled down in a freezing mixture and opened, when 
about 4 litres of a gas escaped, which, agitated with an ammo- 
niacal solution of chloride of copper, gave an abundant red pre- 
cipitate. When this precipitate was treated with dilute hydro- 
chloric acid, it gave off about a litre of a colourless gas with a 
peculiar odour, and which burned with a very fuliginous flaine. 
The analysis of this gas, and its combination with copper, left no 
doubt that it was acetylene. 

Its formation may be thus expressed :-— 


o FJ ll 
‘ i 04+C?H?Br= C?H?+NaBr+@ HO. 
pe ae F Monobrominated Acety- Amylic 
Ba tia ethylene. lene. alcohol. 


This reaction is important, as it will probably lead to the for- 
mation of a new series of hydrocarbons of the general formula 
©; He»-2, of which acetylene, €* H?, is the first member, from 
the hydrocarbons of the general formula C, H.,. In fact 
Sawitsch has subsequently { examined the action of monobromi- 


* Bulletin de la Société Chimique, p. 7. 
+ Phil. Mag. vol. xx. p. 196. 
{ Comptes Rendus, March 4, 1861. 


M. Miasnikoff on Acetylene. 359 


nated propylene on ethylate of sodium, and has obtained a second 
member of the series, al/ylene, C7 H*. The action is quite ana- 
logous to that in the former case: the gas is passed into an am- 
moniacal solution of copper, with which it forms a voluminous 
flocculent precipitate. This is decomposed, when heated, with 
the formation of a reddish flame; with concentrated acids it dis- 
engages a gas even in the cold. 

Allylene is best obtained from this precipitate by the action 
of dilute aqueous hydrochloric acid, from which, when heat is 
applied, there is given off a colourless gas of a strong and dis- 
agreeable odour, but less so than that of acetylene. It burns 
with a fuliginous flame, and precipitates silver and mercury salts, 
the former grey and the latter white. These compounds are 
analogous to the copper compound, and, like it, are very unstable. 
The property of combining with an ammoniacal oxide of copper 
appears to be characteristic of this group, and will probably lead 
to the discovery of the higher members. 

The formation of allylene may be thus expressed :— 

C? H° NaQO+ C? H® Br= Na Br+ €? H*+€? H°O, 
Ethylate of Brominated Allylene. Alcohol. 
sodium. propylene. 


Miasnikoff*, in some experiments with monobrominated ethyl- 
ene, has also noticed a mode of the formation of acetylene, which 
gives a simple and elegant method of preparing this gas. 

When the vapours of crude monobrominated ethylene, prepared 
in the ordinary way, are passed into an ammoniacal solution of 
nitrate of silver, a precipitate forms, which is at first yellow, but 
which quickly becomes converted into grey; at the same time 
an oil collects at the bottom of the vessel, which is brominated 
ethylene, and which can easily be separ ated by heating to 20°. 
When this bromide further acts upon a fresh portion of ammo- 
niacal solution, it produces no change; but after being passed 
through a boiling concentrated solution of potash, it again 
acquires the property of forming this grey pulverulent deposit. 
By arranging the apparatus so that the vapours of brominated 
ethylene pass more than once through solution of potash, a con- 
siderable quantity of the pulverulent deposit can be formed. 

This powder detonates strongly on the application of heat, 
percussion, or friction, and also by the action of chlorine or of 
gaseous hydrochloric acid. Treated with dilute hydrochloric 
acid, it gives a gas which burns with a fuliginous flame, and 
which reproduces the pulverulent precipitate. The analysis and 
the properties of this gas show that it is acetylene; and the 
analysis of the silver compound gives for it the formula 

C* H? Ag’. 
* Bulletin de la Société Chimique, p. 12. 


360 M. Heinz on Glycolic Acid. 


From the mode of its preparation, monobrominated ethylene, 
in passing through strong potash, is simply resolved into acetyl- 
ene and hydrobromic acid, 

€? H® Br—H Br=€? H?. 
Monobrominated Acetylene. 
ethylene. 


By a similar series of actions, M. Morkownikoff has prepared 
what appears to be the gas allylene, described by Sawitsch. 


According to Heinz*, the best method of preparing glycolic 
acid is from monochloracetic acid, which, under the influence of 
alkalies, decomposes into an alkaline glycolate and into an alka- 
line chloridet. | 

The hydrate of glycolic acid may readily be obtained by the 
following method :—To the solution of the mixture of glycolate 
of soda and chloride of sodium obtained in the above reaction, a 
sufficient quantity of solution of sulphate of copper is added. 
The glycolate of copper, C+ H? Cu O®, which forms, is a diffi- 
cultly soluble salt; it precipitates as a crystallme mass, and 
is readily obtained pure by washing. This salt is then dif- 
fused in a large quantity of water, the mixture raised to boiling, 
and saturated with sulphuretted hydrogen. When all the cop- 
per is precipitated it is filtered; and as the filtrate is brownish, 
from the solution of a small quantity of sulphide of copper, it is 
evaporated to a small volume, while a slow stream of sulphuretted 
hydrogen is passed through, and when now filtered, is obtained 
quite colourless. 


By a series of operations analogous to those by which an 
alcohol of the ethyle series may be transformed into the next 
higher acid, Cannizarot has obtained from anisic alcohol an acid 
homologous with anisic acid. 

Anisic alcohol, €® H'®Q?§, appears to contain the group 
€° H® 0, which plays the part of a monoatomic radical. When 
the chloride of this group, C® H9 O, Cl, was treated with cyanide 
of potassium, chloride of potassium was formed, and an oil which 
was the cyanide, C7 H9O EN. This oil was obtained in the im- 
pure state, and was treated directly with potash at the tempera- 
ture of ebullition, by which a large quantity of ammonia was 
disengaged ; and on the subsequent addition of hydrochloric acid 
in excess, an oil deposited which solidified to a crystalline mass. 
This consisted of the new acid which Cannizaro names homoanisic 


* Poggendorff’s Annalen, January 1861. 
tT Plul. Mag. vol. xvi. p. 138. 

{ Comptes Rendus, vol. li. p. 606, 

§ Phil. Mag. vol. xx. p. 294. 


M. Rossi on Homocuminic Acid. 361 


acid. It crystallizes im nacreous lamine. Its formation may be 
thus expressed :— 
CSHIOEN+K HO+ H?O=C9 H® KO8+ NH. 
Cyanide of Homoanisate 
anisyle. of potash. 


Rossi* has applied to cuminic alcohol the same series of trans- 
formations, and has obtained a new acid homologous with cuminic 
acid. He prepared the chloride of cumyle, G!° H'’ Cl, by the 
action of hydrochloric acid on cuminic alcohol, and treated it 
with cyanide of potassium, by which means he obtained the cor- 
responding cyanide. This crude cyanide of cumyle was boiled 
with strong caustic potash until its decomposition was complete ; 
and to the mixture was then added hydrochloric acid in excess, 
by which the new acid was precipitated. On recrystallization it 
was obtained in small needles. Its formation is thus expressed : 

Gl HEN + KHO+ H? O= 6"! H KO?4 NH, 
Cyanide of Homocuminate 
cumyle. of potash. 

Homocuminic acid, G!! H!? 02, can be distilled without decom- 
position. It is difficultly soluble in cold water ; but its solution 
reddens litmus, and decomposes the carbonates. Its salts are 
obtained by double decomposition: most of them crystallize 
well. , 


As the result of a lengthened investigation on filtration of the 
air in reference to fermentation, putrefaction, and crystallization, 
Schroder f is led to the following conclusions :— 

1. A vegetable or animal can only be formed from living vege- 
table or animal organisms. Ommne vivum ex vivo. 

2, There is a series of phenomena of fermentation and putre- 
faction which arise solely from microscopic germs furnished by 
the atmosphere. These are more especially the formation of 
mould, of wine-yeast, of the lactic acid ferment, of the ferment 
which produces the decomposition of urine. 

3. Vegetable or animal substances, boiled and closed while 
hot by means of cotton, remain im that condition quite protected 
against every kind of fermentation, putrefaction, or formation of 
mould, if all the germs in them capable of development are de- 
stroyed by boiling; for the germs which might reach them from 
the air are filtered out by the cotton. 

4, The germs of most vegetable or animal substances are com- 
pletely destroyed by simple boiling. A boiling for a short time 
at 100° C. isalso sufficient to kill all germs furnished by the air. 


* Comptes Rendus, March 4, 1861. 
t+ Liebig’s Annalen, March 1861. 


362 M. Schréder on Fermentation, Putrefaction, &c. 


5: But milk, the yellow of egg, and meat contain germs which 
are not completely destroyed by a short boiling at 100°. But 
boiling at a higher temperature under a pressure of two atmo- 
spheres in the digestor, or long-continued boiling at 100°, is 
sufficient to kill even these germs. 

6. The germs of milk, yellow of egg, and of meat, even when 
they have been submitted to a boiling at 100°, not continued, 
however, too long, are capable of developing themselves as a 
specific putrefaction ferment, and not unfrequently, at least in 
the yelk of egg, in the form of long but inert fibrils. 

7. This specific putrefying ferment is of animal nature. It 
developes and increases at the expense of all albuminous sub- 
stances. It is, however, incapable of increase under conditions 
which are all that are necessary to vegetable formations. 

8. The crystallization of supersaturated solutions is com- 
menced or induced by the action of the surface of solid bodies. 

9. The induction necessary to set up the crystallization of the 
soluble hydrates from a supersaturated solution, is less than that 
necessary for the crystallization of the more difficultly soluble 
hydrates. 

10. The surface of a crystal of the same nature exercises the 
strongest inducing action. Next to that comes the layer of air 
which forms on the surface of solid bodies. These coatings are 
destroyed by heating, continued wetting, or by cleaning, and are 
only formed slowly again in filtered air. 

1]. The crystallization of the more soluble hydrates from 
supersaturated solutions, which is set up even by a feeble induc- 
tion, only experiences a feeble induction on the surface of the 
crystal of the same kind, and hence only progresses very slowly. 

12. Supersaturated solutions closed with cotton keep for a 
long time unchanged, because the cotton filters all the solid 
particles from the air which gains access. Agitation has no 
action on the crystallization ; it only induces it if supersaturated 
solutions are in contact with such places of the surface as are 
fitted to induce the crystallization. 


By oxidizing cymole, €!°H", with dilute nitric acid, Noad 
found that it was converted into toluylic acid, C® H® 0%, and 
oxalic acid; from cumole, €? H'!*, Abel similarly obtained ben- 
zoic acid, G67 H® 8%. Hence it might have been expected that 
toluole, G7 H®, by analogous treatment would yield a new acid, 
€ H? 62, homologous with these. 

This is, however, not the case, as experiments by Fittig * have 
shown. When toluole is oxidized by means of nitric acid, the 
process is different. There is no formation either of oxalic or of 
carbonic acid. <A colourless acid is formed, almost insoluble in 


* Liebig’s Annalen, February 1861. 


MM. Beilstein and Seelheim on Saligenine. 363 


cold water, and but slightly so in hot. It erystallizes from this 
solution in very small needles. 

This body seems to have the composition of salicylic acid, 
€’ H®0®, without, however, beimg identical with it; for it 
does not give the well-known reaction with perchloride ‘of iron, 
characteristic of salicylic acid. The baryta salt has the formula 
G7 H° Ba O38, and the silver salt G’ H® Ag 0°, 


As yet the glycols of the fatty acid series only are known. 
Wicke obtained a compound, €!! H!? 64, which has the compo- 


- @7 He 
sition of an acetate of benzo-glycol, (C2 H3 oy: $s but its pro- 


perties differ from what might be expected of a glycol derivative, 
and it is rather analogous to the compounds which Geuther ob- 
tained by heating the aldehydes of the fatty acids with anhydrous 
acids. Beilstein and Seelheim* have made a series of experiments 
to prepare theglycol,€’ H° 0”, of the aromatic series of acids, which 
stands to benzylic alcohol, €’ H® 0, and benzoic acid, €’ H® O?, 
in the same relation as ordinary glycol, €? H® O?, does to alcohol, 
€* H° O, and acetic acid, C? H*0*. By the action of sulphuric 
acid on benzylic alcohol, they hoped to obtain the bibasie radical 
@’ H° in a manner analogous to that by which ethylene is obtained 
from ordinary alcohol. But the result of the above action was a 
resinous body, which, when treated with bromine in the expecta- 
tion of obtaining €’ H® Br?, gave off hydrobromic acid and un- 
- derwent a complete decomposition. 

The composition of the desired body would be identical with 
that of saligenine, which in many points resembles a biatomic 
alcohol. An attempt was made to prepare from it the biatomic 
chloride, G’ H® Cl?, which did not give the desired result. 

By the action of pentachloride of phosphorus, saligenine was 
resolved into saliretine, 6’ H® Q, and water; at the same timea 
certain quantity of a chlorine compound was formed which 
seemed to contain the chloride €’ H® Cl?, but which could not 
be separated in the pure state. 

Saligenine was heated with anhydrous acetic acid in the ex- 
pectation of forming acetate of saligenine ; but instead of this, 
saliretine and acetic acid were formed :— 


CHS 0? + fopsg bO=C’ W804 20 HO? 


seas Salireti Acetic acid. 
Saligenine. Acetic Hea ree 


anhydride. 


~ When sodium was added to a solution of saligenine in pure 
ether, hydrogen was evolved, and a white pulverulent precipitate 


* Liebig’s Annalen, January 1861. 


364 M. Jolly on Liquid Ammonia. 


formed, which appeared to have the formula €'* H'? Na Q?. 
Iodide of ethyle and chloride of acetyle act on this body, and 
form resinous bodies which could not be purified. 

Saligenine dissolves in baryta water, forming a crystalline com- 
pound, €’ H9 Ba 0? =€’ H’ Ba 0? + H? 0. 

By the action of pentasulphide of phosphorus, saligenine 
appears to become converted into an amorphous variety. 


The law which regulates the contraction of solutions made it 
probable that the specific gravity of liquid ammonia must be less 
than that found by Faraday; and with a view of testing this 
point, Jolly* has made a redetermination of its specific gravity. 

The liquid gas was prepared in the usual way, by heating am- 
moniacal chloride of silver in a bent closed tube, the empty end 
of which was much narrowed in one part and was provided with an 
arbitrary graduation. After the ammonia had been expelled from 
the ammoniacal chloride, and had been condensed in the cooled 
end of the tube, the part containing the liquefied gas was cooled 
down to a temperature of —86° in a mixture of solid carbonic 
acid and ether, and was melted off, which at this temperature 
could be done without danger. 

The tube was now immersed in pounded ice, and the height of 
the liquid read off. A subsequent weighing gave the weight of 
the tube, together with the hquid gas and the compressed gas 
above the liquid. 

The tube was now cooled down to —24° C., and the point 
softened, by which, as the tension of the gas at this temperature 
does not exceed two atmospheres, the gas escaped without danger 
or loss of glass. The opened tube was next transferred from the 
freezing mixture into pounded ice, upon which a violent ebullition 
commenced, after which, when terminated, and there was no more 
escape of NH3, the tube was closed and weighed, by which the 
weight of the vapour at O° was determined. 

At this stage special experiments were made to ascertain if the 
ammonia was anhydrous and quite free from air, which was found 
to be the case. The tube was next weighed empty, and then 
calibrated. 

From the data furnished by these various operations, Jolly 
found the specific gravity in three experiments to be 


0:6239, 0:6261, 0°61938, 


or in the mean 0°6231, which is one-sixth less than the number 


* Liebig’s Annalen, February 1861. 


On the Duration of the Spark of an Electric Discharge. 865 


found by Faraday, 0°73, and agrees with a determination made 
by Andréeff*, who obtained the number 0°6364. 

Jolly also determined the coefficient of absorption of liquid 
ammonia, and found it to be for 1 degree 0°00155, which is 
about half as much as that of air. 


LV. On the Duration of the Spark which accompanies the dis- 
charge of an Electrical Conductor. By P.. RisKe, Professor 
of Natural Philosophy at the University of Leydent. 


1. ‘ N J HEN a Leyden jar is discharged in the ordinary way, 

the spark produced may be considered as instanta- 
neous; its duration, at least, is so short that it has hitherto 
been found impossible to measure it even approximately. This, 
however, is no longer the case when the charge has to traverse a 
body which offers any considerable resistance, as, for instance, a 
copper wire half a mile long. In fact, Mr. Wheatstone found f 
that the spark obtained thr ough a copper wire of ;/;th of an inch 
in diameter, and of the length: above mentioned, lasted for about 
se oooh of a second. 

2. This result, if Mr. Wheatstone had published it by itself, 
would probably have been explained simply - the ground that 
electricity required precisely this time, viz. —1 th of a second, 
to traverse the length of wire in question. This explanation 
would, however, have been, to say the least, incomplete, since in 
the same series of a Mr. Wheatstone proved that elec- 
tricity really requires 1 th of a second to travel that di- 
stance ; and in order to reconcile these results, he considered it 
necessary to have recourse to a new hypothesis, and to suppose 
“that the diameter of the wire was not sufficiently great to allow 
the charge to pass through it except in a successive manner.’ 

3. In reflecting on this question, it appeared to me that the 
results obtained by the above-named illustrious physicist might 
be easily explained on known grounds; and that it was by no 
means necessary to have recourse to a hypothesis, in support of 
which it would be difficult to cite a single direct observation. 

We shall see that it is, in fact, easy to prove a priori the fol- 
lowing proposition :— 

The time required by electricity to traverse a given conductor 1s 
much less than that required to discharge that conductor. 


* Liebig’s Annalen, vol. ex. p. 1. 

+ Communicated by the Author. 

t “On some Experiments to Measure the Velocity of Electricity and the 
duration of Electrical Light,” Phil. Trans. 1834. 


366 Prof. Rijke on the Duration of the Spark which 


Let AB be an isolated conductor of such length that a charge 
of electricity requires a perceptible time, say 7’, to traverse it. 


CA B 


Let C.D be another conductor much shorter than the first, and 
so placed that the extremities C and A of the two conductors are 
at the distance of several millims., the other extremity D of the 
second conductor being in communication with the ground, 

Now suppose that at a given moment a certain quantity of 
electricity be communicated to the extremity B of the conductor 
AB. At the end of 2” this electricity will have spread over the 
whole surface of the conductor. At the same instant, supposing 
the tension sufficient, a luminous discharge will commence be- 
tween A and C. We say will commence, admitting“therefore that 
the discharge will occupy a certain time. In fact, in order that 
the conductor might discharge itself instantaneously, it would be 
necessary that all the electric fluid should be accumulated at A. 
This, however, is not the case; since at the moment when the 
discharge commences, the whole surface of the conductor is 
occupied, though unequally, with electricity. Now it is easy to 
see that the electricity, which at the moment we are considering 
is still at B, will only reach the other extremity 7" afterwards* ; 
and even then it must be carefully noted that ad/ the electricity 
at B will not have passed to A; only part will have done so, and 
the rest will have remained at B, of which a further portion will 
reach A 2¢" after the discharge commences, and a third 3¢"' after 
the same epoch, and so on, 

The above reasoning shows that, during the time oceupied by 
the discharge, successive portions of electricity will arrive at A 
from B at equal intervals of time; and it is clear that the same 
will be the case with the electricity which at the beginning of 
the discharge was at any intermediate part of the conductor, 
only that the intervals of time will be shorter in proportion as 
the part considered is nearer A, It is therefore evident that 
there will be a continuous current of electricity towards this ex- 
tremity, and that the discharge will therefore be equally con- 
tinuous. ‘The passage of the electricity from A to C will of 
course cease immediately the tension at A descends below a cer- 
tain limit; but, on the other hand, it must not be forgotten 


* Tf, as some physicists believe, the rapidity of the propagation of elee- 
tricity diminishes with its density, then the electricity at B would require 
more than ¢" to arrive at A. 


accompanies the discharge of an Electrical Conductor. 867 


that, in order to support the discharge already commenced, a 
much less considerable tension is required than is necessary to 
establish it in the first instance (Riess, Die Lehre der Reibungs- 
elektricitét, vol. 11. p. 636). When electricity once commences 
to pass in the disruptive form from A to C, an expansion is pro- 
duced in the intermediate layers of air, which amply suffices to 
explain the facility with which the same layers of air allow them- 
selves to be traversed by electricity of much lower tension. 

4. It is evident, however, that this expansion will depend on 
the quantity of electricity which in a given time passes from A 
to C. Consequently if the experiment be so conducted that, all 
other things being the same, a less quantity of the electric fluid 
passes from A to C, the expansion of the air will be less, and the 
discharge ought to cease sooner. But if the discharge ceases 
sooner, it will follow that the residwe will be greater. Now it is 
easy to yerify this theoretical conclusion. 


B is a metallic sphere of 0°31 metre diameter. This sphere is 
connected by means of metal wires, on one side with a sinus elec- 
trometer A (Pogg. Ann. vol. evi. p. 438), and on the other with 
an apparatus C, called by Riess an “ Entladungsapparat ” (Riess, 
Die Lehre der Reibungselektricitat, p. 365), and which consists 
of a moveable metal rod gh, turning at 2 on a horizontal axis 
provided with a ratchet and clapper, which can be moved by 
pulling the silk cord ad, so that the knob g can always be 
brought to a fixed distance from the metal ball f 

The ball f and the moveable rod g / are both supported on glass 
pillars, the former being united by means of a metal wire with 
one branch of the universal excitator D, of which the other 
branch communicates by similar means with one of the knobs 
of the spark-micrometer E. The other knob of the spark-micro- 
nieter is in connexion with the ground. Between the branches 
of the excitator D the substances are placed whose action on the 
residue we wish to determine. 

I confined myself to the comparison of the actions of brass 
wire and a cord of hemp steeped in water. Both these conduc- 
tors were 0°3 metre long, the diameter of the brass wire being :08 
millim., that of the hempen cord 2 millims. In each experiment 
the sphere B received the same charge measured by the electro- 
meter. The clapper which supported the rod gf was then 
pulled by means of the silk cord ad, the knob g descended 


868 On the Duration of the Spark of an Electric Discharge. 


towards the ball f, establishing a metallic communication between 
ABCD and FE, and at the same instant a spark passed between 
the two knobs of the spark-micrometer. The amount of residue 
was then determined by the electrometer. The results I ob- 
tained are collected in the following Table,in which the amount 
of residue is represented by R, that of the charge by L:— 


| 
Name of the _ | Deviation of the magnetic needle 


| 
Distance between | substance placed | Value of 
R 


excitator. discharge. | discharge. 


| 
__ 


the knobs of the between the i aa ee : 
micrometer. | branches of the | Before the After the & 


0°88 millim. | Hempen cord. | 52 20 


5 18 0-117 

+ 7 Brass wire. ie 3 18 0-073 

+ at Hempen cord. +i 4 42 0-103 

1 millim. | Hempen cord. 64 26 vor 0:137 
7 . Brass wire. 9 3 56 0-076 

“ Es Hempen cord. 5 6 56 0-134 


From this Table it is obvious that the residue is more con- 
siderable when the body through which the discharge takes place 
offers more resistance. | 

- 5. Itis possible that the above theory may not at first meet 
with universal assent. I trust, however, that those physicists 
who hesitate to admit it will find their doubts dispelled on con- 
sidering the following experiment :—A BC D is a hollow cylin- 
der closed at the end C D and fitted at the other end AB witha 
sucker-valve opening outwards. Near the end CD there isa 
slide GH pierced with a large opening at I. The anterior por- 


Gq 
ot ald 
AURA RARE! ure re 
eee? 2 ee eee Se z£ 
F D 
HL 


tion ABEF of the tube must be supposed exhausted of air, 
while in the remaining part E F C D the air is ina state of great 
compression. Now suppose the slide GH suddenly depressed 
until the centre of the opening I coincides with the axis of the 
cylinder. It is evident that the air enclosed in E FC D will im- 
mediately begin to spread throughout the anterior portion of the 
tube until it reaches AB, where, if its tension be sufficiently 
great, it will commence escaping from the tube. If the air has 

taken z" to arrive at A B, it will of course begin to escape z" after — 
the slide has been depressed; but no one will imagine that the 


On the unsymmetrical Six-valued Function of six Letters. 369 


escape of the air will cease in ?’. In fact it would suffice to 
Yepeat, mutatis mutandis, the reasoning in (8) to see that the 
escape must necessarily last more than ¢". : 


P.S. In my note on the Inductive Spark, which was inserted in 
the December Number of this Journal, the expression point of light 
should have been streak of light. 


et 


LVI. Note on the Historical Origin of the unsymmetrical Siz- 
valued Function of six Letters. By J. J. Sytvuster, Professor 
of Mathematics at the Royal Military Academy, Woolwich*. 


iene discovery and first announcement of the existence of the 
& celebrated function of six letters having six values, and not 
symmetrical in respect to all the letters, is usually assigned to 
my illustrious friend M. Hermite, to whom M. Cauchy expressly 
ascribes it in a memoir inserted in the Comptes Rendus of the 
Institut for December 8, 1845, p. 1247, and again, January 5, 
1846, p. 30. | 

M. Cauchy adds that the conversation he held with M. Her- 
mite on this subject excited in himself a lively desire to sound to 
its depths the question of permutations, and to develope the 
consequences to be deduced from the application of the princi- 
ples relative thereto, which he had himself long previously laid 
down. | 

I was not at that date in the habit of consulting the Comptes 
Rendus, or I should at once have made the reclamation of priority 
which I now do, not from any unworthy motive of self-love in so 
small a matter, but out of regard to historic truth. It isa year or 
two since I first learnt that the origin of this function was 
usually referred to M. Cauchy or M. Hermite; but although 
aware that its existence was known to myself long previous to 
the dates quoted, I did not recollect that I had ever communi- 
cated it to the world through the medium of the press, and I 
therefore kept silence on the subject. 

Turning over, a few days ago, for another purpose, the pages 
of a back volume of this Magazine, my eye chanced to alight on 
a footnote to a paper of my own inserted therein, under date of 
April 1844, “On the Principles of Combinatorial Aggregation,” 
which I will take the liberty of quoting at length, as it proves 
incontestably the priority which I lay claim to. 

“When the modulus is four, there is only one synthematic 
arrangement possible, and there is no indeterminateness of an 
kind; from this we can infer, @ priori, the reducibility of a bi- 


* Communicated by the Author. 


Phil. Mag. 8. 4. Vol. 21. No, 141. May 1861. 2B 


370 Prof. Sylvester on the Historical Origin of the 


quadratic equation ; for using ¢, f, F to denote rational symme- 
trical forms of function, it follows that . 


a, b, be, 
F 3 I pine . ee, d is itself a rational symmetric function 
pdt , of a, b, ¢, d. 
tba, d, pb, c) 

Whence it follows that if a, b, c, d be the roots of a biquadratic 
equation, f(a, b, ded) can be found by the solution of a cubic: 
for instance, (a+b) x x (c+d) can be thus determimed, whence 
immediately the sum of any two of the roots comes out from a 
quadratic equation. 

“To the modulus 6 there are fifteen different synthemes 
capable of being constructed. At first sight it might be sup- 
posed that these could be classed in natural families of three or 
of five each, on which supposition the equation of the sixth degree 
could be depressed ; but on inquiry this hope will prove to be 
futile, not but what natural affinities do exist between the totals ; 
but in order to separate them into families, each will have to be 
taken twice over; or in other words, the ‘fifteen synthemes to 
modulus 6 being ‘reduplicated, s subdivide into six natural families — 
of five each.” 

The six families above referred to (in which it is to be under- 
stood that p.g and q.p are identical in effect) are the followmg :— 


a0 Ca err Ore. ee ye aid exp ee 
G6 OLE) a.) ese V6.7 tere Ge GOA Pe 
We OL ewe ce Qe C.0 C.F af ad, t exe 
ave On eer bl ea Ee) a.0° af Bae 
Gop Ole We ATO ce Ce 4.0 GON 
ae f.6 ‘e.d Gf) bie die &.8) c,d oeef 
aifiivceve. Gvd a8. f.d5 exe a.c b.e d.f 
Gb eds fre a.c f.e b.d ad b. frie ce 
a.ee.b fid ad» fre bie a.6@ bd -0.f 
aud ef Bie a.e) f.b ed af bie! dle 


And it will be observed that every two families have one, and 
only one, syntheme in common between them ; and precisely m 
the same way as in the note above quoted, it is especially shown 
that the one single natural family 


a.b ec.d 
a.c b.d 
aya be 


gives rise to a function of four letters with only one value, so 
the six functions analogously formed with these six families ob- 
viously give rise to six functions, which change into one another 


unsymmetrical Six-valued Function of sia Letters. 871 


when any interchange is effected between the letters which enter 
into them; so that any oue of these is a function of six letters 
having only six values. I conceive that, after this reference, no 
writer on the subject wishing to specify the function in question 
would hesitate to call it after my name. 

I may also take occasion to observe that, in connexion with 
my researches in combinatorial aggregation, long before the 
publication of my unfinished paper in the Magazine, I had 
fallen upon the question of forming a heptadic aggregate of 
triadic synthemes comprising all the duads to the base 15, 
which has since become so well known, and fluttered so many a 
gentle bosom, under the title of the fifteen school-girls’ problem ; 
and it is not improbable that the question, under its existing 
form, may have originated through channels which can no longer 
be traced in the oral communications made by myself to my 
fellow-undergraduates at the University of Cambridge long years 
before its first appearance, which I believe was in the ‘ Lady’s 
Diary’ for some year which my memory is unable to furnish. 

In order to relieve this notice from the mere personal cha- 
racter which it may thus far appear to bear, I will state another 
question concerning the combinatorial aggregation of fifteen 
things which may serve as a pendant to the famous school-girl 
problem. 


The number of triads to the base 15 is ae =5~x9l1. 


Let it be required to arrange these into 91 synthemes, in other 
words, to set out the walks of 15 girls for 91 days (say a quarter 
of the year) in such a manner that the same three shall never all 
come together more than once in the quarter. Of the various 
ways in which it is probable this problem may be solved, the 
following deserves notice. Let 15 letters be arbitrarily divided 
into 5 sets, viz. 


Mb, 6,3 Ag bg lg3 Wg bgeg3 My by Cy; 5 5 C5 
The sets as they stand will represent one of the 91 arrangements 
sought for, which I call the basic syntheme. The remaining 90 
may be obtained as follows in 10 batches of 9 each. Write down 
the 10 index distributions following :— 


123;45 145;28 
hee 3 6 2°38 4; 15 5 
126;3 4 2 3°53; 1 4 
134; 25 2465;18 
1835; 2 4 § 45: 1.2 


Take any one of these distributions, as for instance 2 35; 1 4, 
and proceed as follows:—In respect of 2, 3, 5, conjugate the 
2B2 


~ 


372 Prof, Sylvester on the Historical Origin of the 


fl, b, Co 
three sets a, 6, cs; and in respect of 1, 4, conjugate the two 
a, b. Ce 


gh a, b, ¢, 
remaining sets 


4 04 Ca 
From the ternary conjugation form the nine arrangements, 

Ug Ag as by by Os Co Cy Cs 
a2 as bs by bs Cs Cy ¢, ds 
fy Ag Ce by bs as Co Cy Og 
a3 bs ds by c3 55 Cg 43 ¢s 
dy bs bs by os ¢5 C9 a ds 
Aq bs. Cs by C3 ds Co a; b; 
lg Cg As be as Ob; Co by Cz 
a, Cy 6. bg fg C. Cy bs as 
fly Cy Cs by a3 as Co by 6, 


which call 

L, L, L, i, L; L, L, L, Lig. 
Again, from the binary conjugation, form the nine arrange- 
ments, 


a, b, e4 ay b,c, 
a, b, b, Gy C, Cy 
a 6, ay C) by Cy 
QC) Ca a, 6, 5, 
ay C, b, ay by ey 
@ Cy ay b, bs 4 
b, cy C, a, b, ¢, 
b, c, by Ay a C4 
b, cy a, by ey 


which call 
M, M, Mg M, M; Mg M, Mg Mog. 


Now combine the L with the M system, each L with some 
M im any order whatever; the 9 combinations or appositions 
thus obtaimed will give a batch of 9 synthemes; and proceeding 
in like manner with each of the 10 distributions of the indices 
1, 2, 3, 4, 5, we shall obtain 90 synthemes, which together with 


unsymmetrical Siv-valued Function of six Letters. 373 


the basic syntheme complete the system required. The M system 
corresponding to any distribution of the imdices is the system 
which contains the synthematic arrangement of the bipartite* 
triads which can be constituted out of six things, separated in 
two sets or parts, and is unique. The L system is one of those 
which represents the synthematic arrangement of the tripartite t 
triads of nine things separated mto three sets or parts. I have 
set out above one in particular of these for the sake of greater 
clearness; but any other system having the same property will 
serve the same purpose, and a careful study will serve to show 
that the total number of L’s corresponding to a given distribu- 
tion of indices will be ( ) +. Consequently the total number 
of LM’s that we can form for a given distribution will be (_ ) 
xX1.2.3.4.5.6.7.8.9; and the number of distinct syn- 
thematic arrangements satisfying the given conditions corre- 
sponding to any assumed basic syntheme will be this number 
raised to the tenth power; and as this vastly exceeds the total 
number of permutations of fifteen things, we see, without even 
taking into consideration the diversity that may be produced by 
a change of the base, that this method must give rise to man 
distinct types of solution (arrangements being defined to belong 
to the same or different types, according as they admit or not 
of being deduced from each other by a permutation effected 
among their monadic elements), ‘The common character of all 
these allotypical aggregations, and which serves to constitute them 
into a natural order or family, consists in their being derived from 
a base formed out of five sets, such that the monopartite triads 
corresponding to the base form one syntheme, and the other 90 
synthemes each contain a conjugation of the tripartite triads 
belonging to three out of the five sets of the base with the bipar- 
tite triads belonging to the other two sets thereof. There is, 
moreover, no reason to suppose, or at all events no safe ground 
for affirming, that this family exhausts the whole possible num- 
ber of types to which the arrangements satisfying the proposed 
condition admit of bemg reduced. A further question which I 
have somewhere raised, and which brings the two problems of 
the school-girls into rapport, is the following :—* To divide the 
_ system of 91 synthemes satisfying the conditions above stated 
into thirteen minor systems, each of which satisfies the conditions 
of the old problem, 7. e. of containing all the duads that can be 
made out of the fifteen elements once and once only ;” or to put 
the question in a more exact form, to exhibit thirteen systems, 

* See note at end of paper. 

+ Some day or another a newcombinatorial caleulus'must come into being 
én furnish general solutions to the infinite variety of questions of multifa- 


riousness to which the theory of combimatorial aggregation, alias compound 
permutations, gives rise. 


374: Prof. Sylvester on the Historical Origin of the 


each satisfying this last condition, which shall together include 
between them all the triads that can be made out of the fifteen 
elements. 

The reader would have reason to be dissatisfied with the 
author’s reticence, were he to leave altogether unmentioned the 
synthematic aggregation of the dinomial triads appertaining to 
the same three triliteral sets or nomes ; but space forbids my doing 
more at present than giving one of these aggregates, and indica- 
ting the number and mode of generation of all from this one. 
It will readily be seen that any such aggregate will be made up 
of two sub-aggregates, which I shall call A and B respectively, 
of which one bears the same relation to the disposition of the 
nomes in the order 123 456 789, as the other to their disposi- 
tion in the order 123 789 456. Thus we may take for our A 
and B the following, which will each contain 9 synthemes, the 
total number of synthemes in the two together being 18* :— 


(A.) (B.) 
124 567 893 127 894. 768 
125 468 739 128 795 436 
126 459 783 129 786 453 
1384 568 279 137 895 246 
185 469 278 188 796 245 
136 457 289 139 784 256 
934 569 187 937 896 154 
935 467 189 238 794 156 
236 458 179 2939 785 146 


The system of triads contained in A may be arranged in 
twelve different aggregates similar to the one given, and the 
same will be true for the triads in the B; ‘so that the total num- 
ber of the combined systems will be 144. All the permutations 
which leave A or B (separately considered) unaltered will form 
a natural group,—the theory of groups in this, as in every other 
case, standing in the closest relation to the doctrine of combina- 
torial aggregation, or what for shortness may be termed syntax. 
I have elsewhere given the general name of Tactic to the third 
pure mathematical science, of which order is the proper sphere, 


* Thus, since there is evidently one mononomial syntheme, the total 
8x 
number of synthemes of all three kinds will be 1+18+9=28= 9 > as 
, ists 
it should be, the total number of triads being 8.f and 3 of them going 


to a syntheme. 


unsymmetrical Six-valued Function of six Letters. 375 


as is number and space of the other two. Syntax and Groups 
are each of them only special branches of Tactic. I shall on an- 
other occasion give reasons to show that the doctrine of groups 
may be treated as the arithmetic of ordinal numbers. With 
respect to the twelve varieties of the A or B aggregates, they 
may be obtained from the one given by combining the substitu- 
tions corresponding to the six permutations of the three consti- 
tuents of one nome, as 7, 8, 9, with the permutation of any two 
constituents of another, as 5,6. But I have said enough for 
my present purpose, which is to point out the boundless un- 
trodden regions of thought in the sphere of order, and especially 
in the department of syntax, which remain to be expressed,mapped 
out, and brought under cultivation. The difficulty indeed is not 
to find material, of which there is a superabundance, but to dis- 
cover the proper and principal centres of speculation that may 
serve to reduce the theory into a manageable compass. 

I put on record (as a Christmas offering on the altar of science) 
for the benefit of those studying the theory of groups, or com- 
pound permutations (to which the prize shortly to be adjudicated 
by the Institute of France for the most important addition to the 
subject may tend to give a new impulse), and with an eye to the 
geometrical and algebraical verities with which, as a constant of 
reason, we may confidently anticipate it is pregnant, an exhaust- 
ive table of the monosynthematic aggregates of the trinomial 
triads that are contained in a system of three triliteral nomes. 
Let these latter be called respectively 123; 456; 789; then 
we have the annexed :— 


Table of Synthemes of Trinomial Triads to Base 3.3. 


(1.) (2.) (3.) (4.) 
147 258 369 147 258 369 147 258 369 147 258 369 
148 259 367 148 259 367 148 259 367 148 259 367 
149 257 368 149 257 368 149 257 368 149 267 358 
157 268 349 157 268 349 157 269 348 157 268 349 
158 269 347 158 269 347 158 267 349 158 269 347 
159 267 348 159 267 348 159 268 347 159 247 368 
167 248 359 167 249 358 167 248 359 167 248 359 
168 249 357 168 247 359 168 249 357 168 249 357 
169 247 358 169 248 357 169 247 358 169 257 348 
(9.) (6.) 7.) (8.) 
147 258 369 147 258 369 147 258 369 147 258 369 
148 267 359 148 267 359 148 269 357 148 269 357 
149 268 357 149 257 368 149 257 368 149 267 358 
157 249 368 157 268 349 157 268 349 157 268 349 
158 269 347 158 269 347 158 249 367 158 249 367 
159 248 367 159 248 367 159 267 348 159 247 368 
167 259 348 167 259 348 167 248 359 167 248 359 
168 257 349 168 249 357 168 259 347 168 259 347 
169 247 358 169 247 358 169 247 358 169 257 348 


A 


376 On the unsymmetrical Siz-valued Function of six Letters. 


The discussion of the properties of this Table, and the classi- 
fication of the eight aggregates into natural families, must be 
reserved for a future occasion. 


Note.—A triad is called tripartite if its three elements are 
culled out of three different parts or sets between which the 
total number of elements is supposed to be divided; bipartite 
if the elements are taken out of two distinct sets ; unipartite if 
they all lie in the same set. The more ordinary method for 
the reduction of synthematic arrangements from a given base 
to a linear one which I employ, consists in the separate synthe- 
matization inter se of all the combinations of the same kind as 
regards the number of parts from which they are respectively 


9 
drawn. ‘Thus, ex. gr., if the distribution of the oo dae 2 — 
triads to the base 30 into 20609 synthemes be required, this 


2 
may be effected by dividing the 30 elements in an arbitrary 
manner into 15 parts, each part containing 2 elements. These 
15 parts being now themselves treated as elements, are first to be 
conjugated as in the old 15-school-girl problem, and each of these 
7 -conjugations can be made to furnish 6 synthemes containing 
exclusively bipartite triads. The same 15 parts are then to he 
conjugated as in the new school-girl problem, and the 91 conju- 
gations thus obtained will each furnish 4 synthemes, containing 
exclusively the tripartite triads. These bipartite and tripartite 
synthemes will exhaust the entire number of triads of both 
kinds, and accordingly we shall find 
7x6491 x 4=406 
_ 29 x 28 
OnE 

A syntheme, I need scarcely add, is an aggregate of combina- 
tions containing between them all the monadic elements of a 
given system, each appearing once only. In the more general 
theory of aggregation, such an aggregate would be distinguished 
by the name of a monosyntheme. A disyntheme would then 
signify an aggregate of combinations containing between them 
the duadic elemienits; each appearing once only, and so forth. 
Thus the old 15-school-girl question in my nomenclature would 
be enunciated under the form of a problem “to construct a triadic 
disyntheme, separable into monosynthemes to the base 15 ; ” the 
new school question, as a problem “ to divide the whole of the 
triads to base 15 into monosynthemes ;”’ the question which 
connects the two, as a problem “to exhibit the whole of the triads 
to base 15 under the form of 13 disynthemes, each separated 
into 7 monosynthemes. 


On. the Galvanic Polarization of buried Metal Plates. 377 


_ A question of a more general kind, and embracing this last, ° 
would be the problem of dividing the whole of the same system 
of triads into 13 disynthemes, without annexing the further con- 
dition of monosynthematic divisibility. So there is the simpler 
question of constructing a single disyntheme to the base 15 
without any condition annexed as to its decomposability to 7 
synthemes. 


K, Woolwich Common, 
December 1860. 


LVII. On the Galvanic Polarization of buried Metal Plates. 
By Dr. Pu. Caru*. 


AST year, in consequence of the disturbances which were 
observed in the telegraphic wires during the appearance 
of the northern lights, Professor Lamont was induced to contrive 
an apparatus at the observatory of Munich in order to examine 
more closely into the occasional motion of the earth’s electricity, 
and to determine its magnitude and direction. For this purpose 
large zinc plates were buried on the north, south, east, and west 
sides of the observatory garden ; the north plate being connected 
with the south, and the east with the west, by means of copper 
wires, which were brought into the observatory and connected 
with galvanometers. As Professor Lamont, in testing this appa- 
ratus, remarked certain phenomena which he attributed to gal- 
vanic polarization, it appeared to me advisable to subject the 
matter to a more careful examination, and to obtain more accu- 
rate measurements. 

_ Through the wire that connects two of the above-mentioned 
zinc plates, a current, which I shall call the terrestrial current, 
is perpetually circulating, the intensity of which is indicated by 

a fixed deviation of the galvanometer. If a galvanic element be 
inserted in these conducting wires and again removed, then, pro- 
vided it has caused no modification in the conductor, the needle 
of the galvanometer will return to its former position. But if, 
on the other hand, a state of galvanic polarization has been pro- 
duced in the zinc plates, then the deviation of the needle of the 
galvanometer, after the removal of the element, will be greater 
or less than that exhibited by it originally, accordingly as the 
direction of the galvanic current has been opposite to, or the 
same as that of the terrestrial current. 

On trial, the latter result exhibited itself so unmistakeably that 
no further doubt could be entertained of the occurrence of galvanic 
polarization. In order to measure the magnitude of the effect 
produced, I made use of a weak Daniell’s cell, which I inserted 


* Translated by F, Guthrie from Poggendorft’s Annalen, No. 10, 1860, 


378 On the Galvanic Polarization of buried Metal Plates. 


for five minutes in the wire conductor, and I thereby obtained 
the numbers exhibited in the following Table ; in which G indi- 
cates the effect of the galvanic current, E that of the terrestrial 
current, and P that of the polarization expressed in divisions of 
the galvanometer. The effect of the polarization was observed 
1 minute 30 seconds after the removal of the cell. 

I. When the two currents passed in the same direction. 


P 
E. are a 

ES G-+E 
129-8 34 0-026 
129:3 3-4 0-026 
123-0 20 0-021 
108-2 24 0-022 


II. When the current passed in opposite directions. 


P 

ak: 

: es Gan 
1245 54 0-043 
122-7 51 0-041 
107-4 3:8 0-035 
109-2 3:5 0-031 


From these experiments, it follows that the mean value of 
ee Spas 
Gan * 0:0237, that of GE 0:0375 ; so that when the gal- 


vanic and terrestrial currents pass in opposite directions, the 
polarization of the buried metal plates is greater than when they 
pass in the same direction. 7 

Immediately on the removal of the cell, the effect of the gal- 
vanic polarization was greater by two or three divisions of the 
galvanometer scale than it was after the lapse of 1 minute 30 
seconds ; and after that period the effect still continued gra- 
dually to diminish. In order to exhibit the law of this diminu- 
tion I subjoin the following Table :— 


Time after the removal, Deviation of the gal- 
of the cell. vanometer needle. 
1 minute. 23:0 divisions. 

” 21°38 ” 

” 211, 

” 20°7 ” 

” 20:3 39 

20:0 a 

” 19-9 ” 

”? 19:7 bP 

” 19°5 ” 

” 19°4 ”? 


SUMMONS Str CS bo 


— 


On Transcendental and Algebraic Solution. 379 


At the commencement of the experiment, the deviation of the 
galvanometer caused by the terrestrial current was read off at 
19-2 divisions. 

The above experiments disclose nothing at variance with the 
known laws of galvanism; but it nevertheless appeared to me 
advisable to make them known, as they afford a simple expla- 
nation of certain phenomena which Professor Thomson has de- 
scribed*, and which he seems to attribute to entirely different 
causes. 


LVIII. On Transcendental and Algebraic Solution. By JamMEs 
Cocks, M.A., F.R.A.S., F.C.P.S., Barrister-at-Law, of the 
Middle Temple. 

Saga fe=0 be an algebraic equation of the nth degree, all 

the coefficients of which are functions of one parameter a. 

By differentiation we obtain a result of the form 


oe =Fr = +fe=0. 

But, since F and f are rational functions, 
de fe 
da ‘Fe 


Ue ee Oe ee 

~ Fa.Fu,.Fa,..Fa, 
where R is a rational and integral function of z And 

Ra=A,a"-!+A,a"-?+..+A,, 
where A is a function of a. Moreover 

2 
= Poa’. espace a 

Hence, repeating this process, we are conducted to the system _ 


= Raz, 


@ —Re= Aya +A,2™-?4+..+A,, 

d? 

eg le 14 Boa"-?+ .. +B,, 
Biot 
eT oe G,2"-1 + G,a"-2+ ..4+G, ; 


and if we assign n—2 indeterminates A, u,..v so as to satisfy 


* Report of the Twenty-ninth Meeting of the British Association for the 
Advancement of Science (Transactions of the Sections), p. 26. 
+ Communicated by the Author. 


380 Mr. J. Cockle on Transcendental and 
the n—2 conditions 

AA, +B, +..+v0,4+G,=0, 

AA, +uHB,+..+vC,+G6,=0, 


NAn—2 + MBy_2+ ++ +VOn2+ Gn-2=0, 
we shall arrive at a linear differential equation, 


d”®— a d™—24 d?ax 
da"- de gees B+ ae 
5 ad oe 
da 


For, when the above conditions are satisfied, 2"-!, 2*-?,.. x?, 
all the powers of x in short, save a itself, disappear; and 
v,..#, A, L, M are each of them known functions of a, inasmuch 
as A, B,..C, G are known functions of a. 

Thus the roots of any equation whereof the coefficients are 
functions of only one parameter may be expressed in terms of 
algebraic, circular, or logarithmic functions, and of integrals of 
algebraic functions. These integrals depend upon the quantity M. 

To a form involying only one parameter, Mr. Jerrard has shown 
that the general quintic may be reduced. Its resolvent sextic 
may also be reduced to the same form. 

Mr. Jerrard’s memorable discoveries also show that the general 
sextic may be regarded as involving two parameters only. The 
general sextic leads us to the consideration of the equation 


dfe=Fr.da+fr.db=0, 


where a and b are the independent parameters, of which the co- 
efficients may be considered as functions, and 6 is the character- 
istic of the Calculus of Variations. 
If, in art. 62 of my “ Observations,” &c. (vol. xvii. p. 342), we 
take the suffixes of @ to the modulus 6, the equations become 
0,04 + 0.09 + O:05=Ys=P(x5)s 
8109+ 9205+ O;0,=Y1="(2)), 
0,03 + 0284+ 0;09=Ya=7 (22); 
6,4, + 0,03+ 0,05=¥3=7(2#3); 
@, 19 + 6365+ 8,0;=y4=7(2,). 
And this system has a certain relation to the formula 
6,2 Oar a 6424200245 a 424300244) 
which, taking the suffixes to the modulus 6, is, for all mtegral 
values of a, equal either to y, or to yy. But all the values of y 


are not thence evolved ; and in order to obtain a convenient repre- 
sentation of the system, I avail myself of certain cyclical forms 


Algebraic Solution. 38] 


which may be given to it when one of the roots is supposed to 
become fixed. 

The form here used will admit of an exceedingly simple repre- 
sentation if, throughout my “ Observations,’”’ we replace 0, by 
@,, and vice versd. This requires that in art. ‘48 (vol. xviil. p. 52) 
we write 

Oras =O's, Ofas) =O, 
a change of definition which I shall accordingly suppose to be 
made. 

Further, I shall suppose that we replace 0, by 0;, where i is 
an imaginary suffix defined by the congruence 

t+ a=z1 (mod. 5), 
a being an integer. Or, if we agree to regard the infinite suffix 
oo as satisfying the congruence 

o-+a=o (mod. 5), 
we may replace 6, by 9,,. Lastly, I shall suppose the suffixes, 
after these changes, to be taken to the modulus 5. 

The changes being made, it will be found that all the fune- 
tions y are deducible from the expression 


0; 82+ Oa41 9044+ 80429043 
by writing, successively, 0, 1, 2, 3,4 for a. In fact we have 
9;09+ 994+ 9,0;=y2=1(xo), 
9,0, + 9,9) + 8,0,=9,=7(2)); 
0; 05+ O30; + O,99=Yo=7 (Xo) 
9,0; + 0495+ 697, =Y3=r(#s), 
0,0, +0,03+ 9,0,=Y4=" (2,4) 5 


and if, in these equations, we change 


“ 


‘ 0, 9, 93 8% Yo % 
into 
Oe 95, Oy 5, 5 2s 
respectively, we shall be reconducted to the system of art. 62 of 
my “Observations.” More extensive changes in our funda- 
mental formule and definitions would enable us to express the 
system with a greater concinnity between the suffixes of 0 and 
those of a, and provided that, on the right of the last system, 
we interchange 2, and 2, the system may be deduced from the 

equation 
0:0.+ 60419044 + 904200+3=YVy=T (aa). 
If, in the expression 
2 0. 6, =f 644104 +3 =e 64420044) 
we make a equal to 0, 1, 2, 3, 4: successively, we find the follow- 


3882 Mr. J. Cockle on Transcendental and 


ing relations between it and the « and 8 functions of art. 70 of 
my “ Observations” (vol. xvii. p. 508), viz. :— 

6;0,+ 0,0; +0,0,= a, 

0,0, + 0,0,+ 6,9,=P;, 

0;0,+60)+ 6,0,=8.; 

003+ 040, + 0,94 = ea, 

0;0,+ 005+ 9,0,;= Bo; 
and in like manner from* 


0.0,+ 6410 a4+2+ 00430044 
we deduce 

0,49 + 010+ 0;0,= e4, 

0:0, + 005+ 6,0,=e,, 

G,0q+t 0304+ 99, =Bs, 

0;03,+0,0,+ 0,0,=R4, 

0; 0+ 0.0; + 9,03= a3. 

A contemplation of these systems of equations seems to lead 
to the conclusion that a certain equation of the fifteenth degree, 
which Mr. Jerrard supposes to be capable of decomposition into 
five cubics, is not irreducible, but composed of a quintic and a 
10-ic factor. 

I cannot think that Abel’s conclusion is at all shaken by the 
researches of Mr. Jerrard. Of his cardinal proposition, the 
en 

Py tiFnagt=9 
of art. 106 of his ‘ Essay,’ Mr. Jerrard gives no proof. Direc- 
tions to compare (ab) and (ac) are insufficient instructions for 
attaiing a result fraught with difficulties so serious. For rea- 
sons already assigned, I believe the proposition to be erroneous, 
and incapable of proof. And with it the whole argument of Mr. 
Jerrard falls. 

I need not the warning from my own oversight to restrain me 
from dwelling unduly upon what I believe to be an error of Mr. 
Jerrard’s. But, with every recognition of his great claims to 


* Mr. Harley has completely determined these « and 8 functions; and I 
regret that he has not as yet published the whole of his investigations on 
quintics. The proposition of Mr. Jerrard, which Mr. Jerrard supposes that 
Mr. Harley has ignored, is, when considered in reference to processes which 
do not involve transformation to a soluble form, rather an axiom than a 
theorem. It may be stated thus: If © be equal to ©’, it is not in general 
equal to 6”. 

I would here add the expression of a hope that Mr. Harley, to whom I 
have communicated the above results on the theory of transcendental roots, ~ 
may soon publish some developments of them to which he has been led. 


Algebraic Solution. ; 383 


the gratitude of mathematicians, it is scarcely possible to ignore 
the fact that Mr. Jerrard’s hope (expressed at the conclusion of 
his paper of 1845), to discuss the resolution of the trinomial 
equation z°+ A,v#+A,=0, has not been realized, and that little 
or no approach has yet been made towards its realization. Mr. 
Jerrard’s subsequent researches on quintics seem to me, for rea- 
sons already adduced, to enhance rather than dispel any diffi- 
culties which arise upon the paper in question. It is perhaps 
to be desired that the mathematical world should be made ac- 
quainted with the whole of Mr. Jerrard’s views on this import- 
ant subject. 

Does an absolutely impossible, or rootless, equation, exist ? 
MM. Terquem and Gilain have discussed this question in the 
Nouvelles Annales de Mathématiques*, with reference ‘to the 
equation 

+V1+2e4+ V1—2=1. 

But this equation does not in reality raise the question under 
consideration. Jor (as I had occasion to write to Mr. Harley 
durmg last autumn) every one of the congeneric equations 


is soluble. And some one of the four values of a given by 
e= +(+1)?3./3 
will satisfy any one of the above four congeners. I shall there- 
fore again (S. 3. vol. xxxvii. p. 281) have recourse, for illustra- 
tion, to the equations 
1+ Vz—44+ Vz—1=0, 
1— Vx—4— Wx—1=0, 
each of which must, I think, be deemed impossible or rootless. 
The only gleam of a solution of the last is, so far as I can see, 
one which springs from the assumptions 
v=4(+1)?4+(—1)?, 
A= 4( tg De; l= Ss. 
while, for the first, we have the system 
#=4(—1)? +(+))?, 
4=4(—1)?, T=(+1)* 
But how can that be called a solution which depends upon a mo- 
dification of the constants of a problem (compare 8. 4. vol. ii. 
p. 439)? The safer conclusion seems to be that the two equa- 
tions are rootless. 
Midland Circuit, at Lincoln, 
March 15, 1861. 
* See Mr. Wilkinson’s Note Mathematice, Mechanics’ Magazine, 
vol, lxii. p. 582. 


[ 384 ] 


LIX. Proceedings of Learned Societies, 


ROYAL SOCIETY. 
(Continued from p. 233.] 


May 24, 1860.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 


> me following communications were read :— 
“Qn a new Method of Approximation applicable to Elliptic 
and Ultra-elliptic Functions.’ By C. W. Merrifield, Esq. 


On the Lunar-diurnal Variation of Magnetic Declination at the 
Magnetic Equator.’’ By John Allan Broun, F.R.S., Director of the 
Trevandrum Observatory. 

This variation, first obtained by M. Kreil, next by myself, and 
afterwards by General Sabine, presents several anomalies which re- 
quire careful consideration, and especially a careful examination of 
the methods employed to obtain the results. The law obtained seems 
to vary from place to place even in the same hemisphere and in the 
same latitude, and this to such an extent, that, for example, when the 
moon is on the inferior meridian at Toronto it produces a minimum 
of westerly declination, while for the moon on the inferior meridian 
of Prague and Makerstoun in Scotland it produces a maximum of 
westerly declination. No two places have as yet given exactly the 
same result ; though the result for each place has been confirmed by 
the discussion of different periods. 

In order to obtain the lunar diurnal action, it has been usual to 
consider the magnetic declination at any time as depending on the 
sun’s and moon’s hour-angles and on irregular causes. Thus, if 
at conjunction, H, be the variation due to the sun on the meridian, 
and h, be that due to the moon on the meridian, H, the variation 
for the sun at 1, 4, for the moon on the meridian of 1", and so on; 
it is supposed that we may represent the variations for a series of 
days by the following expressions, where the nearest values of / to 
the whole hour-angles are given :— 


Ist day. H’, +A’, +2), H+’, +2, ... H’,, +2, +2’. 
2nd day. H",+h",, +2" H" +h", +2", ics HA", "5 


nth day. H) +4, +e, Hy +h) +a. ... H+A +, 


where 2 is qos to imaeatalit causes, and n is 7” aed of days ina 
lunation nearly, 


Summing these quantities we have nae 
2H, +3) ji+3e, 3H, +2, Atde, , ++. SH, +23, Ate, (A) 
saa the means are, 
H+ ¢ +=", H+ ¢+=,... ul eee 


Here the aa means are affected by the spine due to the total 
action of the moon on all the meridians, and by variables depending 
on disturbing causes. If, on the other hand, we arrange the series as 


On the Magnetic Declination at the Magnetic Equator. 385 


follows, 
H’, +h’, A HW’ +A) +0’, ... HY", +h", 42", 
H+", 42" en Pr eee 


n—1 n—-l A-1 : n n n 34 n n 
Ht” +h, +v,, Ho +h +a,... Hi +h),+z,,- 


Bhisisintng these quantities we have, 


eh) 0 (td) ,0 i O (24) 
2) f+ 2h, + Ew ? H+ 2h +4, 1% H+ dh +%,,% (C) 


and for the A 


O+Ah, $= 


In this case © is the mean di it observations, of which 24 give 
the true means for the total solar influence, and the remaining n—25 
being equally distributed through the hour-angles also give the mean 
approximately. 

Instead, however, of combining the observations in this way, the 
following method has been preferr ed. Let, in the quantities (B), 


(H,) = 1,4 ¢ += 


a ae opis ee ape. 


Gs Untig 


Then H’,+ 2’, e a’, — aj h', +. (@',. ye; 
a + i" ot a” i- CH, fen Es + wn = d", 
ol ae ig nu— nt )= a (ae 1) = ee 
Summing the fi two shinies we have 


awe 
2d, ab fag 2 (#’) 


nm—\1 } n—1 


Similarly we obtain 
xd, 2. a 
af eis and so on. 


n—1| 


Loh + 


It will be observed that in these summations there are two assump- 
tions ; one, that the lunar diurnal law is constant throughout the 
lunation, or series of lunations, for which the means are obtained ; or 
that the quantity € in the expressions (B) is constant. If this be 


not exact, thea the quantity — will contain the variation due to this 
n 


cause, and depend in part on the lunar hour-angle ; so that the mean 
(H.) which is employ ed in taking the differences will eliminate part 
of the lunar action and partially distort the law. The other assump- 
tion is that the mean solar diurnal variation, represented by (H,),(H,) 
»..., 18 nearly constant throughout the period ; for, if not, the dit- 


Phil. Mag. S. 4. Vol. 21. No. 141. May 186}. 2C 


386 Royal Society :— 


ferences due to such changes might be sufficient to mask any lunar 
law, the latter having a small range compared with the former. 
Also it should be remarked that the means /,, 4,, &c. are combined 


0 
with the irregular effect 25(%), This effect, as far as it is due to 
n—1 

disturbance, we know obeys a solar diurnal law ; and if independent 
of lunar action, a sufficiently large series of observations might suffice 
to eliminate it, as combining with and forming part of the regular 
solar diurnal variation. If, however, the series is not very large and 
the irregular disturbance considerable compared with the variation 
sought, it may be desirable to omit or modify the marked irregu- 
larities. 

As regards the first assumption referred to above, the results 
obtained hitherto seem to show the error to be small, and the only 
way to determine its amount will be to consider it zero in the first 
instance, and thereafter a more accurate calculus may be employed. 
For the second assumption, it is certain that the solar diurnal law 
varies considerably in some cases within a lunation. At the mag- 
netic equator, for example, the law of magnetic declination is inverted 
within a few weeks near the equinoxes. The attempt to correct the 
error due to considerable change in the solar diurnal variation by 
taking the means, as has been done, from shorter periods than a 
lunation, is liable to the serious objection that the resulting hourly 
means are affected unequally by the lunar action, so that the sums 
(A) take the form, 


2H) + 2,A+ 2%, BH, + WA+Be,......2Hy3+ Bh 4 Baro, 


where the second term in each expression is a variable. In the 
discussion to which I am about to allude, the following pian has been 
followed. ‘The hourly means for the following series of weeks were 
taken, namely— 

m, from Ist, 2nd, 3rd, and 4th weeks of the year. 

m, ,, 2nd, 3rd, 4th, and 5th te is 
yo. org, 4th, Sth; and. Ott Bs ~ 


The means of m, and m, were then taken as normals for the 3rd 
or middle week, of m, and m, as normals for the 4th week, and so 
on: these means were then employ red for the differences from the 
corresponding hourly: observations of the weeks to which they 
belonged. 

With reference to the irregular effect, it is evidently desirable that 
we should know in the first instance whether it may not be a function 
of the lunar, as well as of the solar, hour-angle ; for this end it is 
essential in the first instance to obtain the result including all the 
supposed irregular actions, and afterwards to eliminate these in the 
best manner possible. 

In the discussion of the Makerstoun Observations I had substi- 
tuted for certain observations, which gave differences from the mean 
beyond a fixed limit, values derived by interpolation from pre-. 


On the Magnetic Declination at the Magnetic Equator. 3887 


ceding and succeeding observations. General Sabine in his discussions 
has rejected wholly the observations which exceeded the limit chosen 
by him. The omission of observations accidentally or intentionally, 
and the taking of means without any attempt to supply the omitted 
observations by approximate values, require consideration. 

Let m be the true hourly mean for an hour /, derived from the 
complete series of x observations; let m' be the mean derived from. 
n—1 observations, one observation o being accidentally lost ; then 


,__2m—o 
m= > 
n—1 
es m! —o , m—o 
m=m'— =m — . 
n n— 1 


If, however, we supply the omitted observation by an interpolation 
between the preceding and succeeding observations, and if the inter-. 
polated value be 0+, we have 
“i nm+ x 
. nu 


lene 


> 


m—m 


. The comparative errors of m! and m" are therefore 


aS aT sa 

. n—1 n 
We may for any given class of observation determine the mean values 
of these errors. 
Example :—At Hobarton, in July 1846, the mean barometer 
for 3° (Hobarton mean time) was 29°848 in., and the mean differ- 
ence of an observation at that hour from the mean for the hour was 
0-403 in. ; if an observation had been omitted with such a difference, 
or for which o—m=0°403 in., we should have an error in the resulting: 


mean of o408 = 0-016 in., and the error might have been twice as» 
great had the observation with the greatest difference been rejected. . 
If we now seek the error of m!', where the observation is interpolated, 
we shall find for the same month that the mean value of x=0-005 in. 
‘ 2 0°005 i vi 
nearly ; whence the error > =—5--=0:0002 in. only, and the error 
would never exceed 0°001 in. A similar though less advantageous. 
result will be found in all classes of hourly observations. 

In the case where observations are rejected which differ from the 
mean for the corresponding hour more than a given quantity, let 
us suppose, to simplify the question, that the sums of n—1 out of 
m observations for each of two successive hours are each equal M, 
and that the observations for the same hours of the nth day are 


h : “ite 
respectively m'+/ and m'+/+.2, where m= uthe, Zis the limit 


beyond which observations are ‘rejected, and # is the excess of the’ 
observation to be omitted. The means retaining all the observations: 


2C2 


388 Royal Society :— 


are, 
M+ m'+1 l 
ne a 
n n, 
M+ m'+l+e« Ite 
IE Tae a eT ‘ 
a iL n 


but if we reject the observation m!'+/+., we have 


It is assumed that m,!—m,'=0 (any other hypothesis of variation 
would give the same final result), and therefore the error of the 
change from the first hour to the second, when all the observations 


° e x . . e . 
are retained, is —; but if the observation be rejected, the change is 
nN F 


ay ES eal: 

m +——m =— 

n n 

This error, therefore, will be greater than the other if / > ; so that 

the error in the resulting change from one hour to the Mext will be 

less by retaining an observation than by rejecting it, if the difference 

from the preceding observation be not greater than the difference 

from the hourly mean; that this will most frequently be the case 

will be obvious from the following fact :—At Makerstoun, in 1844, 

at 1 a.m. the number of observations which exceeded the monthly 

means by 3! and less than double that, or 6', was 99, while the whole 
number which exceeded by more than 6! was only 16. 

It will be evident also that the difference / of an observation from 
the corresponding hourly mean may not be due to irregular causes, 
or to causes which affect the changes from one hour to the next in a 
perceptible manner, but to gradual and regular daily change. If we 
examine the daily means most free from irregular or intermittent 
disturbance, we shall find that they vary plus or minus of the monthly 
mean; if the difference amounts to / in any case, then the whole 
observations of the day may be rejected though they follow the nor- 
mal law. By taking a proper value of J this case may not happen fre- 
quently, but cases like the followmg will. At Hobarton the daily means 
of magnetic declination differ in some months from the monthly means 
by 2'0 nearly ; as the limit chosen by General Sabine is 2'4, any 
observation in such days differing by 04 from the normal mean 
would be rejected. The 25th ‘and 26th days of March 1844 had 
been chosen by me as days free from magnetic disturbance, and fol- 
lowing the normal law at Makerstoun (Mak. Obs. 1844, p. 339), 
yet the means of horizontal force for these days differed 0°00064 and 
0:00075 from the monthiy means; had the former quantity been 
the linit, all the observations on these days might have been rejected. 

Altogether it appears to me that the method of rejecting observa- 
tions beyond certain limits .should. not be employed at all, or if 
employed, only when interpolated observations are substituted ; and ° 


On the Magnetic Declination at the Magnetic Equator. 889 


that this interpolation should constitute a second part of the discus- 
sion, the first including all the observations*. 

These considerations may appear somewhat elementary, but it is 
essential that results which present such anomalies as the lunar 
diurnal variation of magnetic declination should be obtained in a 
manner the most free from objection, even though the objections 
should touch on quantities of a second order compared with those 
obtained.: 

The discussion of which I now proceed to note the results, 
includes all the hourly observations without exception, made in the 
Trevandrum Observatory (within a degree and a half of the magnetic 
equator) during the five years 1854 to 1858; the second part of the 
discussion, in which days of great magnetic irregularity have been 
wholly rejected, not being completed, I ‘shall reserve the details for a 
more formal communication to the Royal Society. The results 
obtained are as follows :— 

Ist. At the magnetic equator the lunar diurnal law of magnetic 
declination varies with the moon’s declination and — the sun’s 
declination. 

2nd. This variation is so considerable that the attempt to combine 
all the observations to form the mean law for the year gives results 
that are not true for any period. Hence evidently the impossibility 
of relating the laws at different places. The so-called mean law for 
the year at Trevandrum obtained for the moon furthest north, on the 
equator going south, furthest south, and on the equator going north, 
consists of ¢hree maxima and three minima,—a result wholly false, 
excepting as an arithmetical operation due to combination of very 
different laws. 

3rd. The lunar diurnal lawvaries chiefly with the position of the sun, 
the variation being comparatively small with the position of the moon. 

4th. At the magnetic equator the range of the variations is mark- 
edly greatest in the months of January, February, November and 
December, or about perihelion. 

The following results are derived after grouping the means for differ- 
ent positions of the moon in periods of six months, October to March, 
and April to September ; they are therefore, for the reason given in 
the 2nd conclusion, not quite accurate ; but the change of the law from 
month to month will be followed when the details are presented to the 
Society. The following will give a general idea of the changes :— 

Sth. When the moon is fur thest north. 

a. About perihelion. The lunar diurnal law of magnetic declina- 
tion consists of two maxzimat when the moon is near the upper and 
lower meridians, the maximum for the latter being much the great- 


* T should note here my belief that a peculiarity noticed by General Sabine in 
his discussions as requiring explanation, namely, that the excursions of the decli- 
nation needle east and west in the lunar diurnal variation have very different 
magnitudes, is due to the rejection of observations, while the means by which the 
differences were obtained included the rejected quantities. 

+ The declination is easterly at Trevandrum, and the maxima indicate greater 
easterly declination. 


a 


390 Royal Society :— 


est; of the two minima at intermediate epochs, that for the setting 
moon is the most marked. 

6. About aphelion. The law consists of two nearly equal minima 
near the upper and lower transits: of the two intermediate maxima, 
that near the moonset is the most marked. 

e. Thus the law about the winter solstice is inverted about the 
summer solstice, and the one law passes into the other at the epochs 
of the equinoxes, exactly as for the solar diurnal variation. 

6th. For the moon on the equator going south. 

a. About perihelion. The lunar diurnal law consists of two 
nearly equal maxima near the superior and inferior transits: of the 
two intermediate minima, the moonset minimum is by far the most 
marked. 

6. About aphelion. The law consists of two nearly equal minima 
near the superior and inferior transits: of the two intermediate 
maxima, that near moonrise is by far the most marked. 

e. In this case also the laws for the solstices are the opposite of 
each other, and the one law passes into the other near the epochs of 
the equinoxes. : 

7th. For the moon furthest south. 

a. About perihelion. The lunar diurnal law consists-of maxima 
near the upper and lower transits, that at the upper transit being by 
far the most marked: of the intermediate minima, that near moon- 
set is the greater. : 

6, About aphelion. The law consists of two minima, the most 
marked at the inferior transit, the other about three hours before the 
superior transit; and of two equal maxima, one near moonrise, the 
other near the superior transit, but varying little till 3 hours before 
the inferior passage. 

_ ¢. In this instance the inversion is not so complete as in the other 
cases ; this, it is believed, will be found to be due to the fact that the 
change from one law to the other takes place after the vernal and 
before the autumnal equinox ; so that in the means for six months, 
from which the above conclusions are drawn, the lunations following 
the law a are combined with those belonging to 0. 

8th. The moon on the equator going north. 

a, About perihelion. The lunar diurnal law consists of two nearly 
equal maxima when the moon is near the superior and inferior meri-. 
dians ; of the two intermediate minima, that near moonrise is by far 
the most marked. 

b. About aphelion. The law consists of two minima at the infe- 
rior and superior transits ; and of two maxima, the greatest at moon- 
set, the other between the meridians of 16" and 21"; between these 
points there is an inflexion constituting a slight minimum. . 

c. In this case also the opposition of the laws is sufficiently well 
marked ; the only divergence from opposition being that due to the 
minor miininreed about the meridian of 19", due, it is believed, as 
noted 7th c, to the partial combination of opposite laws in the 
aphelion half-year. 

9th. It will be observed that the variations of the law with refer- 


On the Nature of the Light emitted by heated Tourmaline. 891 


ence to the moon’s declination for any given period of the year, con- 
sists chiefly in the difference of the relative values of the maxima and 
minima, the differences of epochs being small. Thus for perihelion, 
the moon furthest north, the principal maximum occurs at the infe- 
rior passage ; the moon on the equator going south, the two maxima 
are nearly equal; the moon furthest south, the maximum at the 
superior passage is by far the greatest: on the equator going north, 
the two maxima are again nearly equal; and so on for other epochs. 

10th. The moon’s action is chiefly, if not wholly, dependent on 
the position of the sun, or (which is the same thing) on the position 
of the earth relatively to the sun; and the law of the lunar action at 
the magnetic equator resembles in some points that for the solar 
action at the same epochs. ‘Thus about aphelion there is a minimum. 
of easterly (maximum of westerly) declination produced by the Junar 
action, as well as by the solar action, for these two bodies near the 
superior meridian; whereas about perihelion both actions for the 
sun and moon near the superior meridian produce maxima of easterly 
declination. A like analogy holds for near the epochs of sun- 
rise and moonrise. 


June 14.—General Sabine, R.A., Treasurer and Vice-President, in’ 
the Chair. : 


The following communication was read :— 

“On the Nature of the Light emitted by heated Tourmaline.” By 
Balfour Stewart, Esq., M.A. : 

Some months ago I had the honour of submitting to the Royal, 
Society a paper on the light radiated by heated bodies, in which it 
was endeavoured to explain the facts recorded by an extension of 
the theory of exchanges. 

Having mentioned the difficulty which I had in maintaining the 
various transparent substances at a nearly steady red heat for a 
sufficient length of time in experiments demanding a. dark back- 
ground, Professor Stokes suggested an apparatus by means of which 
this difficulty might be overcome; and it is owing to his kindness in 
doing so that I have been enabled to lay these results before the 
Society. 

The apparatus consists of a thick, spherical, cast-iron bomb, about 
5 inches in external and 3 inches in internal diameter—the thickness 
of the shell being therefore 1 inch. It has a cover removeable at 
pleasure. There is a small stand in the inside, upon which the sub- 
stance under examination is placed, and when so placed it is pre- 
cisely at the centre of the bomb. Two small round holes, opposite 
to one another, viz. at the two extremities of a diameter, are bored in 
the substance of the shell. If, therefore, the substance placed upon 
the stand be transparent, and have parallel surfaces, by placing these 
surfaces so as to front the holes, we are enabled to see through the 
substance, and consequently through the bomb. Let the bomb with 
the substance on the stand be heated to a good red heat, and then 
withdrawn from the fire and allowed to cool. It is evident that the 
eooling of the substance on the stand will proceed very slowly, as it 


392 Royal Society. 


is almost completely surrounded with a red-hot enclosure. It is also 
evident that, by placing the bomb in a dark room, we may view the 
transparent substance against a dark background. By this method 
of experimenting, therefore, the difficulty above alluded to is over- 
come. 

Before describing the experiment performed on tourmaline, it may 
be well to state what result the theory of exchanges would lead us to 
expect when this mineral is heated, and we shall perceive at the same 
time the importance of the experiment with tourmaline as a test of 
the theory. When a suitable piece of tourmaline, with its faces cut 
parallel to the axis, is used to transmit ordinary light, the hight which 
it transmits is nearly completely polarized, the plane of polarization 
depending on the position of the axis. The reason of this is, that if 
we resolve the incident light into two portions, one of which consists 
of light polarized in a plane perpendicular to the axis of the crystal, 
and the other of light polarized in a plane parallel to the same axis, 
nearly all the latter is absorbed, while a notable proportion of the 
former is allowed to pass. 

Suppose now that such a piece of tourmaline is placed in a red-hot 
enclosure; the theory of exchanges, when fully carried out, demands 
that the light transmitted by the tourmaline, say in a direction per- 
pendicular to its surface, plus the light radiated by the tourmaline 
in that direction, plus the small quantity of light reflected by the 
surface of the tourmaline in that direction, shall together equal in 
quantity and quality that which would have proceeded in the same 
direction from the wall of the enclosure alone, supposing the tour- 
maline to have been removed. Let us neglect the small quantity of 
light which is reflected from the surface of the tourmaline, and, 
standing in front of it, analyse with our polariscope the light which 
proceeds from it. This light consists of two portions, the trans- 
mitted and the radiated, both of which together ought to be equal 
in quality and intensity to that which would reach our polariscope 
from the enclosure alone were the tourmaline taken away. But the 
light which would fall on our polariscope from the enclosure alone 
would not be polarized; hence the whole body of light which falls 
upon it from the tourmaline, and which is similar in quality to the 
former, ought not to be polarized. Now part of this light, or that 
which is transmitted by the tourmaline, is polarized; hence it fel- 
lows, in order that the whole be without polarization, that the light 
which is radiated should be partially polarized in a direction at right 
angles to that which is transmitted. 

Another way of stating this conclusion is this. The light which 
the tourmaline radiates is equal to that which it absorbs, and this 
equality holds separately for light polarized in a plane parallel to the 
axis of the crystal, and for light polarized in a plane perpendicular 
to the same. , 

The experiment was made. with a piece of brown tourmaline 
having a few opake streaks, procured from Mr. Darker of Lambeth. 
It was placed in a graphite frame between two circular holes made 
as above described in opposite sides of the bomb, the diameter of the 


Intelligence and Miscellaneous Articles. 393 


holes being about ;*,ths of an inch. On Icoking in at one of these 
holes you could thus sce through the tourmaline and the opposite 
hole, or, in other words, see quite through the bomb. An arrange- 
ment was also made by which part of the tourmaline might be viewed 
with the graphite behind it. 

The apparatus thus prepared was heated to a red or yellow heat 
in the fire, placed on a-brick in a dark room, and the tourmaline 
viewed by a polariscope which Mr. Gassiot kindly lent me. The 
following was the appearance of the experiment :— 

Without the polariscope the transparent parts of the tourmaline 
were slightly less radiant than the field around them. When the 
polariscope was used, the light from the transparent portions of the 
tourmaline was found to vary in intensity as the instrument was 
turned round. No change of intensity could be observed in the 
light radiated by the opake streaks of the tourmaline, or by the 
graphite. 

The light from the transparent portions was therefore partially 
polarized. The polariscope was then brought to its darkest position, 
and a light from behind allowed to pass through the tourmaline. 
The light was distinctly visible in this position, but by turning round 
the polariscope about 90° it became eclipsed. The mean of four 
sets of experiments made the difference between the position of dark- 
ness for the two cases 883°. It appears, therefore, that the light 
radiated by the tourmaline was partially polarized in a plane at nght 
angles to that which was transmitted by it. It was also ascertained 
that the light from the tourmaline which had the graphite behind it 
gave no trace of polarization. | 


LX. Intelligence and Miscellaneous Articles. 


ON THE MOTION OF THE STRINGS OF A VIOLIN. 
BY PROFESSOR H,. HELMHOLTZ, 


if HAVE been studying for some time the causes of the different 

qualities of sound ; and as I found that those differences depended 
principally upon the number and intensity of the harmonic sounds 
accompanying the fundamental one, I was obliged to investigate the 
forms of elastic vibrations performed by different sounding bodies. 
Among such vibrations, the form of which is not yet exactly known, 
the vibrations of strings excited by the bow of a violin are peculiarly 
interesting. ‘Th. Young describes them as very irregular ; but I sup- 
pose that his assertion relates only to the motions which remain after 
the impulse of the bow has ceased. At least, I myself found the 
motion very regular as long as the bow is applied near one end of the 
string, in the regular way commonly followed by players of the 
violin. I used a method of observing very similar to that of 
Lissajoux. Already, without the assistance of any instruments, one 
can see easily that a stiing moved by the bow vibrates in one plane 
only—the same plane in which the string itself and the hairs of 


394 Intelligence and Miscellaneous Articles. 


the bow are situated. This plane was horizontal in my experi- 
ments. The string was powdered with starch, and strongly illumi- 
nated. . One of the little grains of starch, looking like a bright point, 
was observed by a vertical microscope, the object lens of which was 
fixed to one of the branches of a tuning-fork. ‘The fork, making 120 
vibrations in the second, was placed between the branches of a horse- 
shoe electro-magnet, which was magnetized by an interrupted electric 
current, the number of interruptions being itself_120 in the second. 
In that way the fork was kept vibrating for as long a time as I de- 
sired. The lens of the microscope vibrated in a direction parallel to 
the string, and therefore perpendicular to its vibrations. ‘The string 
I used was the second string of a violin, answering to the note A, 
tuned a little higher than common, to 480 vibrations, and therefore 
it performed four vibrations for every one of the tuning-fork. Look- 
ing through the microscope, I observed the grain of starch describing 
an illuminated curved line, the horizontal abscissze of which corre- 
sponded to thedeviations of the tuning-fork, and the vertical ordinates 
to the deviations of the string. I found it a matter of importance to 
use a violin of most perfect construction, and I was fortunate in get- 
ting a very fine instrument of Guadanini for these experiments. On 
the common instruments of inferior quality I could not keep the curve 
constante nough for numbering the little indentures which I shall 
describe afterwards, although the general character of the curve was 
the same on all the instruments I tried: the curve used to move by. 
jerks along the line of abscissze ; and every jerk was accompanied by- 
a scratching noise of the bow. On the contrary, with the Italian 
instrument, and after some practice, I got a curve completely qui- 
escent as long as the bow moved in one direction, the sound bere 
very pure and free from scratching. 

We may consider the motion of the string as being compen 
of two different sets of vibrations, the first of which is the principal 
motion as to magnitude. Its period is equal to the period of the 
fundamental sound of the string, and it is independent of the situation 
of the point where the bow is applied. The second motion produces 
only very smali indentures of the curve. Its period of vibration 
answers to one of the higher harmonics of the string. It is known 
that a string, when producing only one of its higher harmonics, is 
divided into several vibrating divisions of equal length, being sepa- 
rated by. quiescent points, which are called nodes. In all the nodes 
of the second motion of the string in the compound result at pre- 
sent considered, the principal motion appears alone; and also in the 
other points of the string the indentures corresponding to the second 
motion are easily obliterated, if the line of light is too broad. 

The principal motion of the string is such that every point of it 
goes to one side with a constant velocity, and returns to the other 
side with another constant velocity. 

PlateV. fig. 7 represents four such vibrations, corresponding to one _ 
vibration of the fork. The horizontal abscisse are proportional to the 
time, the vertical ordinates to the deviation of the vibrating point. 
Every vibration is formed on the curve by two straight lines. The 


Intelligence and Miscellaneous Articles. 395 


curve is not seen quite in the same way through the microscope, 
because there the horizontal abscisse are not proportional tu the time 
but to the sine of the time, It must be imagined that the curve 
(fig. 7) is wound up round a cylinder, so that the two ends of 
it meet together, and that the whole is seen in perspective froma 
great distance ; thus it had the real appearance of the curve, as repre- 
sented in two different positions in fig. 8. If the number of vibra- 
tions of the string is accurately equal t to four times the number of the 
_tuning-fork, the curve appears quietly keeping the same position. If 
there is, on the contrary, a little difference of tuning, it looks as if the 
cylinder rotated slowly about its axis, and by the motion of the curve * 
the observer gets as lively an impression of a cylindrical surface, on 
which it seems to be drawn, as if looking at a stereoscopic picture. 
The same impression may be produced by combining, stereoscopically, 
the two diagrams of fig. 8. 

_ We learn, therefore, by these experiments, — 

1. That the strings of a violin, when sleick by the bow, heats 
in one plane. 
_ 2. That every point of the string moves to and fro with two con- 
stant velocities. 
_ These two data are sufficient for finding the complete equation of 
the motion of the whole string. It is the following ; — 


y= Ad 1a ; = )sin(= = ‘) } ah ocainy ste as 


y is the deviation of the point whose distance from one end of the 
string is 7; /, the length of the string; ¢, the time; T’, the duration 
of one vibration ; A, an arbitrary constant; andz, any whole number; 
and all values of the expression under the sign %, got in that way; 
are to be summed. r 

A comprehensive idea of the motion represented by this equation 
may be given in the following way :—Let a 4, fig. 9, be the equili- 
brium position of the string. During the vibration its forms will be 
similar to a ¢ b, compounded of two straight lines, ac and c 6, inter- 
secting in the point c. Let this point of intersection move with a 
constant velocity along two flat circular arcs, lying symmetrically on 
the two sides of the string, and passing through its ends, as repre~ 
sented in fig. 9. A motion the same as the actual motion of the 
whole string is thus given. 

- As for the motion of every single point, it may be deduced froth 
equation (1), that the two parts ad and bc (fig. 7) of the time of 
every vibration are proportional to the two parts of the string which 
are separated by the observed point. The two velocities of course 
are inversely proportional to the times a6 and 6c. In that half of 
the string which is touched by the bow, the smaller velocity has the 

same direction as the bow; in the other half of the string it has the 
contrary direction. By comparing the velocity of the bow with the 
velocity of the point touched by it, I found that this point of the 
string adheres fast to the bow and partakes in its motion during the 


396 Intelligence and Miscellaneous Articles. 


time ab, then is torn off and jumps back to its first position during 
the time &c, till the bow again gets hold of it. 

With these principal vibrations smaller vibrations are compounded, 
the nature of which I can define accurately only in the case where 
the bow touches a point whose distance from the nearer end of the 
string is > - 7 &c. of its whole length, or generally — if mis a 
whole number. Because the point where the bow is applied is not 
moved by any vibration belonging to the mth, 2mth, &c. harmonic, 
_ it is quite indifferent for the motion of that point, and for the impulses 
exerted by the bow upon the string, whether vibrations corresponding 
to the mth harmonic exist or not. Th. Young has proved that if 
we excite the vibrations of a string by bending it with the finger, as 
in the harp, or hit it with a single stroke, as in the piano, in the 
ensuing motion all those harmonics are wanting which have a node 
in the touched point. I therefore concluded also that the bow 
cannot excite those harmonics which have a node at the point where 


it is applied; and I found, indeed, that if this point is distant 4 from 
m 


the end, the ear does not hear the mth harmonic sound, although it 
distinguishes very well all the other harmonics. Therefore, in the 
equation (1), all those members of the sum will be wanting in which 
n is equal to m, or 2m, or 3m, &c.. ‘These members, taken together, 
constitute a vibration of the string with m vibrating divisions. Every 
such division performs the same form of vibration we have described 
as the principal vibration of the whole string. ‘These small vibra- 
tions must be subtracted from the principal vibration of the whole 
string for getting its actual vibration. Curves constructed according 
to this thecretical view represent very well the really observed curves. 


If m=6 and the observed point is distant, | from the other end of the 


string, the motion is represented in fig. 10. Near the end of the 
string, where the bow is commonly applied by players, the nodes of 
different harmonics are very near to each other, so that the bow is 
nearly always at, or at least very near to, the place of a node. 
Striking in the middle between two nodes, I could not get a curve 
sufficiently constant for my observations. If I strike very near the 
end, the sound changes often between the fundamental and the 
second or third harmonic, which is indicated by gradual corresponding 
alterations of the curve.—From the Proceedings of the Glasgow Philo- 
sophical Society for Dec. 19, 1860. 


ON CLAIRAUT’S THEOREM. BY PROF, HENNESSY, F.R.S. 


Laplace has shown that this theorem follows, whatever may be the 
density of the interior parts of the earth, provided it consists of similar 
concentric strata, and that the form of the outer stratum is ellipsoidal. 
In the ‘ Philosophical Transactions’ for 1826, Mr. Airy (the present 


Intelligence and Miscellaneous Articles. 397 


Astronomer Royal of England) has presented an equivalent result ; 
more recently, Professor Stokes has shown that we can deduce the 
law of variation of terrestrial gravity without any hypothesis what- 
soever as to the earth’s interior structure. He assumes merely that 
its surface is spheroidal, and that the equation of fluid equilibrium 
holds good at that surface. In vol. vi. of the ‘ Cambridge Mathe- 
matical Journal,’ Professor Haughton presented a demonstration, 
founded upon the same assumptions as those of Professor Stokes, 
and in which he uses certain propositions relative to attractions 
which had been enunciated by Gauss and Maccullagh. While 
studying the labours of those mathematicians, it appeared to me 
that the question could be entirely divested of the hydrostatical 
character, and that Clairaut’s theorem may be directly deduced from 
the equations to the normal of any closed surface, without any con- 
siderations as to the physical condition of the matter forming that 
surface. ‘Thus every surface concentric with the earth, and per- 
pendicular to gravity, will possess the property of exhibiting this 
relation in the intensity of gravity at its various points. 

Let X, Y, Z represent the components parallel to the rectangular 
axes of the forces by which a point is retained at rest on a given 
surface whose equation is L=Q. ‘Then from the equations of the 
normal we have : 


y te xo =0, 7 il yah 


dx dy da dz 


when the resultant of these forces is perpendicular to the given sur- 
face. If we represent by V the potential of the earth on the-par- 
ticle in question, by w the angular sa of rotation, we have 


dV dV 
X= — wy “he ’ scape Ale 


and the above equations become 


Ee a Ce 
dy dx dx dy dy “dx}’ 
dV dl_dVdb_, al 

dzdx dx dz "ie 


If, in conformity with General Schubert’s* recent determinations, 
we assume the earth’s surface to be that of an ellipsoid, with three 
unequal axes, we should substitute for L 


Pe y 2 ies 
et ae 
or 
dL _ 20 di_y dl pind’ 


de @' dy @ dz @ 


* Memoires de ’ Académie Impégriale des Sciences de St. Hee, sér. 7, 
tom. i. 


398. Intelligence and Miscellaneous Articles. 


whence we have’ 


ba 7 _ ay SN =w'ay (a . b°), tae —a°z = ware. 


Each of these partial differential equations can be easily integrated ; 
and the value of V, finally obtained, is equivalent to the equation 
of fluid equilibrium, or 


VtS@+y)=c. 


Let 6 represent the complement of the latitude, and ¢ the longitude, 
, counted from the meridian of the greatest axis, then 


z=r cos 0, =r sin 6 cos ¢, y=r sin 6 sin g, 
and 
- rw" . 

V+ = sin? @6=C. 


In the case of an ellipsoid having the ellipticity e, we have, neglect- 
ing small terms, 
r=a (1—e cos’). 


From these equations, and from the properties of Laplace’s functions 
into which V can be expanded, an expression can be obtained of the 
same kind as that deduced by Professor Stokes from his own and 
Gauss’s theorems relative to attractions.—Proceedings of the Royal. 
Irish Academy, Feb, 25, 1861. 


ON A METHOD OF TAKING VAPOUR-DENSITIES AT LOW TEMPERA- 
TURES. BY DR. LYON PLAYFAIR,:C.B., F.R.S.. AND J. A. WANK- = 
LYN, F.R.S.E. 


The authors refer to Regnault’s experiments, which have shown 
that aqueous vapour in the atmosphere has the same vapour-density 
at ordinary temperatures as aqueous vapour above 100° C.; and 
they bring forward fresh experiments upon alcohol and ether to show 
that when mixed with hydrogen these vapours preserve their normal 
density at 20° or 30°C. below the boiling-points of the liquids, and 
infer generally that vapours, when partially saturating a permanent 
gas, retain their normal densities at low temperatures. 

From their researches the authors deduce the consequence—re- 
markable, but quite in harmony with theory—that permanent gases 
have the property of rendering vapour truly gasecus. Stated in 
more precise terms, the proposition maintained by the authors is, 
«The presence of a permanent gas affects a vapour, so that its ex- 
pansion-coefiicient at temperatures near its point of liquefaction 
tends to approximate to its expansion-coefficient at the highest tem- 
peratures.” 


Intelligence and Miscellaneous Articles. 399 


--The authors anticipate that admixture with a permanent gas may 
serve as akind of reagent to distinguish between cases of unusually 
high expansion-coefficient in a vapour, and cases where chemical 
alteration takes place. It will also be possible, by the employment 
of a permanent gas, to obtain vapour-densities of compounds which 
will not bear boiling without undergoing decomposition. 

In experimenting upon substances which may be heated above the 

boiling-point, the authors employ Gay-Lussac’s process for taking 
the specific gravity of vapours. A slight modification, however, is 
necessary. Previous to the introduction of the bulb containing the 
weighed substance, dry hydrogen is introduced into the graduated 
tube and measured with all the precautions belonging to a gas ana- 
lysis. It will be obvious that in the subsequent calculation the 
volume of hydrogen corrected at standard temperature and pressure 
must be subtracted from the volume of mixed gas and vapour, also 
corrected at standard temperature and pressure. 
_ When the substance will not bear heating to its boiling-point, the 
authors employ a process resembling that of Dumas in principle, but 
differing very widely from it in detail. Dumas’s flask with drawn- 
out neck is replaced by two bulbs, together of about 300 cub. cent. 
capacity, joined by a neck, and terminating on either side in a nar- 
row tube. Oneof the narrow tubes has some very small dilatations 
blown upon it (0), the other is merely bent (D). (See Plate V. fig. 6.) 
The apparatus, whose weight should not exceed 70 grms., is weighed 
in dry air, then placed in a bath, being secured by a retort-holder 
grasping the neck joining the large bulbs Cand C. The end A, 
projecting over the one side of the bath, is made to communicate 
with a hydrogen apparatus; the end D passes through a hole -in 
the opposite side of the bath, which is plugged up water-tight by 
means of putty. Dry hydrogen is transmitted through the whole 
arrangement, and escapes at D through a long narrow tube joined 
to it by a caoutchouc connecter. 

The bath is next filled with warm water until the bends a and a 
are covered. The connexion with the hydrogen apparatus is then for 
a moment interrupted, to allow of the introduction of a small quantity 
of the substance at A. The substance, which should not more than 
half-fill the small bulb 4, is partially vaporized in the stream of hydro- 
gen, and in that state passes into the part CC. All the while the 
temperature of the bath is kept uniform throughout by constant 
stirring, and .made to rise very slowly. When within a few degrees 
of the temperature at which ‘the determination is to be made, the 
current of hydrogen is almost. stopped, so that the bulbs C and C 
may contain less vapour than will fully saturate the gas at the tem- 
perature of sealing. The water of the bath is then made to subside, 
by opening a large tap placed near the bottom. The bends a and a 
are thus exposed, the bulbs CC remaining covered. Immediately 
the current of hydrogen has been stopped, the flame is applied at. 
aa, so as to seal the apparatus hermetically. The temperature of the 
bath, as well as the height of the barometer, must now be observed. 


400 Intelligence and Miscellaneous Articles, 


After being cleaned, the apparatus (which now consists of three 
portions, viz, the portion CC hermetically sealed and the two ends 
6 and D) must be weighed, 

‘The capacity of the apparatus is found by filling it completely with 
water and weighing; but previously to this operation the volume of 
hydrogen enclosed at the time of sealing must be found. On break- 
ing one extremity under water, the water will rise in the bulbs, and, 
after a while, will have absorbed all the vapour, but will leave 
the hydrogen, ‘The bulbs must then be lifted out of the water, 
without altering their temperature, and, with the water that has 
entered, weighed. ‘The difference between the latter weighing and 
the weight of the bulbs quite full of water gives the weight in 
grammes, which expresses in cubic centimeters the volume of hy- 
drogen enclosed; the pressure is the height of the barometer minus 
the column of water which had entered the bulbs; the temperature 
is that of the water, 

An example of a determination of the vapour-density of alcohol 
at 30° C. below its boiling point is subjoined ;— 


Height of the barometer (at O° C.) ...... 763°09 millims, 


Temperature of the balance case ......., 75 C, 
Weight of apparatus in dry air,......... 69°959 grms, 
‘Temperature at time of sealing. ......... 48°C, 


Weight of apparatus + hydrogen+vapour,, 69°5275 grms, 
Weight of apparatus+ water (at 3°2C.)., 191°76 grms, 
Weight of apparatus filled with water.... 545°36 grms. 
Height of water column .. ..00. 6 ce eens 122 millims, 


From which is deduced—~ 


Volumes corrected 
at 0 C. and 760 millims. pressure, 


eubie centimeters. Grn, 
Hydrogen+ vapour ...... 40643 weighing 0°1695 
Hydrogen, , .. weap oe Ue 341°27 ”» O0306 
65°16 Or 1389 
Therefore, 65°16 cub. cent. of alcohol-vapour weigh +1389 
but 65°16 cub. cent. of air weigh... ...... ‘0843 
"1389 


Vapour-density of alcohol = = 1648, 


‘OS43 

The authors have extended their experiments to acetic acid and 
other substances. At low temperatures the vapour-density of acetic 
acid approximates to 400, no matter how much hydrogen be em- 
ployed. At higher temperatures an approximation to 2°00 is ob- 
tained, but without heating so high as Cahours found necessary, 

The authorsare continuing these researches. — From the Proceedings 
of the Royal Society of Adindurg’, January 21,1386). 


THE 
LONDON, EDINBURGH ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 
JOURNAL OF SCIENCE. 


[FOURTH SERIES, ] 


JUNE 1861, 


eee 


LXI. On a Law of Liquid Kxpansion that connects the Volume of 
a@ Liquid with its Temperature and with the Density of its satu- 
rated Vapour. By Joun Jamns Warenstron*, sq. 

| With a Plate. | 

$1. 1 tee the archives of the Royal Society for 1852, there is 

an account of observations on the density of hquids 
and their superjacent vapours at high temperatures, made in sealed 
graduated tubes filled with the same liquid in different propor- 
tions of their volumes. The general law of density in saturated 
vapours deduced from these observations, and from the various 
observations of vapour-tension already published by other phy- 

sicists, is therein set forth, with the assistance of a chart (No. 2 

chart) in which the observations are all projected, and lines 

drawn, that enables the eye to judge of the accordance between 

theory and observation. (See Note A.) 

An account of this general law is also given in the Philoso- 
eel Magazine for Mareh 1858, in a paper entitled “On the 
§vidence of a Graduated Difference between the ‘Thermometers 
of Air and Mereury between 0° and 100° C.” 

By the same mode of observing in sealed graduated tubes, | 
afterwards extended the observations up to the transition-point 
of three of the liquids, viz. aleohol, ether, and sulphate of carbon, 
and found that the law of vapour-density was maintained in them 
Without deviation to their extreme limiting temperatures, As 
these extensive series of observations supplied the curves of ex- 
pansion of the three liquids, I have occasionally tried by means 
of them to discover a general law of liquid expansion, T submit 
the following account of the last attempt of this kind, as it ap- 
pears to be successful. 

* Communicated by the Author. 


Phil, Mag. 8. 4, Vol. 21, No, 142, June 1861, 2D 


402 Mr. J.J. Waterston on a Law of Liquid Expansion 


§ 2. The curves of expansion, drawn to a large and distinct 
scale, were examined by the following graphical process :—At 
four or five points nearly equidistant, tangents were drawn 
(carefully judging of the direction to be given to the straight 
edge by the sweep of the curve to the right and left of the point 
of contact). Thus were obtained several values of the quotient 
of the differential of volume by the volume or proportionate dif- 


d 
ferentials for constant element of temperature EA . These 


were set off as ordinates to the temperatures, and the curve 
drawn through the points appeared to be the common equilateral 
hyperbola, havin g one asymptote coinciding with the axis of tem- 
perature and the other perpendicular to it, and intersecting it at 
a temperature [y] that evidently was above the transition- -point. 
If this were the case, the product of the coordinates to each point 
of the curve, reckoning from the point y as origin, ought to be 
constant [=p]; and accordingly it was found that when the 
inverse of the quotients were projected as ordinates to the tem- 
peratures, the points ranged in a straight line, which being pro- 
duced, cut the axis in the pomt y. The differential equation is 
thus 

dv y—t 

He Uo ag 
the integration of which is 


+ k 

v=4 —— 

y— 

in which k=(y—z) when v=1. (See Note B.) 

§ 3. There is a relation between this expression and that for 
saturated vapour-density which ‘seems to prove that it is not em- 
pirical, but the true exponent of the physical condition of the 
molecules of a body in the liquid state. The following is a state- 
ment of it. 

In the papers above referred to, there will be found an account — 
of the law of saturated vapour-density, and the proofs on which 
it rests. It is expressed by the equation 


so soma 


If we put A= 2 the law of liquid density is 


Bata" L 
(ayaa 
On comparing the constants for different liquids, I find as a 


general rule that the quotient is a constant quantity [KE]. 


that connects the Volume of a Liquid with its Temperature. 403 


Thus for Alcohol my observations give E=1717 
»  Sther pS 5 K=1739 
» Sulphate of carbon _,, H=1725 


M. Muncke’s observations on sulphuric acid from 50° to 230° C, 
E=1600 to 1800. (See Note C.) MM. Dulong and Petit’s 
observations on the expansion of mercury between 0° and 300° C. 


give p= ie The line passing through M. Avogadro’s ob- 


servations on the vapour of mercury from 230° to 300° C. gives 
h=1160. These combined give H=1727. I have adopted 
1717 as the nearest probable value at present, because the most 
labour was bestowed on the alcohol series of observations. 

These values of E are derived from English measures of pres- 
sure and temperature, viz. inches of mercury and degrees of 
Fahrenheit scale. The value of this constant derived from French 
measures is F=504°44, which corresponds with H=1717. The 


ah ats Df 3x 29°922 1% bas 
ratio of reduction is a= a4 eee , so that Ka=F, 
a F=2-70282 
rine =0°53195 
ue a 


§ 4. M. Regnault’s observations on the tension of the vapour 
of mercury from low temperatures up to 200° C., respond to the 
same value of / as those at the higher temperatures by M. Avo- 
gadro, but with g augmented 12 degrees, showing a boiling-point 
12 degrees higher. It is remarkable that M. Regnault’s obser- 
vations on the expansion of liquid mercury differs so far from 
those of MM. Dulong and Petit as to be represented with p=4 
and HE=870. At 300° C. this difference amounts to about the 
equivalent of 84° C. The acceleration of the rate of expansion 
is in M. Regnault’s observations only one-half what is shown by 
those of MM. Dulong and Petit. (See Note D.) This 1s a re- 
_markable discrepancy, both being so eminent in this class of ob- 
servations. r 

§ 5. In all cases I have worked with temperatures reduced to 
the air-thermometer by scales of correction computed from the 
formula given in Appendix III. to the paper in the Philosophical 
Magazine for March 1858 above referred to. 

The formula is founded on MM. Dulong and Petit’s observa- 
tions. I annex exact tracings of these scales (Plate VI.). In 
two cases (petroleum and sulphuric acid) the temperatures were 
taken uncorrected and compared with the results when corrected. 
In both, the differences between theory and observation were 
less when the temperatures were corrected. 

2D2 


404 Mr. J.J. Waterston on a Law of Liquid Expansion 


It is not absolutely necessary to correct the temperatures in 
order to recognize these laws of density, and for practical pur- 
poses may not be required; but it seems best to accustom our- 
selves to do so, in order to be prepared for the recognition of 
any other relations of harmony that may exist in the thermo- 
molecular physics of different bodies. 

§ 6. Water is, as might be expected, an exception to the law 
of liquid density, as itis to the law of capillarity and compressi- 
bility (see papers by M. Grassi and M. Simon in the Annales 
de Chimie). Ihave traced its curve of expansion by observations 
in sealed tubes up to 210° C. air-thermometer (see Note E), and 
projected the densities to the value of p required by its vapour- 
gradient ; also those of M. Despretz from 0° to 100° C.; but 
they do not conform to the line required at any point of its 
range even at the highest temperature. These abnormal features 
in this first of liquids have had a prejudicial effect on the pro- 
gress of science in this department. There is no other liqmidas 
yet found with such point of maximum density that remains a 
liquid under its maximum ; yet such a point seems invariably to 
be sought for. M. Muncke and M. Pierre have bestowed much 
unavailing labour on this question. (See Note F.) 

§ 7. To determine the constants of these two equations for 
the density of the liquid and of its vapour, not more than four 
exact observations are strictly required; two of the vapour, and 
two of the liquid. 

If the series of observations on the dilatation of a liquid extend 
over a considerable range of temperature, and have had their 
inequalities equalized by graphical processes equivalent to weigh- 
ing by the method of least squares, the three constants of the 
equation may be directly determined. 

Thus let fo, 4, ¢ be the three temperatures, and v9, 0), vg the 
corresponding volumes observed, to find p and & we have 


=; 
———}__9___ = ___#__0___ 


y-@y @y-Qy 


which may be solved by trial and error. But few observations 
as yet published will stand this test, the range of temperature 
being too small, and the irregularities proportionably too great. 
§ 8. A simple and satisfactory way to test both of these laws 
of density by published observ ations, is to take two of the vapour- 
tensions not far from the boiling-point and compute the value 
of A. Ex. gr., let eo, e, be the two observations of the pressure 
of vapour in contact with its generating liquid; To, T, the cor- 
responding temperatures by air-thermometer reckoned from the 


that connects the Volume of a Liquid with its Temperature. 405 


zero of gaseous tension [ —461° F.,or —273°-89C.]; then we have 
T,—Ty 


| Fe — SENT 


2@)-G 


and since p= : , we obtain the index of the power of the density 


of the liquid, which being set off as ordinates to the temperature, 
ought to range in a straight line; and this line produced, cuts 
the axis of temperature at y. If, when these points are con- 
nected by distinct lines, a general convexity in the range can 
be discovered, viewing it foreshortened with the eye close to the 
plane of projection, then we may infer that p requires to de di- 
minished if the convexity 1 is directed upwards from the axis of 
temperature, and vice versd. 

§ 9. Having found p and k and y, the next step is to compute 
the values of ¢ from the volumes by the equation, and tabulate 
the differences between the computed and observed temperatures. 
This will be found attended with but little additional labour. If 
we now project these differences as ordinates on an exaggerated 
scale to the temperatures, we obtain a distinct impression of how 
far theory and observation accord. 

§ 10. Mercury and alcohol being the most important liquids 
for thermometric purposes, may serve as examples of the mode 
of computation. 

I. Mercury. 


M. Avogadro’s observations on the tension of the vapour of 
mercury :—At 260° C. the observed tension was 13362 millims., 
at 290° it was 252°51 millims. The correction to reduce the 
temperatures to the air-thermometer from the scale is 5°:60 at 
260°, and 6°91 at 290°. Hence— 

260— 5°60 + 273'89=528:29=T,, 133-62 millims. =e, 
290—6'91 +273'89=556'98=T,, 252°51 millims. =e, ; 
and we arrive by computation at log h=2°54796 and g=247°-45, 

[I have computed the temperatures for M. Avogadro’s other 
six observations. The computed, minus the observed, is, at 


300= + 0°15 
290= -0 

280= + 0°42 
270= —0°26 
260= 0O 

250= —0°26 
240= — 1:90 
230 = —4'56 


= difference in tension amounting to one-third inch mercury. ] 


406 Mr. J. J. Waterston on a Law of Liquid Expansion 
This value of A being derived from French measures, is to be 
applied to F to find us which thus comes out 1:4284. 


The following are MM. Dulong and Petit’s volumes of mer- 
cury computed with this index :— 


Temp. Inverse of volumes 
Cent. Volumes. raisedtothe power _ First Second 
Air. 1 1.4984. differences. _ differences. 
0 1:000000 —'1-000000 aie 
100 1:0180180 "974815 025213 ‘000028 
200 1:0368664 "94.9602 025236 "000023 
300 = 1:0566037 "924366 


The second differences indicate a slight convexity in the line 
upwards. This shows that : requires augmentation. The fol- 
lowing is the result of computing the same observations with 
t = 1-489 :— | 
' First diff. Second diff. 


CE MMEH LS 0 opie a 


100 973760 | 000001 
200 947521 aoeen 000005 
300 —--921287 


To find y, we have 1—0:947521 : 200°: : 1: 3811°05=y, 


8811:05—¢ 1 a, 1 fees in 
and | ae 3811-05 =A=-,or(3811 05 —#)v'4°9 = 3811-05. 


This expresses MM. Dulong and Petit’s observations with a 
difference at 100° amounting to +,4,5th of a degree, and at 300° 
the difference is =,th of a degree. 

$11. To bring the D of the vapour formula to the same 
standard as the A of the liquid formula, it is requisite to change 
the value of / in the one and & in the other, so that the weight 
in grains of a cubic inch of either may be indicated. | 

Let n='0216216 = weight in grains of a cubic inch of hy- 

drogen at the ‘temperature 0° C. and pressure 760 
millims. 

5= vapour-density of the body on the hydrogen scale. 

T= temperature (reckoned from the zero of gaseous ten- 
sion) at which the pressure of the saturated vapour 
is 760 millims. 

f= required factor 


TGA BBO i, 2 
ion hae 


that connects the Volume of a Liquid with its Temperature, 407 


By the formula, 

r= 24745, 

g=611°28, 
also 5=101; hence ph= "=", and log wh=2'56247. Thus 
we obtain 

T—247-45 1 5 _ 

[256247] f 


the general expression for the weight in grains of a cubic inch 
of the saturated vapour of mercury at T° (C. A. G.), temperature 
reckoned by Centigrade Air-thermometer from the zero of 
Gaseous tension. 

§ 12, The weight of a cubic inch of mercury at 0° is 87544 
grains, hence 

| 
37544 _ § 3811-05 — (T—273:89) | 480 ; 
v tL Mx8811:05 —? 


1°489 
and M= (aera) ; hence 


Ree cit ate 
[8:25857 | a el 
the weight of a cubic inch of mercury in grains at T° 
(C. A. G. temperature). 

We may thus find the temperature at which a=W, or that at 
which liquid and vapour would be of equal density if the laws 
were maintained. 

With alcohol, ether, and sulphate of carbon, transition occurs 
a few degrees below the theoretical temperature of equal density. 


II. Alcohol. 


— § 18. M. Regnault’s observed tensions of saturated vapour :— 
At 40° C. the tension is 134°1 millims.; at 70°, 589°2 millims. 


40 +. 0°48 + 27389 =314'37 C.A.G.=T, | logh= 2°15392 


70+ 0:41 + 27389 = 34430 =T,f  g=190-70 
ao = 3:5892 


This gives 78°83 C. A. as boiling-point at pressure 760 millims. 
M. Pierre’s observations on the expansion of aleohol were made 
on a specimen that boiled at 78°°63 C. A. under pressure 758 
millims., and its specific gravity at O° was 0°8151. 

The following are his second series of observations computed 
with the above index, 3°5392 :— 


408 Mr.J. J. Waterston on a Law of Liquid Expansion 


Computed 
temp. minus 
(=) 35392 observed 
V temp. 
(1) 33-46 + 0:47 = 33-93 108714 87890 = +0°21° 
(2) 47:524+0°51=48-:03  1:05356 —-83140 0 
(3) 50°33+0°5]=50°84 1:05676 82248 —0:19 
(4) 56:26+0:50=56:76 1064.16 980245 —O0°25 
(5) 60:41 +0°48=60°89 1:06989 "78736 +0°03 
(6) 73°70+0°38=74:'08 1:08780 74238 0 
(7) 76°73+0°35=77:08 1:09168 ‘73310 = —0°27 


The computed densities (87890, &c.) set off as ordinates to 
the temperatures, show atrend without any appearance of curva- 
ture. The straight line seems to pass exactly through the points 
of the second and fifth and sixth. Assuming it to pass through 
the second and sixth, we have 

83140 —°74238 = -08902 : 74°08 — 48°'03 = 26°05 : : *74238 : 217°24, 
and 74°08 + 217:24=291°32=y. This line gives unity volume 
at —1°-30, hence k=292°62=y—t when volume equal unity, 
and the equation is (291°°32 — t)v99 = 29262. The differences 
between the observed temperatures and those computed from the 
observed volumes by this equation are given in the last column. 

§ 14, This equation answers well to the observations of M. 
Pierre above 10°; also to those of M. Muncke (St. Peters- 
burgh Memoirs) above the same temperature; but in both the 
trend of the points below this lies in a line inclined to that of 
the equation. The divergence is the greatest in M. Pierre’s. In 
neither is it a general convexity, but distinctly the contour shows 
two lines diverging from about 15° to 20° C. This is most 
distinct in M. Muncke’s observations. I have computed them 
by the above equation, and tabulated the differences between the 
observed and computed temperatures, which are set off in Pl. VI. 
fig.3asordinatesto the temperatures on ten times the natural scale. 
Above these, in fig. 2, M. Pierre’s differences are set off to the 
same scale, and in fig. 4 the differences in my series of observa- 
tions on alcohol, described in the paper above referred to as being 
in the archives of the Royal Society. This alcohol was not 
absolute ; it had 19 per cent. water, and the index of its power 
derived from its line of vapour-density was 3°60; also y=290°89, 
k=209°81, and its equation (the volume being reckoned as unity 
at the boiling point) } 


(2909-89 —#) v3=209°81 C. A. G. 


§ 15. The deflection in M. Pierre and M. Muncke’s observa- 
. sions, it will be remarked, occurs in those below atmospheric tem- 


C. C. A. Ne 


that connects the Volume of a Liquid with its Temperature. 409 


peratures, where the reduction of temperature had to be artifici- 
ally produced by mixtures of broken ice and muriate of lime, and 
it represents the temperature of the mercury to be higher than 
that of the alcohol. This is precisely what took place in some 
observations I made on the contraction of ether about 20° below 
the atmospheric temperature. A similar deflection, but in a 
greater degree, appears in the ether observations of the same 
authors. They are projected in figs. 5 and 6 to the same scale 
as the others. (See Note G.) 

The application of cold to maintain a constant temperature is 
by no means under the same command as the application of 
heat ; and, besides, conductibility is very much reduced at low 
temperatures. There is an evident dislocation, the law of con- 
tinuity is broken, but it is at the part of the scale where the mode 
of obervation underwent a change. I submit, therefore, that 
the verdict should be against the observations at the lower tem- 
peratures, not against the law of expansion, which, if in fault, 
would cause the trend of the points to have a general curvature 
throughout the range. 

In judging of the evidence afforded by these graphical projec- 
tions, it should be kept in view that the vertical scale magnifies 
the amount of the differences tenfold. The accordance of theor 
with observation is in some casesremarkable. Thus, for 40° C., 
Muncke’s alcohol and Pierre’s ether do not show a difference 
greater than one-sixth of a degree. We have also to keep in 


mind that the power . that reduces the densities to a straight 


trend, is not arbitrarily assumed to suit a particular series of ob- 
servations, but that it is determined @ priori from the vapour, 


If we take any other value of that that which is thus deter- 
mined, the graphical projection of the computed densities shows 
a general bend. If — is too great, the bow is turned downwards ; 
if too small, the bow is turned upwards. The string of the bow 
only makes its appearance when the value of 4 is that deduced 


from the gradient of vapour-density above described. 

§ 16. The time has not perhaps yet arrived for deducing these 
laws of density from the dynamical theory of heat; but if we are 
ever to arrive at a conception of the true ultimate nature of mo- 
lecular force, it seems clear that the inductive path of least difficult 
approach (if not the only one) is that which sets out from the study 
of the gaseous state, and proceeds by way of that of the equili- 
brated condition of saturated vapours in communication with their 


410 Mr. J.J. Waterston on a Law of Liquid Expansion 


generating liquids, to the molecular condition of the liquids, where 
the dynamic condition of the chemical element is constrained by 
the cohesive force; and the struggle in which this dynamic force 
is gradually subdued by the increase of temperature is, as now 
ascertained, represented by one quantitative relation throughout, 
that seems to indicate a certain simplicity in the ultimate recon- 
dite principle on which molecular force is based. 

We know that the physics of gases conform to the physics of 
media that consist of perfectly free elastic projectiles*. Their 
free concourse and perfectly elastic recoil determines the resolu- 
tion of their vis viva into the six rectangular directions of space ; 
and it is this number that probably fixes the ratio of the propor- 
tionate increment of density in a saturated vapour to the corre- 
sponding proportionate increment of temperature reckoned from 
the fixed limit g. But the absolute increment of density corre- 
sponding to constant increment of temperature differs in different 
vapours, being ruled by a gradient, the sixth root of which has a 
constant ratio to the index of density of the generating liquid 
expressed as a function of the temperature. 

The next step that seems within reach, if we had a few more 
observations to work from, is the discovery of the relation which 
no doubt exists between the increase of volume and decrease of 
latent heat or capillarity regarded as the integral of cohesion. 
The density and the capillarity both diminish as the temperature 
rises. (See Note H.) If there is a simple law of quantitative rela- 
tion between them, its discovery would supply all that is now 
wanting to bring the dynamical theory of heat to bear upon the 
molecular physics of liquids. 


Notes. 


Note A. § 1.—The title of the paper is ‘‘On a General Law of 
Density in Saturated Vapours,”’ illustrated by Chart No. 2. Inthe 
Philosophical Transactions for 1852 there is a paper with the same 
title, illustrated by a Chart No.1. (This paper was originally sent to 
the British Association.) In Chart No. 1 the sixth root of density 
is laid off as ordinate to the square root of the temperature reckoned 
from the zero of gaseous tension. In Chart No. 2 the sixth root of 
density is laid off as ordinate to the temperatures simply. In Chart 
No. ] the lines appear straight at the upper part of their course, but 
with an increasing flexure at the lower part of the range convex to 
axis of temperature. Also there is no relation of harmony apparent 
betweenthem. In No. 2 Chart (of which a tracing is to be found in 
the archives of the Royal Society for 1852-53) the lines are straight 

* See paper “On the Physics of Media that consist of perfectly elastic 
ery in a state of Motion,” in the archives of the Royal Society, 


that connects the Volume of a Liquid with its Temperature. 411 


throughout, and relations of paralellism appear ; also several radiate 
from the same point in the axis of temperature, showing that, as a 
general law, vapours in contact with their generating liquids have, at 
the same temperature, or at the same constant difference of temperature, 
densities that have a constant ratio. 


Note B. § 2.—This mode of graphical analysis seems a natural 
mode of operating when a law of nature has to be unmasked. If the 
proportionate differentials of volume had been laid off as ordinates, 
not to the temperature, but to the volume, the result would be the 
logarithmic curve, which might not be so easy to recognize with only 
a few points to lead from. We must be guided in the selection of 
the coordinate axis by the causal relation of dependent phenomena. 
Heat being, as it were, the instrument of action in molecular physics, 
claims the preference as a standard by which to measure the propor- 
tionate differentials, and to which other variables may be referred to 
as coordinate axis. As an example, the’following is the analysis of 
the law of saturated vapours by this process. 

The vapour-tensions being divided respectively by the correspond- 
ing temperatures reckoned from the zero of gaseous tension, the quo- 
tients represent densities of saturated vapour. Setting off these quo- 
tients as ordinates to the temperatures, we next draw the curve, and 
equalize the irregularities as far as possible; then take off the ordi- 
nates of the finished curve at equal intervals of temperature, say 10° 
or 5°; next take the differences of adjacent ordinates and divide each 


by the intermediate ordinate. These quotients, 7 are to be laid 


off as ordinates to the temperatures. The points appear to range in 
a conic hyperbola, having the axis of temperature as an asymptote. 
This conjecture is to be tested by laying off the inverse of these 
quotients as ordinates to the temperatures. The conjecture is con- 
firmed by the points ranging in a straight line which cuts the axis 


at a certain temperature g. Hence (t—g)f= Gr) tod eee Gis 


FO D hidit wey 
1 1 
The integration of this gives D=(t—g)f x = in which H=(t—g)f 


when D= unity; or let A4/=H, then Df= (2) Comparing the 


value of f in different vapours, it is found to be constant for all and 
equal to 4. 

As another example, but unconnected with heat, we may inquire 
as to the possibility of ascertaining the law of gravitation from the 
changes in the moon’s apparent size and motion, its actual distance 
_ and the earth’s radius being supposed unknown, but assuming that 
the difficulty caused by an unknown parallax and augmentation of 
diameter might be evaded by taking lunar distances at equal altitudes 
on both sides of the meridian. 

By observations on consecutive nights, while the diameter is in- 
creasing or diminishing at the maximum rate, we might obtain two 


412 Mr.J. J. Waterston on a Law of Liquid Expansion 


angular velocities and two measurements of diameter; hence the pro- 
portionate differential of the diameter and the correction to be applied 
to the angular velocities to reduce them to the same radius. We 
might thus obtain the velocity, the increment of velocity, and incre- 
ment of distance expressed in terms of r, the radial distance of the 


moon from the earth at the middle epoch. Now since ar 2Qvdy, if 
x 
we had these same quantities for different values of p or 7, and pro- 


jected the, different values of a as ordinates tothe correspon- 
vdv 

ding values of r, the points would converge in a straight line to the 
zero of r; and if an approximate parallax was obtained, the point 
corresponding to the value of 2vdv at the earth’s surface would fit in 
and confirm the propricty of the projection. If it is a question what 
should direct us to this particular projection, it might be answered 
the increment of square velocity is a square quantity, and the inverse 
form of function is applicable to a power depending on distance. 


Note C. § 3.—The longest series of observations on the expansion 
ofa liquid that I have met with is that of M. Muncke, on sulphuric 
acid from —30° to +230°C. Ihave been enabled to put them to the 
test by the following equation for the tension of its vapour, viz. 


Sa) = p (English measures). In this the value of g=354°7 


is assumed to be the same as that for steam, and for the vapours of 
several hydrates of sulphuric acid observed by M. Regnault, and 
referred to in § 1. of paper in the Philosophical Magazine for March 
1858. ‘The value of 4(=1288) is derived from the boiling-point. 


seal aeunh ea = is thus 1°33. The inverse volumes being com- 
p hk 

puted to this power, and laid off as ordinates to the temperatures, 
were found to range well in a straight line above 30°. The line 
drawn through 45° and 220° is expressed by the equation 


(1433°-2—2)v5= 14361 C. A. 


The differences between the temperatures computed from the volumes 
by this equation and those observed are laid off in fig.1 (PI. VI.) as 
ordinates to the temperatures, the scale vertical to horizontal being 
10 to l. 

The law of continuity is evidently broken at about 40°, the de- 
flection being similar to the other cases referred to in §§ 14, 15, and 
probably due to the same cause. 

Fig. 7 (Plate VI.) represents the differences of Muncke’s observa- 
tions on petroleum projected in the same way. ‘The equation is 

(489°°5 —2) v*14=4895 C., 


in which Liia.ge has been deduced from Ure’s observations on the 
Pp 


that connects the Volume of a Liquid with its Temperature. 413 


vapour of petroleum. It is unlikely that the liquids were exactly the 
same. A slight convexity directed upwards is apparent in the trend of 


the points, which a small augmentation in — would correct. 


Note D. § 4.—M. Regnault stands so high as an authority, that an 
error in his observations that can be clearly demonstrated from in- 
ternal evidence is of importance to science. Erroneous observations 
from eminent observers are serious obstacles to progress, as are un- 
sound deductions from eminent men of science. ‘They are weeds 
difficult to root up, and the attempt to do so is a task so ungracious 
and so irreverent as to incur every discouragement. 
The projection of M. Regnault’s observations on the tension of 
steam above and below 100° C. is given in fig. 8. The dotted line 
represents the empirical formula which had to be altered at 100°, 
the point at which the method employed in making the observations 
was changed. They are projected with temperatures uncorrected, in 
. the manner described in § 1 of paper in the Philosophical Magazine 

for March 1858, and they are orthographically foreshortened as de- 
- scribed in the latter part of § 4. See also § 6, and Appendix I. of 
the same paper. 

The question to ask ourselves when looking at the figure 8 is, Do 
the points conform to the law of continuity? Is their trend not clearly 
broken at 100°? To put a series of observations to the test of this 
law can always be done, but it is attended with considerable labour, 
and seems to require a speciality different from that which charac- 
terizes the eminent observer and experimentalist. 


Note E. § 6.—The following are those observations in series along 
with those of M. Despretz, both equalized graphically by elaborate 
processes, and the temperatures corrected and reduced to the air- 
thermometer. My observations from 100° up’to 212° F. agree so 
well with M. Despretz’s, that those at the higher temperatures will, I 
think, be found nearly correct, although there was some uncertainty 
in consequence of absorption by corrosion of glass. 


C. A. Volume. C.A. | Volume. C. A. Volume. C, A. Volume. 


—10 | 1-00184 || 55 | 1-:01413 |] 100 | 1-04333 || 153 | 1-09847 
— 5] 1-00068 || 6O| 1-01668 || 105 | 1-04743 || 160 | 1-10456 
0} 1:00013 || 65! 1-01940 || 110] 1-05172 || 165 | 1-11083 
51 100001 || 70) 1-02230 || 115 | 1-05620 || 170 | 1-11731 
10 | 1-00025 || 75 | 1-02538 || 120] 1-06086 || 175 | 1-12400 
15 | 1-00083 || 80! 1-02863 || 125 | 1-06570 || 180 | 1-13093 
20 | 100168 || 85 | 1-03205 || 130 | 107073 || 185 | 1-13811 
25 | 1-00280 || 90] 1-03563 || 135 | 1-07593 || 190 | 1-14553 
30 | 1:00416 || 95 | 1-03939 || 140] 1-08130 || 195 | 1-15323 
35 | 1:00575 || 100) 1-04333 || 145 | 108684 || 200 | 1-16124 
40 | 1-00755 150 | 109257 || 205 | 1-16958 
45 | 1-00955 | 210 | 1:17829 
50.| 101175 


rr rer a SS NN 


414 Mr. J.J. Waterston on a Law of Liquid Expansion. 


The following is an extract from note-book of the experiments :— 

“The observations on pure distilled water could only be made up 
to 305° F., in consequence of the glass being corroded and becoming 
opake above that temperature. At the higher temperatures, five 
tubes were employed with water having 3, of carbonate of soda in 
solution. ‘Two only of these five were sufficiently transparent up 
to 413°. But on examining them next day, ;1,th of the volume of 
liquid was absorbed. This allowed for. 

«« The expansion of the solution rather less than pure water. The 
corrosion of the glass began immediately above the surface of the 
liquid. ‘The vapour was computed from formula, assuming the law 
of vapour-density maintained.” 


Note F. § 6.—M. Muncke and M. Pierre have employed the general 
formula 1+ A,=1-+ax+ba’?+ ca’, &c. to represent their observa- 
tions, and have computed the constants for eachseries. They have 
also sought, by means of the roots of this equation, to find points of 
maximum density of each liquid beyond the range of their observa- 
tions. Thus M. Pierre, at p. 358, vol. xv. Ann. de Chim., expresses 


himself as follows :— ‘‘ ... . puisque l’équation ee. =0, dont 
2 


les racines doivent donner la température de ce maximum, a ses deux 
racines imaginaires.” 

I have traced graphically the curve of the equation and of the ob- 
servations, and find that its course through them is similar to fig. 8, 
interlacing at the fixed points, and departing altogether from the line 
of observation beyond the extreme points to which it is bound down. 
The positive and negative differences at the loops sometimes amount 
to 4 degree. A conic section may be drawn to represent almost per- 
fectly a series of observations if the range is not great. The hyperbola 
answers well, and can be simply applied as the increasing rate of ex- 
pansion adapts itself to the curve, referred to an asymptote parallel 
to the axis of temperature. 


Note G. § 15.—The value } 3-98 is taken from Regnault’s ob- 


Pp 
servations on the tension of its vapour at 0° and 20°C. The obser- 


vations at 0° and 30° represent =3°25. Dalton’s observation on 


Pp 
the vapour give it equal to 3:2108, which is probably the most cor- 
rect, as / is thus represented to be the same for sulphuric ether and 
water, their lines of vapour-density being parallel. 


Note H. § 16.—Ina paper on Capillarity in the Philosophical Ma- 
gazine for January 1858, the proofs are given in detail of a law that 
connects molecular volume with capillarity and latent heat. It is ex- 


pressed by the equation mF, in which m is the cube root of the mo- 


lecular volume of aliquid, p the height of the same in a capillary tube 
of constant bore, and L the latent heat of the vapour of the same, all 


Prof. F. von Kobell on Dianic Acid. 415 


taken at the same temperature ¢. According to Wolf and Brunner 
(Ann. de Chim. vol. xlix.), p= A—Odt is the empirical equation for the 
capillary height in terms of the temperature. According to the law 


, ‘ k \p) 
of expansion, m= ) . Hence 


Pein / (GE) 


is the equation which, at present partly empirical, it is so desirable 
to convert into one wholly expressive of a general natural law of 
quantitative relation between L and V. 

Edinburgh, May 6, 1861. 


LXII. On a peculiar Acid (Dianic Acid) met with in the Group 
of Tantalum and Niobium compounds. By Professor F. von 
KoBELu*. 


— G engaged in preparing a new edition of my ‘ Minera-- 

logical Tables,’ I was anxious, among other matters, to 
arrive at as distinct chemical characters as possible for the tan- 
talates and niobates with which we are familiar ; and after various 
experiments, [ came to the conviction that in several of these 
compounds there exists an acid different from the true tantalic 
acid which occurs in the tantalite from Kimito, and also from 
the niobic acid met with in the niobite from Bodenmais. 

As from the previous labours of MM. Rose, Hermann, 
Wohler, and others we are aware that in testing for these acids 
the one is very liable to be mistaken for the other, inasmuch as 
the tests give more or less various indications according to the 
manner of treating the substances and the quality of the reagents 
themselves, I have endeavoured in the first place to avert any 
possible error arising from those causes by conducting the whole 
of the assays in precisely the same manner, which I now proceed 
to describe in detail. 

1:5 grm. of each assay was fused in a silver crucible with 12 
grms. of hydrate of potash, and the mass, which melted quietly, 
was maintained for seven minutes longer in a state of fusion ; hot 
water was then added till the fluid amounted to 20 cubic inches, 
and when cold it was filtered. The filtrate was acidulated with 
hydrochloric acid, then neutralized with ammonia, the precipitate 
allowed to subside, and the liquor poured off; after this, the 
precipitate, which was frequently coloured by manganese, was 
shaken with caustic ammonia and filtered. I had taken somewhat 
more ammonia than would have been required to remove from 
the precipitate an amount of 10 per cent. of tungstic acid. By 


* From the Bulletin of the Academy of Sciences of Munich, Meeting of 
March 10, 1860. Communicated by W.G. Lettsom, Esq. 


416 Prof. F. von Kobell on Dianie Acid. 


this treatment any tungstic or molybdic acids which might have 
caused the reaction described below was got rid of. 

In order to employ in my experiments as equal quantities as 
possible of the precipitates, which must be used when just 
thrown down, I made funnels of tinfoil, which I cut into the 
form of a filter one inch long in the side, and gave them the 
requisite shape in a small por celain funnel. One of these funnels 
was filled with the freshly filtered pasty precipitate by means of 
a spatula, and then laid in a porcelain dish; the tinfoil having 
been opened out, one cubic inch of concentrated hydrochloric 
acid, of the specific gravity of 1:14, was added and heated to 
boiling, that temperature being maintained for three minutes, 
and the foil kept continually well stirred about in the fluid. 
Under this treatment the appearances observed were as follows. 

1. The acid of the tantalite from Kimito, and of the niobite 
from Bodenmais, coloured the liquor bluish (smalt-blue); on 
adding half a cubic inch of water thereto, when poured into a 
glass the colour disappeared rapidly, the precipitate settled 
without being dissolved; on being filtered the liquor gave a 
colourless filtrate, and the precipitate, which at first was of a 
bluish tint, became speedily white on a further addition of water. 

2. The acids of a so-called tantalite from Tammela, the powder 
of which was blackish grey, those of euxenite, zeschynite, and 
samarskite, on being boiled with hydrochloric acid and tinfoil 
as above described, were dissolved to a dark blue cloudy fluid, 
which, when diluted with half a cubic inch of water or rather 
more, became perfectly clear with a deep sapphire-blue colour, and 
gave a transparent deep-blue filtrate. On being further diluted 
by the addition of a twofold or threefold quantity of water, the 
colour becomes indigo-blue and bluish green; and in open 
vessels, after some time, olive-green, maintaining that tint for 
several hours, but becoming paler. The fluid preserves its per- 
fect transparency all the while, and in a closed vessel the colour 
remains unchanged for weeks. 

Both with the assays under (1), and also with those under 
(2), I kept up the boiling for a longer time, indeed till the 
liquors were tolerably concentrated ; I then added half the 
volume of water and poured the whole into a glass. The 
appearances observed were the same as before; the acids of (1) 
remained undissolved and gave a colourless filtrate, while those 
of (2) were dissolved and gave a transparent blue solution, the 
colour of the filtrate being also blue. When treating euxenite 
on one occasion, and conceutrating the liquor by boiling, obtained 
an olive-green fluid, which was, however, transparent; on the 
addition of concentrated hydrochloric acid, and boiling a second 
time with tinfoil, the blue colour was restored. If, on obtaining 


Prof. F. von Kobell on Dianie Acid. 417 


a green fluid of this nature, it is diluted with three times its 
volume of water and then slowly evaporated tillit becomes tur- 
bid, on the addition of a suitable quantity of concentrated hydro- 
chlorie acid and boiling for a few minutes with tinfoil, the blue 
colour of the solution always appears on adding a little water. 

It seems superfluous to say that a transparent blue fluid 
also gives a filtrate of the same colour; and yet the case occurs 
of such a fluid being coloured only from some substance being 
held suspended therein in a state of extreme subdivision, the 
filtrate being colourless. Such, for instance, is the behaviour of 
tungstic acid when it is precipitated from tungstate of potash 
with hydrochloric acid, and the precipitate boiled with con- 
eentrated hydrochloric acid and tinfoil. I obtained thus a dark- 
blue fluid, which, when considerably diluted, was quite trans- 
parent and of a bright sapphire-blue; but both the dark-blue 
and the light-blue diluted fluid gave a colourless filtrate; and 
when left to themselves, both these fluids also became colourless 
when the blue oxide of tungsten suspended therein, and which 
in that condition retains its blue colour, had settled to the 
bottom. 

The tin contained in the blue solution of the acid in question 
is easily got rid of by a stream of sulphuretted hydrogen, and 
the acid is obtained again from the filtrate. by precipitation with 
ammonia. ‘The precipitate, on being boiled with hydrochloric 
acid and tinfoil, again produces the blue fluid. On evaporating 
slowly the liquor filtered from the sulphide of tin (which from 
its diluted state is colourless), it becomes turbid when consider- 
ably concentrated. On adding a little water the cloudiness dis- 
appears, and on the further addition of concentrated hydrochloric 
acid a white precipitate is produced. If the hydrochloric acid 
has been added in suitable quantity, and if the fluid is boiled with 
a slip of tinfoil placed in it, the appearance spoken of above is 
produced. The fluid becomes of a deep blue, and when poured 
into a glass appears turbid; but on the addition of half its 
volume of water it becomes transparent, and presents itself in the 
glass like a clear sapphire. The original precipitate from the 
potash solution may be freed from any manganese it may contain 
by boiling it with a certain-quantity of hydrochloric acid; this 
precipitate can further be boiled with tolerably strong sulphuric 
acid without being deprived of the property of being soluble in 
hydrochloric acid in the presence of tinfoil. The acid thus puri- 
fied is white; on being heated, it assumes a very pale yellow 
colour, which it loses again on cooling, taking somewhat the 
appearance of porcelain. 

Before the blowpipe it is dissolved in borax and salt of phos- 
phorus to a colourless glass, both in the oxidating and the redu- 


Phil, Mag. 8. 4. Vol. 21. No. 142, June 1861, 25 


418 Prof. F. von Kobell on Dianic Acid. 


cing flame. When the borax glass is saturated, it remains trans- 
parent on cooling after exposure to a good heat ; on being warmed 
again it becomes cloudy, and assumes the appearance of enamel. 

When the acid in question is boiled with zinc instead of tin, 
the blue solution is not obtained; the precipitate of the acid is 
blue, it is true, but the filtrate is colourless, and the acid loses its 
colour on the addition of water without being perceptibly dis- 
solved. It was only with a very large quantity of hydrochloric 
acid and zinc that I could obtain a dirty greenish solution, which, 
however, when diluted with half its amount of water, became 
speedily reduced in its colour, assuming a pale green hue with 
opalescence. 

If equal quantities of the acid spoken of, of tantalic acid, and 
of hyponiobic acid, all three bemg measured in a platinum fun- ~ 
nel, are boiled for three minutes with concentrated hydrochloric 
acid without tin in the manner above described, and are then 
poured out into a glass, they all three give yellow milky fluids. 
On the addition of a very moderate quantity of water the acid 
in question becomes perfectly transparent, whereas the tantalic 
acid, and also the hyponiobic acid, even on the addition of four — 
or five times their volume of water, remain undissolved, 

If the metallic acid im question, when freshly precipitated, is 
heated to boiling in diluted sulphuric acid (1 volume of concen- 
trated acid to 5 of water), it forms a cloudy fluid ; and on this being 
poured into a glass with a few grains of distilled zinc, im the course 
of a few minutes the acid, which was previously white, becomes 
of a decided smalt-blue, even deep blue, and retains this colour for 
some time on the addition of water; the filtrate, however, is 
colourless. In this behaviour it resembles hyponiobic acid, whereas 
tantalic acid treated in the same manner is only coloured pale 
blue, which colour immediately disappears on the addition of 
water. The difference in the behaviour of tantalic and hyponiobie 
acids has been already mentioned by HeinrichRose as character- 
istic ; as I modified the experiment, by having recourse to a boil- 
ing temperature, the effect is not only produced more rapidly, 
but also in a more marked manner. I look on this reaction for 
distinguishing tantalic acid from other kindred acids as the most 
certain, that is to say, if one does not wish to investigate the be- 
haviour of the chlorides. For a qualitative testing of an acid of 
this class, the first step of the inquiry would be to precipitate 
it in the manner described from the solution of potash, and then 
to examine the solubility of the freshly obtained precipitate with 
hydrochlorie acid and tinfoil, with due attention to the condi- 
tions above laid down. Should the acid not be dissolved to a blue 
fluid when, after three minutes’ boiling, half a cubic inch or a 
cubic inch of water is added, it is tantalic or hyponiobic acid, and 


Prof. F. von Kobell on Dianic Acid, 419. 


recourse must be had to an assay with sulphuric acid and zinc to 
determine between these two acids. I am at least inclined to think 
that our determinations, as far as correctness is concerned, will 
have as great a probability in their favour as with the other 
methods hitherto employed, which, as is shown by the constantly 
varying indications of the acids of euxenite, yttrotantalite, 
samarskite, &c., have not given any thoroughly reliable results. 

With respect to the acid discovered by me, and which forms a 
blue solution with hydrochloric acid and tin with such remark- 
able facility, it is with certainty and ease distinguishable both 
from tantalic and from hyponiobic acid, and that evidently in 
a more marked manner than those acids mutually are; the me- 
thod of its preparation, moreover, as above set forth, as well 
also as a comparison with kindred acids under closely similar 
circumstances, appear to me to exclude the idea of its being an 
allotropic state, or a not hitherto observed stage of oxidation of 
tantalum or niobium, and to claim for it an existence as a distinct 
acid. Hermann, as is well known, several years since assumed 
the occurrence in samarskite, formerly termed uranotantalite, 
of a peculiar acid which he termed ilmenic acid; he was, how-. 
ever, not enabled to characterize that acid with sufficient pre- 
cision; and Heinrich Rose could at that time establish point by 
point for his own niobic acid, now termed hyponiobic, everything 
that Hermann sought to establish for ilmenic acid, so that at last 
Hermann ranged his acid under niobium, and has pronounced 
it to be a niobous-niobic combination*. That the acid discovered 
by me is an oxide of niobium is, as far as present experience 
-goes, not to be assumed ; for if it were a lower grade of oxidation 
than the hyponiobic acid we are acquainted with, it must, on 
being fused with potash in an open crucible, be converted to 
this hyponiobic acid, inasmuch as, according to Heimrich Rose, 
niobium itself is dissolved into hyponiobate of potash by boiling 
potash ; and if it were a higher oxide than hyponiobic acid, it 
must, on being reduced with tin, be also converted into that 
acid, and consequently neither soluble in hydrochloric acid 
‘under the conditions spoken of, nor impart a blue colour to the 
solution, as is, however, the case. 

The same argument holds good if it be regarded as an oxide 
of tantalum: under the treatment referred to, it must be con- 
verted into the tantalic acid with which we are familiar, and 
must agree with it in its reactions, which it does not. Hein- 
rich Rose has duly established that the metallic acid of the 
tantalite of Bodenmais is distinct from that of certain Finland 
tantalites; and to mark the difference, he called the former 


* According to Hermann, it colours salt of phosphorus dark brown 
before the blowpipe. 5 
2K2 


420 Prof. F. von Kobell on Dianic Acid. 


niobie acid, now termed hyponiobic acid, and has called the. 
mineral formerly designated as tantalite by the name of nio- 
bite. According to my experiments, the same case occurs with 
the acids of the tantalite from Kimito, and of that from Tammela 
which I have examined. I will therefore name the latter, in 
which I first remarked the difference, after Diana, and term it 
Dianie acid; the element I shall name Dianium (D1), and the 
mineral from Tammela which contains this acid, Dianite. 

Besides occurring in the mineral here mentioned, this acid, 
though in a less pure state, appears to occur in the Greenland 
tantalite, im the pyrochlore-from the IlImen Mountains, and in 
the brown Wohlerite (I have not examined the yellow). I could 
only employ small quantities, however, of these minerals, and it 
was not in my power to carry out the requisite investigations in 
sufficient detail. A small fragment of yttrotantalite, professedly 
from Ytterby, gave the reaction of dianic acid; in another assay 
of a specimen, the specific gravity of which I ascertamed to be 
5°5, from the collection of the late Duke of Leuchtenberg, the 
acid proved to be tantalic acid. ‘The former assay refers there- 
fore to a different species, the specific gravity of which I could 
not determine. 

When combinations of this nature contain at the same time 
titanic acid, the latter is found in the residue of the potash-lye, 
in which it can be easily detected even when this residue con- 
tains also a small portion of dianic acid. The residue is boiled 
with concentrated hydrochloric acid and filtered, the filtrate, 
with a strip of tin laid in it, bemg then boiled longer. If no 
dianic acid, but tantalic acid is present, the liquor on becoming 
concentrated assumes a violet-blue colour, which on diluting 
with water is changed very characteristically to pnk. The fluid 
retains this latter colour for several days or longer. When the 
solution, in addition to titanic acid, contains a portion of dianic 
acid as well, the blue colour of the latter predominates ; on di- 
luting it in an open glass, the pink colour due to titanic acid 
makes its appearance in the course of a few hours, owing to the 
colouring of the dianic acid disappearing gradually. In this 
way I recognized the presence of titanic acid (as it had been esta- . 
blished previously by other methods) in sschynite, pyrochlore, | 
and euxenite. 

I cannot of course say whether my dianic acid is contained in 
all varieties, and from all the localities, of the above-named 
species; with respect to the tantalites from Tammela, it is indeed 
established that perhaps the majority of them contain tantalic 
acid. ‘The specific gravity should probably be particularly at- 
tended to. ‘The mineral from Tammela examined by me (dia- 
nite) has a specific gravity of 5°5, while the tantalites from that 


Prof. F. von Kobell on Dianie Acid. 42] 


locality analysed by H. Rose, Weber, Jacobson, Brooke, Wornum, 
and Nordenskiold, had a specific gravity of from 7°38 to 7:5 and 
more. The tantalite from Kimito, moreover, from which I pro- 
cured the tantalic acid employed for my investigation, has a spe- 
cific gravity of 7:06. The colour of the streak of dianite is, as 
before remarked, black-grey, while that of the Tammela tanta- 
lites analysed by Jacobson is stated to be dark brownish red, as 
is also the case with the Kimito tantalite. 

In appearance dianite very closely resembles Finland tanta- 
lites. The assay analysed was taken from a large tabular broken 
crystal about 2 inches in size, on which, however, only two 
planes occur. Their angle of inclination, as measured by the 
hand-goniometer, amounts to about 151°; whether those planes 
are T and R of Naumann’s tantalite, or T and G, or other ones, 
cannot of course be determined. Lefore the blowpipe, dianite 
affords no marked difference when compared with the Kimito 
tantalite. 

The samarskite which I examined is from the IImen Moun- 
tains; I employed quite fresh, pure fragments, with a conchoidal 
fracture and strong, somewhat metallic, vitreous lustre. The 
euxenite is from Alva near Arendal (procured from Dr. Krantz) ; 
the eschynite, from the IImen Mountains, was from the Leuch- 
tenberg collection. 


While preparing the above, I forwarded a portion of the 
dianic acid in question to Professor Heinrich Rose, and communi- 
cated to him the leading points of the paper, requesting his 
opinion on the matter. Professor Rose was so good as to pre- 
pare the chloride of this acid, and wrote to me that, in doing so, 
he had met with a trace of tungstic acid, adding that the re- 
action described by me might be brought about from that cireum- 
stance; and he advised me, as a first step, to purify the acid by 
the method suggested by him, namely, by fusing it with car- 
bonate of soda and sulphur. The case might be similar to the 
one which had misled Hermann. 

Now I had, it is true, established, by the very ready solubility 
of dianic acid in hydrochloric acid when compared with true 
tantalic and hyponiobic acids under similar conditions, a 
characteristic distinction for the first of these three acids; 
but it was none the less essential to prove that the property 
of becoming blue with hydrochloric acid and tin belonged 
to the acid in question, and is not attributable to tungstic acid. 
After the treatment with ammonia, to which reference has been 
made, but little tungstic acid could, it is true, contaminate the 
dianic acid; nevertheless the turning blue might be ascribed to 
that. A plan to clear this pomt up was soon formed. [I first 


422 Prof. F. von Kobell on Dianice Acid. 


sought to impart to the non-colouring tantalic and hyponiobic 
acids the quality of becoming coloured by an addition of tungstic 
acid, and then endeavoured to ascertain how far an acid. thus 
mixed was to be purified by ammonia, the process which I fol- 
lowed in my original experiments. I prepared tungstate of pot- 
ash of a determined strength, and mixed it with a lye of tantalic 
acid in such proportions that 84 parts of tantalic acid were united 
to 16 parts of tungstic acid, corresponding, as it were, to a pot- 
ash solution of a tantalite that consisted of tantalic and tungstic 
acids only. The mixture was divided into two portions. (by 
means of a graduated glass), and precipitated with hydrochloric 
acid. The precipitate of one portion was decanted and filtered, 
and a tinfoil filter, one inch long in the side, being filled there- 
with, it was boiled for three minutes in | cubic inch of hydro- 
chloric acid as described above; 14 cubic inch of water was 
added, and it was filtered. ‘The filtrate was greenish yellow; 
on adding 1 cubic inch more water the fluid was yellowish, the 
precipitate was not dissolved, and after the lapse of twenty- 
four hours the fluid which was poured off deposited a dark blue 
precipitate. The same experiment, performed in the like manner 
with a similar quantity of the hyponiobic acid, gave an olive-green 
filtrate, which did not materially change im twenty-four hours. 
When boiled again it became of a blue colour, which was also 
the hue of the filtrate. The hyponiobic acid was a little dissolved 
in this experiment, as the tantalic acid was in the corresponding 
one. When, however, I agitated the precipitates of the mixed 
acids with ammonia (the approximate quantity required to dis- 
solve the amount of tungstic acid contaied therein having been 
ascertained by experiment), and then allowed them to subside, 
decanted and filtered them, the precipitates thus treated, 
on being boiled for three minutes, as above described, with hy- 
drochloric acid and tinfoil, and diluted with half a cubic inch of 
water, behaved almost entirely like the acids prepared directly 
from the minerals themselves; the fluid of the tantalic acid 
passed through the filter colourless, that of the niobic acid had 
a slight greenish tint. These experiments prove that tantalic 
and hyponiobic acids, even when containing a great amount of 
tungstic acid, may be at least so far purified by ammonia as not 
to produce the deep blue colour given by dianic acid; and fur- 
ther, that the presence of tungstic acid in those acids, under the 
conditions spoken of, does not increase their solubility in hy- 
drochloric acid. The latter circumstance, although to be antici- 
pated, was of more importance to me than the absence of the 
blue colour; for similar experiments to these had already fully 
convinced me that the removal of tungstic acid by means of am- 
monia is not a perfect one. To remove, however, the last doubts 


Prof. F. von Kobell on Dianic Acid. 423 


as to the possible cooperation of the tungstic acid in the produc- 
tion of the blue colour alluded to, the acid of the dianite from 
Tammela was purified with the utmost care by the process sug- 
gested by H. Rose. The filtered acid was dried down till it was 
capable of being readily reduced to powder. I took 0:5 grm, 
of it, which was triturated with 1:5 grm of carbonate of pot- 
ash and then with 0°5 grm. sulphur. I fused the mixture in a 
covered porcelain crucible over a gas-lamp, dissolved the mass 
in water, and after decantation transferred the acid remaining 
into a close glass vessel with sulphuretted hydrogen, which I 
agitated well, leaving it thus for twenty-four hours. The liquor 
was then decanted twice, and the residue boiled with diluted 
hydrochloric acid and well washed ; and lastly, the metallic acid 
was attacked a second time with hydrate of potash in a silver 
crucible, precipitated with hydrochloric acid and filtered. <A tin- 
foil funnel was filled, as above described, with the acid, and a cubic 
inch of concentrated hydrochloric acid having been poured into 
it, the fluid was maintained for three minutes at a boiling tempe- 
rature. Having been poured into a glass, it proved to be deep 
blue and turbid; but on the addition of the necessary quantity 
of water, it afforded a splendid sapphire-blue solution, perfectly 
transparent, -without a trace of undissolved precipitate. There 
is therefore no doubt, not only that by its very marked difference 
of solubility under similar conditions dianic acid is distinguish- 
able from tantalic and hyponiobie acids, but also that the pro- 
perty of producing a blue colour, as above described, belongs to 
‘it essentially, a property which the other acids do not possess. 

I purified in the same way the acid of euxenite and samars- 
kite ; and their behaviour was precisely the same as I observed it 
to be on my endeavouring to remove by agitation with ammonia 
any tungstic acid they might possibly contain. The blue solution 
of dianite and samarskite was of a peculiarly deep colour, almost 
black, so that twice or thrice its volume of water had to be added 
to it to recognize the blue colour distinctly, and to see that the 
solution was perfectly transparent. In a stoppered bottle the 
colour maintained itself quite unaltered for weeks. 

The acid of eschynite I have not purified further than by 
agitation with ammonia; and as in two experiments, independent 
of the blue colour, it proves to be quite as thoroughly soluble as 
the acid of dianite, I have no doubt that it is dianic acid. The 
experiments here described have all been repeated several times, 
particularly those with true tantalic acid, with hyponiobic acid, 
and with the dianic acid of dianite. 

The very peculiar behaviour of dianic acid above described 
with respect to zine as compared with tin, and with hydro- 
chloric acid alone, induced me to make some additional ex- 


A2A Mr. A. Cayley on the Partitions of a Close. 


periments. When the solution obtained by employing a large 
quantity of hydrochloric acid and zine is diluted with about 
thrice its volume of water, it has a dirty yellowish colour, and 
for the moment is tolerably transparent ; in the course of a few 
minutes it becomes turbid and loses its transparency, owing to 
a finely-divided grecnish-grey precipitate which forms after a 
while ; on the addition of more water it is deposited, so that the 
liquor may be decanted. An assay with hydrochloric acid and 
tin shows this deposit to be hydrous dianic acid; for it is dis- 
solved to the characteristic sapphire-blue fluid when treated in 
the way so often referred to. If this blue solution is boiled for 
a few minutes with zine, the dianic acid also is thrown down 
with the tin; the precipitate is deposited with readiness in light 
grey flakes on the zine, which is coated with spongy tin, 
and the supernatant fluid is transparent and colourless, On 
filtering the portion containing the flakes and boiling the 
acid collected with hydrochloric ‘acid and tinfoil, the blue solu- 
tion is obtained again on the addition of a little water. ‘Thus 
the behaviour of the acid of the Tammela dianite and that of 
the acid of samarskite from the Iimen Mountains is strictly iden- 
tical. The behaviour of zine and tin therefore with reference 
to the solutions of dianic acid in question, is, to an extent not 
to be anticipitated, entirely different, it may be said antagonistic. 

Those who wish to repeat the investigations described would 
do well to adhere to the quantities mentioned by me, or to em- 
ploy them proportionally; for without this precaution it 1s possible 
that the properties may not be as distinctly brought out as they 
will be re Spa 8 to them. 


—_————_—_— ————— Wo ———S=S=————. 


LXIIL. On the Partitions ut Closes, iis A. hee LEY, Esq.* 


ie F, 8, E denote the number of faces, summits, and edges of 
a polyhedron, then, by Kuler’s w eH-known theorem, 


F+S=E+2 


and if we imagine the polvhedron ah on the plane of any 
oue face in such manner that the projections of all the summits 
not belonging to the face fall within the face, then we have a 
partitioned polygon, m which, if P denote the number of com- 
ponent polygons, or, say, the number of parts, F=P+41, or we 
have | | 


P+S=E--1, 


where 8 is the number of summits and E the number of edges 
of the plane figure. I retain for convenience the word edge, as 
having a different initial letter from swmmt. 


* Communicated by the Author, 


Mr. A. Cayley on the Partitions of a Close.- — 425 


The formula, however, excludes cases such as that of a polygon 
divided into two parts by means of an interior polygon wholly 
detached from it; and in order to extend it to such cases, the 
formula must be written under the form 

P+S=E+1+B, 
where B is the number of breaks of contour, as will be explained 
in the sequel. 

The edges of a polygon are right lines: it might at first sight 
appear that the theory would not be materially altered by re- 
moving this restriction, and allowing the edges to be curved 
lines; but the fact is that we thus introduce closed figures — 
bounded by two edges, or even by a single edge, or by what [ 
term a mere contour; and we have a new theory, which I call 
that of the Partitions of a Close. 

Several definitions and explanations are required. The words 
line and curve are used indifferently to denote any path which 
ean be described currente calamo without lfting the pen from 
the paper. A closed curve, not cutting or meeting itself *, is 
called a contour. An enclosed space, such that no part of it 
is shut out from any other part of it, or, what is the same 
thing, such that any part can be joined with any other part bya 
line not cutting the boundary, is termed a close. The boundary 
of a close may be considered as the limit of a single contour, or 
of two or more contours lying wholly within the close. The 
reason for speaking of a limit will appear by an example. Con- 
sider a circle, and within it, but wholly detached from it, a figure 
of eight; the space imterior to the circle but exterior to the 
figure of eight is a close: its boundary may be considered as the 
limit of two contours,—the first of them interior to the close, 
and indefinitely near the circle (in this case we might say the 
circle itself) ; the second of them an hour-glass-shaped curve, 
interior to the close (that is, exterior to the figure of eight) and 
indefinitely near to the figure of eight. The figure of eight, as 
being a curve which cuts itself, is not a contour; and in the 
case in question we could not have said that the boundary of the 
close consisted of two contours. A similar instance 1s afforded by 
a circle having within it two circles exterior to each other, 
but connected by a line not cutting or meeting itself; or even 
two points, or, as they may be called, summits, connected by a 
lime not cutting or meeting itself; or, again, a smgle summit: 
im each of these cases the boundary of the close may be con- 
sidered as the limit of two contours. But this explanation once 
given, we may for shortness speak of the close as bounded by a 


* Tt is hardly necessary to add, except in so far as any point whatever 
of the curve may be considered as a poimt where the curve meets itself. 


4.26 Mr. A. Cayley on the Partitions of a Close. 


single contour, or by two or more contours ; and I shall throngh- 
out do so, instead of using the more precise expression of the 
boundary being the limit of a contour, or of two or more contours. 
The excess above unity of the number of the contours which 
form the boundary of a close is the break of contour for such 
close ; in the case of a close bounded by a single contour, the 
break of contour is zero. 

Any point whatever on a curve may be considered as the point 
of meeting of two curves, or, in the case of a closed curve, as the 
point where the curve meets itself, but it is not of necessity so 
considered. A point where a curve cuts or meets itself or any 
other curve, is a summit; each point of termination of an un- 
closed curve is also a summit; any isolated point may be taken 
to be a summit. It follows that, in the case of a closed curve 
not cutting or meeting itself (that is, a contour), any point 
or points on the curve may be taken to be summits; but 
the contour need not have upon it any summit: it is in this case 
termed a mere contour. The curve which is the path from a 
suminit to itself, or to any other summit, is an edge: the former 
case is that of a contour having upon it a single summit, the 
latter that of an edge having, that is, terminated by, two sum- 
mits, and no more. It is hardly necessary to remark that a 
contour having upon it two or more summits consists of the 
same number of edges, and, by what precedes, a contour having 
upon it a single summit is an edge; but it is to be noted that a 
contour without any summit upon it, or mere contour, is noft an 
edge, It may be added that an edge does not cut or meet itself 
or any other edge except at the summit or summits of the edge 
itself. : 

Consider now a close bounded by 8+1 mere contours: if for 
any partitioned close we have P the number of parts, S the 
number of summits, EK the number of edges, B the number 
of breaks of contour; then, for the unpartitioned close, we have 
P=1, S=0, E=0, B= 8, and therefore 


P4+S+@=E+14B; 


and it is to be shown that this equation holds good in whatever 
manner the close is partitioned. The partitionment is effected 
by the addition, in any manner, of summits and mere contours, 
and by drawing edges, any edge from a summit to itself or to 
another summit. The effect of adding a summit is first to in- 
crease S by unity: if the summit added be on a contour, E will 
be thereby increased by unity ; for if the contour is a mere con- 
tour, it is not an edge, but becomes so by the addition of the 
summit ; if it 1s not a mere contour, but has upon it a summit 
or summits, the addition of the summit will increase by unity 


‘Mr. A. Cayley on the Partitions of a Close. 427 


the number of edges of the contour. If, on the other hand, the 
summit added be an isolated one, then the addition of such 
summit causes a break of contour, or B is increased by unity. 
Hence the addition of a summit increases by unity S; and it 
also increases by unity E or else B, that is, it leaves the equation 
undisturbed. The effect of the addition of a mere contour is to 
increase P by unity, and also to increase B by unity: it is easy 
to see that this is the case, whether the new mere contour 
does or does not contain withim it any contour or contours. 
Hence the addition of a mere contour leaves the equation undis- 
turbed. The effect of drawing an edge is first to increase E by 
unity; if the edge is drawn from a summit to itself, or from a 
summit on a contour to another summit on the same contour, 
then the effect is also to increase P by unity; if, however, the 
edge is drawn from a summit on a contour to a summit ona 
different contour, then P remains unaltered, but B is diminished 
by unity. There are a few special cases, which, although appa- 
rently different, are really included in the two preceding ones: 
thus, if the edge be drawn to connect two isolated summits, 
these are in fact to be considered as summits belonging to two 
distinct contours, and the like when a summit on a contour is 
joined to an isolated summit. And so if there be two or more 
summits connected together in order, and a new edge is drawn 
connecting the first and last of them, this is the same as when 
the edge is drawn through two summits of the same contour. 
The effect of drawing a new edge is thus to increase EK by unity, 
and also to increase P by unity, or else to diminish B by unity ; 
that is, it leaves the equation undisturbed. Hence the equation 
P+8+8=E+1-+B, which subsists for the unpartitioned close, 
continues to subsist in whatever manner the close is partitioned, 
or it is always true. 

In particular, if 8=0, that is, if the original close be bounded 
by a mere contour, P+S=H+1+B; and if, besides, B=O, 
. then P+S=E+1, which is the ordinary equation in the theory 
of the partitions of a polygon. 

If we consider the surface of a plane as bounded by a mere 
contour at infinity, then for the infinite plane, @=0, or we have 
P+S=EH+1+B: in the case where the infinite plane is parti- 
tioned by a mere contour, P=2, S=0, E=0, B=1 (for the 
exterior part is bounded by the contour at infinity, and the par- 
titioning contour, that is, for it, B=1), and the equation is thus 
satisfied. And so for a contour having upon it 2 summits, 
P=2, S=n, E=n, B=1, and the equation is still satisfied: 
this is the case of the plane partitioned into two parts by means 
of a single polygon. 

The case of a spherical surface is very interesting: the entire 


428 Prof. Chapman on the Drift Deposits 


surface of the sphere must be considered as a close bounded by 
0 contour, or we have have 8=—1, and the equation thus be- 
comes P+S=H+2+B8B. ‘Thus, if the sphere be divided into 
two parts by a mere contour, P=2, S=0, E=0, B=0O, and 
the equation is satisfied. And in general, when B=O, then 
P+S=E+2; or writing F for P, then F+S=E+42, which is 
Kuler’s equation for a polyhedron. 
2 Stone Buildings, W.C., 
March 8, 1861. 


LXIV. Some Notes on the Drift Deposits of Western Canada, and 
on the Ancient Extension of the Lake Area of that Region. By 
Ei. J. Cuapman, Professor of Mineralogy and Geology in Uni- 
versity College, Toronto*. 


i ie following notes and deductions are the result of a 

careful examination of the Drift deposits of Western 
Canada, undertaken during the last three or four summers in an 
unsuccessful search for marine post-tertiary fossils, such as occur 
so abundantly in many parts of Kastern Canada and throughout 
the New England States. The district more especially investi- 
gated extends from the Bay of Quinté westward to the mouth of 
the Saugeen on Lake Huron, and includes the lime of country 
lying along, and immediately within, the outcrop of the Lauren- 
tian rocks north of that region. Detached observations have 
been made, moreover, at various points on the islands and north 
shore of Lake Huron; and also beyond the limits of the province, 
as in the district south of Lake Ontario, in Michigan, and along 
the southern shore of Lake Superior. 

The notes recorded here are arranged under two sections, of 
which the first comprises a collection of data, and the second a 
corresponding series of deductions. 


§ 1. Data. 


1. The first point observable, with regard to our Drift deposits, 
is the very evident fact that the rock floor on which these accu- 
mulations are spread had been extensively denuded prior to their 
deposition upon it. They cover thus an undulating and more 
or less broken surface ; and their thickness, consequently, apart 
from the denudation to which they have been themselves sub- 
jected, 1s exceedingly variable. 

2. The lowest of these deposits appear to consist of dark-blue or 
greyish clays, with thin layers of yellowish or light-coloured clay 


* Communicated by the Author, 


of Western Canada. 429 


in places. This deposit is often laminated horizontally, and is 
generally very calcareous. It appears also to be free from north- 
ern or large crystalline boulders. Pebbles of limestone and other 
fossiliferous rock, mixed with some small pebbles of water-worn 
gneiss, occur abundantly in it in many localities; but northern 
boulders, properly so called, are either absent or exceedingly rare. 
Amongst the localities in which these lower and boulder-free clay 
deposits are of marked occurrence, the district around Toronto 
and many parts of the valley of the Saugeen and western shores 
of Lake Huron may be especially mentioned ; but wherever our 
Drift deposits are found to consist of clay and other materials, 
the clay-beds are almost invariably seen to occupy the lower 
place. At the same time, as described more fully in the sequel, 
beds of yellow and other-coloured clay, it should be observed, 
are occasionally found with northern boulders in a higher part of 
the series; but these are quite distinct from the lower clays now 
referred to. They are, moreover, of no great thickness, but 
alternate with, and are subordinate to, thick deposits of gravel 
and sand ; whereas the lower clays attain in places to a thickness 
of over 100 feet, and present a general uniformity throughout. 
In these latter beds no traces of contemporaneous fossils have as 
yet been found. 

3. It is generally assumed as an established fact, that the 
harder rocks beneath the Drift exhibit everywhere the marks of 
glacial action. Although we have numerous examples, through- 
out this section of the province, of polished and striated rock, I 
believe it to be still an open question as to whether the rocks 
which underlie these lower clays have been thus affected. I have 
not been able to discover any imstances of it, nor can I find any 
recorded cases in our Geological Reports, or in other trustworthy 
sources. The question hitherto does riot seem to have been 
mooted, the Drift accumulations generally being classed together 
by most observers under one common term. As the point is of 
much interest, however, it should be kept in view. 

4. Above the lower clay deposits, or resting immediately (where 
these are absent) on the foundation rock of the country, we meet 
with a series of sands and gravels of evidently northern origin, 
containing boulders of gneissoid and other rock, and alternating 
occasionally with beds of clay, in which northern boulders are 
also frequently found. ‘This clay, with scarcely an exception, is 
remarkably free from calcareous matter, the cause of which will 
be alluded to further on. In some places the clay and gravel 
are mixed up together, and present no signs of stratification ; but 
more usually they are distinctly stratified, and the boulders are 
mostly accumulated towards the upper part of the series Asa 
general rule, indeed, the boulders occur in by far the greatest 


430 Prof. Chapman on the Drift Deposits 


abundance, scattered, per se, over the surface of the gravels, or 
resting immediately on the underlying rocks where the clays and 
gravels are absent. This appears to have arisen in some cases 
from the subsequent removal or washing away of the looser 
materials in which the boulders were originally imbedded ; but 
the greater number of these were evidently thrown down where 
they now lie, by melting or stranded icebergs, after the deposition 
of the other Drift materials. The boulders, whether of gneissoid 
or other fossiliferous rock, belong always to northern localities 
in relation to the spots on which they now occur. Here 
and there the infiltration of water containing bicarbonate of lime 
has cemented some of these upper Drift deposits into conglome- 
rates of considerable solidity (Burlmgton Heights; vicinity of 
Niagara Falls; Georgetown, &c.). i 

5. Under the gravels and sands, or where the isolated boul- 
ders of this series are found, the rocks are always more or less 
marked by glacial action. The more common effects comprise a 
smoothed and polished surface, and a fine striation, the striz 
running in long straight lines in a general N.E. and 8S. W. direc- 
tion, although following to a certain extent, in hilly and broken 
districts, the natural windings of the rock-slopes on which they 
occur. These effects are seen in Western Canada, at various 
heights above the sea-level, up to an elevation of at least 1500 
feet. They are well shown on the top of the Collingwood es- 
carpment, at about 1000 feet above the level of Lake Huron; on 
the same line of escarpment near Niagara Falls ; on many of the 
rock-exposures on the north shore of Lake Huron ; and through- 
out the country at the junction of the Laurentian and Silurian 
formations, between the river Severn and the County of Fron- 
_tenac ; also in the vicinity of Belleville, Trenton*, &c. 

The isolated boulders scattered over the country frequently 
exhibit in themselves a polished and striated surface; and the 
small boulders and pebbles imbedded in the gravel deposits often 
present the same effects (e.g. the pebbles found in the terraces 
north of Toronto; also those in Drift gravel in the environs of 
Belleville, Marmora, Guelph, Niagara Falls}, &c.). 

6. The gravel and sand beds of this series occur in places in 
oblique stratification, or exhibit what is technically termed “ false 
bedding.” This occurs at or near the upper part of the series, 
and is evidently due to a rearrangement of the materials by the 
action of currents (e. g. Drift-bank seen in Great Western Rail- 


* See a paper, by the writer, ‘‘On the Geology of Belleville and its En- 
virons,”’ in the ‘ Canadian Journal,’ vol. v. (new series), pp. 41-48. 

+ The localities cited in this paper are those which have come more im~ 
mediately under the author’s observation. In most instances the lists 
given might be greatly added to. 


of Western Canada. ~ 431 


way cutting at Toronto, and extending westward several miles ; 
beds at Orillia, on Lake Couchiching ; also near Collingwood, &c. 
A remarkable example, alluded to more fully in the second part 
of this paper, Deduction 3, occurs near the village of Lewiston, 
on the south shore of Lake Ontario). I think it will be rendered 
clear, by what follows, that the currents in question were not 
marine, but were produced in the lake waters when these stood 
at higher levels. In places, moreover, secondary ridges, or ancient 
spits, have been formed by the same action out of these drift 
materials (e. g. Ridge at Weston, near Toronto, described by 
Sandford Fleming, C.E., in the Canadian Journal, new series, 
vol. vi.; also the ridge at Craigleith, in Collingwood Township, 
mentioned by the writer in the same Journal, vol. v. p. 305). 
These secondary ridges, it should be observed, are altogether 
distinct from the terraces of the lake shores and intervening di- 
stricts. A careful search would no doubt reveal their presence 
in very many localities. 

7. We now come to a fact of great interest—the occurrence 
of shells of freshwater mollusca in the sands and gravels of 
these Drift deposits, at various levels above the present surface 
of our lakes. These shells belong to existing species, inhabitants 
of the surrounding waters. They must not be confounded with 
similar shells left in elevated spots by the drying up of streams 
and ponds, or by the cutting back and lowering of river-beds. As 
occurring in our modified Drift deposits, they are imbedded in 
sand or gravel containing northern pebbles and small boulders; 
and in situations, moreover, in which it is evident that no merely 
local causes could have been concerned in their deposition. The 
fragility of most freshwater shells necessarily operates against 
the preservation of these in the coarser sediments, and explains 
their absence, probably, as regards the upper Drift beds of many 
localities. 

In some of these re-sorted beds the bones and teeth of both 
extinct and existing mammals are occasionally found. The ex- 
tinct forms comprise a species of Mastodon (M. Ohioticus? see 
Canadian Journal, new series, vol. ii. p. 856), the Elephas pri- 
migenius, and apparently an extinct species of the Horse. The 
remains of existing species found in these deposits (always con- 
fining our remarks to Western Canada) include the Wapiti, the 
Moose, Beaver, Musk-rat, &c. These two classes of remains 
have been found together. In a railway-cutting through Bur- 
lington Heights near Hamilton, the tusk of a Mammoth (Elephas 
primigenius) and the horns of a Wapiti (Elaphus Canadensis) were . ° 
met with at a depth of about forty feet below the present surface 
of the ground. I have also seen the lower jaw of a Beaver 
(Castor fiber) obtained from the same locality. The flint arrow- 


a 


432 Prof. Chapman on the Drift Deposits 


heads and other wrought implements of Amiens and Abbeville, 
occur apparently in deposits of the same kind and age. 

I have discovered freshwater shells, under the conditions de- 
scribed above, in beds of stratified Drift consisting of coarse 
gravel filled with pebbles of gneiss and other northern rocks, on 
the Kingston road, about two miles east of Belleville, at an ele- 
vation, by rough measurement, of about 40 feet above the pre- 
sent level of Lake Ontario. These belong to Planorbis trivolvis, 
or to some closely related species. Other examples of the same 
shell were obtained from fine gravel in oblique stratification, near 
the village of Orillia, at a height of about 18 feet above the level 
of Lake Couchiching. This lake is about 120 feet higher than 
Lake Huron, and about 700 feet above the sea. Pieces of na- 
creous shell (belonging to a species of Unio?) were also found 
in gravel, in the vicinity of Barrie, at an estimated height of 
about 30 feet above Lake Simcoe. I have found lacustrine and 
terrestrial shells in many other places; but these I omit from men- 
tion, as the shells occurred on the sites of ancient swamps, in 
gullies, or in flat lands adjacent to running streams, or in other 
doubtful situations in which they may have been deposited by 
freshets and other agencies of comparatively recent date. 

Mr. R. Bell, of the Geological Survey of Canada, has added 
greatly to our knowledge of the above localities, in a paper pub- 
lished in the ‘Canadian Naturalist’ for February of this year 
(1861). Amongst other spots in which he has discovered fresh- 
water shells, the environs of Collingwood and Owen Sound may 
be cited. At the former, examples of Planorbis trivolvis, asso- 
ciated with several species of Helix, were found by him at an ele- 
vation of 78 feet above Lake Huron. Specimens of Melania 
conica have been obtained, according to Mr. Bell, from another 
spot in this locality. Dr. Benjamin Workman of Toronto, has 
also communicated the discovery of examples of a Melania and 
Unio ellipsis, on the high banks of the Don, about 30 feet above 
the lake. These may have been deposited by the river, however, 
when flowing at a higher level; but they were covered, accord- 
ing to Dr. Workman, by a considerable deposit of sand. 

The upper deposits of the Drift period are separable with 
difficulty in many places from those of more recent age. As the 
one period merged gradually into the other, this must necessarily 
be the case. Among the more recent deposits of Western Canada, 
however, our river “ flats”” may be more especially cited, as those 
of the Grand River, filled with the remains of land mollusea. 
Also, the closely-similar deposits of the ancient bed of the 
Niagara, so high above the present level of that river; together 
with the shell-marls and. calcareous tufas of our lakes and 
streams ; and our deposits of bog-iron ore and iron ochres, 


of Western Canada. 438 


§ 2. Deductions. 


The following deductions appear to flow naturally from the 
observations recorded above :— 

1. A general depression of the land, at the commencement of 
the Drift period, must have taken place to such an extent as to 
admit of the deposition of the lower clays. These latter were 
evidently derived from the limestones and other Silurian and 
Devonian strata lying beneath and around them. Hence their 
generally calcareous nature. Their derivation from this source 
is proved, moreover, by the pebbles of Trenton limestone and 
other fossiliferous rocks which they frequently contain. Exten- 
sive denudation must thus have occurred both immediately prior 
to and during the deposition of these clays; but it may be 
questioned whether the bolder contours offered by the denuded 
rocks, such as the escarpment that sweeps from the Niagara 
river to Cabot’s Head on Lake Huron, were not produced during 
the first uprise of the palzeozoic strata from the earlier seas in 
which their materials were accumulated, ages before the period 
now under discussion. It appears, at least, to be a well-admitted 
point, that these rocks had been elevated into dry land before 
the deposition of the higher formations in the south and west. 

2. After the deposition of the lower Drift clays, a sudden and. 
abrupt change in the character of the sediments took place. A 
striking example of this may be seen in the natural sections 
about Hoge’s Hollow, a few miles north of Toronto. The 
change in question must have been effected by a still further de- 
pression of the country, bringing the higher lands and gneissoid 
strata of the north within the influence of the waves, and yielding 
the sands, gravels, and boulders of the upper Drift accumulations. 

This depression permitted an invasion and broad extension 
southwards of the ice-covered Arctic seas, the trve cause, in all 
probability, of the cold of this epoch. ‘The depression must have 
exceeded 1500 feet, since northern boulders are found at that 
height above the sea on the Collingwood escarpment. The 
eneissoid boulders there met with must at least have traversed 
the basin of Georgian Bay; but the glacial strize which also occur 
there may have been produced by the action of ice origina- 
ting at the spot itself: the three or four distinct sets of strize 
observed at this locality, however, do not radiate from any fixed 
point, but run in the usual north and sonth direction, some being 
a little east and others a little west of north*. 

3. At the close of this second series of phenomena, a gradual 


* On a visit to this spot, since the publication of the “ Note on the Geo- 
logy of the Blue Mountain Escarpment” in the ‘Canadian Journal,’ vol. v. 
p. 304, some additional sets of striz were observed. 


Phil, Mag.8. 4. Vol. 21. No, 142. June 1861. our 


434: On the Drift Deposits of Western Canada. 


uprise of the land appears to have taken place, and a vast area, 
extending over and around our present lake-basins, then became 
converted into a freshwater sea. This probably found its out- 
let to the ocean through what is now the broad valley of the 
Mississippi. Its waters stood at a great elevation above the 
waters of our present lakes, and were gradually lowered to these 
levels by physical changes in the surrounding country, and more 
especially by the depression of a higher region lying to the east. 
During this gradual fall and retrocession of the great lake-waters, 
the upper layers of the Drift were re-sorted, mixed with newer 
sediments, and thrown up here and there into secondary ridges ; 
and the remarkable terraces which form so salient a feature in 
the general aspect of our lake shores and intervening districts, 
were then in chief part produced. The escarped faces of these 
Drift terraces, it should be observed, always front the present lake- 
basins, and thus look in some places towards the north, and in 
others towards the south, &c., according to the direction of the 
nearest shores. This would necessarily arise if they were pro- 
duced, as here imagined, by a gradual lowering of the waters, 
with intervening periods of repose. The shells of freshwater 
mollusca buried in the modified Drift, at various levels above 
the existing lake-waters, and in localities so far apart—for these 
shells have been found throughout the region south of the lakes, 
in addition to the localities mentioned in this paper—prove in- 
contestably the former expansion and union of our lakes, or, in 
other words, the presence in this part of Western America, of a 
widely-extended freshwater sea covering an enormous area. A 
curious circumstance, and one of great significance in its bear- 
ings on this question, is the fact that all the inclined layers of 
modified Drift (to the east, at least, of Lake Superior) appear to 
slope towards the west or south. A remarkable instance of this, 
hitherto, it is believed, unnoticed, may be seen near the mouth 
of the Niagara river, at Lewiston. At this spot, oblique layers 
of modified Drift, in beds made up of coarse gravel and pebbles, 
point nearly due south, and thus bear witness to the fact that 
the current which occasioned the inclined stratification must 
have set directly up the gorge, or against the direction of the 
present stream. 

The assumption of an immense freshwater lake of this cha- 
racter gradually falling from a high level, necessarily involves 
the additional assumption of an eastern barrier, extending at 
one period between the lake-waters and the Atlantic. This view 
was maintained bysome of the earlier investigators of our geology, 
and notably by Mr. Roy, in his well-known paper on the ter- 
races of Lake Ontario, communicated to the Geological Society 


of London in 1837. The difficulty of finding a satisfactory loca- 


On the Neutralization of Colour in mixtures of certain Salts, 485 


tion for a barrier of this kind led Sir Charles Lyell, however, to 
reject the idea of an original lake extension, and to refer the 
formation of our terraces entirely to the action of the sea during 
the slow uprise of the land at the commencement of the present 
epoch. In this he has been followed by all geologists who have 
subsequently examined these terraces. The difficulty may per- 
haps be surmounted by assuming the earlier and greater eleva- 
tion of that portion of the country lying to the east of the gneis- 
soid belt which connects our northern Laurentian district with 
the Adirondack Mountains of New York. The subsequent de- 
pression of this region would open an eastern outlet to the lake- 
waters, and gradually lower these to their present levels. But 
whatever the explanation, the undoubted fact remains, that, at 
the close of the Drift period, a vast freshwater sea extended over 
the greater portion of Western Canada, and at a level of at least 
500 feet above the present surface of Lake Ontario. 

Whilst the mollusca of this ancient lake were identical with 
existing species, its shores were peopled by the mastodon and 
mammoth, and probably by other extinct forms of life, together 
with various species that still survive. A great question remains 
to be solved. Our gravel beds may perhaps reply to this, and 
reveal to us that here, as in Europe, man and the departed mam- 
moth once trod the earth together. Could this be established, 
the discovery would be fraught with even deeper interest than 
that which attaches itself to exhumed human relics of the ancient 
plains of Picardy and the gravel-beds of Suffolk. Our Indian 
arrow-heads are disentombed by hundreds: the connecting link 
of the extinct tooth or bone may not be long forthcoming*. 


University College, Toronto, Canada. 
March 16, 1861. 


LXV. On the Neutralization of Colour in the mixtures of Solu- 
tions of certain Salts. By Freprrick Fizrp, F.R.S.E.F 


BELIEVE Maumené first pointed out the fact that when 
nitrate of cobalt is added to nitrate of nickel in certain pro- 
portions, the green and pink colours of the solution entirely dis- 
appear, and the liquid becomes colourless, or assumes merely a 
pale neutral tint. ver since the manufacture of the oxides of 


* Since writing the above, Albert Koch’s account of the discovery of the 
Missouri mastodon has come under the author’s notice. In this account, 
published in 1841, it is stated that the mastodon bones were found in more 
or less immediate association with large arrow-heads. The same writer 
also attests to the discovery of wrought implements in connexion with 
Edentate remains in Gasconade county, Missouri. 


+ Communicated by the Author. 
22 


436 Mr. F. Field on the Neutralization of Colour 


nickel and cobalt from the ordinary speiss by the wet method, 
earried on for many years in Birmingham, this phenomenon 
must have been observed by those employed in conducting the 
process ; and to one ignorant of the fact, and who has devoted 
but little time to this particular branch of chemical analysis, the 
solution of speiss must appear rather surprising, as, although very 
rich both in cobalt and nickel, in certain instances the solution 
appears almost destitute of colour, showing no trace either of the 
red of the cobalt or the green of the nickel. Professor Liebig 
(Liebig’s Annalen, vol. xe. p. 112, and Chemical Gazette, vol. xii. 
p- 300), in remarking upon the decolorizing action of binoxide of 
manganese upon glass, does not impute the bleaching effect to 
the oxidation of the protoxide of iron by the reduction of the bin- 
oxide, as neither nitrate of potash nor other strongly oxidizing 
bodies effect the same change, but to the violet colour imparted 
to the glass by the manganese being complementary to the green 
produced by the iron, and hence the two affording a colourless 
mass. And that this is the case is evident, I imagine; for if 
borax be coloured by protoxide of iron, the resulting glass fused 
in a platinum crucible, and a little of the same salt (previously 
coloured by manganese) cautiously added, a point is arrived at 
where the mixture of the two has lost the individual tint of each 
and produced a nearly colourless glass. Liebig also mentions 
that a concentrated solution of sulphate of manganese having a 
slight rose colour, added to a solution of protosulphate of iron 
having a pale green tint, affords a perfectly colourless mixture. 

A few experiments of my own have been extended to some 
other solutions and chemical compounds. 

When nitrate of cobalt is gradually added to a cold solution of 
bicarbonate of soda, a beautiful amethyst-coloured liquid, at times 
almost approaching to violet, is produced. The colour has not 
the pure rose-red of the nitrate or sulphate of the metal, but 
has evidently a considerable portion of blue in its composition. 
If the fluid thus formed be divided into two equal parts, and to 
one of these a few drops of hypochlorite of soda be added, the 
liquid changes to an intense green colour, with no trace of blue, 
but a slightly yellow tinge, very much the colour of chloride of 
copper when dissolved in : strong hydrochloric acid. If the violet 
and green liquids are united, the mixture becomes colourless, more 
strikingly so perhaps than by the union of the cobalt and nickel 
salts: the blue tint in the bicarbonate of cobalt forms green with 
the slight yellow shade of the peroxidized compound; and this, 
together with the remaining green of that liquid, is entirely neu- 
tralized by the pure rose colour. 

Dilute sulphate of nickel (pale green) dissolves erystallized 
sulphate of manganese (pink), forming a colourless solution. 


in the miztures of Solutions of certain Salts. 437 


A solution of permanganate of potash evidently contains two 
colours, red and blue, forming by their union the magnificent 
violet tint so characteristic of that salt. When a little chloride 
of sodium is added to a solution of sulphate of copper, chloride 
of copper is formed by double decomposition, and the liquid as- 
sumes a pure green colour. Permanganate of potash carefully 
added to this compound changes it to a fine bright blue. The 
red tint is neutralized by the green, and the visible blue remains. 
The experiment can also be performed by substituting the chlo- 
ride of copper for the sulphate. When the chloride, free from 
acid, is dissolved in water, the solution has a pale blue tint, and 
the addition of one drop of the permanganate causes a very dark 
blue shade. Ifa little acid be introduced into the copper salt, 
and the permanganate added as before, a similar effect is pro- 
duced, but in about half an hour the pure blue disappears and 
the solution becomes green. The acid in this instance first 
changes the blue colour of the chloride into green, and subse- 
quently decomposes the permanganate, and thus by destroying 
the red which was neutralized by the green, as well as the blue 
which remained intact, the original green tint becomes apparent. 

When permanganate of potash is cautiously added to a solu- 
tion of the bichromate of the same base, a bright-red liquid is 
produced. The solutions, however, must be dilute, and carefully 
managed. ‘The yellow in the bichromate forms a green with 
the blue in the permanganate, which, neutralized by the red in 
both salts, would form a colourless solution, did not an excess of 
the latter tint prevail. 

Most chemists must have observed that, in the estimation of 
iron by means of permanganate of potash, the last drop, which 
shows that the reaction is complete, imparts a rose-red to the 
liquid, differing somewhat from the bluish pink of the perman- 
ganate. ‘The pale yellow of the perchloride of iron has combined 
with the blue of the permanganate, and the resulting green, not 
sufficiently powerful to destroy the whole of the red, has left a 
portion of it visible. 

M. Terreil estimates copper by the same reagent. The cu- 
preous salt is deoxidized by sulphite of ammonia, the sulphurous 
acid expelied by ebullition, and permanganate of potash added 
until the whole is converted into the protoxide. ‘The difference 
of tint which the last drop of permanganate imparts to this liquid 
and to that containing the iron salt, is very apparent. In the 
case of the copper solution it is nearly blue; in the iron, pinkish 
red. These facts are not without their significance in qualitative 
analysis. Gibbs* informs us that the beautiful test for manga- 
nese, first proposed by Mr. Walter Crum, by the action of nitric 

* Silliman’s Journal, September 1852. 


438 M. H. Fizeau on several Phenomena 


acid and peroxide of lead, fails to yield the characteristic tint if 
nickel be present in large quantity, and the manganese only in 
minute traces: the nickel salt destroys, or at all events modifies 
the colour produced by the formation of permanganic acid. If 
cobalt is present, however, or a solution of a salt of that metal 
is subsequently added, the colour of the nickel is nullified, and 
that of the manganese becomes sensible. 

When red fire, composed of nitrate of strontia, chlorate of 
potash, &c., 1s mixed with green fire containing nitrate of baryta 
and ignited, the red and green rays become invisible, and a white, 
or, rather, a bluish-white flame is produced: the crimson of the 
strontian flame has a dash of blue in its composition, and the 
red being removed by the green, is clearly shown. If a rose-red 
fire be prepared by mixing thirty-four parts of carbonate of lime, 
fifty-two of chlorate of potassa, and fourteen of sulphur, or still 
better, perhaps, twenty-three of dry chloride of calcium, sixty- 
one of chlorate of potassa, and sixteen of sulphur, and then 
ignited with the ordinary green fire, pure white light is produced. 


LXVI. Researches on several Phenomena connected with the Po- 
larization of Light. By M.H. Fizpavu*. 


| i has long been observed that when a ray of light is received 
on a mirror whose surface, instead of being perfectly smooth, 
is scratched with a fine point, it is no longer simply reflected. 
Part indeed follows the ordinary course, but a considerable por- 
tion is dispersed in various directions, some of which deviate 
greatly from that of the regularly reflected ray. We may men- 
tion as an example of this species of phenomenon, the singular 
reflexions produced by surfaces of metal, such as brass and steel, 
&c., which have been artificially prepared by beg rubbed con- 
tinually in one direction with emery, the hard angular particles 
of which produce fine parallel scratches on the surface of the 
metal. The amount of light dispersed by surfaces so prepared, 
in directions other than that of the regularly reflected ray, is cal- 
culated to excite some surprise; and it is generally agreed to 
attribute this effect partly to the variously inclined surfaces of 
the minute furrows with which the mirror is covered, partly to 
the diffraction caused by them in conjunction, acting as an irre- 
gular grating, and producing at the same time, and mingled 
with each other, the phenomena observed by Fraunhofer with 
simple gratings of various structure. 

In studying the light dispersed in this manner with respect to 


* Translated from the Comptes Rendus for February 18, 1861, by F. 
Guthrie. . 


connected with the Polarization of Light. 439 


its polarization, I have observed several unexpected and, as I 
believe, hitherto unnoticed phenomena, which appear worthy of 
the attention of some of the learned members of the Academy, 
to whom [ hasten to communicate them. 

Many observers, among whom I may mention Fraunhofer, 
Sir D. Brewster, Foreign Associate of the Academy, and more 
recently Messrs. Stokes, Holtzmann, and Lorenz, have remarked 
certain phenomena of polarization in the light emitted by regular 
gratings. These phenomena, however, seem to be entirely di- 
stinct from those I am about to communicate. 

On a plate of metal, say of silver, perfectly flat and polished, 
suppose a straight line to be drawn with a fine steel or dia- 
mond point, the surface of the metal being disturbed as little 
as possible, and the line so traced becoming finer and finer by 
degrees towards one end until it becomes imperceptible. If the 
plate on which the line has been so drawn be illuminated very 
obliquely, and in a direction perpendicular to the line, the latter 
will be visible in every position comprised in the common plane 
of incidence and reflexion, except its thin end, which, from its 
great tenuity, will be imperceptible. If the plate, illuminated 
in the same manner, be placed in the field of a microscope, a 
much larger portion of the thin end of the line will be visible, 
the amount depending on the power of the lenses employed. 

Under these circumstances, the plate being viewed perpendi- 
eularly to its surface, if a doubly-refracting analysing prism be 
placed between the eye and the eyepiece of the microscope, the 
different intensity of the ordinary and extraordinary images at 
once indicates that the lhght emitted by the brilliant line thus 
drawn is more or less polarized,—the amount of polarization 
being greatest towards the fine end of the line, and the plane of 
polarization being parallel to the direction of the line. Lines 
produced in various ways were observed, and, provided they were 
sufficiently fine, always with the same result. 

It was observed, moreover, that the plane of polarization, which 
was always parallel to the lines at their thinnest extremities, was 
perpendicular to them where they were a little broader, and 
became altogether imperceptible towards their thicker ends. 

On varying the angle of incidence of the light on the plate 
and the angle at which the line was viewed, which could be done 
within certain limits, depending on the shape of the microscope, 
by inclining the plate and shifting the position of the source of 
light, certain changes were observed in these phenomena, of 
which the following are the principal. 

The plate being still observed normally, if the line be illumi- 
nated less and less obliquely, the source of light being brought 
nearer to the eyepiece of the microscope, the amount of polari- 
zation rapidly decreases and soon becomes insensible. 


440 M. H. Fizeau on several Phenomena 


If the plate be illuminated perpendicularly, but observed very 
obliquely though perpendicularly to the line, the phenomena are 
the same as in the first case, the hight reflected from the finest 
extremity of the line being stall polarized in the direction of the 
line itself. 

If the plate be kept in the same position as in the last case, 
but the source of light be brought nearer to the eyepiece, so that 
the plate is both observed and illuminated obliquely and nearly 
in the same direction, the polarization of the bright line is much 
increased, not only the fine end polarizing the hght parallel to 
itself, but the same species of polarization being observed towards 
the thicker part of the hne where the light was formerly polarized 
in the opposite direction, and even where the light was previously 
unaffected. 

The distinct polarizing power of single lines traced on a silver 
surface having been thus demonstrated, it was easily foreseen that 
the same property would be possessed by the innumerable striz 
produced on metallic surfaces by rubbing them with a body 
covered with some hard substance reduced to a fine powder; and 
it was anticipated that the large number of these lines would 
compensate for the want of brilliancy in each individually, so 
that the phenomena would be visible without the need of a 
microscope. 

On a silver surface, a straight striated band about 2 
centims. broad was accordingly traced by means of a ruler and 
a piece of cork charged with emery*. ‘The striated band thus 
produced exhibits in the most striking manner, on account of 
the intensity of the light reflected, the phenomena of polariza- 
tion before observed in the case of single lines. 

If the striated band be placed under the microscope and illu- 
minated obliquely, innumerable lines are observed of different 
degrees of brightness and of various colours, due no doubt to 
accidental phenomena of diffraction and interference: nearly all 
these lines polarize the light in their own direction, some of the 
thicker ones, however, produce the opposite effect. 

If the striated band, mstead of being straight, is in the form 
of an arc of acircle of about 50 centims. radius, and if the 
surface of the plate be horizontal, and the source of light be 
placed vertically above the centre of the band, at such a distance 
from the plate that the incident light may make an angle of 
from 60 to 80 degrees with the normal, then, the eye being 
placed behind the source of light a little on one side, and being 


* Emery powder, No. 40 of the opticians, answers very well for these 
experiments, the mean diameter of its particles being about 5}5 millim. 
Emery powder No. 20, ordivary Tripoli, or English red may also be em- 

] 
ployed. 


connected with the Polarization of Light. 441 


shaded from the direct rays by means of a small screen, the 
striated band will appear illuminated throughout the entire are, 
and the reflected light may be observed directly by means of an 
analyser, which causes it to appear alternately more or less bright. 

The polarization thus produced does not seem to depend on 
the nature of the metal of which the plate is formed. Gold, 
platinum, copper, steel, brass, speculum metal, aluminium, tin, 
&c., have been substituted for silver; and all these metals, when 
suitably striated, have presented the same phenomena without 
sensible difference, except with regard to the colour of the light 
polarized by reflexion. 

Metals which themselves possess least colour, give reflexions 
tinged with yellow, which, when most oblique, become bronze ; 
while in the case of metals that have a marked colour of their 
own, the reflexions possess the same tinge, and sometimes,-indeed, 
in a striking degree, as 1s the case with copper and gold. 

I should mention here that the striated bands on silver and 
copper and some other metals are very brilliant when they have 
recently been made, but that they diminish in intensity on 
account of the action of the vapours accidentally present in the 
atmosphere. Gold and platinum are of course exempt from this 
inconvenience. 

Non-metallic substances present similar phenomena, but 
their reflexions are so dull that the observation is often un- 
certain. Polarization parallel to the lines has nevertheless been 
clearly observed with a plate of specular iron and with one of 
obsidian, both of which I owe to the kindness of M. de Senar- 
mont. With some precautions the phenomenon may even be 
observed with a plate of glass. 

Finally, the groups of lines on silver and copper surfaces have 
been moulded with black wax, gum-lac, and even with galvanic 
copper; and the impressions so obtained presented to all appear- 
ance the same phenomena as the surface actually furrowed. 

Among the various experiments that were tried, I may men- 
tion the case of a scratched metal surface which at first gave a 
reflexion distinctly polarized parallel to the lines, but which was 
afterwards covered with varnish. Under these circumstances the 
polarization became hardly sensible—a result which seems most 
naturally explicable on the ground of the change of the direction 
of the rays owing to the refraction of the varnish, which pre- 
vented the incident light from impinging at that angle which is 
required to produce the polarization in question. In fact, when 
glass plates differently cut were fastened to the striated plate by 
means of a varnish of turpentine or Canada balsam, the polar- 
ization was immediately reproduced in the refracting substance 
whenever the direction of the ray was such that the phenomenon 


44.2 M. H. Fizeau on several Phenomena: 


would have been produced in the air. It is, however, well known 
that instruments constructed of brass, copper, and bronze, which 
are rendered brilliant by polishing, are generally covered with a 
coat of varnish for the purpose of preserving the brightness of 
the metal, and there is therefore no reason for surprise that the 
reflexions from these metals, however bright they may be, pre- 
sent no sensible polarization. When these surfaces have not 
been varnished, and when, moreover, they have been obtained 
by the action of polishing substances not too coarse, the pheno- 
mena are invariably observed. 

No mention has yet been made of the light regularly reflected 
by a striated surface. In this direction the observation is not 
so easy, because the rays reflected by the furrows mingle with 
those reflected from the smooth surface of the mirror. Neyver- 
theless, on observing with a microscope single lines suitably illu- 
minated, a sensible polarization may be detected which varies 
little with the angle of reflexion; but what is strange is that the 
direction of this polarization is opposite to that which is produced 
in the former case, being perpendicular to the lines on the sur- 
face. The same fact may even be observed on regarding a stri- 
ated surface directly by means of an analyser. In this ease, 
to render the phenomenon sensible, it is sufficient to trace 
two bands of lines at right angles on a silver surface, and to 
observe the reflected rays almost normally, the source of light 
being a white surface equally illuminated. The direction of the 
lines being perpendicular in the two bands, and each band po- 
larizing the light perpendicularly to its direction, it results that 
the two bands give opposite polarizations, and that the phe- 
nomenon becomes more sensible by contrast. 

The same effect may be observed, without much difference, 
whether the incident rays are normal or more or less oblique, the 
reflected rays invariably possessing a partial polarization sensibly 
perpendicular to the direction of the lines. 

This phenomenon is rendered very obvious on striating a space 
of some centimetres diameter on a polished plate by means of a 
lathe ; the portion covered with concentric lines, bemg regarded 
with an analyser, presents two dark tufts similar to the tufts dis- 
covered by M. Haidinger. 

This phenomenon may be rendered still more visible by uni- 
formly furrowing the entire surface of two mirrors, placing them 
parallel and opposite to each other, and causing light to be 
reflected repeatedly from one to the other: at each of these 
reflexions an additional portion of light is polarized; so that 
after several reflexions in a direction which may be as near the 
normal as possible, the polarized light greatly exceeds the non- 
polarized in quantity. 


connected with the Polarization of Light. 448 


This polarization of the regularly reflected ray may be ob- 
served with different metals without sensible modification,—the 
metals which have the least effect in producing ordinary polari- 
zation, such as gold and silver, giving results sensibly the same 
as those produced by the metals that polarize the most, such as 
platinum and zinc. This result seems to preclude us from attri- 
buting these effects to partial polarization by the sides of the 
furrows, which is the first idea which naturally occurs to us. 
Such reflexions appear at least not to be the principal cause of 
the phenomenon. 

In order to advance another step in the study of these singular 
phenomena, it was necessary to ascertain the exact dimensions 
of the small furrows which possess properties so singular. For 
this purpose recourse was had to exceedingly thin layers of 
silver deposited on glass from certain chemical solutions, and 
which may not only be used to replace the tin amalgam for sil- 
vering looking-glasses, but have even been employed with success 
by M. Foucault in the construction of a new species of telescope. 

The first glass plate, A, was covered with a very thin, though 
still perfectly opake layer of silver, and a straight band of ~ 
striz was produced on the metallic surface by means of a piece 
of cork covered with very fine emery. This band presented the 
phenomena above described, viz. polarization of the dispersed 
light parallel to its own direction, and polarization of the reflected 
light perpendicular to the same. On examining, by means of 
the microscope, the state of the striated layer by transmitted 
light, it was easy to perceive that the furrows had not in general 
penetrated through the metallic layer, some deeper than the rest 
forming exceptions. 

In order to ascertain the thickness of the metallic layer, a 
piece of iodine was placed on one point of the surface, and the 
coloured rings due to the film of iodide of silver produced by 
the evaporation of the iodine were suffered to spread from this 
point, which itself became completely transparent, owing to the 
change of the silver layer throughout its entire thickness into 
yellow iodide. From the part where the silver had not been in 
any degree affected by the emanations of iodine, to the transpa- 
rent spot of iodide, there was a series of coloured rings commen- 
cing with white, and which, on being observed through a red 
glass, appeared to be nine in number. The series terminated in 
the middle of the ninth brilliant rmg. The index of refraction 
of the iodide of silver being 2°246 (as deduced from the angle of 
polarization, which was 66°), the ninth bright ring gave for the 
iodide of silver a thickness of 34, millim. From the thickness, 
composition, and known density of the iodide, the thickness of 
the layer of silver was calculated to be 34455 millim. 


4.44, M. H. Fizeau on several Phenomena 


A second glass plate, B, was covered with silver-leaf, opake 
like the former, except for rays of more than a certain degree of 
intensity ; for on looking at the sun through this plate, the body 
of that luminary was visible, stripped of his rays, and of a rich 
blue colour. I am persuaded that this silver-leaf contained a 
small quantity of gold. 

The metallic surface so produced was found too unequal and 
too loosely adherent to the glass to be scratched with emery like 
the former. On being rubbed, however, with pure cotton, the 
polarization of the dispersed hght was very distinct. Under the 
microscope it appeared to be torn in every direction, so that 
nothing could be inferred from this experiment; nevertheless, 
for the sake of comparison, the thickness of the metal was deter- 
mined by the same means as before. In this case the rings were 
four in number, the layer becoming transparent in the middle 
of tke fourth, whence it was concluded that the thickness of the 
metal was not more than 5,4, millim. This extreme thinness 
of beaten silver-leaf agrees with what we know with respect to the 
gold leaves used in gilding; these leaves, which, as is well known, 
are transparent and of a green tinge, have a medium thickness 


of about +, millim., as I ascertamed by weighing measured 


quantities of them. ‘Three different specimens gave the values 
0:000108, 0:000095, and 0:000091 millim. 

Returning then to the employment of glass plates covered 
with a layer of silver chemically deposited, one was obtained 
(which we will call C) not so thick as the former, as was proved 
by its greater transparency. ‘The light transmitted by this plate 
was of a greyish blue, the reflected light of a yellowish blue, 
with this property, that towards the angle of maximum polariza- 
tion it became of a pure blue for light polarized normally to the 
plane of reflexion. The rings of iodide formed on this surface 
terminated in the middle of the second bright line, beyond which 
the layer was completely transparent, from which it was con- 
cluded that the thickness of the silver layer was —4,5 mullim. 
This metallic film, when scratched with the same emery as the 
former, polarized the dispersed light very distinctly. On being 
examined microscopically, a very large number of the furrows 
seemed to have penetrated through the metal; but the majority 
did not, and consequently must have been less than 5-45, 
millim. deep. It was ascertained also that the lines which, when 
illuminated obliquely, produced a distinct polarization in their 
own direction, were of the latter lind. 

Lastly, a fourth layer of silver, D, was prepared thinner than 
all the others; it was more transparent than the last, and the 
light reflected by it possessed the same properties to a greater 
degree. Scratched hke the former, the dispersed light was 


connected with the Polarization of Light. AAS 


feebler, but still quite sensible and polarized as before. On 
being viewed with the microscope, it was found that the number 
of furrows that penetrated entirely through the metal was much 
greater than before; but that the polarization of the dispersed 
light was still due solely to those striz which were merely super- 


ficial, and consequently were less than —1+—. millim. deep,—such 


being the thickness of the silver, as estimated by the coloured 
rings of iodide, which terminated in the middle of the first dark 
line. 

A general view of the results just described naturally leads 
one to anticipate that light may suffer changes of the same nature 
as that above described when it traverses extremely fine slits. 
The experiments, with a description of which I am about to close 
this memoir, prove that this is the case, and that under these 
circumstances also phenomena are produced closely related to 
the preceding. 

It is well known that, to reproduce certain experiments of 
interference and refraction, small instruments are constructed 
which are to be found in all physical cabinets: these are slits 
with narrow walls and straight parallel edges, which can be ap- 
proximated to each other from a distance of several millimetres 
to actual contact. If a pencil of light be suffered to pass through 
such a slit, the opening of which has been reduced to such a 
degree as to suffer but a trace of the light to pass, the emergent 
ray is invariably observed to be polarized in a direction perpen- 
dicular to the slit, the polarization being stronger in proportion 
as the slit is narrower. 

If a very bright light be employed, and if the observation be 
conducted with a microscope, openings still narrower may be ob- 
served; and by slightly inclining one edge to the other, a slit 
may be obtained in the field of the microscope which gradually 
decreases until the edges actually meet. Now in this case the 
light which passes near the point of contact is almost entirely 
polarized in a direction perpendicular to the slit. 

This phenomenon was at first attributed to the repeated 
reflexions of the light from one side of the slit to the other, 
reflexions which necessarily give rise to several phenomena of 
polarization; but we shall see directly that there are circum- 
stances hard to reconcile with this explanation. 

The first trials were made with a slit whose edges were of 
brass; steel, copper, and, lastly, silver were substituted for this 
metal: the phenomenon was but little modified, and that in a 
way which by no means agreed with the polarizing power of 
these different metals. Silver, for example, which by itself has 
but little polarizing power, polarizes almost completely the light 
which traverses a very narrow slit of which it forms the sides. 


446 On Phenomena connected with the Polarization of Light. 


Moreover, in reducing the thickness of the sides so as to 
render them mere edges, the phenomenon is equally produced, 
and it then becomes difficult to imagine the existence of reflexions 
sufficiently numerous to cause the observed effect. 

Bodies of the most dissimilar nature, so disposed as to present: 
a narrow slit, give rise to the same phenomenon, provided the 
sides of the slit be well polished. Flint, glass, obsidian, ivory, 
fluor-spar, have in this respect afforded almost the same result. 

Having observed that the edges of the slit require to be well 
polished, which agrees with the theory that the polarization is 
due to repeated reflexions, the effect of removing this cause of 
polarization was tried, the edges of the slit being covered with 
lampblack. Under these circumstances the polarization was 
entirely destroyed, and the idea of repeated reflexions seemed 
thus to be confirmed, only, however, to be again overthrown ; 
since on restoring the polish of one side only, the other being 
still covered with lampblack, the polarization reappeared di- 
stinctly, and in this case the existence of repeated reflexions 
seemed impossible. This experiment, taken in conjunction with 
the preceding, seems to show that there is some particular cause 
for the phenomenon. 

In order to throw some light on this subject, the attempt was 
made to examine the phenomenon when the light undergoes 
total reflexion from the sides of the slit, such reflexion having, 
as is well known, no polarizing effect. 

After several unsuccessful attempts, no better method was 
discovered than that of observing the edge of a soap-bubble 
formed in a straight tube. Under these circumstances the soap- 
bubble forms a very thin film of hquid at the centre, perpendi- 
cular to the axis of the tube, and terminated by two opposite 
concave menisci. Placing this under the microscope and illu- 
minating it properly, it was easy to distinguish through the walls 
of the tube a bright line, formed by the light that had traversed 
the film, either directly, or having undergone none but total 
reflexions from its sides. 

When the bubble was thick, the light thus transmitted exhi- 
bited no sensible polarization ; but when the bubble was suffi- 
ciently thin to give rise to coloured rings by reflexion, par- 
tial polarization was invariably found present in the bright line, 
the plane of polarization being, as before, perpendicular to the 
direction of the slit. This observation was repeated in various 
ways, and always with the same result. . 

Finally, the slits in the thin layers of gold and silver men- 
tioned above, were examined with regard to the above phenomena. 

Leaves of beaten gold were at first examined with the micro- 
scope; they presented numerous rents and slits that offered no 


On the Cubical Compressibility of solid Homogeneous Bodies. 447 


particular characteristics; but in some of the leaves, especially 
in their thicker parts, natural fissures were discovered ex- 
tremely narrow, certainly less than 3,55 millim. across, which 
were clearly polarized, especially towards their narrowest ends, the 
plane of polarization being, as before, perpendicular to the direc- 
tion of the slit. These polarized slits are rather rare in gold- 
leaf; and I never found them in the thinner and more transpa- 
rent parts, but only in those whose thickness cannot be much 
less than 3,555 millim. This property seems to indicate that 
the phenomenon is only produced when the layers have a certain 
thickness, below which it is insensible. 

The same conclusion was come to on observing the thin layers 
of silver already mentioned. In fact layers C and D, which 
were excessively thin and transparent, exhibited no sensible 
polarization even in their finest slits ; while the somewhat thicker 
and more opake layer A, whose thickness amounted to gqb5 
millim., exhibited the phenomenon in a remarkable manner, and 
with certain curious peculiarities. Some of the narrowest of the 
lines which penetrated through the entire thickness of the metal 
were polarized, some partially, others almost totally, the plane 
of polarization being still perpendicular to their length. On 
employing solar light, the phenomenon of coloured light appeared 
in conjunction with that of polarization; for on observing the 
polarized lines with a doubly-refracting prism, the two images 
appeared in certain cases of complementary colours. 

I believe I have now communicated the principal facts which 
I have discovered relatively to the polarization, 

1. Of light dispersed from furrowed metal surfaces, 

2. Of the rays regularly reflected by such surfaces, 

3. Of light which has traversed very narrow slits. 

With the permission of the Academy I shall for the present 
content myself with the foregoing statement of facts, without 
entering on the premature and, as yet, uncertain question of the 
causes and connexion of the phenomena above detailed. 


LXVII. On the Cubical Compressibility of certain sold Homo- 
geneous Bodies. By M. G. WertHEIM*, 


1848 I published a memoir on the proportion between 

the elongation and transverse contraction of a homogeneous 
isotropic elastic bar when subjected to longitudinal traction. 
After having called attention to the fact that the value of this 
ratio as determined by Poisson’s analysis, viz. 4, had never been 
confirmed by any conclusive experiments, I shewed in the case 
of certain substances which I was enabled to submit to direct 


* Translated from the Comptes Rendus, vol. li. p. 969, 


448  M. G. Wertheim on the Cubical Compressibility 


experiment by means of a method susceptible of almost any 
degree of accuracy, that this ratio was really 4. Subsequent 
experiments, less direct, but made on a greater variety of bodies; 
have confirmed this result. 

These researches have given rise to numerous discussions. 
Several distinguished geometricians, without repeating my expe- 
riments, and without disputing their accuracy, have endeavoured 
to bring them into accordance with the ancient theory by vari- 
ous and, unfortunately also, very arbitrary hypotheses. I shall 
shortly mention and discuss these hypotheses before describing 
my new experiments on this subject. 

In a memoir published shortly after mine, M. Clausius ex- 
pressly acknowledged that the bodies on which I had experi- 
mented may be considered as truly homogeneous and isotropic ; 
but he thinks that the secondary elasticity discovered by M. 
Weber in silk threads, and which I have observed in several 
organic bodies, may serve to explain this disagreement between 
experiment and the ancient theory. This secondary action being 
added to the true or primary elongation, will give rise to an ex- 
cessive actual elongation, the numerator of the fraction being 
thus increased to such a degree that, though really equal to + 
when only the primary elongation is considered, it in fact ap- 
proximates to Z. 

Against this explanation it may be objected, in the first place, 
that it is founded on a fact absolutely hypothetical, no one ~ 
having yet observed this secondary action either in metals or in 
glass, which are the only bodies I experimented on. Some ex- 
periments of M. Weber are, it is true, appealed to, according to 
which the transverse note produced by a metallic wire which has 
been suddenly stretched, becomes lower for several seconds. 
Seebeck has in fact endeavoured to explain this phenomenon on 
the ground of the secondary action above mentioned—contrary, 
however, to the very plausible opmion of M. Weber himself, who 
attributes it solely to the diminution of the temperature of the 
wire produced by its elongation, and its gradual return to the 
temperature of the surrounding atmosphere. But even admit- 
ting the hypothesis of M. Seebeck, this lowering of the note 
is at all events far too small for its corresponding secondary 
elongation to account for the numerical result of my experiments ; 
and M. Clausius is therefore obliged to suppose that, in the case 
of metals, this species of elongation principally takes place during 
the first quarter of a second, and consequently produces no sen- 
sible effect on the note. But the primary action itself not being 
instantaneous, how is it possible to fix the limit of time beyond 
which the effect ought to be considered as secondary? Itis thus 
that hypotheses accumulate. 


of certain solid Homogeneous Bodies. 449 


A still graver objection to this hypothesis is that, contrary to 
all our theoretical notions and all the results of experience, we 
should be obliged to suppose that this secondary elongation 
produces no corresponding transverse contraction, since other- 
wise the ratio between the two observed quantities, namely the 
total longitudinal elongation and the total transverse contraction, 
would always remain that indicated by the ancient theory. 

I have been obliged to enter into these details in consequence 
_ of the perseverance with which certain physicists have for twelve 
years opposed this theory to mine, and the manner in which 
they insist on treating as a demonstrated scientific truth that 
which M. Clausius himself only regarded as a hypothesis, and 
one indeed to which no great importance was to be attached. 

MM. Lamé and Maxwell admit that the ratio above defined, 
or, what comes to the same thing, the ratio between the cubic 
and linear compressibilities, may vary in different substances. 
Experience alone can determine whether this is the case, as I 
have not failed to remark, both in my original memoir, and in 
several of those I have since published. M. Verdet is therefore 
wrong in asserting, as he does in the extract of a memoir which 
we shall have to discuss hereafter, and of which M. Kirchhoff is 
the author, that I have “ endeavoured to show by numerous ex- 
periments that this ratio has in all bodies the same constant 
value +.” On the contrary, while affirming and maintaining 
the exactitude of this value for those bodies which were the 
subject of my researches, I excluded those not yet submitted to 
experiment. 

According to an interesting experiment made by M. Clapeyron 


4 1 
on vulcanized caoutchouc, the fraction —, instead of being equal 


to 1 according to the ancient theory, or 2 as my experiments 
require, attains in the case of this substance the enormous value 
of 2201; this fact, to which we shall return hereafter, seems to 
me to be explained by the resuJts of the present memoir. 

Contrary to the opinion of M. Clausius, M. de Saint-Venant 
attributes the disagreement between the results of my experi- 
ments and the ancient theory to.a want of isotropism in the bodies 
on which I experimented: the author thinks “that there are as 
many species of mechanical homogeneousness as there are of 
possible curvilinear systems of coordinates, or of systems of con- 
jJugate orthogonal surfaces”—in fact, that we may imagine as 
many species as we please of non-isotropic homogeneousness ; 
but what he has failed to show is that any such heterotropy 
really exists in the bodies I experimented on, and, which is 
absolutely incredible, that it exists to the same degree in 
them all. 

Phil. Mag. 8S. 4. Vol. 21. No, 142. June 1861. 2G 


450 M. G. Wertheim on the Cubical Compressibility 


But without going so far as this, and without comparing 
bodies chemically different, if we attribute to a body one of the 
species of homogeneousness imagined by M. de Saint-Venant, as 
for instance cylindrical or spherical homogeneousness, or any 
other, we ought at least to be able thus to explain the results of 
the various experiments to which these bodies may be submitted. 

It would, for example, be easy to invent a molecular arrange- 
ment such that a cylindrical piezometer would possess a cubical 
compressibility conformable to that given by the ancient theory ; 
but it would be necessary to show also that this cylinder, when 
subjected to longitudinal traction, would exhibit the elongation, 
and at the same time the transverse contraction, which is shown 
by experiment, that its resistance to torsion might be determined 
beforehand, &c. 

As long as this demonstration has not even been attempted, 
all discussion on these hypotheses is necessarily futile. 

Lastly, M. Kirchhoff has just published an important memoir 
on this point, which it will be necessary for me to examine with 
the degree of attention due to the name of the author and the 
interest of the subject. Instead of indulging in mere conjectures, 
M. Kirchhoff has devised the following experiment :—A weight 
applied to the end of a lever produces simultaneously the flexion 
and torsion of a homogeneous cylinder ; these two displacements 
are measured exactly by means of an ingenious application of 
Gauss’s method; and their ratio, which is independent of the 
modulus of elasticity and the radius of the cylinder, gives by 
known formule the required relation between the elongation and 
transverse contraction. 

This method is lable to numerous objections. It would be 
difficult to imagine one more indirect and consequently more 
subject to error: the coefficient of the change of volume is deter- 
mined by two distortions, which are themselves unaccompanied 
by any change of volume whatever; this at least is what is — 
assumed in order to establish the formule, though it is not 
rigorously true ; the experiment may be considered as the flexion 
of a cylinder which has been rendered non-homogeneous by tor- 
sion, or the torsion of a cylinder rendered heterogeneous by 
flexion ; and the ordinary formule for torsion and flexion, which 
are inexact in themselves (as I think I have sufficiently shown in 
the case of the former, and as I shall hereafter endeavour to 
prove of the latter), become still less trustworthy in the present 
case. 

M. Kirchhoff’s apparatus is one of great delicacy, and. does 
not seem as if it could possess sufficient stability for researches 
of this nature ; the small dimensions of the cylinders subjected 
to experiment (less than 3 millims. in diameter, and only 145 


of certain solid Homogeneous Bodies. 451 


millims. long), the sensible flexions produced originally by the 
mirrors and the levers supported by the cylinders, the necessity 
of soldering the latter in the middle, and lastly the complication 
of the calculations necessary to reduce the observations, are so 
many sources of inconvenience and error. 

The following are, however, the results of these experiments : 
M. Kirchhoff found for yellow brass the value 0-387, for tem- 
pered steel 0-294: these numbers are, it will be seen, decidedly 
greater than 1, while } is very nearly equal to their mean value. 
M. Kirchhoff passes somewhat lightly over the former of these 
results, while he attaches great importance to the second: tem- 
pered steel appears to him to be a body eminently isotropic, 
while yellow brass is neither sufficiently homogeneous nor en- 
tirely free from the secondary effect before spoken of. 

We have already done justice to the latter observation, which 
moreover applies as well to steel as it does to brass, since this 
secondary effect has in fact been observed in neither. As far as 
isotropism is concerned, it is very gratuitous to attribute that 
property peculiarly to a tempered body: the action that tem- 
pered glass exercises on polarized light abundantly proves this ; 
and indeed if the least homogeneous among non-crystallized 
bodies were required, it would undoubtedly be on a tempered 
substance that the choice ought to fall. 

i am far, then, I repeat, from affirming that this ratio ought 
not to be somewhat less than 4 in the case of homogeneous steel ; 
but the present experiment does not seem to me to be conclusive 
on the subject. 

The experiment, on the contrary, made on yellow brass is the 
first in which my results have been attempted to be verified on 
one of the substances [ myself employed. The number 0°387 
is, it is true, greater than 4; but I shall prove, in a memoir on 
flexion I am about to produce, that the denominator of the frac- 
tion which represents in M. Kirchhoff’s results the ratio of the 
torsion to the flexion, is too little, and that this fraction, properly 
corrected, approaches much more nearly to the value $. 

In short, setting aside for the moment the experiment of M. 
Clapeyron, no fact has hitherto been advanced to show that the 
required relation is different in different bodies. The experi- 
ments that have been made, moreover, refer only to a small 
number of bodies; they have been made by means of methods 
all more or less indirect; and the cubical compressibility has 
never itself been the subject of any direct experiment ; so that we 
know not whether the proportion supposed to exist between the 
pressures and the diminutions of volume really does exist for 
changes of pressure, however small. This research will be the 
subject of the memoir which I shall shortly have the honour of 
submitting to the Academy. 

262 


\ 


[ 452 ] 


LXVIII. On a New Electrometer (the Siphon Electrometer) for 
measuring the Electrical Charge of the Prime Conductor of a- 
Machine ; and on the Dispersion of different Liquids by Elec- 
trical Action. By Tuomas Tate, Esq.* 


age electrometer most commonly used by electricians, for 

ascertaining the intensity of the charge of the prime con- 
ductor of a machine, is Henley’s. According to the experiments 
of Sir W. Snow Harris, it appears that the degrees of diver- 
gence of this instrument for high charges are nearly in proportion 
to the quantities of electricity generated; at the same time it must 
be observed that this result does not agree with what theoretical 
imvestigation would give. This instrument therefore would 
serve very well in all ordinary cases for indicating the power of 
any machine, provided that all the instruments used were con- 
structed exactly alike; but this is practically impossible; and 
hence it follows that the degree of divergence of one instrument 
cannot be compared with that of another instrument, as regards 
its indication of electrical charge. The hydrostatic and balance 
electrometers are very complete instruments as regards scientific 
research ; but it must be allowed that they are too delicate in 
their construction and mode of action to be used on ordinary 
occasions, when only an approximate value of an electric charge 
is required; moreover, the thermo-electrometer is only appli- 
cable to high charges of an electrical battery. 

The siphon electrometer, represented in the annexed diagram, 
is sufficiently delicate and reliable in its indications, and admits 
of being constructed so that the results derived from one imstru- 
ment may be fairly compared 
with those derived from an- 
other instrument. It depends 
on the principle, that differ- 
ent quantities of electricity 
discharge different quantities 
of liquid from a siphon-tube 
in which the liquid is sus- 
pended by capillary action. 

A B a glass jar, containing 
water, about 4 inches in dia- 
meter, placed upon the insu- 
latmg stand CD of gutta 
percha; EG a small siphon 
about °15 of an inch diameter, 
cemented to the side of the 
jar, as shown in the diagram ; 
HI a funnel-shaped receiver 


* Communicated by the Author. 


On a New Electrometer (the Siphon-Electrometer). 453 


about 3 inches diameter, connected with the ground by a damp 
cord, and placed directly below the orifice G of the tube, and 
connected with a glass tube, K L, divided into tenths and hun- 
dredths of a cubic inch; N P a conducting wire fixed to the prime 
conductor of the electrical machine and dipping into the liquid 
EF. The instrument is used in the following manner :— 

A sufficient quantity of water is poured into the jar, so as to 
cause the siphon to act; the water then flows through the siphon 
until its pressure in the jar is balanced by the capillary action of 
the tube G E, when it will cease to flow; it will then be found 
that the level of the water in the jar stands somewhat above the 
orifice G of the siphon-tube: scarcely any amount of shaking 
or oscillation will now cause the water to flow from the orifice G. 
The graduated tube K L is then placed below the orifice G, the 
bottom of the funnel being from 24 to 24 inches from this orifice. 
The machine is then turned, and the electric action causes the 
water to flow in a continuous stream or jet from the orifice G, 
filling the tube K L; any proposed number of revolutions being 
given to the machine in a known time, the number of cubic inches 
of water discharged is taken as the measure of the efficiency of 
the machine. 

It will be hereafter shown, the machine being in a fixed state 
of action, that in order to produce a given or constant discharge 
of liquid, the product of the number of revolutions of the machine 
by the time in which these revolutions are made must be a con- 
stant quantity. Thus, if revolutions, performed in ¢ seconds, 
produce a discharge of & cubic inches of water, and n, revolu- 
tions, performed in 7, seconds, produce the same discharge of 
liquid, then nt=nty. 

Hence it follows that (within certain limits) the relative effi- 
ciency of a machine (in different states of action, or of different 
machines) will be inversely as the product of the number of revo- 
lutions by the time requisite for producing a given or fixed 
amount of discharge. Thus, if a machine discharges one-half of 
a cubic inch of water in 20 revolutions per 60 seconds, and another 
machine discharges the same amount of water in 15 revolutions 
per 40 seconds, then the powers of the machines will be as 

1 ‘ 1 
20x60 °° 15 x 40 

The following results of experiments show the uniformity of 
the action of the instrument. 

24 revolutions of the machine, in 45 seconds, produced a dis- 
charge of °61 of a cubic inch of water ; and the experiment being 
repeated for two successive times, the discharges were found to 
be 62 and ‘61. 


wor asl tO 2: 


454 Mr. T. Tate on anew Electrometer for measuring 


When the machine was in a higher state of action, 20 revolu- 
tions, in 60 seconds, produced a discharge of 1:06 cubic inch; 
and upon repeating the experiment the discharge was found to 
be 1:04 cubic inch. 

Within certain limits, the quantity of liquid discharged is not 
sensibly affected by the diameter of the tube GE, or by the 
distance of the cup from the nozzle G: other things being the 
same, the diameter of the tube may vary from ,3,ths to ;4ths of 
an inch; and the distance of the cup from the nozzle may vary 
from 24 to 24 inches without sensibly affecting the amount of 
discharge. In like manner, slight variations in the diameter of 
the jar produced little or no sensible alteration in the amount of 
the liquid discharged. 

At the commencement of the operation, the columns of liquid 
being in equilibrium, the electrical action has simply to over- 
come the cohesion ofthe particles of the liquid for one another ; 
but as the process goes on, the water being more and more dis- 
charged, the equilibrium of the columns is destroyed, and the 
resistance to the discharge increases, so that, with the same elec- 
tric force, the rate of discharge of the water becomes less and 
less; but when the section of the jar is considerable, and the 
volume of the liquid displaced does not exceed a certain limit, 
the velocity with which the liquid is discharged is nearly uniform. 

The following experimental results show that, for equal quan- 
tities of water discharged (the machine being in a fixed state of 
action), the product of the number of revolutions by the correspond- 
ing time is (approximately) a constant quantity. 


Experiment I. 


Number of : Corresp. dis- | 
. Correspondin : 
hemmachine, |HHEIM seonds | Pe EStotaen, | Vaugot 
nN. : 
15 70 69 1050 
25 42 70 1050 
18 60 69 1080 
12 90 “69 1080 


The following experiment was made when the machine was in 
a different state of action. 


Experiment II. 


24: revolutions of the machine, performed in 80 seconds, pro- 
daced a discharge of 72 cubic izch of water; and 33 revolutions, 
in 60 seconds, produced the same amount of discharge. 

In this case 24 x 80=1920, and 38 x 60=1980. 


the Electrical Charge of the Prime Conductor of a Machine. 455 


Experiment III. 


10 revolutions, performed in 50 seconds, produced a discharge 
of *41; and 20 revolutions, in 25 seconds, produced nearly the 
same discharge. . 

Here 10 x 50=20 x 25=500. 

Now, assuming that the quantity of electricity generated is in 
proportion to the number of revolutions of the machine, then it 
follows that a certain quantity of electricity, acting for 50 
seconds, produces the same (or nearly the same) discharge as a 
double quantity of electricity acting for half the time; and so 
on, similarly to the results of the other experiments. 

If ¢ be put for the quantity of electricity generated in ¢ seconds, 
and e, for the quantity generated in ¢, seconds, then for equal 
amounts of discharge we shall have 


ext=e, Xt; 


that is, for equal amounts of discharge the quantities of electricity 
are in the inverse ratio of the times. 

In Experiment III. the angular velocities of the machine are 
as 1 : 4, and therefore the intensities of the electricity generated 
would be in the same ratio, provided that no electricity had been 
carried off by the discharge of the liquid; but the deflections 
of Henley’s electrometer dicated that the ratio of the itensi- 
ties of the electricity in the two states of the conductor was only 
about 2 to 3. 

Although equal volumes of water are discharged, we cannot 
infer that the dynamic effects are equal; for the liquids are re- 
spectively discharged with different velocities. 

Let & = the cubic inches of water discharged in each case, w 

~ being its weight in units of lbs. 

n = the corresponding number of revolutions in ¢ seconds 
in the one case, e being the amount of electricity 
generated, and v the velocity with which the liquid 
is discharged. 

n, = the corresponding number of revolutions in ¢, seconds 
in the other case, e, being the quantity of electricity 
generated, and v, the velocity with which the liquid 
is discharged. 

u, U,= the accumulated work or dynamic effect in each case 
respectively. 
vw 


v 
Then v= Wg? and u, = —— ; 


456 Mr. T. Tate on a Siphon Electrometer. 


t : sith : 
but = = ne on the assumption that the velocities are uniform, 


1 
eee a) 
e = Z e 
Now by experiment we have 


ni=n,t,, and .. —=-; 


e Uu n : e 
= — aa > 
Uy Ny 


that is, the discharge being constant, the dynamic effects are in the 
ratio of the squares of the number of revolutions of the machine. 


If n=20, and n,;=10, as in Exp. III., then i that is, in 


this case the dynamic effects will be as 1 to 4, or a double num- 
ber of revolutions produces a quadruple effect. 

Let x be put for the number of revolutions of the machine (its 
state being constant) performed in 60 seconds, or 1 minute, to 
produce the same discharge as 7 revolutions in ¢ seconds; then 


nt 
x x 60=nt, or <= 60" 
Similarly, we have for the relation of equal discharge corre- 
sponding to any other state of the machine, 
ately 
re GOR 
Now it may be presumed that the efficiency of the machine is 
inversely proportional to the number of revolutions per minute 
requisite to produce a given discharge; but we find 
pc WALL 


x nt ” 


that is, the efficiency of a machine varies inversely as the product 
of the number of revolutions by the corresponding time requisite to 
produce a gwen discharge. 

ff 7775, then TERR 


that is, im this case the efficiency of a machine varies inversely as 
the number of revolutions (the time being constant) requisite to 
produce a given discharge. 

Thus, if a machine discharges half of a cubic inch of water in 
twenty revolutions in a certam time, and another machine dis- 
charges the same amount of water in ten revolutions in the same 


time, then the latter machine will have double the power of the 
former. 


Royal Society. 457 


On the Dispersion of different Liquids by Electrical Action. 


The siphon-electrometer enables us to determine the rate at 
which electrical charges will disperse different liquids. The 
liquid to be examined being placed in the jar A B, and the siphon 
being brought to act in the usual manner, the discharge pro- 
duced by a given number of revolutions of the machine in a 
given time is determined; and having previously found the 
amount of pure water discharged by the same number of revolu- 
tions performed in the same time, we are enabled to estimate the 
dispersiveness of the particular liquid, as compared with that of 
pure water, under the same electrical action. In this manner, 
saturated solutions of chloride of sodium, carbonate of soda, and 
other salts were examined ; and it was found that, under the same 
electrical action, the volumes of the liquid discharged were in the 
inverse ratio of their specific gravities. It will be observed that 
these liquids are all good conductors of electricity. But the case 
is very different with respect to liquids which are imperfect con- 
ductors of electricity, such as turpentine, fixed oils, and alcohol. 

In twenty revolutions per minute the discharge of pure water 
was about three-fourths of a cubic inch; whereas with the same 
electrical action only about one-fourth of a eubic inch of turpen- 
tine was discharged, and not more than one-tenth of a cubic inch 
of fixed oil. Under the same electrical action, the volume of 
alcohol discharged did not exceed one-fifth of a cubicinch. Now 
although the specific gravities of these-liquids are less than that 
of water, yet their dispersiveness, under the same electrical action, 
is considerably less than that of water. 


Hastings, May 18. 


LXIX. Proceedings of Learned Societies. 


ROYAL SOCIETY. 
[Continued from p. 393. ] 


June 14, 1860.—General Sabine, R.A., Treasurer and Vice-President, 
in the Chair. 


ee following communications were read :— 

“Notes of Researches on the Poly-Ammonias.’”’—No. VIII. 
Action of Nitrous Acid upon Nitrophenylenediamine. By A. W. 
Hofmann, LL.D., F.R.S. 

The experiments of Gottlieb have shown that dinitrophenylamine, 
when boiled with sulphide of ammonium, is converted into a remark- 
able base, crystallizing in crimson needles, generally known as nitra- 
zophenylamine, and for which, in accordance with the views I enter- 
tain regarding its constitution, I now propose the name Nitrophe- 
nylenediamine. I owe to the kindness of Dr. Vincent Hall a con- 


458 Royal Society :— 


siderable quantity of this substance, which is not quite easily pro- 
cured. 

I have made a few experiments with this compound in the hope of 
obtaining some insight into its molecular constitution. If, bearing 
in mind the numerous analogies between the radicals ethyle and 
phenyle, we assume that the latter, by the loss of hydrogen, may be 
converted into a diatomic molecule, phenylene C, H,, corresponding 
to ethylene, the existence of a group of bases corresponding to the 
ethylene-bases cannot be doubted. 


C,H, (C, Hy)” 
Ethylamine H }N*. Ethylenediamine UH, N,. 
H H, 


C,H, (, H,)" 

Phenylamine H fx. Phenylenediamine H, Ly, 

H H, 

With the last-named body agrees in composition the compound 
known as semibenzidam, or azophenylamine, which Zinin obtained 
by exhausting the action of sulphide of ammonium on dinitro- 
benzole. 

Those chemists, however, who have had an opportunity of be- 
coming acquainted with the well-defined properties of ethylenedia- 
mine, will not be easily persuaded to consider the uncouth dinitro- 
benzol-product—sometimes appearing in brown flakes, sometimes as a 
yellow resin, rapidly turning green in contact with the air—as stand- 
ing to smooth phenylamine in a relation similar to that which obtains 
between ethylenediamine and ethylamine; we much more readily 
admit a relation of this description between phenylamine and Gott- 
lieb’s crimson-coloured base, in which the clearly pronounced cha- 
racter of the former is still distinctly visible, although of necessity 
modified by the further substitution which has taken place in the 
radical. 


C, H, i 

Phenylamine Tae Ns 
H 

(C, Hy)" 
Phenylenediamine H, pe 

(C,[H, (NO.)})" 
Nitrophenylenediamine H, } N,. 

H 


Does the latter formula really represent the molecular constitution 
of the crimson needles? The degree of substitution of this body 
might have been determined by the frequently adopted process of 
ethylation. But even a simpler and a shorter method appeared to 
present itself in the beautiful mode of substituting nitrogen in the 
place of hydrogen, lately discovered by P. Griess. ‘The red crystals 


* H=1; 0=16; C=12, &. 


On the Action of Nitrous Acid upon Nitrophenylenediamine. 459 


undergo, indeed, the transformation, which he has already proved for 
so many derivatives of ammonia, with the greatest facility. 

On passing a current of nitrous acid into a moderately concen- 
trated solution of the nitrate of the base, the liquid becomes slightly 
warm, and deposits on cooling a considerable quantity of brilliant 
white needles, the purification of which presents no difficulty: spa- 
ringly soluble in cold, readily soluble in boiling water, the new com- 
pound requires only to be once or twice recrystallized. Thus puri- 
fied, this substance forms long prismatic crystals, frequently inter- 
laced, white as long as they are in thé solution, but assuming a 
shghtly yellowish tint when dried, and especially when exposed to 
100°: they are readily soluble both in alcohol and in ether. The 
new body exhibits a distinctly acid reaction ; it dissolves on applica- 
tion of a gentle heat in potassa and in ammonia, without, however, 
neutralizing the alkaline character of these liquids; it also dissolves 
in the alkaline carbonates, but without expelling their carbonic acid. 
The new acid fuses at 211° C., and sublimes at a somewhat higher 
temperature, with partial decomposition. The sublimate consists of 
small prismatic crystals. 

Analysis proves this substance to contain 


C, H, N, 0,, 
a formula which is confirmed by the analysis of a silver-compound, 


| C, (H, Ag) N,O,, 
and of a potassium-salt, 
C, (H, K) N, O,. 


The analysis of the new compound shows that, under the influence 
of nitrous acid, nitrophenylenediamine exchanges three molecules of 
hydrogen for one molecule of nitrogen, three molecules of water 
being eliminated. 


C, H, N, 0,+H NO,=2H,0+C, H, N’’N, O,. 
—_.+=,-——_—’ —————---—-—_—— 
Nitrophenylene- New acid. 
diamine. 


I do not propose a name for the new compound, which can claim 
but a passing interest, as throwing, by its formation, some light on 
the constitution of nitrophenylenediamine. 

The composition of the new acid, and of its salts, shows that in the 
crimson-red base four hydrogen molecules are still capable of re- 
placement ; in other words, that this body contains four extra-radical 
molecules of hydrogen. The result of these experiments appears to 
confirm the view which, in the commencement of this Note, I have 
taken of the constitution of this body; at all events, the mutual 
relation of the several bodies is satisfactorily illustrated by the 
formulze— : 


4.60 Royal Society :— 
(C.[H, (NO,)])" } 
N.. 


Nitrophenylenediamine Ss 


C.CH, (NO.)])" 
(C.{H, (N0,)}) \y, 


New acid 
H 
(C,[H, (NO,)])" 
Silver-salt NI!" Ng. 
Ag 


If the admissibility of this: interpretation be confirmed by further 
experiments, the reaction discovered by Griess furnishes a new and 
valuable method of recognizing the degree of substitution in the 
derivatives of ammonia. 

The new acid differs in many respects from the substances pro- 
duced from other nitrogenous compounds. As a class, these sub- 
stances are remarkable for the facility with which they are changed 
under the influence of acids, and more especially of bases. The new 
acid exhibits remarkable stability; it may be boiled with either 
potassa or hydrochloric acid without undergoing the slightest change. 
Even a current of nitrous acid passed into the aqueous or alcoholic 
solution is without the least effect. The latter experiment appeared 
of some interest ; for if the action of nitrous acid, im a second phase 
of the process, had assumed the form so frequently observed by Piria 
and others, it might have led to the formation of the diatomic nitro- 
phenylene-alcohol, according to the equation 


(C, [H, (NO,)])” 
H, 


H 


It deserves to be noticed that nitrophenylenediamine, although 
derived from two molecules of ammonia, is nevertheless a decidedly 
monacid base. Gottlieb’s analyses of the chloride, nitrate, and sul- 
phate left scarcely a doubt on this pomt. However, as some of the 
natural bases, quinine for instance, are capable of combining with 
either one or two molecules of acid, I thought it of sufficient interest 
to confirm Gottlieb’s observations by some additional experiments. 
The crystals deposited on cooling from a solution of nitrophenylene- 
diamine in concentrated hydrochloric acid, were washed with the 
same liquid and dried zn vacuo over lime. 

Analysis led to the formula 


L (C,[H,(NO,)])" | 
H H N, | 


(C, [H, (NO,)] x O 
N,+2H NO,=2H, 0+N,+ H, 2 


2 


2 


H, 

The dilute solution of this chloride is not precipitated by dichlo- 
ride of platinum, nor can the double salt of the two chlorides be 
obtained by evaporating the mixed solutions, which, just as Gott- 
lieb observed it, is readily decomposed with separation of metallic 
platinum. I had, however, no difficulty in preparing a platinum salt, 


On the Action of Nitrous Acid upon Nitrophenylenediamine. 461 


crystallizing in splendid long brown-red prisms, by adding the dichlo- 
ride of platinum to the concentrated solution of the hydrochlorate. 
The platinum determination led to the formula 


fe #(@2(H, (NO,)})")° 7 
A Be NIC Pele 
H, val 


These experiments prove that, even under the most favourable cir- 
cumstances, nitrophenylenediamine combines only with 1 equiv. of 
acid, while the ethylene-derivatives are decidedly diacid. The dimi- 
nution of saturating power in nitrophenylenediamine, at the first 
glance, seems somewhat anomalous, but the anomaly disappears if 
the constitution of the body be more accurately examined. It can- 
not be doubted that the diminution of the saturating power is due to 
the substitution which has taken place in the radical of the diamine. 
I have pointed out at an earlier period*, that the basic character of 
phenylamine is considerably modified by successive changes intro- 
duced into the phenyl-radical by substitution. Chlorphenylamine, 
though less basic than the normal compound, still forms well-defined 
salts with the acids; the salts of dichlorphenylamine, on the other 
hand, are so feeble, that, under the influence of boiling water, they 
are split into their constituents; in trichlorphenylamine, lastly, all 
basic characters have entirely disappeared. Again, on examining the 
nitro-substitutes of phenylamine, we find that even nitrophenylamine 
is an exceedingly weak base, whilst dinitrophenylamine is perfectly 
indifferent. What wonder, then, that a molecular system, to which 
in the normal condition we attribute a diacid character, should, by 
the insertion of special radicals, be reduced to monoacidity? The 
normal phenylenediamine, which remains to be discovered, will doubt- 
less be found to be diacid, like the diamines derived from ethylene. 
Even now the group of diacid diamines is represented in the naphtyl- 
series : 


: C,, H, 
Naphtylamine H +N monoacid. 
H 
(C,, H.)" 
Naphtylenediamine 4H, N diacid. 
3 HH 


The body which I designate by the term Naphtylenediamine, is the 
base which Zinin obtained by the final action of sulphide of ammo- 
nium upon dinitronaphtaline. This substance, originally designated 
seminaphtalidam, and subsequently described as naphtalidine, com- 
bines, according to Zinin’s experiments, with 2 equivalents of hydro- 
chloric acid +. . 


“Qn the Formula investigated by Dr. Brinkley for the general 
Term in the Development of Lagrange’s Expression for the Summa- 
tion of Series and for Successive Integration.” By Sir J. F. W. 
Herschel, Bart., F.R.S. &c. 


* Mem. of Chem. Soc. vol. ii. p. 298. 
+ Liebig’s Annalen, vol. lxxxv. p. 328. 


4.62 Royal Society :— 


June 21.—Sir Benjamin C. Brodie, Bart., President, in the Chair. 
The following communications were read :— 


*‘ Experimental Researches on various questions concerning Sen- 
sibility.” By E. Brown-Séequard, M.D. 


“On the Construction of a new Calorimeter for determining the 
Radiating Powers of Surfaces, and its application to the Surfaces of 
various Mineral Substances.”?’ By W. Hopkins, Esq., M.A., F.R.S. 

When the author's Memoir on the Conductivity of various sub- 
stances was presented to the Society, it was intimated to him on the 
part of the Council of the Society, that it might be advisable to de- 
termine absolute instead of relative conductivities, the latter only 
having been attempted in his previous experiments. It is partly 
in consequence of this intimation, and partly from the desire to make 
his former -investigations more complete, that the author has given 
his attention to the construction of a calorimeter which might serve 
for this purpose. His present memoir contains a description of this 
instrument, with the results obtained from its application to the 
surfaces of various substances. 

The apparatus used by Messrs. Dulong and Petit was more deli- 
cate and complete than the simpler instrument devised by the author 
of this paper, but it was calculated only to determine the radiatimg 
powers of substances of which the bulb of a thermometer could be 
constructed, or with which it could be delicately coated. The only 
substances to which, in fact, it was applied, were glass and silver, 
the radiation taking place, in the first case, from the naked bulb of 
the thermometer, and, in the second, from the same bulb coated 
with silver paper. In these cases, too, it was the whole heat radi- 
ating In a given time from the instrument, and not that which radiated 
from a given area, that was determined. For this latter purpose the 
apparatus was not well calculated, on account of the difficulty of ob- 
taining with accuracy the area of the surface from which radiation 
took place. The instrument here described can be easily applied to 
any plane radiating surface, while the area of that surface can be easily 
determined to any required degree of accuracy. The quantity of 
heat radiating under given conditions, froma unit of surface ina unit 
of time, can thus be easily ascertained. The paper contains a detailed 
description of the instrument, and of the experiments made with it. 

The following are experimental results thus obtained,—the unit 
of heat being that quantity of heat which would raise 1000 grs. of 
distilled water 1° Centigrade. ‘The formula is that of Dulong and 
Petit, where 

0= temperature of the surrounding medium (the air in these ex- 
periments), expressed in Centigrade degrees ; 

¢= the excess of the temperature of the radiating surface above 
that of the surrounding medium, in Centigrade degrees ; 

p= pressure of the surrounding medium (the atmosphere in these 
experiments), expressed by the height of the barometer in metres ; 

a= 1:0077, a numerical quantity which is always the same for all 
radiating surfaces and surrounding media. 


On the Construction of a new Calorimeter. 463 


Then if Q denote the quantity of heat, expressed numerically, 
which radiates from a unit of surface (a square foot) in a unit of 
time (one minute), we have the following results for the substances 
specified :— 

Glass. 


9-566 a%(at'—1)+°03720 (5) 
Dry Chalk. 
Q= 8:613 a%(a'—1)+-03720 (5) ° 
Dry New Red Sandstone. 
= 8:377 a%(a'—1)+-03720 (4) prs 


Q 


Sandstone (building stone) 
Q= 8-882 a%(at—1)++03720 (4) 


45 
fe 


Polished Limestone. 
45 
Q= 9:106 a%(aé'—1)+°03720 (4) gi298 


Unpolished Limestone (same block as the last). 
"45 
@=—12:808 a9(at—1)+-03720 (4) 2233 


‘On Isoprene and Caoutchine.” By C. Greville Williams, Esq. 


This paper contains the results of the investigation of the two prin- 
cipal hydrocarbons produced by destructive distillation of caout- 
chouc and gutta percha. 

Isoprene. 

This substance is an exceedingly volatile hydrocarbon, boiling 
between 37° and 38° C.; after repeated cohobations over sodium, it 
was distilled and analysed. The numbers obtained as the mean of 
five analyses were as follows :— 


Experiment. Calculation. 
oe a 
Carbon % 1)..; «8870 Ces 160 88-2 
Hydrogen. . 12°1 eats 11°8 

68 100:0 


Three of the specimens were from caoutchouc and two from gutta 
percha. + The vapour-density was found to be at 58° C. 2°40. Theory 
requires, for C** H®=4 volumes, 2°35. The density of the liquid 
was 0°6823 at 20°C. 


Action of Atmospheric Oxygen upon Isoprene. 


Isoprene, exposed to the air for some months, thickens and acquires 
powerful bleaching properties owing to the absorption of ozone. On 


464 Royal Society :— 


distilling the ozonized liquid, a violent reaction takes place between — 
the ozone and the hydrocarbon. All the unaltered hydrocarbon distils 
away, and the contents of the retort suddenly solidify to a pure, 
white, amorphous mass, yielding the annexed result on combustion :— 


Experiment. Calculation. 
—__-_s*—————--_ Eres Ce 
Carbon. °.ay73'5 C260 78°95 
Piydroseny 077 Bp 8 10°52 
Oxysen i. 10" O 8 10°53 

76 100°00 


This directly-formed oxide of a hydrocarbon is unique, as regards 
both its formula and mode of production. 


Caoutchine. 


Himly’s analysis was correct. The mean results of three analyses 
are compared in the following Table with those of M. Himly :— 


Mean. Himly. Calculation. 
—— at 
Carbon’) >> S381 88°44 Ce 120 88°2 
Hydrogen . 11:9 11°56 He! AS 11°8 
136 100°0 


Two of the determinations, the results of which are incorporated 
in the above mean, were made on a substance from gutta percha. 
The vapour-density was :— 


Experiment. Himly. Calculation = 4 vols. 


4°65 4°46 4°6986 


We now for the first time see the relation between the two hydro- 
carbons. Itis the same as between amylene and paramylene. The 
author discusses the boiling-point of these bodies, and shows that 
they form most decided exceptions to Kopp’s empirical law. 


Action of Bromine on Caoutchine and its isomer Turpentine. 

Caoutchine and turpentine act on bromine in precisely the same 
manner. One equivalent of the hydrocarbon decolorizes four equi- 
valents of bromine. To determine this point quantitatively, eight 
experiments were made, four with turpentine and four with caout- 
chine. The quantity of bromine-water employed was 20 cub. cents. 
=0'2527 gramme bromine. 


Mean of four turpentine experiments. Mean of four caoutchine experiments. 


0°1074 grm. 0°1091 grm. 


Conversion of Turpentine and Caoutchine into Cymole. 


By the alternate action of bromine and sodium on caoutchine or 
turpentine, two equivalents of hydrogen are removed, the final result 
being cymole, having exactly the odour hitherto considered charac- 
teristic of the hydrocarbon obtained from oil of cumin, and quite 
distinct from that of camphogene. The liquid was identified by the, 


Mr. C, G. Williams on Isoprene and Caoutchine. 465 


annexed analyses. No. I. was from turpentine, II. and III. from 
caoutchine. 


Experiment. Calculation. 
ca — a 
i II. IIT. Mean. 


Carbon . . 89'2 89:5 89°5 89°4 OE 120.,.1,89:6 
Hydrogen . . 10°5 10°4 10°4 10°4 H“ 14 10:4 

134 100°0 
Agreeing perfectly with the formula C”? H™*, 


Paracymole. 


At the same time that cymole is formed, there is a production of 
an oil having the same composition, but boiling about 300°C. The 
author has provisionally named it paracymole. 


Action of Sulphuric Acid on Caoutchine. 


Sulphuric acid acts on caoutchine, converting it almost entirely into 
a viscid fluid like hévééne, at the same time a very small quantity of a 
conjugate acid is formed, having the formula 

ex H’ S? O°: ; 
the composition was determined from that of the lime salt, which on 
ignition, &c., gave a quantity of sulphate of lime equal to 8:3 per 
cent. of calcium; C* H” CaS? O° requires 8°5. 

The author considers the action of heat on caoutchouc to be merely 
the disruption of a polymeric body into substances having a simple 
relation to the parent hydrocarbon. He deduces this view from the 
similarity in composition between pure caoutchouc, isoprene, and 
caoutchine. 

The following Table contains the principal physical properties of 
isoprene and caoutchine :— 


Table of the Physical Properties of Isoprene and Caoutchine. 


Vapour-density. 


Name. Formula. | Boiling-point. a gee ee 
; Ghanieye Expt. Calculated. 
Tsoprene C10 HS Sf 0°6823 at 20° 2°44 2°349 
Caoutchine| C?? H16 UALS 0°8420 4°65 4-699 


In the calculations rendered necessary by the numerous vapour- 
density determinations contained in this paper, and more especiall 
in those ‘‘On some of the products of the Destructive Distillation of 
Boghead Coal,’ the author has so repeatedly had to ascertain the 


: 1 : 
value of the expression ——_—______, that he was induced to calcu- 

: P 1+0-00367 1" 

* (Note received July 27.) Both the cymole from turpentine and that from 
caoutchine were converted into insolinic acid by bichromate of potash and sul- 
phuric acid. The quantitative determinations made on the silver salt of the acid 
were almost theoretically exact. 


Phil, Mag. 8. 4, Vol. 21, No. 142. June 1861, 2H 


466 Royal Society :— 


late it once for all for each degree of the Centigrade thermometer from 
1° to 150°. As it is always easy so to manipulate as to prevent the 
value of T falling between the whole numbers, the Table proved a 
most valuable means of saving time ; the author has therefore appended 
it to his paper in the hope of its proving equally useful to other work- 
ing chemists. 


*‘On the Thermal Effects of Fluids in Motion—Temperature of 
Bodies moving in Air.” By J. P. Joule, LL.D., F.R.S., and Pro- 
fessor W. Thomson, LL.D., F.R.S. 

An abstract of a great part of the present paper has appeared in 
the Phil. Mag. vol. xv. p. 477. To the experiments then adduced 
a large number have since been added, which have been made by 
whirling thermometers and thermo-electric junctions in the air. The 
result shows that at high velocities the thermal effect is proportional 
to the square of the velocity, the rise of temperature of the whirled 
body being evidently that due to the communication of the velocity 
to a constantly renewed film of air. With very small velocities of 
bodies of large surface, the thermal effect was very greatly imcreased 
by that kind of fluid friction the effect of which on the motion of 
pendulums has been investigated by Professor Stokes. 


On the Distribution of Nerves to the Elementary Fibres of 
Striped Muscle.” By Lional 8. Beale, M.B., F.R.S. 


On the Effects produced by Freezing on the Physiological Pro- 
perties of Muscles.” By Michael Foster, B.A., M.D. Lond. 


* On the alleged Sugar-forming Function of the Liver.” By 
Frederick W. Pavy, M.D. 


«A new. Ozone-box and Test-slips.” By E. J. Lowe, Esq., 
F.R.A.S., F.L.S. &c. 

The ordinary form of Ozone-box being very cumbersome, the pre- 
sent one has been contrived to supersede it*. The box is simple in 
construction, small in size, and cylindrical in form; the chamber in 
which the ¢est-slips are hung is perfectly dark, and at the same time 
there is a constant current of air circulating through it, no matter 
from what quarter of the compass the wind is blowing. The air 
either passes in at the lower portion of the box and travels round a 
circular chamber twice, until it reaches the centre (where the test- 
slips are hung) and then out again at the upper portion of the box 
in the same circular manner, or in at the top and out again at the 
bottom of the box. 

Fig. 1 represents a section of the upper portion of the box, showing 
the manner in which the air enters and moves along to the centre 
chamber (where the test-slip is hung at A), and figure 2 represents 
a section of the lower half of the box where the air circulates in the 
opposite direction, leaving the box on the side opposite to that on 
which it had entered. 


* A specimen of the instrument was forwarded with the paper. 


Mr. E. J. Lowe on a new Ozone-box and Test-slips. 467 
Fig. 1. Fig. 2. 


The box has been tested and found to work well. 

On three different dates, when there was much ozone, test-slips were 
hung in one box, whilst others were hung in another which had the 
two entrances sealed up in order that no current of air should pass 
through ; the result was satisfactory, viz. :— 


Example. New ozone-box. New ozone-box sealed up. 
] 10 
2 9 0 
eee gi 0 


Then again, in five examples of test-slips being exposed without 
any box, in comparison with those placed in this new box, the result 
was :— 


Example. In new ozone-box. Exposed to north without 
a box. 
1 10 Ss 
2 9 9 
3 7 7 
4 10 9) 
4) 2 0 


The ozone-box is capable of being suspended at an elevation above 
the ground ; and this appears to be a great advantage, because eleva- 
tion seems necessary in order to get a proper current of air to pass 
across the test-slips ; indeed as an instance it may be mentioned, that 
at an elevation of 20 feet there is almost always more indication of 
ozone than at 5 feet. 

The plan adopted here is to suspend the box to a T support, it 
being drawn up to its proper place by means of a thin rope passing 
over a pulley ; and there is less trouble in examining and changing 
the test-slips in this manner than there was in the old method. 

The box, as described, is made by Messrs. Negretti and Zambra 
of Hatton Garden. 

It has been urged that a box was scarcely necessary for ozone 
test-slips; but as the papers fade on exposure to light, it must be 
evident that in order to register the maximum amount of ozone a 
dark box is required. 

Test-slips.— Paper-slips being so fragile, I have substituted others 
made of calico. The calico is to all intents and purposes chemically 
pure, containing only a few granules of starch, used in the first pro- 
cess of its manufacture, which it is very difficult to remove, being 
enveloped in the cotton fibre ; it is, however, thought to be purer than 


2H2 


468 Royal Society. 


the paper that is used for these test-slips, every precaution having 
been taken to make it so. 

Results of observations.—The following Tables have been con- 
structed from observations made between the lst of May, 1859, and 
the 3lst of March, 1860. 


TABLE I, 


Mean amount of Ozone observed from Test-slips hung for twelve 
hours, both at night and in the daytime, in comparison with others 
hung for twenty-four hours. 


Papers exposed for | Papers exposed for Difference 


twelve hours. twenty-four hours, ayes oa 

During the month of i oe CS RE SSre cwentecoue 

Day. | Night. Pate Day. | Night. oo hours. 

1859. May.........{ O°4 13 0-9 Je 1:9 0:8 0-7 0-6 
Sune, ..dint 03 | 09 | O1 3) 1-5, se 05 | 06 
Tully... .éseck 09 | 10] O1 | 1:2 | 13 | O1 || 08g 08 
August...... 07 14 | 07 1:2 18 0-6 0-5 0-4 
September .| 1:9 2°6 0:7 2°5 30 0:5 0-6 O-4 
October ...| 095 0-7 0:2 0:7 0-9 0-2 0-2 0-2 
November..| 1:5 LZ, 0:2 1:8 2-1 0:3 0-3 0:4 
December...| 1°7 2:0 0:3 2-1 25 0-4 0-4 0:5 
1860. January ...} 2°38 | 2:8 | 0-0 So {oo o, | ees 0-4 | 07 
February ...| 273 2°8 0:5 2°6 3°0 0-4 0-3 0-2 
Marchicvens. 49 5:2 0:3 5-2 5°6 0-4 0:3 0-4 

Mean scsi: 17 2-0 0:3 2-1 2°5 0-4 0:4 0-5 


The ozone being always in excess in the night, and the tests exposed 
for twenty-four hours showing always an excess over those only ex- 
posed for twelve hours. 


Mareh ..:... 0 


ed 
e 
=) 
oa 
@ 
a] 
fo) 
rh 
fo 
~ 
<< 
6 
— 
— 
Go 
for] 
oO 


TaBxe II. 
Number of observations without any visible ozone. 
During the night. During the day. 
Month. 
Twelve hours’ | Twenty-four || Twelve hours’ | Twenty-four 
exposure. hours’ exposure. exposure. hours’ exposure. 

1859. May......... a 4 19 12 
VONE sexiness 18 10 15 9 
SLY chino ab 18 12 | 18 13 
August...... 10 4 15 9 
September.. 2 0 0 0 
October ... 16 12 18 14 
November.. 10 7 10 10 
December... 10 sf) 7 5 
1860. January ... 8 6 “, 5 
February ... 12 6 9 9 
0 0 0 


Cambridge Philosophical Society. 469 


Mean amount of ozone with the box suspended at the height of 


25 feet. 
1859. December 24 hours’ exposure =3°0 48 hours’ exposure =5:0 
1860. January... 24 hours’ exposure =3°9 48 hours’ exposure =4'5 
February 24 hours’ exposure =3°7 48 hours’ exposure =5°4 
? b] 


March ... 24 hours’ exposure =5°9 48 hours’ exposure =6°4 


Mean amount of ozone with the box suspended at the height of 
40 feet, March 1860, with twenty-four hours’ exposure =7'l. 


CAMBRIDGE PHILOSOPHICAL SOCIETY. 
[ Continued from‘vel. xvii. p. 316.] 


October 31, 1859.—A communication was made by Mr. Hopkins 
«“‘On the construction of a new Calorimeter for determining the 
Radiating Power of the Surfaces of Heated Bodies.” 


November 14.—A communication was made by the Master of 
Trinity College ‘‘On the Mathematical part of Plato’s Meno.” 


November 28.—The Rev. Dr. Donaldson read a paper “On the 
Origin and proper value of the word ‘ Argument.’ ”’ 

The author first investigated the etymology and meaning of the 
Latin verb arguo, and its participle argutus. He showed that arguo 
was a corruption of argruo = ad gruo; that gruo (in argruo, ingruo, 
congruo) ought to be compared with xpotw, which means ‘to dash 
one thing against another,”’ especially for the purpose of making a 
shrill, ringing noise; that arguo means ‘‘ to knock something for the 
purpose of making it ring, or testing its soundness,” hence “to test, 
examine, and prove anything;”’ and that argutus signifies ‘“‘ made to 
ring,” hence ‘making a distinct, shrill noise,” or “tested and put 
to the proof.” Accordingly argumentum means id quod arguit, ‘ that 
which makes a substance ring, which sounds, examines, tests, and 
proves it.” 

It was then shown that these meanings were not only borne out 
by the classical usage of the word, but also by the technical appli- 
cation of ‘‘argument” as a logical term. For it is not equivalent 
to ‘argumentation,’ or the process of reasoning; it does not even 
denote a complete syllogism; though Dr. Whately and some other 
writers on logic have fallen into this vague use of the word, and 
though it was so understood in the disputations of ;the Cambridge 
schools. The proper use of the word ‘‘argument”’ in logic is to 
denote ‘‘ the middle term,” 7. e. ‘‘the term used for proof.” Ina 
sense similar to this the word is employed by mathematicians; and 
there can be no doubt that the oldest and best logicians confine the. 
word to this, which is still its most common signification. 

_ The author@entered at some length into the Aristotelian definition 
of the enthymeme, which may be rendered approximately by the word 
“argument.” He also explained how the words ‘topic’ and 
‘‘argument”’ came to denote the subject of a discourse or even of a 


470 Cambridge Philosophical Society :— 


‘picture. He showed, by a collection of examples from the best 
English poets, that the established meanings of the word ‘“argu- 
ment’”’ are reducible to three: (1) a proof or means of proving; 
(2) a process of reasoning or controversy made up of such proofs; 
(3) the subject matter of any discourse, writing, or picture. And he 
maintained that the second of these meanings ought to be excluded 
from scientific language. 


December 12.—The following paper from the Astronomer Royal 
was read, ‘‘Supplement to the proof of the Theorem that ‘ Every 
Algebraic Equation has a Root.’ ” 

‘he author expressed his want of confidence in every result ob- 
tained by the use of imaginary symbols, and in this supplement 
demonstrated that the left-hand member of every algebraic equation 
of the form ¢(#)=0 admitted of resolution, either into real linear 
factors, or into real quadratic factors. 


Professor Miller also made a communication ‘‘ On a new portable 
form of Heliotrope, and on the employment of Camera Lucida prisms 
and right-angled prisms in surveying.” 


February 13, 1860.—The Rev. H. A. J. Munro read a paper . 
“On the Metre of an Inscription copied by Mr. Blakesley, and 
printed by him in his ‘ Four Months in Algeria,’ p. 285.” 


February 27.—The Rev. Professor Sedgwick made the following 
communications :— 

1. ‘* Anaccount of Mr. Barrett’s progress in the Survey of Jamaica, 
with some remarks on the Distribution of Gold Veins.” 

2. ‘“Some account of the Geological Discoveries in the Arctic 
Regions.” 


March 12.—The Rev. Professor Challis made a communication 
‘On the Planet within the orbit of Mercury, discovered by M. 
Lescarbault.” 

By a recent comparison of the theory of Mercury’s orbit with 
observation, M. Leverrier found that the calculated secular motion 
of the perihelion of that planet requires to be increased by 38", and 
that this difference between observation and theory cannot be ac- 
counted for by the attractions of known bodies of the solar system. 
In a letter addressed to M. Faye, and published in the Paris Meteo- 
rological Bulletins of October 4, 5, and 6, 1859, he suggested that 
the difference might be due to the attraction of a group of small 
planets circulating between Mercury and the Sun. On December 22 
of the same year, M. Lescarbault, a physician and amateur astro- 
nomer, residing at Orgéres, about sixty miles south-west of Paris, 
announced in a letter to M. Leverrier that he had seen on March 26, 
1859, a small round spot traversing the sun’s disc, which he con- 
sidered to be a planet inferior to Mercury. Naturally much inter- 
ested by this information, M. Leverrier went to Orgéres on Decem- 
ber 31, and after closely interrogating M. Lescarbault respecting the 
particulars. of the observation, and the instrumental means by which 


Prof. Challis on the Planet within the Orbit of Mercury. 471 


it was made, he returned with the conviction that the observation 
was trustworthy, and that a new planet had been discovered 
(Comptes Rendus, January 2, 1860, p. 40). 

M. Lescarbault had long conceived the idea of detecting inferior 
planets by watching the sun’s disk for transits, and in 1858 he put 
his project into execution. He was in possession of a good telescope 
of 33 inches aperture and 5 feet focal length, mounted with an alti- 
tude and azimuth movement, and provided with a finder magnifying 
6 times. The power of the eyepiece employed in the observations 
of March 26 was 150. Not being furnished with a position-circle, 
he adopted the following means of obtaining angular measurements. 
The eyepiece of the telescope and the eyeviece of the finder each 
had at its focus two wires crossing at right angles, and the wires of 
the latter were so adjusted that a star seen at their intersection was 
seen at the same time at the intersection of the wires of the telescope. 
There were also in the eyepiece of the finder two wires parallel to, 
and on opposite sides of, each cross-wire, and distant by about 16’. 
A circular card about 6 inches in diameter, and graduated to half 
degrees, was placed concentric with the tube of the eyepiece of the 
finder, and apparently could be moved both about the tube and, with 
the tube, about the axis of the finder. A cross-wire of the telescope 
and a cross-wire of the finder were adjusted vertically by looking at 
a distant plumb-line, and the diameter of the card containing the 
zero of its graduation was placed vertically by means of a small plumb- 
line and eye-hole approximately arranged for that purpose. ‘The 
mode of using this apparatus for anguiar measurements will be seen 
by the following account of the observations. The observer had 
also a small transit-instrument by which he obtained true time, using 
for timepiece his watch, which, as it only indicated minutes, required 
the supplement of a temporary seconds’ pendulum. 

In the account which M. Lescarbault gives of his observations, he 
says that it had been his practice to examine with the telescope the 
contour of the sun for a considerable interval on each day in which 
he had leisure, and that at length, on March 26, 1859, he saw a small 
round spot near the limb, which he immediately brought to the inter- 
section of the wires of the telescope. ‘Then, according to his state- 
ment, he quickly turned the graduated card till two of the wires of 
the finder were tangents to the sun’s limbs, or equidistant from them. 
But it is evident that to effect an angular measurement in this way, 
one of the middle wires of the finder must have been placed tangen- 
tially to the sun’s limb at the point of their intersection, to which 
point the spot had just been brought. Assuming that this operation 
was performed, the angular distance of the point from the vertical 
diameter of the sun might be read off, as the account states that it 
was, by applying the plumb-line apparatus to the graduated card. 
This method could only give a rough measure of the angular position 
of a point very near the sun’s limb; and in fact M. Lescarbault does 
not appear to have attempted to determine the position of the spot 
during the interval between the beginning and the end of the 
transit. He states that the spot had entered a little way on the sun 


4.72 Cambridge Philosophical Society :— 


when he first saw it, and that the time and place of entrance were 
inferred by estimation. 

The following are the immediate results of the observations :— 
The spot entered at 45 5™ 36° mean time of Orgéres at the angular 
distance of 57° 22' from the north point towards the west, and de- 
parted at 55 22™ 44s, at 85° 45! from the south point towards the 
west, occupying consequently in its transit 1" 17™ 88. The length 
of the chord it described was 9! 14", and its least distance from the 
sun’s centre 15! 22, M. Lescarbault also states that he judged the 
apparent diameter of the spot to be at most one-fourth of that of 
Mercury, when seen by him with the same telescope and magnifying 
power during its transit across the sun on May 8, 1845. ‘The lati- 
tude of Orgéres is 48° 8' 55", and longitude west of Paris, 2™ 355. 

From these data M. Leverrier ascertained, by calculating on the 
hypothesis of a circular orbit, that the longitude of the ascending 
node is 12° 59!, the inclination 12° 10’, the mean distance 0°1427, 
that of the earth being unity, and the periodic time 19°7 days. Also 
he found that the greatest elongation of the body from the sun is 8°, 
the inclination of its orbit to that of Mercury 7°, the real ratio of 
its diameter to Mercury’s 1 to 2°58, and that its volume is one- 
seventeenth the volume of Mercury on the supposition of equal den- 
sities. This mass is much too small to account for the perturbation 
of Mercury’s perihelion. According to these results, the periods at 
which transits may be expected are eight days before and after 
April 2 and October 5, the body being between the earth and sun 
near its descending node at the former period, and near its ascend- 
ing node at the latter. 

After the announcement of this singular discovery, it was found 
that other observations of a like kind had been previously made. 
Several instances are collected by Professor Wolf in the tenth num- 
ber of his Mittheilungen tiber die Sonnenflecken, eight of which are 
quoted in vol. xx. (p. 100) of the Monthly Netices of the Royal 
Astronomical Society. ‘I‘wo of these, the observation of Stark on 
October 9, 1819, and that of Jenitsch on October 10, 1802, agree 
sufficiently well with the calculated position of the node of the object 
seen by Lescarbault. But the spot seen by Stark is stated to have 
been about the size of Mercury. 

Capel Lofft saw at Ipswich, on January 6, 1818, at 11 a.m.,a 
spot of a ‘sub-elliptic form,’ which advanced rapidly on the sun’s 
disc, and was not visible in the evening of the same day (Monthly 
Magazine, 1818, part 1, p. 102). 

Mr. Benjamin Scott, Chamberlain of London, saw about mid- 
summer of 1847 a large and well-defined round spot, comparable in 
apparent size with Venus, which had departed at sunrise of the next 
day (Evening Mail, January 11, 1860). 

Pastorff of Buchholz records that he saw on October 28 and 
November 1, 1836, and on February 17, 1837, two round black, 
spots of unequal size, moving across the sun at the respective hourly 
rates of 14’, 7", and 28’. Also he announced, January 9, 1835, to 
the Editor of the Astronomische Nachrichten, that ‘‘ six times in the 


Prof. De Morgan on the Syllogism No. IV. 473 


previous year he had seen two new bodies pass before the sun in dif- 
ferent directions and with different velocities. ‘The larger was about 
3" in diameter, and the smaller from 1” to 1°25. Both appeared 
perfectly round. Sometimes the smaller preceded, and at other 
times the larger. The greatest observed interval between them was 
1’ 16": at times they were very near each other. Their passage 
occupied a few hours. Both appeared as black as Mercury on the 
sun, and had a sharp round form, which, however, especially in the 
smaller, was difficult to distinguish.” Schumacher considered it his 
duty as editor to insert the communication, but evidently did not 
give credit to it (Astron. Nachr. No, 273). 

In vol. ii. of the Correspondence between Olbers and Bessel, 
mention is made in p. 162 of an observation at Vienna by Steinhtibel, 
of a dark and well-defined spot of circular form which passed over 
the sun’s diameter in five hours. Olbers, from these data, estimates 
the distance from the sun to be 0°19, and the periodic time thirty 
days. It is remarkable that Stark saw about noon of the same day 
a singular and well-defined circular spot, which was not visible in 
the evening. ‘This is one of the instances in vol. xx. of the Monthly 
Notices of the Astronomical Society. 

These accounts appear to prove that transits of dark round objects 
across the sun are real phenomena; but it would perhaps be prema- 
ture to conclude that they are planetary bodies. If the object ob- 
served by Lescarbault be a planet, it is certainly very surprising that 
it has not been often seen. Schwabe, after observations of the sun’s 
face continued through thirty-three years, has recorded no instance 
of such atransit. It is probable that now attention has been espe- 
cially drawn to the subject, future observations, accompanied by 
measures (of which Lescarbault’s are the first instance), may throw 
light on the nature of these phenomena. 


April 23.—Professor De Morgan read a paper ‘‘ On the Syllogism, 
No. IV., and on the Logic of Relations.” 

In the third paper were presented the elements of a system in 
which only onymatic relations were considered; that is, relations 
which arise out of the mere notion of nomenclature—relations of 
name to name, as names.. The present paper considers relation in 
general. It would hardly be possible to abstract the part of it 
which relates to relation itself, or to the author’s controversy with 
the logicians, who declare all relations material except those which 
are onymatic, to which alone they give the name of formal. Mr. 
De Morgan denies that there is any purely formal proposition except 
“there is the probability a that X is in the relation L to Y;” and 
he maintains that the notion ‘ material’ non suscipit magis et minus ; 
so that the relating copula is as much materialized when for L we 
read identical as when for L we read grandfather. 

Let X..LY signify that X stands in the relation L to Y; and 
X.LY that it does not. Let LM signify the relation compounded 
of L and M, so that X..LMY signifies that X isan L of an M of Y. 
In the doctrine of syllogism, it is necessary to take account of 


474, Cambridge Philosophical Society :— 


combinations involving a sign of inherent quantity, as follows :— 

By X..LM’Y is signified that X is an L of every M of Y. 

By X..L,MY it is signified that X is an L of none but Ms of Y. 

The contrary relation of L, not -L, is signified by 7. Thus X. LY is 
identical with X..7Y. ‘The converse of L is signified by L~*: thus 
X..LY is identical with Y..L7'X. ‘This is denominated the 
L-verse of X, and may be written LX by those who prefer to avoid 
the mathematical symbol. 

The attachment of the sign of inherent quantity to the symbols of 
relation is the removal of a difficulty which, so long as it lasted, pre- 
vented any satisfactory treatment of the syllogism. There is nothing 
more in X..LM/Y than in every M of Y is an L~’ of X, or 
MY))L~'X, X and Y being individuals; and nothing more in 
X..L,MY than in L~'X))MY, except only the attachment of the 
idea of quantity to the combination of the relation. 

When X is related to Y and Y to Z, a relation of X to Z follows: 
and the relation of X to Z is compounded of the relations of X to Y 
and Y to Z. And this is syllogism. Accordingly every syllogism 
has its inference really formed in the frst figure, with both premises 
affirmative. For example, Y.LX and Y..MZ are premises stated 
in the third figure: they amount to X..L7'Y and Y..MZ, 
giving X../~*MZ for conclusion. This affirmative form of conclu- 
sion may be replaced by either of the negative forms X .L~’M’Z or 
Re WL 

The arrangement of all the forms of syllogism, the discussion of 
points connected with the forms of conclusion, the extension from 
individual terms in relation to quantified propositions, the treatment 
of the particular cases in which relations are convertible, or transi- 
tive, or both—form the bulk of the paper, so far as it is not contro- 
versially directed against those who contend for the confinement of 
the syllogism to what Mr. De Morgan calls the onymatic form. 

An appendix follows the paper, on syllogism of transposed quan- 
tity, in which the number of instances included in one premise is 
equal to the whole number of existing instances of the concluding 
term in the other premise. 


Mr. J. H. Rohrs also read a paper ‘“‘ On the Motion of Bows, and 
thin Elastic Rods.” 


May 7.—The Rev. Professor Sedgwick made a communication 
“On the Succession of Organic Forms during long geological 
periods; and on certain Theories which profess to account for the 
origin of new species.” 

May 21.—The Public Orator read a paper ‘‘ On the Pronunciation 
of the Ancient and Modern Greek Languages.” 

He gave a rapid sketch of the ‘‘ Reuchlin and Erasmus” contro- 
versy in the sixteenth century, especially the part taken in it at 
Cambridge by Cheke, Smith, Ascham, and Bishop Gardiner; and 
then proceeded to show how the proper sounds of the Greek letters 
may be determined from the following sources ;—~ 


Pronunciation of the Ancient and Modern Greek Languages. 475 


1. Distinct statements of grammarians. 

2. Incidental notices in other ancient authors. 

3. Variations in writing of inscriptions and MSS. 

4. Phonetic spelling of cries of animals. 

5. Puns and riddles. 

6. The value of the respective letters in other languages employ- 
ing the same alphabet, especially Latin. 

7. The way in which Latin proper names are spelt in Greek, and 
vice versd. 

8. The traditions of pronunciation preserved in modern Greek. 

He concluded that, on the whole, the method of Erasmus ap- 
proached more nearly to the ancient pronunciation than that of 
Reuchlin. 

‘«« But,” he proceeded, ‘“‘ when we consider the untrustworthiness 
of each of these sources of evidence taken singly, and when moreover 
we find them often in conflict with one another, it cannot be ex- 
pected that the result should be very certain or very satisfactory. 
There are also other considerations which enhance the difficulty of 
the inquiry. As there were very marked dialectic varieties in Greece, 
so there may have been local variations even in Attica itself. 

“The pronunciation, too, changed from time to time. Plato gives 
us proof of this in the ‘ Cratylus.’ ” 

After quoting several instances, and showing that great changes 
both in pronunciation and spelling had taken place in modern lan- 
guages, French, Spanish, and English, ‘it would,” he said, ‘be 
hopeless to attempt to determine the pronunciation of any language 
by a reference to its orthography at a time when both were perpe- 
tually changing. But in the history of every nation there arrives a 
time when the creative energy of its literature seems to have spent 
itself; when, instead of developing new forms, men begin to look 
back and not forward, to comment and to criticise. ‘Then it is that 
a language begins to assume, even in minor and merely outward 
points, such as pronunciation and spelling, a fixity and rigidity 
which it retains with scarcely any change so long as the nation 
holds together. Such a period in Greek history was that which 
began with the grammarian sophists in the fifth century B.c., and 
culminated in Aristarchus and Aristophanes of Byzantium. In the 
spelling and pronunciation of Greek there was probably very little 
change from that time to the end of the third century a.p.” 


October 19.—Dr. Paget made a communication ‘“‘ On some Points 
in the Physiclogy of Laughter.”’ 


November 12.—The Public Orator read a paper (a sequel to that 
on May 21) ‘‘On the Accentuation of Ancient Greek.” 

The question of accents was not discussed in the Reuchlin and 
Erasmus dispute. At that time all pronounced according to the 
system of accents introduced by the Greeks of Constantinople, who 
first taught the ancient language to the Italians. 

It was probably in Elizabeth’s reign that we began to disuse the 
old pronunciation of vowels both in Greek and Latin; and concur- 
rently with this change we, as well as the other nations of Europe, 


476 Cambridge Philosophical Society. 


began to pronounce Greek, not with the modern Greek, but with 
the Latin accent. Jhe reasons were :— 

1. Teachers speaking the modern Greek were no longer required, 
so the tradition was not kept up. 

2. It saved much trouble to pronounce both languages with the 
same accentuation. 

3. The Greek accent perpetually clashes with quantity; the 
Latin much more rarely; never, indeed, in that syllable of which 
the quantity is most marked—the penultima. 

Isaac Vossius (1650-60) advocated the disuse of accentual marks 
altogether, as the invention of a barbarous age to perpetuate a bar- 
barous pronunciation. 

After showing the meaning of the word ‘accent’ as applied to 
modern languages, and discussing the accentuation of the German, 
English, French, &c., he proceeded to say: 

‘There are three methods of emphasizing a syllable:— 

1. By raising the note; 

2. By prolonging the sound ; 

3. By increasing its volume. 

‘«Scaliger, De Causis Lingue Latine, lib. ii. cap. 52, recognizes 
this division when he says that a syllable may be considered of three 
dimensions in sound, having height, length, and breadth. 

«‘ Now in our own language, when we accent a syllable, which 
of these dimensions do we increase? Generally all three, but not 
necessarily ; for when the prayers, for example, are intoned, 2. e. 
read upon one note, the accent is marked by increasing the volume 
of sound (the third method), which involves also a longer time in 
utterance, 7. e. a lengthening of quantity. In speaking, all three 
methods are employed, but one more prominently than the other, 
according to individual peculiarities of the speakers. What we 
blend, the Greeks kept distinct. 

‘«* We cannot understand the Greek system unless we bear this in 
mind. ‘They never confounded accent with quantity. Ineradicable 
habit prevents us from reverting in practice to their method, just as 
they would have been unable to comprehend ours. 

«Tt is clear from Dionysius, De Comp. Verb. lib. xi. cap. 75, that 
the dialogue in tragedy preserved the ordinary accentuation, which 
was disregarded only in choral passages set to music.” 

The practical conclusion was this: that while it would be desirable, 
if possible, to return to the Erasmian system of pronunciation, it 
would be extremely absurd to adopt the barbarous accentuation of 
modern Greek, which has quite lost the old essential distinction 
between accent and quantity. In this respect, as we cannot recover 
practically the ancient method, it is better to keep to our own system 
of the Latin accent, which does not confuse the learner’s notion of 
quantity in verse as the modern Greek does. 

An Athenian boy has the greatest difficulty in comprehending the 
rhythm of Homer or Sophocles. Hence it is not blind prejudice 
(as Professor Blackie asserts) which makes us keep to our old usage, 
but a well-grounded conyiction that we should lose more by changing 
than we should gain. ‘rae 


Intelligence and Miscellaneous Articles. 477 


November 26.—Professor Challis made a communication “‘ On the 
Solar Eclipse of July 18, 1860.” 


December 10.—Mr. Seeley read a “‘ Notice of Opinions on the 
Red Limestone at Hunstanton.” 


Professor Miller also described “ An Instrument for measuring the 
radii of arcs of Rainbows.” 


February 11, 1861.—Mr. H. D. Macleod read a paper ‘‘ On the 
present State of the Science of Political Economy.” , 

The writer took a general survey of the science as it at present 
exists, testing several generally received doctrines by the principles 
of inductive logic, and earnestly enforcing the necessity of a thorough 
reform of the whole science, which must be constructed on prin- 
ciples analogous to those of the other inductive sciences. 

February 25.—Dr. Humphry made a communication ‘On the 
Growth of Bones.” } 


March 11.—The Master of Trinity made a communication ‘‘ On 
the Timzeus of Plato.” 


LXX. Intelligence and Miscellaneous Articles. 


ON THE OPTICAL PROPERTIES OF THE PICRATE OF MANGANESE. 
BY M. CAREY LEA. 

So and Haidinger have described a remarkable property 

possessed by certain crystalline surfaces, of reflecting, besides 

the ray normally polarized in the plane of incidence and reflexion, 

another ray, polarized perpendicularly to that plane, and differing 

from the former in being coloured—a property rendered more con- 

spicuous by the fact that the colour of the ray so polarized abnormally 

is either complementary to, or at least quite distinct from the colour of 
the crystal itself. 

I find that this property is possessed to a remarkable degree by the 
picrate of manganese. ‘This salt crystallizes in large and beautiful 
_ transparent right-rhombic prisms, sometimes amber-yellow, some- 
times aurora-red, exhibiting generally the combination of principal 
. prism, and macrodiagonal, brachydiagonal and principal end planes. 
In describing this substance in a paper on picric acid and the picrates*, 
I mentioned that in a great number of specimens examined, no planes 
except those parallel with or perpendicular to the principal axis had 
been met with. Since then I have obtained in several crystalliza- 
tions specimens exhibiting a brachydiagonal doma; but this appears 
to be rather unusual. 

The optical properties of this salt are very interesting. It exhihits 
a beautiful dichroism. If the crystal be viewed by light transmitted 
in the direction of its principal axis, it appears of a pale straw-colour, 
in any other direction, rich aurora-red in some specimens, in others 
salmon-colour. A doubly refracting achromatized prism gives images 
of these two colours, unless the light be transmitted along the principal 
axis of the crystal of picrate, in which case both are pale straw-colour. - 


* Silliman’s American Journal, Noy. 1858. 


478 Intelligence and Miscellaneous Articles. 


But it also possesses in a high degree the property of reflecting 
two oppositely polarized beams ; and the great size of the crystals in 
which it may readily be obtained renders it peculiarly fitted for 
optical examination. If one of these crystals be viewed by reflected 
light while it is held with its principal axis lying in the plane of in- 
cidence and reflexion, the reflected light is found to be not pure 
white, but to have a purpleshade. Examined witha rhombohedron 
or an achromatized prism of Iceland spar, having its principal axis 
in the plane of incidence and reflexion, the ordinary image is white 
as usual, while the extraordinary is of a fine purple colour, the phe- 
nomenon having the greatest distinctness when the light is incident 
at the angle of maximum polarization. 

The experiment may be varied and the purple light beautifully 
seen without the use of a doubly reflecting prism, by allowing only 
light polarized perpendicularly to the plane of incidence to fall on 
the crystal; in this case the surface of the crystal appears rich deep 
purple, no white light reaching the eye. 

This property is not possessed by all the planes of the crystal, but 
is limited to the principal prism and brachy- and macrodiagonal end 
planes, in other words, to the planes parallel with the principal axis 
of the crystal. The brachydiagonal doma and OP planes do not 
possess it. Nor is it exhibited by the first-mentioned planes when 
the crystal is turned with its prismatic axis at right angles to the 
plane of incidence. 

All specimens of picrate of manganese do not possess this pro- 
perty to an equal extent. The crystals vary considerably in colour, 
and those which are full red exhibit it more strongly than the amber- 
coloured. Picric acid boiled with aqueous solution of cyanhydro- 
ferric acid and saturated with carbonate of manganese, gives crystals 
of a rich deep colour, which exhibit the purple polarized beam par- 
ticularly well. 

These properties are not possessed by the manganese salt alone, 
but also by the picrates of potash and ammonia ~ (especially when 
crystallized by very slow spontaneous evaporation in prisms of suffi- 
cient size), and the picrates of cadmium and peroxide of iron—with 
this difference, however, that while the prismatic axis of the crystal 
in the case of the cadmium and manganese salts must be in the plane 
of incidence, in the alkaline salts it must be perpendicular to that 
plane. As they all crystallize in the right-rhombic system, it is pro- 
bable that either the alkaline salts on the one hand, or the manganese 
and cadmium on the other, are prismatically elongated in the direction 
of a secondary axis. 

It is convenient that distinct phenomena should have distinct 
names; and none appears to have been assigned to this. Brewster 
speaks of it as a ‘‘ property of light,” and Haidinger uses the word 
“Schiller” for it. The terms dichroism, trichroism, and pleiochroism 
are limited to properties of transmitted light. I therefore suggest 
for the phenomenon here in question the name catachroism, using the 
preposition cara in the same sense as in the word xarorzpigw, to 
reflect (as a polished surface), applying it to express the property of 


Intelligence and Miscellaneous Articles. 479 


reflecting two beams—one normally polarized in the plane of in- 
cidence, and the other polarized in a plane perpendicular to it, 

The chromatic properties exhibited by the picrates of ammonia 
and potash are very remarkable in their variety. Their crystals 
possess :— 

Ist. The well-known play of red and green light. If a little very 
dilute solution of pure picrate of potash be spontaneously evaporated 
in a hemispherical porcelain basin, so as to form a network of ex- 
tremely slender needles, and these be viewed by gas-light, the play 
of colours is singularly brilliant. 

2nd. Dichroism. When by spontaneous evaporation of large quan- 
_ titres of solution of potash, or, better, of ammonia salt, transparent 
prisms of =); to ;4 inch diameter are obtained; these, viewed witha 
doubly refracting prism by transmitted light, give two images—one 
pale straw-colour, and the other deep brownish red. 

3rd. The above-described property of catachroism, or reflexion in 
the plane of incidence of oppositely polarized beams.—Silliman’s 
American Journal, November 1860. 


EXPERIMENTS ON THE POSSIBILITY OF A CAPILLARY INFILTRA- 
TION THROUGH POROUS SUBSTANCES, NOTWITHSTANDING A 
STRONG COUNTERPRESSURE OF VAPOUR. POSSIBLE APPLICA- 
TION TO GEOLOGICAL PHENOMENA. BY M. DAUBREE. 


In the grand phenomena which are to us the principal manifesta- 
tions of the activity of the interior of the globe, we see every day 
enormous quantities of water disengaged as steam from great depths. 
It may be asked if these incessant losses are not partially at least 
made up by a supply from this surface; and if so, in what way are 
these infiltrations effected ? 

It would be difficult to imagine that this supply was produced by a 
free circulation; for the way open for a descent would at the same 
time form an outlet also for the escape of vapour; and this objection 
would apply more especially to the volcanic regions, where the in- 
ternal vapour has sufficient tension to send columns of lava with a 
density two or three times that of water, to great heights above the 
level of thesea. In trying to reconcile these apparent contradictions, 
I have been led to inquire if water could not reach the deep and 
heated reservoirs, which yield it in a variety of ways, not by means 
of extended fissures, as has hitherto been supposed, but also by the 
porosity and capillarity of rocks. 

M. Jamin’s ingenious experiments* have shown how considerable 
is the influence which capillarity exerts in changing the conditions 
of equilibrium, established through the intervention of a liquid 
column, between two opposite pressures. 

But in previous experiments the temperature was the same in all 
parts of the capillary tube. It appeared important, more especially 
in reference to the geological problemewhich I have indicated, to see 
what would happen if the temperature was much higher at one part of 


* Phil. Mag. vol. xix. p. 204, 


480 Intelligence and Miscellaneous Articles. 


the capillary passage, so as to convert the liquid into vapour, and 
thus change it into a state in which it would probably not be subject 
to the laws which at first had caused its infiltration. 

I have constructed an apparatus, the principal object of which was 
to connect, by a porous plate of fine close-grained sandstone, on the 
one end a closed space in which the tension of vapour measured by 
a manometer was 14 atmosphere, and on the other a space in direct 
communication with the air, half-filled with water, which soon 
reached the boiling-point, but where the pressure could not exceed 
that of the atmosphere. 

Although the thickness of the interposed plate was only 2 centi- 
metres, the apparatus showed that the water is not driven back by 
the counterpressure of vapour; the difference of pressure on the two 
sides of the plate does not prevent the liquid from passing from the 
relatively cold region towards the relatively hot one, by a sort of 
capillary process, favoured by the rapid evaporation and drying of the 
latter. 

The effects of this apparatus, which I cannot explain in detail, 
will manifestly be materially augmented by increasing the thickness 
of the porous plate, and working with vapour at a higher temperature. 

But even these results prove that capillarity, acting in conjunction 
with gravity, can, in spite of very powerful internal counterpressures, 
force water from the superficial and cold regions of the globe to the 
deep and heated parts, where, in consequence of the temperature and 
pressure which it acquires, the vapour becomes susceptible of pro- 
ducing great mechanical and chemical effects*. Do not the prece- 
ding experiments thus touch the fundamental points of the mecha- 
nism of volcanos, and of the other phenomena generally attributed 
to the development of vapours in the interior of the globe, espe- 
cially earthquakes, the formation of certain thermal springs, the fill- 
ing metalliferous veins, as well as to various cases of the metamorphism 
of rocks? Without excluding the primitive water generally supposed 
to be incorporated in the internal melted masses, do not the same 
experiments show that infiltrations from the surface may also be 
operative, so that the deeper parts of the globe would be in a daily 
State of giving and taking, and that by a most simple process, 
although very different from the mechanism of the siphon and of 
ordinary springs? A slow, continuous, and regular phenomenon 
would thus become the cause of sudden and violent manifestations, 
like explosions and ruptures of equilibrium. —Comptes Rendus, Janu- 
ary 28, 1861. 


* It is known that water penetrates into the pores of most rocks, espe- 
cially those belonging to the stratified formations, as is shown by the water 
which they generally contain in nature. Bischoff has long called the atten- 
tion of geologists to this fact. Although the granite on which the sedi- 
mentary rocks rest is usually very impermeable, it has been traversed in 
many places by injections of eruptive rocks. Among the latter there are 
some, like the trachytes, so porous that they might well be particularly sus- 
pected of establishing a permanent capillary communication between the 
water of the surface and the heated masses which form the base of this 
kind of column. 

ere, A any | 


- 


if 


| Therm: below dt.) Phil. Mag. Ser.A.Nol, 21. PLVL. 
| 20 
bo 


2. Lee J | 


| 


a 


750° 


See OTL STII 


oO 


9) | 
a eee 


| 
| RBerres 
| 
: 
| 


J) Basie litho. 


‘ 


Scale: Scale of Cor ee Oe lo be applied to Cont: Merc: therm: below OC. ( Note. the minus readings of the Thermometer to be augmented.) Phil. Mag Sev-U.Nol.2\. PLY 
5 eae : |, May Ser.A.Nou. 21. PLU. 


—___tecorrect the : 0" | Bess 205 30) 
e AG gs : ese Se eeeeer SSS z Sa eee ese 
* and 100 0°70 0°20 a: 30 a40 0-50 060 0°70 0280 0°90 7200 710 


fe eae | 
Reece | ‘ 5 ‘ % a p : “3 
° 2 ° ° © 2 a ° © A ¢ ° S ° 2 2 co] 2 a ae) 
. pane Seues E S S S S te) S g S S S & S iq S r ‘ S 8 3 2 Wi SW oe Se, 
————+ 60 oa & = Ss S a & 3 & 8 Pet S$ 5 Ss Sy) rr) Ss S ~ 3 at S 3 S$ S = Ss = S S us S S § S Ss Moy, : 
a {i a 
aerator rel z a = g E 
) at a 2 2 is = 33 
= iam S8 
| Nn a8 
aaa = : : : : ; % si 
ese ale S ES 3 2 S S : ss 
ema ie & 
! ~. 


NOTE. The dotted Line x9,t5 the empirical formula below 
450° 100° and bbb the ernpwical formula above 100° 


— eee ee Celica =e? aa 
an Manches Sulphur — —}—— . Ac 
Lea wee A Wa ise |e BS 
(eh ree pee 1002 ae : : 2002. 7 ; : 

= S| ae re SSX TAL ET = OS M. Regnaulis Observations on Steam’ 

p———_} 80" a6 \e A | NS tronv 70° to 130°C. x 

eam 9 eC eee 8h -- tp ges Ye 

a = 5 

| ae Prares kither: 
pa | A ese suo 

aS | a a A 450° 

=a i Bg. 2. 
ss FPrrre’s Alcohol’ 

pee | : 100° is 
I *p 
i rey 


BB,BBBrepresent the aclual observations, 


| ete Ys 4 
: Munckes——~ Petroleam: ~~~ } 


“Le __uricorre, 


50° Se 


20 C=RSO.. Te Sone es 


"50° 


TEE ran cere AMeohol 


Fes 


A 


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THE 
LONDON, EDINBURGH ann DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE, 


SUPPLEMENT to VOL. XXI. FOURTH-SERIES. 


LXXI. On the Reflexion of Light at the Boundary of two Isotropic 
Transparent Media. By L. Lorenz*. 


AMIN, as is well known, discovered that Fresnel’s formule 
for the intensity of the rays reflected and refracted at the 
boundary of two isotropic transparent media do not perfectly 
agree with experiment, the difference bemg very considerable 
when the angle of incidence approaches to the angle of polariza- 
tion. Cauchy had already proved that, under these circum- 
stances, waves must be produced with longitudinal vibrations ; 
and having assumed that these waves were absorbed very rapidly 
(though not instantaneously, since in that case he would have 
returned to the formule of Fresnel), he now introduced a cor- 
rection into the formule which caused them to agree with ex- 
periment. 

All calculations, however, which have hitherto been made 
concerning the reflexion and refraction of light, have proceeded 
on the hypothesis of an instantaneous passage from one medium 
to the other, and a consequent instantaneous change of the 
index of refraction. Such a passage is, however, a mere meta- 
physical abstraction, which cannot possibly exist in nature; and 
the calculation would be more exact and more satisfactory if a 
gradual passage were admitted between the two media through 
a space which might afterwards be assumed to be as small as we 
please. It is, moreover, a fact that bodies are really surrounded 
by an atmosphere which must produce such a gradual change of 
refraction. 

The object of this paper is to show that Jamin’s experiments 
can only be reconciled with Fresnel’s formule when the calcula- 
tion is made on the above hypothesis. — 

In what follows, the case of total reflexion will not be con- 
sidered. 

If the incident light be polarized in the plane of incidence, 


* Translated by F. Guthrie, from Poggendorff’s Annalen, vol. cxi. p. 460. - 
Phil, Mag. 8, 4. No. 148, Suppl, Vol. 21. 21 


482 M. L. Lorenz on the Reflexion of Light at 


the angle of incidence being called x, and that of refraction z,, 
the ratio of the amplitudes of the incident, refracted, and reflected 
light, according to Fresnel, is 
2cosasinz, sin (#—z2z,) 
"sin (w+ 2) ‘sin (w@+a,) (2) 
1 1 
For the light polarized perpendicularly to the plane of incidence, 
the ratio of the same three amplitudes is 
2cosx sin 2, _ _ tan (e@—2,) (2) 
"sin (@+2,)cos(w—az,) © tan (w@+ 2) 
Assume now that these formule are correct when the difference 
between x and 2, is infinitely small, so that 2, =x+dz. - Sub- 
stituting this value of x, the above expressions become - 
dz dx 
sin 22 ) sin 2a" 
de dz 
sin 2a ° tan 2a” 


L:1+ 


1+ (4) 
We suppose that the incident ray approaches the bounding sur- 
face of the media at an angle a, and that its direction is there 
gradually changed by having to traverse successive parallel refrac- 
tive layers, until it emerges completely into the other medium 
at the constant angle £. 

In order to simplify the calculation, we will in the first in- 
stance neglect the retardation of the ray. 

Let A be the amplitude of the incident ray, and let this 
become y and y+dy for the refracted ray, when the angle of 
incidence, a, becomes xz and x+dz. Then, whatever may be 
the polarization, we have, according to (3) and (4 (4), 

dy 22 dx 
y sin Qa? 


from which, by integrating and determining the constants, 
we get 


tan @ 
a tan a 
The ray reflected from this layer, if it be polarized in the plane 
of incidence, has, according to (3), the amplitude a 


and if polarized perpendicularly, it has, according to (4), the 


amplitude OY These two values we indicate by xdu, 


‘x 
tan 22 
where, in the first case, 


scies doe tara). 2s: sy elena 


the Boundary of two Isotropic Transparent Media. 483 


and in the second, 
uo led sin Dye eee eee 2 6} 


The amplitude of the reflected ray is therefore 


tan @ 
xXdu= A A/a a 


and when this ray encounters a layer whose angle of refraction 
is @,, its amplitude becomes 


qf 2 ay / 22 ay 
bane 


At the boundary between this layer and the following, where 
the angle of refraction is z,—dvz,, a portion of the light is again 
reflected ; and uw, being the same function of z, that w is of iz 
the amplitude of the twice reflected ray 1S 


—A oa du du, 3 


and when this ray ae traversed all the layers until its angle of 


refraction has become constant and equal to @, its amplitude is © 


—A 2s B du dup. 
tan e 


_The angle x, may now have all values between « and x, and 


a all values between « and 8. The sum, therefore, of the am-_ 
plitudes of all the twice reflected rays will be represented by: 


the definite double integral 
VE: 
DEVE eng di a Fr : 


where wu, and ug indicate the me a of u mt x equal to a, and a. 


equal to £. 
In this manner the sum of the amplitudes of the rays reflected 


4, 6,.... times can easily be calculated; and as the sum of the 


different rays that have been 0, 2, 4, 6... times reflected make 
up the whole of the refracted ray, the amplitude of the latter is 


Ee aw i au" du +f ae" anf" "a4 ditg— 
tan @ 
which we shall indicate by 


A tana) 


tan a 


jp @ 


48 4, M. L. Lorenz on the Reflexion of Light at 


where 
Ji) = -{" du (Jan sea) 
U Uy 
From the last equation we get by differentiation 
f(uy= (“au fea) 
Uy 
and 
flu =f(u) 2 
flu) = cel + eye, 


where the constants ¢ and e¢, are to be determined by the equa- 
tions 


which gives 


Wh f(ua) =1, and f"(u,)=0. 
ence 

U—U ue —U 
4 —_ € a +e€ a 2 
fe) Or eae 
€ tea 8B 


and the value of (7) or the amplitude of the refracted ray is 
oA tan 8 
ee 
ee Vee a 
If now we wish to find the amplitude of the refracted ray 
polarized in the plane of incidence, which we will call B, we 
must in the above expression substitute 


eae PR 
u=—tlogtanz, 


and we shall find 
2) cos aisinye 
Ba2A— eae: aa (9) 
If, on the other hand, in (8) we substitute 
u= + log sin 2a, 
we find for B’, the amplitude of the portion of the refracted ray 
polarized perpendicularly to the plane of incidence, 
eis cosasin 8 
Rae sin («+ 8) cos («—£)’ 
We return, therefore, exactly to Fresnel’s formule, which is a 
remarkable property of those expressions. The calculation only 
assumes the relations indicated by (3) and (4); and these expres- 


sions might have been deduced from many other formule than 
Fresnel’s. 


The amplitude of the reflected ray, which is the sum of the 


(10) 


the Boundary of two Isotropic Transparent Media. 485 


amplitudes of the rays reflected 1, 3,5... times, may be simi- 
larly found, and may be expressed as follows: 


» ? ? u 
u u u u u u u Ve B 

7, ( P du ( du, ( Plus+ | P du du, "dua ing | duUy—... 
c e Uy e Un e Uy e uy et e uy e Vy Ug 


for which we will put 


A { *8 ul fu) 


Ua 
and 


asi - ("i aes) 


o uy 
From the last equation we get 


flu)= aes 
et Uae 
whence (11) or the amplitude of the reflected ray is 


Ug—Ug__ Ug—Uq 
oT ie ea 


Pia va 2s euig—Ua 


And substituting w= —4}logtanz, we get for the amplitude of 
the portion polarized in the plane of incidence, which we will 


call R, 
_, sin (a—£) 
Beran (2+) 
If KR! is the amplitude of the ray polarized perpendicularly to 


the plane of incidence, and if in (12) we substitute u= 4 log sin2z, 
we get 


(18) 


1, tan (a—8) 
Se oe (2+) 


In this case also, therefore, we return to Fresnel’s formule. 

The result is, that even if there be a gradual change of the 
index of refraction between the two media, and consequently an 
infinite number of reflexions at the boundary, Fresnel’s formule 
nevertheless remain true so long as the thickness of the inter- 
mediate layers is infinitely small as compared with the length of 
a wave. If this be not the case, then the retardations of the dif- 
ferent rays must be taken into consideration. 

For the refracted light this correction is very small, and could 
hardly be confirmed by experiment. We shall therefere proceed 
to calculate it in the case of the reflected hght. 


|) 


heal 


- 486 M. L. Lorenz on the Reflexion of Light at 


A wave which is reflected by the layer whose angle of refrac- 
tion is 2, Or 2), Y,-.., and afterwards interferes with the wave 
reflected by the first layer, will be retarded relatively to the latter ; 
and we may indicate the successive retardations of phase by the 
letters 6, 5,, 6,,.... These quantities are functions of a, 2, 
X_q.-.3 but may also be regarded as functions of wu, wu, Ug)... - 

We ‘may therefore represent the amplitude of the ray reflected 
once at the layer whose angle of refraction is 2, by ; 

A cos (At—96) du, 
where ¢ is the time, and £ a constant. 

For reasons analogous to those stated above, it is easy to see. 
that the amplitude of all the reflected rays may be expressed by | 


“8 “B 
A \ du cos (kt—8) — ( inf du, 
Uy ”~ Uy 


This series is the real part of 


* (kt—8) V1 
af du «€ Tu); 


Uy 


Pi, inthe 5 28 — 92) +.. J. 08) 


“where 
FL =f ay dug €6:-5:)¥=1 f(g). 
Uy Uy 


From this last equation we may deduce the differential equation 
d | -wai |= aS ea a 8; | 
<p) | =e) 


from which we obtain another expression for series (15), since it 
is the real part of 


(kt—6)V—1 dis ; 
Ale fw | 
or since for u=u,, we have f'!(ug)=0 and 5=0, the real part of 


AA Mag”. 
If in the above differential equation we substitute 
Ast 
ola ee Ug—Uy 
» will be determined as a function of wu by the following eqnse 
tion : 
aN tee d(Qa—8) | dd dA—8) 
"Spt 2 SP ag du dus du 


A=0 for U=Uny and wath, for u=Ug. 
du 


the Boundary of two Isotropic Transparent Media, 487 


-. We confine ourselves now to the case in which the values of 
dx 
du 


gives by integration, since the last member vanishes, 


and = are very small. The differential equation for > then 


an _ alee ie 2(u— 2(Upg— do 7 
aT oc Seemmmer B ‘G (u—ug) __ 2(ug )) = du. 


If in this expression we substitute the value of wu, it is obvious 
a" dn. 
that for all angles of incidence aa 8 small so long as 7 1S 80, 


which is the only hypothesis. 
If now we substitute for /(w) its values as found in (15), then 
series (15) becomes the real part of 


— Pp la Ug Mga as 
3 eae oe ar bet de 
ela— Up 4 lp Me du . 


and its sum is therefore 


Ug—Ug __ Ug—U, Ug 2(u—Ug) __ 2(ug—u) d, 
: [ cos e+ inf Se SSeS Te eee oF : 


2s > au 
elas 4 Mp Ya Uy e2(u,—Ug)_ _2(U,— Mn) des 


And substituting again in this expression for u its value 
—tlogtanz, we get for R the amplitude of the reflected ray 
polarized in the plane of incidence, 


epee -/) [cos kt+ sin kt tan A] 
sin (2+) ! ‘ey 
_  sindcosa BD ee ee: dé 
tan A= Se (cos? 6 tan 2— sin? cot A sn dz. 
If, on the other hand, for u we substitute $ log sin 2z, we get 
for the amplitude of the reflected ray polarized perpendicularly 
to the plane of incidence, 


1 _ , tan (a—P) : - 
R/=—A tan (2 +8) [cos A¢-+sin kt tan A’) 
sin2asin28 (8 ie 2¢ sin ad db 


SS —— - = — dk. 
sin? 2a—sin?26} Lsm28 sin 2z 


. dz 


From these equations it may be seen that tan A, for all angles 


(17) 


tan A! = 


of incidence, is small provided Ta is so also; while, on the con- 


trary, tan A’ may be infinite, as when sin 2¢=sin 28; that is, 
when the angle of incidence is equal to the angle of polarization, 
in which case # and 6 are complementary. m: 


488 M. L. Lorenz on the Reflewion of Light at 

If A’, for a given angle of incidence, is a small positive quan- 
tity, it gradually approaches = as the angle of incidence ap- 
proximates to the angle of polarization, and afterwards approaches 
givclf, on:-the contrary, A’ is a small negative quantity, on 
changing the angle of incidence A! approaches -3 and —7r. 

The retardation of the phase of the reflected ray R!, compared 
with the other polarized in the plane of mcidence R, may be ex- 
pressed by A’—A if the coefficients of cos kt have the same sign 
for both rays, that is to say, when the angle of incidence is 
greater than the angle of polarization. If, however, A’ and A 
be always taken in the first positive or negative quadrant, we can 
introduce any multiple we please of 27, and therefore express the 
retardation by A!—A + 2pzr, where p is a whole number. 

If now A is positive for this angle of incidence, it will increase 
as the angle of incidence diminishes ; and when the angle of in- 
cidence becomes less than the angle of polarization, and A! is 
taken in the first quadrant, the retardation of phase will be ex- 


pressed by 
A'—A+(2p+41)7r 


If, on the other hand, A! is negative for an angle of incidence 
greater than the angle of polarization, the retardation of phase 
will become A!—A + (2p—1)z7, if the angle of incidence is made 
less than that of polarization. These results agree with those of 
Jamin. In the first case Jamin puts y=—1, whereby the re- 
tardation of phase becomes 


A'—A—27 for a+B> =, 


A'—A—wa for atp<s; 


and bodies in which this is the case he calls “bodies of negative 
reflexion.” 


vm - 


In the second case (A! negative for «- ao 5) he puts p=1; 


and the retardation of phase of these sites which he calls 
“bodies of positive reflexion,” then becomes 


A'—A +20 for a+8> ZF; 


Al—A-+ @ for atB<s 


Jamin found, moreover, that most bodies whose index of re- 
fraction is less than a given amount (about 1°46) give negative 


the Boundary of two Isotropic Transparent Media. 489 


reflexions, while those whose index of refraction is greater than 
that amount give positive reflexions. Between these are bodies 
which at the angle of polarization produce a sudden change of 
phase from 0 to 7. These remarkable relations between the 
difference of phase and index of refraction could not have been 
anticipated from Cauchy’s theory, while on the other hand they 
can be immediately deduced from the theory above enunciated. 

Let p be the distance of the first intermediate layer from that 
in which the angle of refraction is z, and dp the distance of the 
latter from the next whose angle of refractionisa+dz. It will 
easily be seen that if a wave be reflected at these two consecutive 
layers, the difference of path of the two reflected waves will 
be equal to 2dp cos z. 

If ae / be the wave-length in the first medium, and there- 


length in the layer under consideration, we 


have for the difference of phase corresponding to this difference 
of path, 


Qc sin « ds 
Teng 4 cos aes dx. 


Instead of « we might introduce, as a new variable, the square 
of the index of refraction. If this variable be called v, we have 
_ sinta 
~ sin? av 
The limits of the variables p and v are, for e=a, 0 and 1; and 
for c= they may be denoted by p, and v,, where p, is the 


thickness of all the intermediate layers, and v, the square of the 
observed index of refraction. 


If now the new values of és and x be substituted in (16) and 


dx 
.(17), and these expressions be integrated by parts, we have 
tan A = <7. 5 ("pdty Sh een eee nae Sue TEE) <2) 


one _ sin? 87) 
2 j@: (19 


4 


T Ee 
ae 
— Tv, cos? —aeccere | ? 


From which it is obvious that tan A is always positive, 
whereas tan A! may either be positive or negative. 

In one particular case A’ passes suddenly. from 0 to +7 at the 
angle of polarization; this is when for this angle | 


*% [eost 8 sin? 8 
Wal FT cine |a=o; 


vl vy 


490 On the Reflexion of Light of Transparent Media. 


As this integral includes positive as well as negative elements, 
it is evident that this equation is possible for some values of 2. 
And if it be now supposed that for different bodies p is generally 
only approximately the same function of v, when v, increases by 
the positive increment dv,, this integral increases by 


i % af 
[e(1—) -\ pa | 


which is less than 


1 % dv 
[a(1—=) -p.{ 3 |e =0. 


This increase is therefore positive; and it follows that. the 
definite integral in (19), when v, exceeds a certain amount, 
is positive, and consequently A! negative for v, cos? «— cos* B <0 


or fore+ i if the light, as in Jamin’s experiments, passes 


from a less refracting to a more refracting body (e>). But 
we have, however, seen above that this case answers to that of 
bodies with a positive reflexion. 

Calculation therefore, like experiment, proves that positive 
reflexion occurs in the case of bodies with a greater index of 
refraction, negative reflexion in the case of bodies with a smaller 
index, while the difference of phase in the case of bodies which 
lie between these passes suddenly from 0 to +7. 

The intensity of the reflected light polarized perpendicularly 
to the plane of incidence is, according to (17), 


tan? (2—£) 

2 2 Al). 

tan? ere is. 
the intensity of the reflected light polarized in that plane is, 
according to (16), 


“ULL ow (1-+ tan? A), 


sin? (@ + B) 
If the ratio of these two intensities be expressed by k*, we get 
p= 0% (2+) cosA (20) 


~ cos (a—Z£) cos Al” 


These results agree with those of Cauchy. 
As Jamin has in his experiments determined these magnitudes 
directly, it is possible from his experiments, that is, from the 


Mr. A. Cayley ona Surface of the Fourth Order. 491 


principal angle of incidence, and the index of refraction, to de- 
cae the value of A, and consequently by (18) the value of 


e dv. If now it be supposed that p can be approximately de- 


I — 
termined by a , the thickness of the intermediate layers 
= 


can be deduced from the experiments. 

In this way we have a new means of testing the theory, since 
this requires that the thickness in question should be small and 
positive. The calculation from Jamin’s experiments shows that 
this is actually the case, though, as might be expected, no great 
degree of exactness can be thus attained in the determination 
of these quantities. Ihave found that the thickness of the layers 
a the case of the bodies experimented on lies between 55 and . 
rho of the length of a wave. 

It appears, therefore, that the result of Jamin’s experiments. 
can be completely explained on the simple supposition of an ex-. 
ceedingly thin stratum of intermediate layers in which there is 
a gradual change of refractive power, a supposition which we. 
have obyiously- more right to make than to omit. 


- Copenhagen, June 28, 1860. 


LXXII. On a Surface of the Fourth Order. 
By A. Cavity, Esq.* 


iP! A, B, C be fixed points; it is required to investigate 

the nature of the surface, the locus of a point P such that 
AAP + ~BP+rvCP=0, 

where A, p, v are given coefficients; the equation depends, it is 
clear, on the ratios only of these quantities. 

_ The surface is easily seen to be of the fourth order; it is ob- 

viously symmetrical in regard to the plane ABC; and the section 


by this plane, or say the principal section, is a curve of the fourth 
2 hee the locus of a point M such that 


AM + pBM +7CM=0. 


The curve is considered incidentally by Mr. Salmon, p. 125 
of his ‘ Higher Plane Curves ;’ and he has remarked that the two 
circular points at infinity are double points on the curve, which 
is therefore of the eighth class. Moreover, that there are two 
double foci, since at. each of these circular points there are two 
tangents, each tangent of the one pair intersecting a tangent of 
the other pair in a double focus; hence, further, that there are 


* Communicated by the Author. 


492 Mr. A. Cayley on a Surface of the Fourth Order. 


four other foci, the points A, B, C, and a fourth point D lying 
in a circle with A, B, C, and which are such that, selecting any 
three at pleasure of the points A, B, C, D, the equation of the 
curve is in respect to such three points of the same form as it is 
in regard to the points A, B, C. 

Consider a given point M, on the principal section, then the 
equations 

gain Se! gel) eee meh FN 
BM CM’ CM AM’ AM’ BM 

belong respectively to three spheres: each of the spheres passes 
through the point M. The first of the spheres is such that, 
with respect to it, B and © are the images each of the other; 
that is, the centre of the sphere hes on the line BC, and the pro- 
duct of its distances from B and C is equal to the square of the 
radius; in like manner the second sphere is such that, with 
regard to it, C and A are the images each of the other; and the 
third sphere is such that, with regard to it, A and B are the 
images each of the other. The three spheres intersect in a 
circle through M at right angles to the principal plane (that is, 
the three spheres have a common circular section), and the equa- 
tions of this circle may be taken to be 


Oe ee 
AM” BM” CM’ 
It is clear that the circle of intersection lies wholly on the surface. 

The spheres meet the principal plane in three circles, which 
are the diametral circles of the spheres ; these circles are related 
to each other and to the points A, B, C, in hke manner as the 
spheres are to each other and to the same points. The circles 
have thus a common chord; that is, they meet in the point M 
and in another point M’. And MM! is the diameter of the circle, 
the intersection of the three spheres. 

It may be shown that M, M! are the images each of the other 
in respect to the circle through A, B, C. In fact, consider in 
the first place the two points A, B, and a circle such that, with 
respect to it, A, B are the images each of the other; take Ma 
point on this circle, and let Q be any point on the line at right 
angles to AB through its middle point, and join OM cutting the 
circle in M’; then it is easy to see that M, M’ are the images 
each of the other, in regard to the circle, centre O and radius 
OA (=OB). Hence starting with the pomts A, B, C and the ~ 
point M, let O be the centre of the circle through A, B, C, and 
take M! the image of M in respect to this circle ; then considering 
the circle which passes through M, and in respect to which B, C 
are images each of the other, this circle passes through M’; and 


Mr. A. Cayley on a Surface of ihe Fourth Order. 493 


so the circle through M, in respect to which C, A are images 
each of the other, and the circle through M, in respect to which 
A, B are images each of the other, pass each of them through M’ ; 
that is, the three circles intersect in M!. 

It is to be noticed that M’, being on the surface, must be on 
the principal section; that is, the principal section is such that, 
taking upon it any point M, and taking M! the image of M in 
regard to the circle through A, B, C, then M! is also on the 
principal section. It is very easily shown that the curve of the 
fourth order possesses this property ; for M, M’ being images. 
each of the other in respect to the circle through A, B, C, then 
A, B, C are points of this circle, or we have 

MA MB MC” 

WA MB MC? 
that is, the equation : 

AM +»BM+rvCM=0 


being satisfied, the equation 
VAM! + wBM!'+vCM'=0 


is also satisfied. 

The points M, M! of the curve, which are images each of the 
other in respect to the circle through A, B, C, may be called 
conjugate points of the curve. The above-mentioned circle, the 
intersection of the three spheres, is the circle having MM! for 
its diameter; hence the required surface is the locus of a circle at 
right angles to the principal plane, and having for its diameter 
MM’, where M and M! are conjugate points of the curve. 

In the particular case where the equation of the surface is 


BC.AP+CA.BP+AB.CP=0, 


the principal section is the circle through A, B, C, twice repeated. 
Any point on the circle is its own conjugate, and the radius of 
the generating circle of the surface is zero; that is, the surface 
is the annulus, the envelope of a sphere radius 0, having its 
centre on the circle through A, B,C. Or attending to real 
points only, the surface reduces itself to the circle through 
A, B, C. But this last statement of the solution is an incom- 
plete one. ‘The equation of an annulus, the envelope of a sphere 
radius c, haying its centre ona circle radius unity, is 


Vxrty=l+ V¥e—2?; 
and hence putting c=0, the equation of the surface is, 


Va? +y2=ltzi 


494 Mr, A. Cayley on a Surface of the Fourth Order. 
(if, as usual, i= “—1), or, what is the same thing, it is 
af + y* + (2+1)?=0; 
that is, the surface is made up of the two spheres, passing through 
the points A, B, C, and having seach of them the radius zero ; 


or say the two cone- spheres through the pots A, B,C. In 
other words, the equation 


BC,.AP+CA.BP+AB.CP= 


is the condition in order that the four points A, B, C, P may lie 
on a sphere radius zero, or cone-sphere. Using 1, 2, 8, din 
the place of A, B, C, P to denote the four points, the last-men- 
tioned equation becomes 


12,34+18.42414.23=0; 


and considering 12, &c. as quadratic radicals, the rational form 
of this equation 1s 


— 9 ee & 


Oo= 0, 19, 18, ie pein oi 
2] . ) 0 > 93, 24 
Shin Haier oQepiaide 


—ew) | ———en DB ——9 


47, 42, 48, 0 


In my paper “On a Theorem in the Geometry of Position,” 
Camb. Math. Journ. vol. uu. pp. 267-271 (1841), I obtained 
this equation, the four points being there considered as lying in 
a plane, as the relation between the distances of four points in a. 
circle, in addition to the relation 


a AO node 

Sn Ge aam o RROnramene 
iy ssT 

] 


which exists between the distances of any four points in a plane, 
The present investigation shows the signification of the equation 
O = 0 between the distances of four points in space; viz. it 
expresses that the four points he in a sphere radius zero, or 
cone-sphere. But the formula in question is im reality eluded 
in that given in the paper for the distances of five pomts in. 
space. Por calling the points 0, 1, 2, 3, 4, the relation between 
the distances of these five points is 


Chemical Notices :—Preparation of solid Carbonic Acid, 495 


peste) aciqe phe wig | ‘eal 
Bie tlh geo Dk ». OR gh DBrytrer OH 
er. Ye ie te 
ed Ba tO eae 


eee a 2, ORR 
Hence if 1, 2, 3, 4 are the centres of spheres radii a, B, y, 8, 
and if O is the centre of a tangent sphere radius 7, we have 
Ol=r+a, O2=r+P, O8=rty, 04=r4+6; 

so that, for any given combination of signs, it would at first 
sight appear that r is determined by a quartic equation; but by 
means of a simple transformation (indicated to me by Prof. Syl- 
vester) it may be shown that the equation for 7 is really a qua- 
dratic one ; morcover, the equation remains unaltered if the signs 
of a, B, y, 6 and of r, are all reversed; and 7? has thus in the 
whole sixteen values. In particular, if «, 8, y, 6 are each equal 
0, then r? is determined by a simple equation (r the radius of 
the sphere through the four points) ; and if, moreover, r=O, 
then we have for the relation between the distances of the four 
points, the foregoing equation 0=0., 


2 Stone Buildings, W.C., 
March 25, 1861. 


cn A a = pescmmasitainnntnmmntiieniiil 
- 
ana a = —— = = TT 


LXXIII. Chemical Notices from Foreign Journals. 
By i. Arxinson, Ph.D., FCS. 
[Continued from p. 365. | 

M. LOIN and Drion* describe the following method of ob- 
taining solid carbonic acid, merely requiring for its prepa- 

ration apparatus within the ordinary reach of the laboratory. It 
depends on the great cold produced by the evaporation of liquid 
sulphurous acid. Liquid ammonia is placed in a glass vessel, 
and connected with the receiver of an air-pump by a vessel con- 
taining pumice impregnated with sulphuric acid. On exhausting, 
the temperature of the liquid ammonia rapidly sinks, and it com- 
mences to solidify at —81° C.; when the pressure is reduced to 
1 millim., the temperature of the liquid ammonia is —89%5, 
This is sufficient for the liquefaction of carbonic acid under the 
ordinary atmospheric pressure ; for when a current of dry carbonie 


* Comptes Rendus, April 15, 1861. 


496 M. Deville on the Formation.of Staurotide and Zircon. 


acid is passed through a U-tube dipping in the’ammonia, a small 
portion of it liquefies. 

By increasing the pressure to some extent, considerable quan- 
tities of carbonic acid may be readily solidified. About 150 
cubic centims. of liquid ammonia are introduced into an inverted 
bell-jar provided with a collar, on which a plate perforated with 
two apertures is hermetically fitted. In the central aperture there 
is a tube closed at one end and reaching to the bottom of the 
jar; the other aperture serves to connect the apparatus with the 
air-pump. ‘The carbonic acid is produced -by heating dried bi- 
carbonate of soda to reduess in a copper flask. This flask is con- 
nected with the tube dipping in the liquid ammonia, and also 
with a small air-manometer. All the air having been expelled 
from the apparatus, and the temperature of the liquid ammonia 
reduced to near solidification, the flask is heated until the mano- 
meter indicates a pressure of 3 to 4 atmospheres. Crystals of 
carbonic acid soon begin to form on the inside of the tube, 
and in half an hour about 25 grammes of solid carbonic acid 
are obtained, forming a thick layer on the inside of the tube 
which dips in the liquid ammonia. 

This solid carbonic acid is a colourless mass, as transparent as 
glass ; it may be detached from the tube by touching it with a 
glass rod, and is seen to consist of small cubical crystals. Iix- 
posed to the air, these crystals slowly evaporate without leaving 
any residue; they may be placed on the hand without producing 
any sensation either of heat or of cold: they can be scarcely 
seized between the fingers. Mixed with ether and exposed to 
the air, they form a freezing mixture, the temperature of which 
is —81° C. 

The temperatures were observed by MM. Loir and Drion, by 
means of an alcohol thermometer on which two fixed points 
had been marked; that is, 0° the temperature of melting ice, 
and —40° the temperature of melting mercury. The liquid 
ammonia was prepared by Bussy’s method*, of passing gaseous 
ammonia into a flask surrounded by liquid sulphurous acid, the 
evaporation of which was promoted by the air-pump. In this 
way 6 to 7 fluid ounces may be obtained without difficulty in 
the course of two hours. 


The following experiments by Deville} throw considerable 
light on the formation of some native minerals. 

When fluoride of silicon was passed over calcined alumina 
heated to whiteness in a porcelain tube, fluoride of aluminium 
was disengaged, and staurotide formed analogous in all its pro- 


* Phil. Mag. vol. xx. p. 202. 
+ Comptes Rendus, April 22, 1861. 


M. Schiitzenberger on some New Salts. 497 


perties to the natural mineral. This experiment was repeated in 
a modified manner. 

In a porcelain tube placed vertically, a series of alternate layers 
of alumina and quartz were arranged, the alumina being at the 
bottom, and the quartz at the top; fluoride of silicon was then, 
passed through the tube at a white heat. In this way the fluo- 
ride of silicon meeting alumina was decomposed, and staurotide 
formed; but the fluoride of aluminium which was formed at the 
same time was decomposed on coming in contact with the layer 
of quartz, with the formation also of staurotide and regeneration 
of fluoride of silicon. The same process followed with all the 
successive layers ; so that the quartz and alumina were both con- 
verted into staurotide, and, as the last layer was quartz, as much 
fluoride of silicon left the apparatus as entered it. None of the 
fluorine was fixed, and it served no other purpose than to cause 
the combination of two of the most stable bodies in nature. 

From the formula of topaz, which is a silicate of alumina and 
fluoride of silicon, it was probable that it might be formed in a 
similar way. But direct experiments showed that this is not the 
ease; and Deville is inclined to think that it is formed in the 
moist way. 

In the expectation of obtaining phenakite, Deville heated glucina 
in fluoride of silicon. He obtained a mineral which crystallizes 
well, and consists of silica and glucina, but could not be iden- 
tified with any known mineral species. 

When fluoride of silicon was passed over zirconia, beautiful 
octahedral crystals were obtained which had all the characters of 
the native zircon. An experiment of Deville’s seems to show 
that a very small quantity of fluorine can produce an indefinite 
quantity of this mineral. 

Alternate layers of zirconia and quartz were placed in a por- 
celain tube, commencing with the former and ending with the 
latter, anda current of fluoride of silicon was passed through the 
tube at a white heat. The zirconia in contact with fluoride of 
silicon was changed into zircon and volatile fluoride of zircon ; 
the latter meeting quartz, gave zircon also and fluoride of silicon ; 
and so on with the whole of the layers. The contents of the 
tube were entirely mineralized, and the quantity of fluoride of 
silicon which left the tube was equal to that which entered it. 
No fluorine had been fixed. 

In a subsequent communication Deville will describe a method 
for obtaining metallic sulphurets by the dry way. 


Schiitzenberger* has described a new class of salts, in which 
the electro-negative elements chlorine, bromine, iodine, &c. 


* Comptes Rendus, January 238, 1861. 


Phil. Mag, 8. 4. No, 143, Suppl. Vol, 21. 2K 


498 M. Schiitzenberger on some New Salts. 


are substituted’ for the basic hydrogen, the metals, &. He 
has effected this by acting on salts with such compounds as 
chloride of iodine and iodide of cyanogen. The formation of 
acetate of iodine will illustrate this class of actions, which is sus- 
ceptible of great extension. 

C4 H8 NaO4 + IC] = NaCl+C* H3I 04. 

Acetate of | Chloride Acetate of 
soda. of iodine. iodine. 


These bodies, as may be expected, are endowed with special 
properties, and especially are very unstable. 

Anhydrous hypochlorous and acetic acids mixed in equivalents 
form a red mixture, which soon becomes decolorized. A slight 
excess of hypochlorous acid imparts to it a red tint, which is 
removed by heating the mixture to a temperature not exceeding 
30°. This body is the acetate of chlorme, C+ H? ClO*; its com- 
position is that of chloracetic acid, but it differs greatly in pro- 
perties. It dissolves immediately in water, producing hypo- 
chlorous and acetic acids, and explodes at 100°, with formation 
of chlorine, oxygen, and anhydrous acetic acid. Singularl 
enough it is attacked by mercury even in the cold, with libera- 
tion of chlorine, and formation of acetate of mercury and a little 
calomel— 

C* H® ClO*+ Hg =Cl+ C* H? Hg O*4,— 
Acetate of Acetate of 
chlorine. mercury. 
a curious instance of the replacement of chlorine by a metal. _ 

It dissolves iodine instantaneously without becoming coloured, 
and disengages chlorine; acetate of iodine is formed, a white 
crystalline solid isomeric with iodacetic acid. 

C* H® ClO* + T= C* H31I 04+. 
Acetate of Acetate of 
chlorine. iodine. 


Another mode of forming this body has been given above. It 
is decomposed at 100° into iodine, oxygen, and acetate of 
methyle. 

2(C* H 104) = I? + C? O44 C4 H8 (C? H3) Of. 
Acetate of Acetate of 
iodine, methyle. 


It is decomposed by water into iodic acid, iodine, and acetic acid. 
Butyrate of iodine is formed by the action of chloride of iodine 
on butyrate of soda. Acetate of bromine is obtained by the 
action of bromine on acetate of chlorine. 
Sulphur dissolves in acetate of chlorine with disengagement 
of chlorine; but the acetate of sulphur which forms is very un- 
stable, for it soon decomposes into anhydrous acetic acid, sul- 


M. Lourengo on Polyglyceric Alcohols. 499 


phurous acid, sulphur, and chlorine. The action of iodide of 
cyanogen on acetate of silver forms iodide of silver, and appa- 
rently iodide of cyanogen. 

These interesting facts are capable, as Wurtz suggests*, of 
another interpretation, by assuming that the bodies are mixed 
anhydrous acids. Thus the acetate of chlorine is hypochlor . 
acetic anhydride, and Wurtz expresses its formation in the fol- 
lowing manner :— 


ayo + GeH96 $= 9 Ineghengieel Xe) 


Cl C* H°0 
Anhydrous Anhydrous Lt hypo- 
hypochlorous acetic acid. -  chioracetic acid. 
acid, 


Lourengo has described} a series of new compounds, the 
polyglyceric alcohols. They bear the same relation to glycerine 
that the polyethylenic alcohols { do to glycol. These latter bodies 
were obtained by the action of hydrochloric glycol on glycol in 
excess: the formation of the new bodies is quite analogous; it 
ensues when hydrochlorate of glycerme acts on glycerine im 
excess. Lourengo saturated a portion of glycerine with hydro- 
chloric acid gas, and having added to it an equal quantity of 
elycerine, he heated the whole to 180° C. for several hours in a 
flask connected with a condenser so that the distillate fell again 
into the flask. The result of this action was a very thick brown 
liquid, which was distilled under a pressure of 10 millims. A 
body was obtained boiling at 220°—230° under this pressure. 
It had the composition €° H™ 0°, and its formation may be thus 
expressed :— 


3 yI5 3 FS 3H 
a ida ee }O-+ HCL 
moet New Me 
RErOOhS a 
glycerine. 

This body, which Lourengo names pyroglycerine, or diglyceric 
alcohol, is formed by the condensation of two molecules of gly- 
cerine and elimination of one molecule of water. It is analogous 
in its chemical eet ae to Graham’s pyrophosphoric acid. 


eons" PO, 

ce He" Los PO, 40%, 
H+ H 

Pyroglycerine. Pyrophosphoric acid. 


* Répertoire de Chimie, April 1861. 
t+ Comptes Rendus, February 25, 1861. 
t Phil. Mag. vol. xix. p. 124. 

2K2 


500 M. Lourengo on Polyglyceric Alcohols. 


Besides this there was formed at the same time another body 
of analogous properties, but possessing a greater viscosity. It 
boils at 275° to 285° under the pressure of 10 millims. ; it has 
the composition €9 H®°@7, and is derived from three molecules 
of glycerine with elimination of two molecules of water. It is 
analogous to triethylenic alcohol in the series of condensed 
glycols. 

In the crude product from which these bodies were obtained, 
there were several chlorine compounds which distilled at the 
ordinary atmospheric pressure, and were separated by fractional 
distillation. A portion of this, boiling between 230° and 270°, 
which chiefly consisted of hydrochlorate and dihydrochlorate of 
pyroglycerine, was treated with potash, by which chloride of 
potassium was formed, and a body obtained which, on purifica- 
tion and analysis, was found to have the composition 


C3 H° 
(6 F1294— C3 Hs} 
H2 
It is metameric with glycide, the existence of which has been 
placed out of doubt by Reboul’s researches*. Lourenco names 
it pyroglycide ; it stands in the same relation to pyroglycerine 
that glycide does to glycerine, being formed from it by the eli- 
mination of water. 


€° H® ¢? H° 
13 pO" —H?O= : how 
Glycide. 
2(€3 He 2(C8 HP; 
(E Ht }O°—H?O= (G He + 
Pyroglycide. 


There is another way of obtaining these polyglyceric alcohols, 
which throws some light on their formation. When glycerine 
was heated, and the part collected which distilled between 130° 
and 266°, and this portion treated with ether, an insoluble residue 
was left. This body gave distillates up to 300°, under a pres- 
sure of 10 millims., consisting of pyroglyceric alcohols. It is 
highly probable that in this decomposition, glycerine losing 
one molecule of water forms glycide, and this combining with 
one, two, or three equivalents of glycerine, forms polyglyceric 
compounds ; just as oxide of ethylene, in acting upon one, two, 
or three equivalents of glycol, forms polyethylenic alcohols. 

Lourenco points out that the formation of these polyethylenic 
alcohols suggests a plausible explanation of the formation of the 
different modifications of metaphosphorie acid, which are ob- 


* Phil, Mag. April 1861. 


M. Freund on Butyryle. 501 


tained by heating microcosmic salt, or acid phosphate of soda. 
i Graham’s metaphosphate of soda acts lke glycide or oxide of 
ethylene, and by successive condensations gives rise to the differ- 
ent modifications of the acid. 


PO CH? 1: 
20h 2 
Ht 0?—H? O= Nat O?, corresponding to ~ yy to ‘ 

Acid phosphate Metaphosphate Glycide. 

of soda. of soda. 
3 ys 
fo + - Nat po asg-* © Nae f Q*, corresponding to ac me ro 
[? 

Maddrell’s meta- ee) renee 


phosphate of soda. 


Freund* has made a series of experiments on the preparation 
of the oxygen radicals of the formic acid series by the action of 
metals on the chloride of these acids, a method analogous to that 
of the preparation of the ether radicals. 

When chloride of acetyle was treated with sodium-amalgam 
no action ensued in the cold, and the action set up at a higher 
temperature produced a complete decomposition with forma- 
tion of empyreumatic substances. The action of chloride of 
butyryle, €¢*H’ OCI, on sodium-amalgam gave better results. 
When slightly warmed together, an action was induced which 
disengaged heat sufficient to continue it ; the flask was connected 
with a Liebig’s condenser, so that the distillate flowed back. 
After a short time the mixture was distilled; the unaltered 
chloride passed off; the residue, consisting of mercury, chloride 
of sodium, and butyryle, was digested with water, and the buty- 
ryle which rose to the surface removed. The chloride of buty- 
ryle which had distilled off was treated again with sodium- 
amalgam, and the process repeated until a large quantity of 
butyryle had been accumulated. This was digested with car- 
bonate of potash, washed, dried over chloride of calcium, and 
rectified. No product of constant boiling-point was obtained ; 
but a portion distilling between 260° and 280° gave on analysis 
numbers agreeing with the formula of butyryle, or rather dibu- 


tyryle, €? H'™# on Sl oo Its formation may be thus ex- 


pressed :— 
ieee +2Na= Gaya f 4+ 2NaCl. 
Chloride of Sodium. Butyryle. 
butyryle. 


* Liebig’s Annale, April 1861. 


502 | M. Martius on the Platinum Metals. 


' The action of strong potash on butyryle is very energetic ; 
butyrate of potash is formed as well as a substance of a pleasant 
odour, which has the composition of the ketone of butyric acid, 
but in properties appears to be quite different. 


Martius* has published an investigation on the cyanides of the 
metals associated with platinum. In their preparation he used 
the residues obtained from the manufacture of Russian platinum. 
The method of separating the metals which he adopted is a com- 
bination of several methods, and presents some interesting points. 

The residues were finely powdered, and the larger grains of 
osmium-iridium separated by decantation. The residue having 
been dried and heated, was fused with a mixture of lead and oxide 
of lead, by which all the silicates and other similar impurities 
passed into the slag, and a lead regulus was obtained containing © 
all the platinum metals. When this was treated with diluted 
nitric acid, a residue was left consisting principally of iridium and 
osmium-iridium. The latter was separated by decantation. To 
bring it into a state of fine powder, which could not be effected 
in the ordinary way on account of its hardness, it was melted 
with zinc in a carbon crucible, by which it was dissolved ; when 
this mass was afterwards heated! in a wind furnace, the zinc was 
expelled and the mineral left in a state of fine powder. 

The osmium-iridium was then heated in a current of oxygen ; 
some osmic acid was formed, which volatilized, and was collected 
in a well-cooled receiver. The residue and the iridium were 
then mixed with an equal weight of common salt, and heated in 
a current of chlorine; the mass was dissolved in water, and the 
solution which contained the double chlorides was boiled with 
aqua regia, by which osmium was removed as osmic acid, and 
was received in a solution of ammonia. The residual solution 
was then mixed with sal-ammoniac, which precipitated everything, 
excepting a little rhodium, as ammonium double salt. The pre- 
cipitate consisting principally of iridium, but containing also some 
platinum and ruthenium, was fused with cyanide of potassium 
to convert it into eyanides; this was boiled with hydrochloric 
acid to decompose excess of cyanide of potassium, and then sul- 
phate of copper added, which gave a red precipitate of the cop- 
per salt. 

By digesting this precipitate with baryta water, oxide of copper 
was formed and the barium double cyanides. They were easily 
separated by crystallization, the platimocyanide of barium being 
more insoluble than the iridiocyanide of barium. The small 
quantity of ruthenium was contained in the mother-liquor of this 
latter salt. 


* Liebig’s Annalen, March 1861. 


M. Martius on the Platinum Metals. 5038 


- Osmiocyanide of Potassium, Os Cy, 2 KCy -+-3HO.—This salt 

was prepared byadding cyanideof potassium to a solution of osmie 
‘acid, evaporating to dryness, and heating to redness in a covered 
crucible. On dissolving out the mass in a small quantity of 
water and crystallizing, the salt was obtained in fine yellow 
laminz, which belong to the dimetric system, like the ferrocya- 
nide of potassium: the osmiocyanide of potassium, besides being 
analogous in composition and crystalline form to this salt, has 
the still closer resemblance that it exhibits (as a special investi- 
gation by Kobell showed) the same abnormities in its optical 
relations which have lately been found characteristic of ferro- 
cyanide of potassium. 
_ By the action of nitric acid on osmiocyanide of potassium a 
nitro-compound appeared to be formed. Experiments made to pre- 
pare a series of compounds analogous to the ferricyanides were 
unsuccessful. Chlorine passed into a solution of osmiocyanide 
of potassium, produced a red colour, but on evaporation only 
erystals of the double salt of chloride of osmium and chloride of 
potassium were obtained. 

Osmiocyanide of Hydrogen: Osmiocyanic Acid, Os Cy, 2HCy.— 
This substance was obtained in a way analogous to the ferrocyanic 
acid: by treating a cold saturated solution of osmiocyanide of 
potassium with fuming hydrochloric acid, 


_ Os Cy, 2KCy+2HCl = Os Cy, 2HCy + 2KCl, 


—a reaction which distinguishes osmium and ruthenium from 
other platinum metals—a precipitate was obtamed, which was 
filered, washed with strong hydrochloric acid, dissolved in alcohol, 
and ether added. In this way the body was obtained in trans- 
parent columnar crystals of strongly acid properties. 

Perfectly stable in the dry state, osmiocyanic acid decomposes, 
when exposed to the air in a moist state, ito cyanide of osmium 
and hydrocyanie acid. 

When any osmiocyanide is boiled with strong hydrochloric 

acid, hydrocyanic acid is disengaged, and a dark-violet precipitate 
is formed, which is cyanide of osmium, Os Cy. 

When osmiocyanide of potassium is mixed with a persalt of 
iron, a splendid violet precipitate is formed, which is as delicate 
a test for iron as the ferrocyanide. This precipitate could not be 
analysed, on account of its retaining a quantity of water, which 
eould not be expelled without decomposition ; but it 1s doubtless 
formed according to the equation 

2¥e? CB + 30s Cy, 6(KCy = 30s Cy, 2 Fe? Cy? + 6KCL. 

When this precipitate was treated with baryta water, sesqui- 
oxide of iron was formed, and osmiocyanide of barium passed into 
solution and was afterwards obtained in reddish-brown crystals 


504 Prof. Challis on Theoretical Physics. 


of the trimetric system. Its composition is Os Cy, 2Ba Cy +6HO, 
and it is isomorphous with ferrocyanide of barium. 

Tridiocyanide of Barium, Ix? Cy*, 3Ba Cy + 18HO.—This salt 
was obtained in the process of separating the platinum metals. 
It forms well-defined crystals of the trimetric system. When 
treated with a proper quantity of sulphuric acid and the mass 
exhausted with ether, the iridiocyanide of hydrogen or zridto- 
cyanic acid, Ir? Cy?, 3KCy, is obtained in crystalline crusts on 
evaporating the etherial solution. It is strongly acid, and its 
solution decomposes carbonates. Crystallized from ether it is 
anhydrous. he iridiocyanide of potassium, Ir? Cy®, 3KCy, has 
been already described by Wohler and by Booth. According to 
Martius, the iridiocyanide of barium, which is easily obtained pure, 
affords a convenient means of preparing it. 
— Rhodiocyanide of Potassium, Rh? Cy?, 3 K Cy.—This salt is ana- 
logous in composition and mode of preparation to the preceding 
salt, but is acted upon by acetic acid, which is not the case with 
the iridium salt. When treated with acetic acid, hydrocyanic 
acid is disengaged and a red powder is precipitated, which is the 
eyanide of rhodium, Rh? Cy®. This deportment furnishes a means 
of separating the two metals. 

Martius further remarks upon the preparation of the platino- 
cyanides of potassium, and describes some new double cyanides. 


LXXIII. On Theoretical Physics. 
By Professor CHaruis, /.R.S., F.R.A.S.* 


| HAVE been induced to make the following remarks chiefly 

because I am unwilling to appear inattentive to the repeated 
notices which Mr. Glennie has taken of my mathematical theory 
of the physical forces. But I have occasion to do little more 
than give my reasons for concluding that nothing which Mr. 
Glennie has urged calls for a reply. Of course I do not object 
to my hypotheses being tested and scrutinized in all possible ways 
that are legitimate: at the same time I must maintain the New- 
tonian doctrine, that no arguments can be adduced either for or 
against a hypothesis which are not drawn from experience, or 
from a comparison of the mathematical results of the hypothesis 
with experience. Also it is a necessary condition of a hypo- 
thesis that it be expressed in terms which experience makes in- 
telligible. Myr, Glennie has not said that the statement of my 
hypotheses does not fulfil this condition ; neither has he adduced 
any facts contradictory to results mathematically deduced from 


* Communicated by the Author. 


Prof. Challis on Theoretical Physics. - 505 


them. He has not even alluded to my mathematics. I say, 
therefore, that there is no argument which I have to meet. 

In prosecuting physical inquiry, it appears to be necessary to 
proceed by way of hypotheses. But hypotheses of themselves 
teach nothing: we /earn by mathematics, as the very name im- 
plies, because by mathematics the truth of a hypothesis may be 
tested or established. The existence of gravity as a force, and 
the law of gravity, are truths which could not be ascertained 
by observation alone; but being taken to be true hypothe- 
tically, they are proved to be actually true, by the aid of mathe- 
matics. 

Hence hypotheses respecting the physical forces are deserving 
of consideration only so far as they afford a basis for mathemati- 
cal reasoning. In fact this quality of a hypothesis is a criterion 
of its truth, because all quantitative laws are deducible mathe- 
matically from ¢rwe hypotheses. In selecting hypotheses for the 
foundation of a general theory of the physical forces, [ had 
regard, in the first place, to their conformity with the antecedents 
of physical science, and then to the possibility of arguing from 
. them mathematically. I have not met-with any which in the 
latter respect are preferable to those I have selected, which, con- 
sequently, I have good reason to adhere to. 

To assume that an atom is of constant form and magnitude, 
is, | admit, virtually to call it an indivisible particle, and not, as 
Newton does, an undivided particle, “ particula indivisa.” But 
as the hypothesis is expressed in perfectly intelligible terms, it 
is open to no objection, provided we admit with Newton, that if 
by a single experiment it can be shown that the supposed indi- 
visibie. particle is divided when a solid mass is broken, the theory 
of atoms is untenable. When a physical hypothesis satisfies the 
condition of being expressed in terms which common experience 
renders intelligible, special observation and experiment, or com- 
parisons of its mathematical consequences with facts, alone deter- 
mine whether or not it be true. I do not admit that any meta- 
physical argument can be adduced either in support of, or against, 
a physical hypothesis. Meta-physics come after physics. Ifa 
general physical theory should be established on verified hypo- 
theses, we should have a secure basis for metaphysical reasoning; 
and possibly it might then appear that some of the speculative 
metaphysics which have prevailed during the last century are 
without foundation. 

By the same mode of reasoning, the hypothesis of a universal 
fluid ether, the pressure of which varies proportionally to its 
density,.1s unobjectionable as a hypothesis, simply because it is 
expressed im terms which experience has made intelligible. 
Whether it be a true hypothesis, that is, whether such an ether 


506 Prof. Challis on Theoretical Physics. 


be a reality, is another question. It does not admit of @ priori 
proof or disproof, but may be disproved by a single contradictory 
fact, or may receive accumulative evidence by the agreement of 
its mathematical results with many facts. Now I venture to 
assert respecting this particular hypothesis, that the mathema- 
tical evidence of its truth and of the reality of a fluid ether 
is so varied and comprehensive, that it may be pronounced to 
be all but conclusive. My reasons for this assertion are the fol- 
lowing :—When a mathematical inquiry is made into the laws of 
the motion and pressure of a fluid constituted as above supposed, 
certain results are obtained by the formation and solution of par- 
tial differential equations which correspond to various pheno- 
mena of light. The difference of the intensities of different rays, 
the variation of intensity with the distance from a centre, and 
the law of the variation, the coexistence at the same instant of 
different portions of light in the same portions of space, the 
interference and non-interference of different rays, the composite 
character of light, its colour, results of compounding colours, 
and lastly the polarization of light, are all phenomena which 
have their exact analogues in the motions, as mathematically 
deduced, of a fluid medium whose pressure varies as its density. 
When the number, variety, and speciality of these analogies are 
considered, it seems difficult to resist the conclusion that proper- 
ties of the fluid ether explain phenomena of light, and that the 
phenomena reciprocally give evidence of the reality of the ether. 
Some of the properties—for instance, that of transverse vibration, 
which accounts for polarization—have been deduced by mathema- 
tical reasoning for which I am responsible. I have, however, 
given to mathematicians the fullest opportunity of discussing 
these parts of the general argument ; and when, as I hope to be 
able to do, I go through a revision of the propositions, further 
opportunity will be given. ‘The proof of the reality of the 
eetherial medium, drawn from the explanations which the hypo- 
thesis of such a medium gives of phenomena of light, is an essen- 
tial preliminary of my general theory of physical force, and I am 
well aware that on this ground the truth of the theory must be 
contested. If this point be carried, the rest, I think, must 
follow. | 

There is already evidence from experiment that the action of 
physical force may be explained hydrodynamically. In the Phi- 
losophical Magazine for May (p. 348), Professor Maxwell has 
referred to a paper by M. Helmholtz on Fluid Motion, in which 
the author points out that lines of fluid motion are arranged 
according to the same laws as the lines of magnetic force. This, 
which Prof. Maxwell chooses to call a “ physical analogy,” I of 
course take to be confirmatory of the hydrodynamical theory of 


~ On the Presence of a Medium pervading all Space. 507 


magnetic force. In the same light I regard the experiments of 
Professor Wiedemann, mentioned in vol. xi. No. 42 of the ‘ Pro- 
ceedings of the Royal Society,’ the results of which point to the 
same conclusion. 


Cambridge Observatory, 
May 22, 186]. 


ney 


LXXIV. On Phenomena which may be traced to the Presence of 
a Medium pervading all Space. By Daniex VauGHAN. 


i the permanent change which seems to have been detected 

in the revolution of Encke’s comet be not sufficient to 
establish the doctrine of a space-pervading ether, it may afford 
reasonable motives for examining other indications of the im- 
pediments of such a fluid to celestial motion. The direct in- 
formation which can be obtained on this subject is at present very 
limited and uncertain. The approximate investigations hitherto 
given by mathematicians of the cause of the perturbation of the 
planets, necessarily overlook many slight effects of their mutual 
attraction ; and we are thus prevented from discovering the un- 
periodical changes which a small resistance to their movements 
might occasion. In addition to this, we are ncommoded by the 
want of observations made during very long periods of time; for 
these are as necessary in tracing the course of remote physical 
events, as an extensive base-line is in determining the distances 
of the fixed stars. But by investigating the necessary conse- 
quence of a resisting medium, and testing the result by a com- 
parison with observed facts, we may be enabled to base our con- 
clusions respecting this important question on evidence no less 
satisfactory than that which has already served to establish many 
of the received doctrines of physical science. 

As there has prevailed among some astronomers an impression, 
not unwholly unfounded, in regard to a modification which the 
sun’s attractive power 1s supposed to experience from the emis- 
sion of his light, it seems advisable to give special attention to 
cases in which the central body is not luminous; and certain 
phenomena, observed in the secondary systems and in the dark 
systems of space, afford evidence not vitiated by any effects which » 
light might be expected to produce. In my communication in 
the Philosophical Magazine for last April, 1 showed that a 
satellite impeded by the resistance of a medium would, by an im- 
perceptibly slow diminution of its orbit, be finally introduced 
into the region of instability, where its dismemberment must be 
inevitable, and where it must be transformed into a ring, similar 


* Communicated by the Author. 


508 Mr. D. Vaughan on Phenomena which may be traced 


in all respects to those of Saturn. Butit might be premature to 
suppose that the annular appendage of Saturn has originated in 
this manner, or that it is to be regarded as an index of mutability 
in the heavens, if the conclusion were not supported by investi- 
gations of a different character. Were the rings two integral 
solid masses, the imner one, even with the most favourable 
velocity of rotation, would require to be composed of materials 
having over two hundred times the tenacity of wrought iron to 
escape being ruptured, in consequence of the enormous strain 
arising from a preponderance of centrifugal force on one part, and 
of gravity on the other. Even if this danger were removed, solid 
rings could not be prevented from striking the planet, unless 
each were loadedwith some inequality; and, according to the inves- 
tigations of Professor Maxwell, the load must contain about four 
anda half times as much matter as the remainder of the ring. 
A slight excess or deficiency in the amount of this load would be 
fatal to stability ; and the tendency of any fluid or loose solid 
matter to the locality where it occurs must add much to the 
serious perils and the infirmities of the annular structure. 

Regarding the hypothesis of two solid rings as untenable, 
Professor Maxwell considers the case of their fluidity, and he 
arrives at the conclusion that the fluid composing them would 
break up into satellites, unless its density were less than {', 
of that of the primary. But, from the result deduced in my 
articles in the Philosophical Magazine for December 1860 
and April 1861, it is evident that, in so great a proximity to the 
central body, any liquid matter would require a far greater 
density to exist in the form of independent satellites. In inyes- 
tigating the case of a rig of numerous solid satellites, or frag- 
ments, he finds a combination of very extraordinary conditions 
necessary to prevent the derangements and permanent changes 
which collisions and friction are expected to occasion. The bodies 
are to be all equal in mass, and placed in regular array around 
Saturn; but the intervals between them must be very great 
compared with the linear dimensions; and the ratio between 
the planet and the ring must, according to his formule, be 
greater than 4352 multiplied by the square of the number of 
satellites composing the latter. When we consider the vast 
number of such bodies required to maintain the continuity of 
the ring, and the great improbability that all the immense group 
should have the peculiar conditions for preventing one from 
striking another, we may regard the essay of the eminent mathe- 
matician as a proof that the disconnected matter composing the 
annular appendage, whether it be fluid or solid, cannot be main- 
tained in its present condition without the occurrence of friction — 
and collisions between its parts. 


to the Presence of a Medium pervading all Space.. 509 


Besides the valid objections which Professor Maxwell urges 
against the common idea which regards the rings as two flat 
solids, others of a somewhat different character have been 
suggested by Mr. Bond, who has embraced the opinion that the 
ring is fluid. But whatever be its composition, or whatever 
proportions of fluid and solid matter it may consist of, all its 
parts must have independent movements around Saturn, and 
velocities depending on their distance from his centre. The 
attraction of the planet will be an insurmountable obstacle to 
their conversion into satellites, and will even prevent them from 
concentrating in excessive numbers in any locality; but their 
incessant action must be attended with a constant development 
of heat and a gradual destruction of motion. In consequence 
of the necessary alteration in the orbit of its parts from this 
cause, the dimensions of the ring cannot always remain the 
same ; and though it is not likely that the nearest edge is ap- 
proaching the planet so rapidly as the researches of Struve 
and Hansen would indicate, yet, as some change of this nature 
is unavoidable, we cannot resist the conclusion that the rings 
have been introduced into the zone which they now occupy, 
from one in which their matter could only exist im the form of 
two satellites. Accordingly there appears to be no ground 
for any other inference than that I have adopted, in regard 
to the imperceptible diminution of the orbits of secondary 
planets by the action of a resisting medium. 

In tracing the ultimate effects of a similar impediment to 
motion in the dark systems of remote space, we deduce so satis- 
factory an explanation of the temporary stars, that we may regard 
these celestial apparitions as indicating the existence of the 
same ethereal fluid, and manifesting the great revolutions to 
which it leads in the condition of the heavenly bodies. In my 
last article, I have shown that the instantaneous manner in 
which a secondary or a primary planet must undergo a total 
dismemberment on coming into fatal proximity with the central 
sphere harmonizes in a very decided manner with the astonish- 
ing rapidity with which temporary stars attain their greatest 
brillancy. This peculiarity, taken in connexion with the com- 
paratively slow and gradual decline, is sufficient to set aside the 
theory which ascribes such ephemeral exhibitions of light to the 
rotation of great orbs, self-luminous on one side and dark on 
the other. But this theory, though adopted by Arago and 
other eminent astronomers, is liable to a more fatal objection. 
This will be apparent when we investigate the circumstances 
necessary to make a partially luminous sphere or spheroid display 
its brilliancy to the inhabitants of the earth for only seven- 
teen months, while its period of rotation has been estimated ‘at 


510 Mr. D. Vaughan on Phenomena which may be traced 


309 or 318 years. Under the most favourable circumstances 
for manifesting such an extraordinary inequality between its 
periods of light and darkness, the surface of the supposed 
distant sphere must be nearly 200,000,000 times as great as 
the part of it sending light to our planet during the period of 
maximum brightness. The light, moreover, must have pro- 
ceeded from the verge of the invisible disk; and this circum- 
stance, taken in connexion with the surprising brilliance of 
the star of 1572, together with the invariability of its position, 
will compel us to ascribe to the spectral orb in question a dia- 
meter far exceeding that of Neptune’s orbit. We must also 
regard these vast bodies as solid; for, if composed of liquid or 
gaseous matter, they could not have the luminosity confined to 
particular localities. Even if stellar movements could permit 
us to suppose the existence of such stupendous spheres, the 
explanation would be applicable to one or two cases only; and 
we must therefore reject a hypothesis whose claims rests solely 
on the greater imperfections of others proposed to account for 
the same phenomena. 

But investigations respecting the necessary course of physical 
events in the dark systems afford still more important evidence 
in regard to the ethereal contents of space. Were the central 
body composed of solid matter, or surrounded with an atmo- 
sphere of oxygen, nitrogen, or carbonic acid, a development of 
heat and light might be expected to attend the dilapidation of 
one of the satellites, or the ultimate incorporation of its matter 
with the great orb; but the appearance would not correspond 
to that exhibited by the temporary stars. Admutting that a 
solid globe, almost as large as the sun, may be rendered so 
highly meandescent as to shine like the star of 1572 in its 
greatest brilliancy, it would be impossible for it to cool so 
rapidly as to become invisible in the course of seventeen months. 
Besides this, it may be easily shown that, if our earth had a 
diameter of 80,000 miles, with its present density and superfi- 
cial temperature, our atmosphere would have its density reduced 
a millionfold with an elevation of six or seven miles. Thus, 
the greater mass we assign to the central body, the more nar- 
row must we regard the atmospheric region where light can be 
developed by aérial compression ; and the less display of lustre 
could we expect from this cause when a satellite fell from its 
stage of planetary existence. But this difficulty will disappear 
when we suppose that the ether of space forms for the several 
great celestial bodies extensive atmospheres, which are rendered 
luminous by adequate compression, or rather by the chemical 
action it induces—a theory which becomes necessary to account 
for the luminosity of meteors and the perpetual brilliancy of suns, 


to the Presence of a Medium pervading all Space. 511 


The theory which ascribes the sun’s light to the incessant 
fall of meteors to his surface, and which I have controverted in 
my article in the Philosophical Magazine for December 1858, 
appears to have been suggested by the recently discovered rela- 
tion between heat and mechanical energy. From this it may be 
estimated that a pound of solid matter, falling to the sun from 
a distance of 35,000,000 miles, is capable of generating at 
his surface an amount of heat about 4000 times as great as 
could be developed by the combustion of a pound of coal in 
oxygen gas. But the large amount of heat arising from the 
combustion of hydrogen, and other facts and principles con- 
nected with thermal agencies, give support to the opinion that 
the development of heat must be proportional to the intensity 
of the chemical forces by which it is produced; and these must 
be commensurate with the degree of elasticity between the 
elements concerned in the calorific or the illuminating action. We 
have therefore no grounds for supposing that the accession of 
temperature imparted to the solar orb by the fall of a body, 
even from an infinite distance, is necessarily greater than that 
originating from the chemical action of an equal amount of 
matter, the elements of which were so elastic as to diffuse them- 
selves into space, in opposition to the attractive power of suns 
and planets. If the undulatory theory of light be admitted, 
the medium which conveys it with nearly a million times the 
rapidity of sound, must have a modulus of elasticity almost 
1,000,000,000,000 times as great as that of common air. But 
though not regarding the ether which gives birth to solar light as 
sO Inconceivably elastic, we may safely presume that no matter is 
better adapted for sustaining the great fountain of brilliancy by 
energetic chemical action, than that whose particles are asso- 
ciated with forces sufficiently powerful to cause its diffusion 
through universal space. 

That the fall of meteors is far more frequent and more con- 
spicuous on the sun than on the earth cannot be questioned. If 
these small bodies are to be regarded as independent occupants 
of space, two large spheres, moving with the same velocity through 
the region in which they are located, would each be likely to 
receive a number of them proportional to its mass multiplied by 
its diameter. The circumstances in which the earth and sun 
are placed will change, to some extent, their relative capabilities 
of receiving these foreign bodies; but the facts which Mr. Car- 
rington’s observations have made known in regard to meteoric 
phenomena on the solar disk are not inconsistent with what 
might be reasonably expected, and do not indicate any special 
provision for feeding our central luminary with regular supplies 
of meteorites. 


512 Mr. D. Vaughan on Phenomena which may be traced 


The definite information which Arago was enabled to furnish 
respecting the sun by means of his polariscope, has recently 
received an important accession from the labours of Bunsen and 
Kirchhoff. A comparison of the spectrum of the sun with that 
of various metallic vapours in a state of incandescence, enabled 
these chemists to show that potassium, sodium, calcium, and 
other elements widely diffused on our globe, enter into the com- 
position of the solar atmosphere. Their observations proved, 
however, that these substances, while abundant in the sun’s en- 
velope, instead of being concerned in producing his light, only 
exerted a negative influence—absorbing certain rays, and causing 
dark lines to replace the bright ones peculiar to their luminous 
vapours. It is therefore evident that the light from the vapours 
of the elements alluded to must be overpowered by the rays 
emanating from some other source. Professor Kirchhoff has 
embraced the opinion that the solid globe of the sun must have 
a far higher temperature and a greater illuminating power than 
his atmosphere; but the observations with Arago’s polariscope 
have afforded positive evidence that solar light does not emanate 
from an incandescent solid or liquid body. It appears more 
philosophical to conclude that the hght of our great luminary 
originates, not from the vapours discoverable in its atmosphere, 
but from a more subtle ethereal medium combined with them, 
and possessed of far greater illuminating power. 

The periodical changes recently discovered in the sun’s spots 
seem to furnish a fatal objection to the idea that the self-luminous 
condition results from the high temperature of his solid nucleus, 
or from the heat developed by its compression. It can scarcely be 
doubted that the periodicity of the spots is dependent on the 
movements of the planets; and the position of Jupiter seem to 
exert the greatest influence on their cecurrence; as recent ob- 
servations show, the period of his revolution agrees very closely 
with the interval between the times at which the spots are most 
numerous. Although it may be premature to express a decided 
opinion on so obscure a subject, there seem to be legitimate 
motives to justify an examination of the more obvious ways in 
which it would be possible for a planet to affect the luminous 
condition of the solar disk. If, as Helmholtz contends, the 
ocean of heat and light be maintained by the compression of the 
sun, the planets can only exert their influence on his spots by 
diminishing the weight and pressure of his materials, in the same 
manner in which the moon acts to raise tides on our oceans. 
But the alteration in the weight of terrestrial matter from lunar 
attraction, though extremely small, is about 80,000 times as great 
as that which the component parts of the sun experience from the 
attractive force of Jupiter. ‘This planet holds the highest place 


to the Presence of a Medium pervading all Space., 513, 


in its capability of affecting the pressure of the solar matter: it 
is almost equalled by Venus, but it. is far superior to the other 
members of our system. If, however, the planets moved in circles, 
the peculiar action alluded to could only increase the tendency, 
of the spots to appear on certain sides of the sun, without mate- 
rially increasing the numbers visible during the year. When we 
take into consideration the changes occasioned by the eccentri- 
city of their orbits, the greatest effect must be ascribed to 
Mercury; Jupiter holds the next place; after which we must 
rank Saturn and the earth. But even admitting the compressi- 
bility of the sun’s materials, his mean diameter could not be 
altered more than the ;oth of an inch by the attraction of any of 
his planetary attendants; and the variation of temperature from 
this peculiar action cannot exceed giath part of a degree (F.). 
That so small a variation could be manifested in the appears 
ance of the sun’s disk, seems wholly improbable, especially if we 
adopt the estimate of Mr. Waterston, which assigns to the great 
orb a mean temperature of one thousand million degrees. 

Any effect which the planets may be supposed to occasion by 
their electric or magnetic forces must be also rendered extremely 
feeble in consequence of their great distance. If the great ocean 
of solar light is sensitive to the electricity or magnetism of Ju- 
piter, the nearest satellite of this planet must feel the power of 
his mysterious influence to an extent several million times as 
great ; yet no indications of such a fact have been observed. 
But supposing the sun’s motion through space to be concerned 
in maintaining his effulgence, the planets would derive a far 
more considerable influence from the general movement around 
the centre of gravity of our system. The position of Jupiter 
would change the progressive motion of the great luminary about 
twenty-four miles an hour; and the other planets will be at- 
tended with results proportional to their masses multiplied by 
the square roots of their distances. Now the amount of ether 
which the sun collects from space, and the density it attains on 
his surface, will depend on the rapidity of his translatory motion; 
but I have shown in the Philosophical Magazine for May 1858 
another way in which the position of the planets would increase 
or diminish the supply of ethereal fuel which sustains the great 
solar conflagration. 

The idea that the space-pervading medium is condensed by 
the attraction of the celestial orbs, is not to be considered a new 
hypothesis, but rather a necessary inference from that of Pro- 
fessor Encke. Were the density of the subtle fluid uniform, 
small and large planets would be so unequally affected by its re- 
sistance, that their orbits could not retain the relation necessary 
for their stability, and they must be destroyed by collisions long 

Phil, Mag. 8. 4, No. 143, Suppl, Vol. 21, 2 1L 


514 On the Presence of a Medium pervading all Space. 


before the natural term of their existence. This difficulty will, 
however, disappear when the effects of planetary attraction in 
condensing the medium are taken into consideration. How far 
observation of primary or secondary worlds give evidence of un- 
periodical changes in our system has not been yet determined 
with positive certainty. The constant acceleration of the moon’s 
orbital velocity, during the past 2000 years, has been traced by 
Laplace to a periodical change in the eccentricity of the earth’s 
orbits. But an error in his investigations being lately pointed 
out by Mr. Adams, there appears to be some definite ground for 
regarding the lunar orbit as subject to a very slow permanent 
diminution, which, after some allowance for the effects of tidal 
action, we may consider as depending, to some extent, on the 
resistance of a medium. The great oblateness which Arago and 
Sir William Herschel assign to Mars would indicate that the 
time of its rotation has been considerably lengthened, since the 
remote period at which it was moulded into its present form ; 
and this may be looked upon as circumstantial evidence of the 
effects of an ethereal resistance in changing the diurnal motion 
of planets. It is only to smaller worlds that we could look for 
such results, for in larger orbs the strength of their solid matter 
can have little influence in preventing alterations of form to cor- 
respond with the relations of gravity and centrifugal force. 

As doubts are entertained by some eminent astronomers as to 
the sensible ellipticity of Mars, it may be well to refer to certain 
appearances which show a slight deviation, at least, in his form 
from a figure of equilibrium. The marked indications of atmo- 
spheric phenomena around his poles, while they are either wholly 
absent or only faintly exhibited in the vicinity of his equator, is so 
much opposed to everything we might expect from the condition 
of our own globe and the belted appearance of Jupiter, that we 
cannot avoid concluding that the aérial ocean of Mars is much 
deeper in his polar than in his equatorial regions. Perhaps this 
may account for the very discordant results of observations in 
determining the extent of the atmosphere of this planet by oc- 
cultations of the fixed stars. 

It is to the revolutions of comets that astronomical curiosity 
has chiefly turned for evidence of the contents of interplanetary 
space ; but the advantages of low density in these bodies have 
been counterbalanced by the great elongation of their orbits, 
which exposes them to very great disturbances from the planets. 
During the past eighteen centuries Halley’s comet has occupied 
in its revolution a period varying from 74°88 to 79°34 years, ac- 
cording to the Table in Mr. Hind’s work on Comets (page 57): 
Of the twenty-four consecutive revolutions here recorded, the 
first eight average 77°59 years, the next eight 76°84, and the last 


On a Four-valued Function of three sets of three-letters each. 515- 


76°54 years. This would seem to favour the idea of a perma- 
nent diminution of the orbit ; and I understand that: De Vico 
regards the movements of his own comet as indicative of a similar 
‘result from the widely diffused ether. But the information on 
this subject hitherto deemed worthy of the most confidence, has 
been derived from the successive returns of Encke’s comet. The 
advantages which this body affords for such inquiries depend. 
chiefly on the moderate eccentricity of its orbit and the position 
of the transverse axis, which is. nearly perpendicular to the line- 
of the. sun’s progressive motion. This arrangement must give 
a more decided preponderance to the perihelion resistance, which 
has the greatest. influence in diminishing the size of the orbit. 
As shooting stars are now regarded as small bodies describing 
very elongated ellipses around the sun, they seem calculated to 
furnish perhaps the most satisfactory means of testing the per- 
fection of the celestial vacuum. Supposing these bodies to be 
more sensitive to the resistance of the medium than to planetary 
disturbances, the transverse axes of their orbits will have a ten- 
dency to assume a uniform direction in consequence of the sun’s 
progressive motion. From the same cause the planes in which 
they move will have their intersections confined for the most 
part to a very limited range, and will also exhibit, though im a 
less degree, a tendency to coincidence. This peculiar arrange- 
ment of their orbits must cause vast swarms of these minute 
cosmical bodies to congregate from the most distant parts of the 
solar domain to a comparatively narrow region at their perihelion 
passage. For the appearance of the zodiacal light and the perio- 
dical fall of meteors, I have endeavoured to account in this man- 
- ner in a paper sent to the meeting of the British Association 
and. published in the Sections (1854, p. 26). My late researches 
on the subject exhibit a closer accordance with observed facts 
than I could then obtain, and they give much support to the 
ideas very prevalent in scientific circles, with regard to the agency 
of meteors in reflecting the zodiacal light. 


Cincinnati, May 11th, 1861. 


LXXVI. Ona Problem in Tactic which serves to disclose the ex- 
istence of a Four-valued Function of three sets of three letters 
each. By J.J. Syuvester, M.A., F.R.S., Professor of Mathe- 
matics at the Royal Mihtary Academy, Woolwich*. 


x page 375 of the May Number of the Magazine (in that 
paragraph commencing at the middle of the page) I gave 
a Table of Synthemes, correct as far as it went, but left in a very 


* Communicated by the Author. 
212 


516 Prof. Sylvester on a Four-valued Function 


imperfect state. It was intended to be supplemented with a 
material addition which escaped my recollection when, after a 
long delay, the proofs of the paper passed through my hands. 
The question to which this Table refers is the following :— 

Three nomes, each containing three elements, are given; the 
number of ¢rinomial triads (1. e. ternary combinations, composed. 
by taking one element out of each nome) will be 27, and these 
27 may be grouped together into 9 synthemes (each syntheme 
consisting of 3 of the triads in question, which together include 
between them all the 9 elements). It is desirable to know :— 
lst. How many distinct groupings of this kind can be formed. 
2nd. Whether there is more than one, and, if so, how many 
distinct types of groupings. ‘The criterion of one grouping 
being cotypal or allotypal to another is its capability or incapa- 
bility of being transformed into that other by means of an inter- 
change of elements. Be it once for all stated that the question 
in hand is throughout one of combinations, and not of permuta- 
tions; the order of the elements in a triad, of a triad in a syn- 
theme, of a syntheme in a grouping is treated as immaterial. 
As we are only concerned with the elements as distributed into 
nomes, the number of interchanges of elements with which we 
are concerned is 6x 6? or 1296; the factor 6° arises from the 
permutability of the elements of each nome inter se, the remain- 
ing factor 6 from the permutability of any nome with any other. 
I find, by a method which carries its own demonstration with 
it on its face, that the number of distinct groupings is 40, of 
which 4 belong to one type or family, and 36 to a second type 
or family. 

Let the nomes be 1.2.3, 4.5.6, 7.8.9, and let 


ce, denote 1.4, 2.5, 3.6 C; denote 1.4, 2,6, 3.5 
eno! fired SRY 6y iB o4h) hep gle) Phe, 
Gog. 168, 204, B65) ey lah) de 
FG 9 7, 9, 8 
y denote 8, 9, 7 y' denote 9, 8, 7 
apts 8, 7,9 
b, denote 1.7, 2.8,3.9 6, dencte 1.7, 2.9, 3.8 
bg 5p 41 26080 eee >) A 
By ii ar en OF BAT PBB By, A ee 


“ 


1 OD 
ee OOD 
QO KC 


“ 


“ 


4, 5, 6 
B denote 5, 6, 4 B' denote 
6 5 


“ 


of three sets of three letters each. 517 


a, denote 4.7, 5.8, €.9 a, denote 4.7, 5.9, 6.8 
Rie ets 5.9, 6. 7:..° hag. 5 apednBy, 3.76 Ga8 
RIS 7628 gen gh) MeO, 5-8, 6x7 

1, 2, 3 ENE 

a denote 2, 3, 1 «#' denote 2, 3, 1 

3, 1,2 5. Le 


I 


I take first the larger family of 36 groupings ; these may be 
represented as follows : 


! ! 
| aye aye aya aya aya! ay! 


Ri I ty 
Ae |A\a A,% |A\% Aye a 
I 


~ 


! I ! ! 
dae | get! |agee | age! |dgn ae! | aoe | dou Age aoa Aga | a% 


I ! n| ee AAP. ! 
Azh |Azt |Ag% |Axe |Agh Aza || Age | Axe set (get age! Age 


b,8\b,8 |b,6'|b,8 |b,8'|b,8')b,8 \b,8 |b,8'|6,8 | 6,8'\5,8" 
BB | ba! by | by!) By8 |b.8' by8 | ba8'|by8 |by8!| bo |b,8' 
DB bof | by | By! |ba(3!|048 | by(3' b48 |b58 |b,6"| 848" b48 
ay | ay ey levy | evry! iat ci ov ey! Cy ey! ey! 
Cay | Coty! | C27 | Cay CoY Cary CY the cary’ eof cory! Col co! 
est | Cay | cay \esty!) esty oy est! C3 cosy ext! egy! cst 


An example of the development of any one of the above sym- 
bolisms into its correspondent grouping will serve to render 
perfectly intelligible the whole Table. 

Let it be required to develope 


6,8 
b, (3! 
bs oy : 
Since 
Pi 7 2.9. 3.8 Aus eG 4» thee 
mot. 2.7, 3.9. Soh 64 B= 6, d44 
pebie.94) 2.8, 8.7 6) 4,5 a ag) 


the development required is the following :— 


om Samed fh fee fed famed fame fore famed 
e e ° ° e. ° . . e 
DD QD Sr Or Or 
CD OWOONOON 


518 Prof. Sylvester on a Four-valued Function 


1.7.4 2.97235 5.5.6 
127.25 92.9.) 3.8.4 
1.7 .6_-2.9 435 48..p 
1.8.4" 27 uate), D 
128.6282 .7 0: 73.9.4: 
1.8.0 2a ok ps aD 
1 ls eee: eee 
1.9.06 -2.8.50.3.%.4 
19.09. 2.6. Od 20 


The whole of this family of 36 may be represented under 
the following condensed form, according to the notation usual 
in the theory of substitutions. 


123 123 .1238 . oct! ax aa bB °”) 
123 281 312 cn! oly aa aa ae 
It remains to describe the principal and most symmetrical 


family. This contains only 4 groupings, and may be repre- 
sented indifferently under any of the three following forms: 


ay 


a 
a\x 
As & 


as 


aa aa aa aa 1,8 b,f' 6,8 5, ay ey ey ey 

Aint Age! det doe! or 6,8 5,6! 5,8 6/3! or Coy Cay! Coty Cony! 

age dget! age age 058 0,8! 6,8 6,8! — egy egy! Cay Cty’ 
In developing, it will be found that each of these three represen- 


tations gives rise to the same family of groupings, which from 
its importance it is proper to set out in full as follows :— 


2.5.8 3.6.9|/1.4.7 2.5.9 3.6.8/1.4.7 2.6.8 3.5.9|1.4.7 2.6.9 3.5% 
2.5.9 3.6.7/1.4.9 2.5.8 3.6.7|1.4.8 2.6.9 3.5.7|1.4.9 2.6.8-8.5 
2.9.7 3.6.8/1.4.8 2.5.7.3.6.911.4.9 2.6.7 3.5.8/1.4.8 2.627 S.b5 
2.6:8 3.4.9/1.5.7 2.6.9 3.4.8/1:5.7 2.4/8 3.6.9|1.5.7 2.4.59 3.6 
2.6.9 3.4.7/1.5.9 2.6.8 3.4.7/1.5.8 2.4.9 3.6.7|1.5.9 2.4.8 3.6. 
2.6.7 3.4.8/1.5.8 2.6.7 3.4.9)1.5.9 2.4.7 3.6.8)/1.5.8 2.4.7 3.6 
2.4.8 3.5.911.6.7 2.4.9 3.5.8|1.6.7 2.5.8 3.4.9|1.6.7 2.5,.950.45 
2.4.9 3.5.7/1.6.9 2.4.8 3.5.7/1.6.8 2.5.9 3.4.7/1.659 Jane 
2.4.7 3.5.8/1.6.8 2.4.7 3.5.9/1.6.9 2.5.7 3.4.8|1.6.8 2.5.7 3.4 


OHO WNI OD CONT 


It bios at once from the above Table, that if 3 cubic equa- 
tions be given, we may form a function of the 9 roots, which, 
when any of the roots of any of the equations are interchanged 
inter se, or all the roots of one with all those of any other, will 
receive only four distinct values. . 

It also follows that we may form with 9 letters an intransitive 


group (of Cauchy) containing ™°, i. e. 54, or a transitive group 


of three sets of three letters each. 519 
containing = ® or 324 substitutions, So the family of 36 
groupings lead to the formation of an intransitive substitution 
== 

- Or 16 


group of i. e. 18, and of a transitive group ie 


substitutions. 


Since 9 letters may be thrown, in at x a : i. e. 280 differ- 


an ways, into nomes of 3 letters each, it further follows that by 
repeating each of the above two families 280 times we shall 
obtain new families remaining unaltered by any substitution of 
any of the nine elements inter se, and consequently indicating 
the existence of substitution-groups containing 
1.°2.3894.5.6.7.38.9 Fl bs 2h Bin Fe Guy 1:8; 9 
280 x 36 ia 280 x 4 

1. e. 86 and 324 substitutions respectively. 

~ In the above solution a little consideration will show that the 
method is essentially based on the solution of a previous question, 
viz. of grouping together the synthemes of binomial duads of two 
nomes of three letters each, which can be done in two distinct 
modes, which (if, ex. gr., we take 1.2.8, 4.5.6 as the two 
nomes in question) are represented j in the notation used above by 


Cy 
C5 4a | és Rowe TEly, So, more generally, the groupings of the 
Cg Cs 


g-nomial g-ads of 7 nomes of s oars may be made to depend 
on the groupings of the (g—l)-nomial (g—1)-ads of (r—1) 
nomes of selements each. The more general question is to dis- 
cover the groupings and their families of the synthemes composed. 
of p-nomial g-ads of r nomes of s elements, of which the simplest 
éxample next that which has-been considered and solved is to dis- 
cover the groupings of the synthemes composed of 54 binomial 
triads of 3 nomes of 3 elements each *. 

The chief difficulty of calculating @ priort the number of such 
groupings is of a similar nature to that which lies at the bottom 
of the ordinary theory of the partition of numbers, namely, the 
hability of the same groupings to make their appearance under 
distinct symbolical representations. Of this we have seen an 
éxample in the threefold representation of the principal family 
ef 4 groupings just treated of. But for the existence of this 


‘* T have ascertained, by a direct analytical method, since the above was. 
el that the number of different groupings of the ‘synthemes composed. 
of these binomial triads is 144. The number of distinct types or families 
is three, one containing 12, another 24, and the third 108 groupings. 


520 Notices respecting New Books. 


multiform representation of the same grouping we could. have 
affirmed: @ priori the number of groupings to be 2 x 3 x 2° or 48, 
whereas the true number is only 40. I believe that the above 
is the first instance of the doctrine of types making its appear- 
arice explicitly, and illustrated by example in the theory of taetie. 
It were much to be desired that some one would endeavour to 
collect and collate the various solutions that have been given of the 
noted'15-school-girl problem by Messrs. Kirkman (in the Ladies’ 
Diary), Moses Ansted (in the Cambridge and Dubtin Mathematical 
Journal), by Messrs. Cayley and Spottiswoode (in the Philosophi- 
cal Magazine and elsewhere), and Professor Pierce, the latest and 
probably the best (in the American Astronomical Journal), besides 
various others originating and still floating about in the fashion- 
able world (one, if not two, of which I remember having been com- 
municated to me many years ago by Mr. Archibald Smith, F.R.S.), 
with a view to ascertain whether they belong to the same or to 
distinct types of aggregation. 


——— 


LXXVII. Notices respecting New Books. 


A History of the Progress of the Calculus of Variations during the 
Nineteenth Century. By 1. Topuunter, M.A., Fellow and Prin- 
cipal Mathematical Lecturer of St. John's College, Cambridge. 
Cambridge: Macmillan and Co. 1861. 


R. ‘TODHUNTER, whose name is already so familiar to the 

mathematical student, has at length produced a work of much 

greater originality and research than any of his former and more ele- 
mentary treatises. 

The ‘Calculus of Variations,” one of the most difficult branches 
of pure mathematics, has been the subject of the labours of several 
eminent mathematicians, Euler, Lagrange, Gauss, Poisson, &c., 
whose successive researches and improvements form an exceedingly 
interesting department of scientific history, which, however, has 
hitherto been specially treated by only one writer in our own lan- 
guage, viz. Woodhouse, whose ‘Treatise on Isoperimetrical Problems 
and the Calculus of Variations’ was published in 1810, and is now 
an extremely scarce book. 

Woodhouse’s work has always received very high praise by such 
competent judges as Messrs. Peacock, Herschel, and Babbage, in their 
‘Examples ;’ Professor De Morgan, in his ‘ Differential and Inte- 
gral Calculus ;’ and Professor Jellett, in his ‘Calculus of Variations.’ 
But since its publication the calculus has been greatly advanced and 
improved ; and it is to record this progress that Mr. ‘l’odhunter has 
written the volume before us, which commences where Woodhouse 
left off. It is evidently the work of one who thoroughly understands 
the science itself, and who has most conscientiously and labo- 
riously consulted and studied all the available materials and sources 
of information. He unites the qualifications of a sound mathe- 


Roval Society. 521 


matician and a good linguist—a rare combination. The Memoirs 
and ‘l'reatises in the German and Italian languages, as well as those 
in the French and Latin, have been completely mastered and ana- 
lysed: and some account is given even of a dissertation in the Rus- 
sian language. Of those works which are difficult of access to the 
English student, a more copious account is given; and throughout 
the whole history, ‘‘numerous remarks, criticisms, and corrections 
are suggested relative to the various treatises and memoirs which are 
analysed. The writer trusts that it will not be supposed that he 
undervalues the labours of the eminent mathematicians in whose 
works he ventures occasionally to indicate inaccuracies or imperfec- 
tions, but that his aim has been to remove difficulties which might 
perplex a student’”’ (Preface). We would specially point out the 
last chapter in the book (pp. 505-530) as deserving attention in 
this respect. 

Fully agreeing with Mr. Todhunter as to the “ value of a history 
of any department of science, when that history is presented with 
accuracy and completeness,” we congratulate him on having pro- 
duced a History which so well merits this character of ‘‘ accuracy 
and completeness ;” and we sincerely hope that the success of his 
present contribution to scientific history may induce him to carry out 
the intention expressed in the conclusion of his Preface, viz. ‘‘ to 
undertake a similar survey of some other department of science.” 


ee - ee 
—ee 


LXXVIII. Proceedings of Learned Societies. 


ROYAL SOCIETY. 
(Continued from p. 469.] 
June 21, 1860.—Sir Benjamin C. Brodie, Bart., Pres., in the Chair, - 


tae following communications were read :— 

“Qn the Sources of the Nitrogen of Vegetation ; with special 
reference to the Question whether Plants assimilate free or uncom- 
bined Nitrogen.” By J. B. Lawes, Esq., F.R.S.; J. H. Gilbert, 
Ph.D., F.R.S. ; and Evan Pugh, Ph.D., F.C.S. 

After referring to the earlier history of the subject, and especially 
to the conclusion of De Saussure, that plants derive their nitrogen 
from the nitrogenous compounds of the soil and the small amount of 
ammonia which he found to exist in the atmosphere, the Authors 
preface the discussion of their own experiments on the sources of the 
nitrogen of plants, by a consideration of the most prominent facts 
established by their own investigations concerning the amount of 
nitrogen yielded by different crops over a given area of land, and of 
the relation of these to certain measured, or known sources of it. 

On growing the same crop year after year on the same land, with- 
out any supply of nitrogen by manure, it was found that wheat, over 
a period of 14 years, had given rather more than 30 lbs.—barley, 
over a period of 6 years, somewhat less—meadow-hay, over a period 
of 3 years, nearly 40 lbs.—and beans, over 11 years, rather more than 
50 lbs. of nitrogen, per acre, perannum. Clover, another Leguiminous 


———. 


522 Royal Society :— 


crop, grown in 3 out of 4 consecutive years, had giver an-average of 
120 lbs. Turnips, over 8 consecutive years, had yielded about 45 lbs: 
~ The Graminaceous crops had not, during the periods referred to, 
shown signs of diminution of produce. The yield of the Legumi- 
nous crops had fallen considerably. Turnips, again, appeared greatly 
to have exhausted the immediately available nitrogen in the soil. The 
amount of nitrogen harvested in the Leguminous and Root-crops was 
considerably increased by the use of “‘ mineral manures,” whilst that 
im the Graminaceous crops was so in a very limited degree. 

' Direct experiments further showed that pretty nearly the same 
amount of nitrogen was taken from a given area of land in wheat 
in 8 years, whether 8 crops were grown consecutively, 4 in alterna- 
tion with fallow, or 4 in alternation with beans. 

Taking the results of 6 separate courses of rotation, Boussingault 
obtained an average of between one-third and one-half more nitrogen 
in the produce than had been supplied in manure. His largest 
yields of nitrogen were in the Leguminous crops; and the cereal 
crops were larger when they next succeeded the removal of the 
highly nitrogenous Leguminous crops. In their own experiments 
ttpon an actual course of rotation, without manure, the Authors 
had obtained, over 8 years, an average annual yield of 57°7 lbs. of 
nitrogen per acre; about twice as much as was obtained in either 
wheat or barley, when these crops were, respectively, grown year after 
year on thesameland. The greatest yield of nitrogen had been in a. 
clover crop, grown once during the 8 years; and the wheat crops 
grown after this clover in the first course of 4 years, and after beans 
in the second course, were about double those obtained when wheat 
succeeded wheat. 

Thus, Cereal crops, grown year after vear on the same land, had 
given an average of about 30 lbs. of nitrogen, per acre, per annum ; 
and Leguminous crops much more. Nevertheless the Cereal crop 
was nearly doubled when preceded by a Leguminous one. It was 
also about doubled when preceded by fallow. Lastly, an entirely 
unmanured rotation had yielded nearly twice as much nitrogen as 
the continuously grown Cereals. 

Leguminous crops were, however, little benefited, indeed fre- 
quently injured, by the use of the ordinary direct nitrogenous ma- 
nures. Cereal crops, on the other hand, though their yield of ni- 
trogen was comparatively small, were very much increased by direct 
nitrogenous manures, as well as when they succeeded a highly nitro- 
i Leguminous crop, or fallow. But when nitrogenous manures 

ad been “employed for the increased growth of the Cereals, the 
nitrogen in the immediate increase of produce had amounted to-little 
more than 40 per cent. of that supplied, and that in the increase of 
the second year after the application, to little more than one-tenth 
of the remainder. Estimated in the same way, there had been in 
the case of the meadow grasses scarcely any larger proportion of 
the supplied nitrogen recovered. In the Leguminous crops the pro- 
portion so recovered appeared to be even less; whilst in the root- 
erops it was probably somewhat greater. Several possible explana- 


On the Sources-of the Nitrogen of Vegetation. 523 


tions of this-real- or- apparent loss of the nitrogen supplied by 
manure are enumerated. 

The question arises—what are the sources of all the nitrogen of 
our crops beyond that which is directly supplied to the soil by arti- 
ficial means? The following actual or possible sonrces may be 
enumerated :—the nitrogen in certain constituent minerals of the 
soil; the combined nitrogen annually coming down in the direct 
aqueous depositions from the atmosphere; the accumulation of 
combined nitrogen from the atmosphere by the soil in other ways ; 
the formation of ammonia in the soil from free nitrogen and nascent 
hydrogen; the formation of nitric acid from free nitrogen; the 
direct absorption of combined nitrogen from the atmosphere by 
plants themselves ; the assimilation of free nitrogen by plants. 

A consideration of these several sources of the nitrogen of the 
vegetation which covers the earth’s surface showed that those of 
them which have as yet been quantitatively estimated are inadequate 
to account for the amount of nitrogen obtained in the annual pro- 
duce of a given area of land beyond that which may be attributed 
to supplies by previous manurmg. Those, on the other hand, which 
have not yet been even approximately estimated as to quantity 
—if indeed fully established qualitatively—offer many practical 
difficulties in the way of such an investigation as would afford results 
applicable in any such estimates as are here supposed. It appeared 
important, therefore, to endeavour to settle the question whether or 
not that vast storehouse of nitrogen, the atmosphere, affords to grow- 
ing plants any measurable amount of its free nitrogen. Moreover, 
this question had of late years been submitted to very extended and 
laborious experimental researches by M. Boussingault, and M. Ville, 
and also to more limited investigation by MM. Mine, Roy, Cloez, 
De Luca, Harting, Petzholdt and others, from the results of which 
diametrically opposite conclusions had been arrived at. Before enter- 
ing on the discussion of their own experimental evidence, the Authors 
give a review of these results and inferences; more especially those 
of M. Boussingault who questions, and those of M. Georges Ville 
who affirms the assimilation of free nitrogen in the process of vege- 
tation. 

The general method of experiment instituted by Boussingault, 
which has been followed, with more or less modification, in most 
subsequent researches, and by the Authors in the present inquiry, 
was—to set seeds or young plants, the amount of nitrogen in 
which was estimated by the analysis of carefully chosen similar 
specimens ; to employ soils and water containing either no combined 
nitrogen, or only known quantities of it; to allow the access 
either of free air (the plants being protected from rain and dust)— 
of a current of air freed by washing from all combined nitrogen—or 
of a limited quantity of air, too small to be of any avail so far as any 
compounds of nitrogen contained in it were concerned ; and finally, to 
determine the amount of combined nitrogen in the plants produced 
and in the soil, pot, &c., and so to provide the means of estimating 
the gain or loss of nitrogen during the course of the experiment. 


524 iieN ~ Royal Society :— 


The plan adopted by the Authors in discussing their own experi- 
mental results, was— 

To consider the conditions to be fulfilled in order to effect the 
solution of the main question, and to endeavour to eliminate all 
sources of error in the investigation. 

To examine a number of collateral questions bearing upon the 
points at issue, and to endeavour so far to solve them, as to reduce 
the general solution to that of a single question to be answered by 
the results of a final set of experiments. 

To give the results of the final experiments, and to discuss their 
bearings upon the question which it is proposed to solve by them. 

Accordingly, the following points are considered :— 

1. The preparation of the soil, or matrix, for the reception of the 
plants and of the nutriment to be supplied to them. 

2. The preparation of the nutriment, embracing that of mineral 
constituents, of certain solutions, and of water. 

3. The conditions of atmosphere to be supplied to the plants, 
and the means of securing them; the apparatus to be employed, &c. 

4, The changes undergone by nitrogenous organic matter during 
‘decomposition, affecting the quantity of combined nitrogen present, 
in circumstances more or less analogous to those in which the expe- 
rimental plants are grown. 

5. The action of agents, as ozone; and the influence of other 
circumstances which may affect the quantity of combined nitrogen 
present im connexion with the plants, independently of the direct 
action of the growing process. 

In most of the experiments a rather clayey soil, ignited with free 
access of air, well-washed with distilled water, and re-ignited, was used 
as the matrix or soil. In a few cases washed and ignited pumice- 
stone was used. 

The mineral constituents were supplied in the form of the ash of 
plants, of the description to be grown if practicable, and if not, of 
some closely allied kind. 

The distilled water used for the final rinsing of all the important 
parts of the apparatus, and for the supply of water to the plants, was 
prepared by boiling off one-third from ordinary water, collecting the 
second third as distillate, and redistilling this, previously acidulated 
with phosphoric acid. 

Most of the pots used were specially made, of poreus ware, with a 
great many holes at the bottom and round the sides near to the 
bottom. ‘These were placed in glazed stone-ware pans with inward- 
turned rims to lessen evaporation. 

Before use, the red-hot matrix and the freshly ignited ash were 
mixed in the red-hot pot, and the whole allowed to cool over sul- 
phuric acid. The soil was then moistened with distilled water, and 
after the lapse of a day or so the seeds or plants were put in. 

Very carefully picked bulks of seed were chosen ; specimens of the 
average weight were taken for the experiment, and in similar speci- 
mens the nitrogen was determined. 

The atmosphere supplied to the plants was washed free from 


On the Sources of the Nitrogen of Vegetation. 525 


ammonia by passing through sulphuric acid, and then over pumice- 
stone saturated with sulphuric acid. It then passed through a solu- 
tion of carbonate of soda before entering the apparatus enclosing the 
plant, and it passed out again through sulphuric acid. 

Carbonic acid, evolved from marble by measured quantities of 
hydrochloric acid, was passed daily into the apparatus, after passing, 
with the air, through the sulphuric acid and the carbonate of soda 
solution. 

The enclosing apparatus consisted of a large glass shade, resting in 
a groove filled with mercury, in a slate or glazed earthenware stand, 
upon which the pan, with the pot of soil, &c., was placed. Tubes 
passed under the shade, for the ingress and the egress of air, for the 
supply of water to the plants, and, in some cases, for the withdrawal 
of the water which condensed within the shade. In other cases, the 
condensed water was removed by means of a special arrangement. 

One advantage of the apparatus adopted was, that the washed air 
was forced, instead of being aspirated, through the enclosing vessel. 
The pressure upon it was thus not only very small, and the danger 
from breakage, therefore, also small, but it was exerted upon the 
inside instead of the outside of the shade; hence, any leakage would 
be from the inside outwards, so that there was no danger of unwashe 
air gaining access to the plants. 

The conditions of atmosphere were proved to be adapted for 
healthy growth, by growing plants under exactly the same circum- 
stances, but in a garden soil. The conditions of the artificial soil 
were shown to be suitable for the purpose, by the fact that plants 
grown in such soil, and in the artificial conditions of atmosphere, 
developed luxuriantly, if only manured with substances supplying 
combined nitrogen. 

Passing to the subjects of collateral inquiry, the first question con- 
sidered was, whether plants growing under the conditions stated 
would be likely to acquire nitrogen from the air through the medium 
of ozone, either within or around the plant, or in the soil; that bod 
oxidating free nitrogen, and thus rendering it assimilable by the plants. 

Several series of experiments were made upon the gases contained 
in plants or evolved from them, under different circumstances’ of 
light, shade, supply of carbonic acid, &e. When sought for, ozone 
was in no case detected. The results of the inquiry in other re- 
spects, bearing upon the points at issue, may be briefly summed up 
as follows :— 

1. Carbonic acid within growing vegetable cells and intercellular 
passages suffers decomposition very rapidly on the penetration of 
the sun’s rays, oxygen being evolved. 

2. Living vegetable cells, in the dark, or not penetrated by the 
direct rays of the sun, consume oxygen very rapidly, carbonic acid 
being formed. 7 

3. Hence, the proportion of oxygen must vary greatly according 
to the position of the cell, and to the external conditions of light, and 
it will oscillate under the influence of the reducing force of carbon- 
matter (forming carbonic acid) on the one hand, and of that of the 


526 at Royal Society :— 


sun’s rays (liberating oxygen) on the other. Both actions may: 
go on simultaneously according to the depth of the cell; and the 
once outer cells may gradually pass from the state in which the. 
sunlight is the greater reducing agent to that in which the carbon- 
matter becomes the greater. 

4. The great reducing power operating in those parts of the plant. 
where ozone is most likely, if at all, to be evolved, seems unfavour-: 
able to the oxidation of nitrogen; that is under circumstances in 
which carbon-matter is not oxidized, but on the contrary, carbonic 
acid reduced. And where beyond the influence of the direct rays of. 
the sun, the cells seem to supply an abundance of more easily oxi- 
dized carbon-matter, available for oxidation should free oxygen or 
ozone be present. On the assumption that nitrates are available as 
a direct source of nitrogen to plants, if it were admitted that nitrogen 
is oxidated within the plant, it must be supposed (as in the case of 
carbon) that there are conditions under which the oxygen compound 
of nitrogen may be reduced within the organism, and that there are 
others in which the reverse action, namely, the oxidation of nitrogen, 
can take place. 

5. So great is the reducing power of certain carbon-compounds of 

vegetable matter, that when the growing process has ceased, and all 
the free oxygen in the cells has been consumed, water is for a time 
decomposed, carbonic acid formed, and hydrogen evolved. 
_ The suggestion arises, whether ozone may not be formed under 
the influence of the powerful reducing action of the carbon-com- 
pounds of the cell on the oxygen eliminated from carbonic acid by 
sunlight, rather than under the direct action of the sunlight itself 
—in a manner analogous to that in which it is ordinarily obtained 
under the influence of the active reducing agency of phosphorus? 
But, even if it were so, it may be questioned whether the ozone 
would not be at once destroyed when in contact with the carbon- 
compounds present. It is more probable, however, that the ozone 
said to be observed in the vicinity of vegetation, is due to the action 
of the oxygen of the air upon minute quantities of volatile carbo- 
hydrogens emitted by plants. 

Supposing ozone to be present, it might, however, be supposed to 
act in a more indirect manner as a source of combined and assimilable 
nitrogen in the Authors’ experiments, namely,—by oxidating the 
nitrogen dissolved in the condensed water of the apparatus—by 
forming nitrates in contact with the moist, porous, and alkaline 
soil—or by oxidating the free nitrogen in the cells of the older 
roots, or that evolved in their decomposition. 

Experiments were accordingly made to ascertain the influence of 
ozone upon organic matter, and on certain porous and alkaline 
bodies, under various circumstances. <A current of ozonous air was 
passed over the substances for some time daily, for several months, 
including the whole of the warm weather of the summer; but in 
only one case out of eleven was any trace of nitric acid detected, 
namely, that of garden soil; and this was proved to contain nitrates 
before being submitted to the action of ozone. | 


On the Sources of the Nitrogen of Vegetation. 527 


Tt is not, indeed, hence inferred that nitric acid could under no 
circumstances be formed through the influence of ozone on certain 
nitrogenous compounds, on ‘nascent nitrogen, on gaseous nitrogen in 
contact with porous and alkaline substances, or even in the atmosphere. 
But, considering the negative result with large quantities of ozonous 
air, acting upon organic matter, soil, &c., in a wide range of circum: 
stances, and for so long a period, it is believed that no error will be 
introduced into the main investigation by the cause referred to. 

Numerous experiments were made to determine whether free ni- 
trogen was evolved during the decomposition of nitrogenous organic 
compounds. 

In the first series of 6 experiments, wheat, barley, and bean-meal 
were respectively mixed with ignited pumice, and ignited soil, and 
submitted for some months to decomposition in a current of air, in such 
manner that any ammonia evolved could be collected and estimated. 
The result was, that, in 5 out of the 6 cases, there was a greater or 
less evolution of free nitrogen—amounting, in two of the cases, to 
more than 12 per cent. of the original nitrogen of the substance. 

The second series consisted of 9 experiments; wheat, barley, and 
beans being again employed, and, as before, either ignited soil or 
pumice used as the matrix. In some cases the seeds were submitted 
to experiment whole, and allowed to grow, and the vegetable matter 
produced permitted to die down and decompose. In other cases, 
the ground seeds, or ‘‘ meals,’ were employed. ‘The conditions of 
moisture were also varied. The experiments were continued through 
several months, when from 60 to 70 per cent. of the carbon had 
disappeared. | 

In 8 out of the 9 experiments, a loss of nitrogen, evolved in the 
free state, was indicated. In most cases, the loss amounted to about 
one-seventh or one-eighth, but in one instance to 40 per cent. of the 
original nitrogen. In all these experiments the decomposition of 
the organic substance was very complete, and the amount of carbon 
lost was comparatively uniform. 

It thus appeared that, under rare circumstances, there might be no 
loss of nitrogen in the decomposition of nitrogenous organic matter; 
but that, under a wide range of circumstances, the loss was very 
considerable—a point, it may be observed, of practical importance in 
the management of the manures of the farm and the stable. | 

Numerous direct experiments showed, that when nitrogenous 
organic matter was submitted to decomposition in water, over mer- 
cury, in the absence of free oxygen, there was no free nitrogen 
evolved. In fact, the evolution in question appeared to be the result 
of an oxidating process. 

Direct experiments also showed, that seeds may be submitted to 
germination and growth, and that nearly the whole of the nitrogen 
may be found in the vegetable matter produced. 

It is observed that, in the cases referred to in which so large an 
evolution of free nitrogen took place, the organic substances were 
submitted to decomposition for several months, during which time 
they lost.two-thirds of-their carbon. In the experiments on the 


528 | Royal Society :— 


question of assimilation, however, but a very small proportion of the 
total organic matter is submitted to decomposing actions apart from 
those associated with growth, and this for a comparatively short 
period of time, at the termination of which the organic form is 
retained, and therefore but very little carbon is lost. It would 
appear, then, that in experiments on assimilation no fear need be 
entertained of any serious error arising from the evolution of free 
nitrogen in the decomposition of the nitrogenous organic matter 
necessarily involved, so long as it is subjected to the ordinary 
process of germination, and exhaustion to supply materials for 
growth. On the other hand, the facts adduced afford a probable 
explanation of any small loss of nitrogen which may occur when 
seeds have not grown, or when leaves, or other dead matters, have 
suffered partial decomposition. They also point out an objection to 
the application of nitrogenous organic manure in such experiments. 

Although there can be no doubt of the evolution of hydrogen 
during the decomposition of organic matter under certain conditions, 
and although it has long been admitted that nascent hydrogen may, 
under certain circumstances, combine with gaseous nitrogen and form 
ammonia—nevertheless, from considerations stated at length in the 
paper, the Authors infer that there need be little apprehension of 
error in the results of their experiments, arising from an-unaccounted 
supply of ammonia, formed under the influence of nascent hydrogen 
given off in the decomposition of the organic matter involved. 


Turning to their direct experiments on the question of the assi- 
milation of free nitrogen, the Authors first consider whether such 
assimilation would be most likely to take place when the plant had 
no other supply of combined nitrogen than that contained in the 
seed sown, or when supplied with a limited amount of combined 
nitrogen, or with an excess of combined nitrogen? And again— 
whether at an early stage of growth, at the most active stage, or 
when the plant was approaching maturity? Combinations of these 
several circumstances might give a number of special conditions, in 
perhaps only one of which assimilation of free nitrogen might take 
place, in case it could in any. 

It is hardly to be supposed that free nitrogen would be assimilated 
if an excess of combined nitrogen were at the disposal of the plant. 
It is obvious, however, that a wide range of conditions would be ex- 
perimentally provided, if in some instances plants were supplied with 
no more combined nitrogen than that contained in the seed, in others 
brought to a given stage of growth by means of limited extraneous 
supplies of combined nitrogen, and in others supplied with combined 
nitrogen in a more liberal measure. It has been sought to provide 
these conditions in the experiments under consideration. 

In the selection of plants, it was sought to take such as would 
be adapted to the artificial conditions of temperature, moisture, &c. 
involved in the experiment, and also such as were of importance in 
an agricultural point of view—to have representatives, moreover, of 
the two great Natural Families, the Graminacee and the Legumiuose, 


On the Sources of the Nitrogen of Vegetation. 529 


which seem to differ so widely in their relations to the combined 
nitrogen supplied within the soil—and finally, to have some of the 
same descriptions as those experimented upon by M. Boussingault, 
and M. G. Ville, with such discordant results. 

' Thirteen experiments were made (4 in 1857 and 9 in 1858), in 
which the plants were supplied with no other combined nitrogen 
than that contained in the original seed. In 12 of the cases pre- 
pared soil was the matrix, and in the remaining one prepared 
pumice, _ 

_ Of 9 experiments with Graminaceous plants, 1 with wheat and 2 
with barley were made in 1857. , In one of the experiments with 
barley there was a gain of 0-0016, and in the other of 0:0026 gramme 
of nitrogen. In only two cases of the experiments with cereals in 
1858, was there any gain of nitrogen indicated; and in both it 
amounted to only a small fraction of a milligramme. Indeed, in no 
one of the cases, in either 1857 or 1858, was there more nitrogen in 
the plants themselves, than in the seed sown. A gain was indicated 
only when the nitrogen in the soil and pot—which together weighed 
about 1500 grammes—was brought into the calculation. Moreover, 
the gain only exceeded 1 milligramme in the case of the experiments 
of 1857, when slate, instead of “elazed earthenware stands were used as 
the lute vessels; and there was some reason to believe that the gain 
indicated was due to this circumstance. In none of the other cases 
was the gain more than would be expected from error in analysis. 

The result was then, that in no one case of these experiments was 
there any such gain of nitrogen as could lead to the supposition that 
free nitrogen had been assimilated. The plants had, however, vege- 
tated for several months, had in most cases more than trebled the 
carbon of the seed, and had obviously been limited in their growth 
for want ofa supply of available nitrogen in some form. During this 

long period they were surrounded by an atmosphere containing free 
nitrogen ; and their cells were penetrated by fluid saturated with that 
element. It may be further mentioned, that many of the plants 
formed glumes and palese for seed. 

It is to be observed that the resultseof these experiments with 
cereals go to confirm those of M. Boussingault. 

The Leguminous plants experimented upon did not grow so 
healthily under the artificial conditions as did the cereals, Still, in all 
three of the cases of these plants in which no combined nitrogen 
was provided beyond that contained in the original seed, the carbon 
in the vegetable matter produced was much greater than that in the 
seed—in ¢ one instance more than 3 times greater. In no case, how- 
ever, was there any indication of assimilation of free nitrogen, any 
more than there had been by the Graminaceous plants grown under 
similar circumstances. 

One experiment was made with buckwheat, supplied with no other 
combined nitrogen than that contained inthe seed. The resuit gave 
no indication of assimilation of free nitrogen. 

In regard to the whole of the ‘experiments in which the plants 
were supplied with no combined nitrogen beyond that contained in 


Phil. Mag. S, 4, No, 148, Suppl. Vol. 21. 1 ee 


530 — . Royal Society :— 


the seed, it may be observed that, from the constancy of the amount 
of combined nitrogen present in relation to that supplied, throughout 
the experiments, it may be inferred, as well that there was no evolu- 
tion of free nitrogen by the growing plant, as that there was no 
assimilation of it; but it cannot hence be concluded that there would 
be no such evolution if an excess of combined nitrogen were supplied. 

The results of a number of experiments, in which the plants were 
supplied with more or less of combined nitrogen, in the form of am- 
monia-salts, or of nitrates, are recorded. Ten were with Cereals; 
4in 1857, and 6 in 1858. Three were with Leguminous plants ; and 
there were also some with plants of other descriptions—all in 1858. 

In the case of the cereals more particularly, the growth was very 
greatly increased by the extraneous supply of combined nitrogen ; in 
fact, the amount of vegetable matter produced was 8, 12, and even 
30 times greater than in parallel cases without such supply. The 
amount of nitrogen appropriated was also, in all cases many times 
greater, and in one case more than 30 times as great, when a supply 
of combined nitrogen was provided. The evidence is therefore suffi- 
ciently clear that all the conditions provided, apart from those which 
depended upon a supply of combined nitrogen, were adapted for 
vigorous growth ; and that the limitation of growth where no com- 
bined nitrogen was supplied was due to the want of such supply. 

In 2 out of the 4 experiments with cereals in 1857, there was a 
slight gain of nitrogen beyond that which should occur from error 
in analysis; but in no one of the 6 in 1858, when glazed earthenware 
‘instead of slate stands were used, was there any such gain. It is con- 
‘cluded, therefore, that there was no assimilation of free nitrogen. 
In some cases the supply of combined nitrogen was not given until 
the plants showed signs of decline ; when, on each addition, increased 
vigour was rapidly manifested. In others the supply was given 
earlier and was more liberal. 

As in the case of the Leguminous plants grown without extraneous 
‘supply of combined nitrogen, those grown with it progressed much 
less healthily than the Graminaceous plants. But the results under 
these conditions, so far as*they go, did not indicate any assimilation 
of free nitrogen. 

The results of experiments with plants of other descriptions, in 
which an extraneous supply of combined nitrogen was provided, also 
failed to show an assimilation of free nitrogen. 

Thus, 19 experiments with Graminaceous plants, 9 without and 10 
with an extraneous supply of combined nitrogen—6 with Leguminous 
plants, 3 without and 3 with an extraneous supply of combined 
nitrogen, and also some with other plants, have been made. In 
none of the experiments, with plants so widely different as the 
Graminaceous and the Leguminous, and with a wide range of condi- 
tions of growth, was there evidence of an assimilation of free nitrogen. 


The conclusions from the whole inquiry may be briefly summed 
up as follows :— 7 . 
~* The yield of nitrogen in the vegetation over a given area, within a 


Deviations of the Compass on Iron and Wooden Steam-ships. 581 


given time, especially in the case of Leguminous crops, is not satis- 
factorily explained by reference to the hitherto quantitatively deter- 
mined supplies of combined nitrogen. 

The results and conclusions hitherto recorded by different experi- 
menters on the question whether plants assimilate free or uncom- 
bined nitrogen, are very conflicting. 

The conditions provided in the experiments of the Authors on this 
question were found to be quite consistent with the healthy develop- 
ment of various Graminaceous Plants, but not so much so for that of 
the Leguminous Plants experimented upon. 

It is not probable that, under the circumstances of the experiments 
on assimilation, there would be any supply to the plants of an unac- 
counted quantity of combined nitrogen, due to the influence either 
of ozone, or of nascent hydrogen. 

It is not probable that there would be a loss of any of the com- 
bined nitrogen involved in an experiment on assimilation, due to the 
evolution of free nitrogen in the decomposition of organic matter, 
excepting in certain cases when it might be presupposed. 

It is not probable that there would be any loss due to the evolu- 
tion of free nitrogen from the nitrogenous constituents of the plants 
during growth. 

In numerous experiments with Graminaceous plants, under a wide 
range of conditions of growth, in no case was there any evidence of 
an assimilation of free nitrogen. 

In experiments with Leguminous plants the growth was less satis- 
factory, and the range of conditions was, therefore, more limited. 
But the results with these plants, so far as they go, do not indicate 
any assimilation of free nitrogen. It is desirable that the evidence 
of further experiments with such plants, under conditions of more 
healthy growth, should be obtained. 

Results obtained with some other plants, are in the same sense as 
those with Graminaceous and Leguminous ones, in regard to the 

question of the assimilation of free nitrogen. 

Tn view of the evidence afforded of the non-assimilation of free 
nitrogen by plants, it is very desirablé that the several actual or 
possible sources whence they may derive combined nitrogen should 
be more fully investigated, both qualitatively and quantitatively. 

If it be established that plants do not assimilate free or uncom- 
bined nitrogen, the source of the large amount of combined nitrogen 
known to exist on the surface of the globe, and in the atmosphere, 
still awaits a satisfactory explanation. 


** Reduction and Discussion of the Deviations of the Compass ob- 
served on board of all the Iron-built Ships and a selection of the 
Wood-built Steam-ships in Her Majesty’s Navy, and the Iron Steam- 
ship ‘ Great Kastern’.”’ By Frederick J. Evans, Esq. 

The analysis of the deviations of the compass in this paper com- 
prises the observations made in forty-two iron ships, varying in size 
from 3400 to 165 tons, a selection of wood-built screw and paddle- 
wheel steam-vessels, as also the steam-ship ‘Great Eastern’ at various 

_times prior to her departure from England. 


M2 


532 Royal Society :— 


The observations made in the iron-built ships extend over periods 
varying between thirteen and five years; and having been made with 
the same description of compass—the Admiralty standard—and under 
similar conditions of arrangement and situation, in accordance with 
the system carried out in Her Majesty’s Navy, details of which are 
given, the general results are strictly comparable. 

In the analysis of the Tables, amounting to nearly 250 in num- 
ber, of deviations observed in various parts of both hemispheres, the 
formula deduced from Poisson’s General Equations by Mr. Archi- 
bald Smith, given in the Philosophical Transactions for 1846, p. 348, 
has been employed. 

In this formula, the deviation of the compass on board ship, 
reckoned positive when the north point of the needle deviates to the 
east, is given by the following expression :— 

Deviation (6)=A-+B sin Z'+C cos Z/+D sin 22'+ E cos 22’, 

é' being the azimuth (by compass) of the ship’s head, reckoned 
from the magnetic north towards the east ; 

A, D, E being constant coefficients depending only on the amount, 
quality, and arrangement or position of the iron in the ship: B and 
C, coeflicients depending on these, and also on the magnetic dip and 
horizontal intensity, are each consisting of two parts; one caused by 
the permanent magnetism of the hard iron, the deviation produced 
by which varies inversely as the horizontal force at the place ; and the 
other, caused by the vertical part of the earth’s force inducing the 
soft iron in the ship, the deviation produced by which varies as the 
tangent of the dip: B representing that part of the combined attrac- 
tion acting in a fore-and-aft direction, C that acting in a transverse, 
or athwart-ship direction. 

Ay 
From the equation tan aoe the direction of the ship’s force, and 


V 6*+C?, the total magnetic force of the ship in proportion to the 

‘horizontal force at the place of observation is obtained: for con- 
venience, 1000 has been adopted to represent the value of the earth’s 
horizontal force at the English ports of observation, in order, by an 
easy comparison, to note the changes on foreign stations. 

By comparison of the coefficients of the several descriptions of 
ships, it is observed that in wood-built steam-vessels, the coefficients 
B and C vary nearly as the tangent of the dip; from whence it may 
be inferred, as a general rule, that in steam machinery permanent 
‘magnetism bears but a small proportion to induced; but in ion- 
built ships, B and C generally vary more nearly as the inverse hori- 
zontal force, showing that they depend more on the permanent 
magnetism of the iron of the ship, and thus confirming the view of 
the Astronomer Royal, given in his earliest deductions (Phil. Trans. 
1839), that the effect of transient induced magnetism is in these 
ships small comparatively. Numerous examples are given in detail 
of this permanency of magnetism, as also of the gradual diminution 
of the ship’s force resulting from time. 

- An investigation of the coefficient D, which is caused entirely by 
the horizontal induction of the soft iron in the ship, and which is 


Deviations of the Compass on Iron and Wooden Steam-ships. 538 


known as the “ quadrantal”’ deviation, shows, that while in wood- 
built steam-ships it seldom exceeds 1° or 13°, it rises in iron-built 
ships from 13° to 6° and 7°; the Liverpool Compass-Comiittee 
recording even a point of the compass. ; 

The chief characteristics of the quadrantal deviation, as developed 
in this investigation, are— 

1. That it has invariably a positive sign, causing an easterly 
deviation in the N.E. and 8.W. quadrants ; and a westerly deviation 
in the S.E. and N.W. quadrants. 

2. Its amount does not appear to depend on the size, or mass of 
the vessel, or direction when building; or on the existence of iron 
beams. 

3. That a gradual decrease in amount has occurred, after the 
lapse of a number of years, in nearly every vessel that has been 
observed. 

4, That the value remains unchanged in sign and amount, on 
changes of geographic position. 

5. That a value not exceeding 4°, and rangmg between that 
amount and 2°, may be assumed to represent the average or normal 
amount in vessels of all sizes. 

Numerous examples are given in support of these propositions, as 
also of the uniformity of the amount of quadrantal deviation when 
determined in various parts of the ship; and, assuming the normal 
amount in iron steam-ships as from 2° to 4°, an analysis is given by 
which it is seen that 75 per cent. of the iron ships of the Royal Navy 
are included in this condition. 

Two questions of importance here arise ; are the results of this ana- 
lysis conclusive, and if so, under what conditions do large quadrantal 
deviations occur? Reverting to the Astronomer Royal’s early experi- 
ments in 1838-39, in the iron ships ‘ Rambow’ and ‘Ironsides,’ whose 
values were very small, and presuming that those vessels were built. 
of good material—from their then experimental character—as also 
that similar conditions of material of good quality exist in the iron 
ships of the Royal Navy, it is assumed that the value (2° to 4°) re- 
presents the average condition of a ship built of the best or superior 
Iron. 

On the other hand, can the inference be drawn that large quadrantal 
deviation in an iron ship implies that inferior material has been used 
in her construction? Attention is here directed to the ships ‘ Birken- 
head’ and ‘ Royal Charter,’ which from their well-known magnetic 
coefficients may be regarded as the types respectively of ‘hard’* 
and ‘soft’? iron constructed vessels, and from their consideration, 
as also from a review of the general results, these conclusions are 
derived :— 

1. That in an iron ship of ordinary dimensions, a standard com- 
pass can be placed, the deviations of which will but httle exceed those 
obtaining in wood-built steam-ships ; and further, that on changes of 
geographic position, however distant, these deviations will be within 
smaller limits, and can be approximately predicted. 

2. A divergence from these conditions will arise when the inductive 


534 Royal Society :— 


magnetism of the hull or machinery predominates ; and it is inferred, . 
especially from the example of the ‘ Royal Charter,’ that large qua- 
drantal deviation and fluctuating sub-permanent magnetism (due to 
hull alone) are co-existent, and give rise to conditions of compass 
disturbance which are beyond prediction, and which have hitherto 
baffled inquiry and given a complexion to theoretical deductions 
varying as regarded from different points of view. 

Tn order to examine the change which the original magnetism of 
an iron ship undergoes after launching, a series of compass observa- 
tions were made in the steam-ship ‘ Great Eastern’ prior to her quit- 
ting the River Thames in 1859, and subsequently at Portland, Holy- 
head, and Southampton*—at the three first-named places within 
short periods of time of each other. 

The results, from an Admiralty Standard Compass placed in a 
position the least subject to influence from local masses of iron, were 
as follows :—In the first five days, from Deptford to Portland, the 
ship’s force had diminished from 0°585 to 0°480 [the earth’s force 
=1:000], or nearly one-fifth ; representing a decrease in the ‘‘ semi- 
circular” deviation from 35° 50! to 28° 45!; the direction of the 
force, or neutral points, approaching the fore-and-aft line by 10°, 
or changing from 47° on the starboard bow to 37°. 

At the expiration of the next six weeks, the ship in the interim 
having made the passage to Holyhead, the ship’s force diminished 
from 0°480 to 0°390, or about one-sixth, corresponding toa decrease 
of “semicircular” deviation from 28° 45! to 23° 0', the direction of 
the force changing from 37° to 32°. 

At Southampton, in June 1860, or nearly eight months after the 
experiments made at Holyhead, the force had further diminished 
from 0°390 to 0°235, or by one-half, corresponding to a decrease in 
the “ semicircular’ deviation from 23° 0! to 13° 30’; whilst the 
direction of the force approached the fore-and-aft line 25°, or from 
32° to 7°; the quadrantal deviation remaining nearly constant 
[+4+°] the whole time included in the various observations. 

The unvarying tendency of the direction of the ship’s force in the 
‘Great Eastern’ to assume a fore-and-aft line, supports the view that 
time, with the vibrations and concussions due to sea service, leads to 
a distribution of the magnetic lines, of the nature of a stable equili- 
brium depending on the average of the inducing forces to which the 
ship is exposed ; the respective sections of the hull having north and 
south polarity, being separated by lines approximating more nearly 
a horizontal plane and vertical axis through the body of the ship ; 
instead of the inclined axis and equatorial plane of separation due to 
the magnetic dip of the locality, and divergence from the magnetic 
meridian, of the hull while building. 

The practical information resulting from the example of the ‘Great 
Eastern’ is, that prior to a newly built iron ship being sent to sea, 
her head during equipment should be secured in an opposite direction 
to that in which she was built; and that the magnetic lines should 


* The observations at Southampton were made after the paper was communi- 
cated to the Royal Society, and are introduced by way of supplement. 


Deviations of the Compass on Iron and Wooden Steam-ships. 535 


be assisted to. be ‘shaken down”? by the vibrations of the machinery 
in a short preparatory trip prior to the determination of her compass 
errors, or their compensation ; but especially that in the early voy- 
ages vigilant supervision should be exercised in the determination of 
the compass disturbances. 

- Another important point, generally neglected when compasses are 
adjusted by the aid of magnets in a newly built iron ship, is rendered 
manifest by the results of this investigation; namely, the necessity 
of the errors of the compass being determined and placed on record 
prior to the adjustment. Without the knowledge to be derived from 
these observations of the magnetic force of the ship, all future 
changes of magnetism and consequent errors of the compass are 
mere guesswork both to those who adjust, and those in charge of 
the navigation of the ship. ¥ 

It is recommended that, in any future legislation for the security 
of the navigation of our mercantile marine with reference to iron- 
built ships, the determination and record of these preliminary obser- 
vations should be secured. : 

_ The paper concludes by directing attention to the general prin- 
ciples of practical import which result from the investigation, viz. as 
to the best direction with reference to the magnetic meridian for the 
keel and head of an iron ship to be placed in building, to ensure the 
least compass disturbance; the best position and arrangement for a 
compass to ensure small deviations, and permanency on changes of 
geographic position ; and the changes to which the compass is liable 
from various causes on the foregoing conditions being fulfilled. 

For the best direction in building, it is shown that, from the nature 
of the polarity of the hull, and especially of the top sides in the after 
section of the ship and adjoining the compass, where usually placed, 
the latter is least affected in those vessels built in the line of the mag- 
netic meridian. 7 

For iron steam-vessels engaged in the home or foreign trades in 
the northern hemisphere, it is recommended, from the then antago- 
nistie magnetic influence of the hull and machinery, to build them 
head to the north: for iron sailing vessels, from the top sides, in the 
usual position of the compass, being magnetically weak if built head 
to the south, the latter direction is to be preferred. 

The seleetion for the position of the compass depends on the 
direction of the ship during building; in those built head to north, 
it must be removed as far from the stern as convenience will permit ; 
in those built head to south, as near to the stern as convenient, but 
avoiding especially, in all cases, proximity to vertical masses of iron. 
In ships built head east or west, there is little choice of position: in 
those built on the intercardinal points, a position approximating to 
the stern when the action from the top-sides—to be determined expe- 
rimentally—is at a minimum, is to be preferred. 

Ample elevation above the deck and exaet peaten in the middle 
line of the ship, are primary conditions to be observed; and no com- 
pass should be nearer iron deck beams than 4 feet. As every piece of 
iron not forming a part of, or hammered in the fabrication of the 


536 Geological Society :— 


hull, such as the rudder, funnel, fastenings of deck houses, &c., is of 
a magnetic character differing from the hull of the ship, proximity to 
any such should be avoided, and, as far as possible, the compass 
should be so placed that they may act as correctors of the general 
magnetism of the hull. ! 

As most compasses are affected by the magnetism of the ship to 
an amount depending on their elevation, and the direction of the ship 
in building, the disturbances will be large comparatively, except in 
those vessels built head east or west. 

A series of Tables is appended, wherein the magnetic coefficients 
and ship’s force and direction of the various classes of vessels are 
given, the ships being classed according to the nature of their mate- 
rial and machinery. 


GEOLOGICAL SOCIETY. 
[Continued from p. 311.] 
March 20, 1861.—L. Horner, Esq., President, in the Chair. 
The following communications were read :— 


1. “On a Collection of Fossil Plants from the Nagpur Territory, 
Central India.”” By Sir C. Bunbury, Bart., F.R.S., F.G.S. &c. 

The specimens examined by the author were collected by the Rev. 
Messrs. 8. Hislop and R. Hunter, and presented to the Geological 
Society in 1854 and since. The vegetable remains described in 
this paper are :—1. Glossopteris Browniana, var. Australasica, Ad. 
Brongn. G. Browniana, var. Indica, Ad. Brongn. By much the most 
abundant plant in the collection. 2. G. musefolia, sp.nov. 3. G. 
leptoneura. 4. G. stricta, sp. un. 5. Pecopteris, sp. 6. Cladophle- 
bis (?). 7. Teniopteris daneoides, M‘Celland (?). 8 and 9. Fili- 
cites: possibly Glossopteris. 10. Neggerathia(?). 11. Phyllotheca 
Indica, sp.n. 12. Vertebraria(?). Different from the true Verte- 
braria, and probably roots. 13. Knorria(?). 14. Stigmaria (?). 
15. Part of a stem, somewhat Sigillarian in appearance. 16. Yuc- 
cites (?). The fruits and seeds are reserved for further examination. 
On a general survey of all these plant-remains, the author for the 
present considers the facies of the fossil flora under notice to be 
Mesozoic rather than Paleozoic, but he regards the question as an 
open one, and requiring much further light for its perfect elucida- 
tion. 


2. ** On the Age of the Fossiliferous thin-bedded Sandstones and 
Coal-beds of the Province of Nagpur, Central India.” By the Rey. 
Stephen Hislop. Communicated by the President. 

The author first pointed out the places near the city of Nagpur 
where the plant-bearing sandstone has been best studied. He next 
noticed the carbonaceous shales underlying thick sandstones, at the 
foot of the Mahadewa Hills and the coal-seams of Barkoi, near Umret, 
80 miles and more N.W. of Nagpur; and pointed out their relation- 
ehip to the plant-bearing sandstone near Nagpur, as shown by the 
Glossopteris and other fossils found in each locality. 


On some Reptilian Remains from North-western Bengal. 587. 


_At Mangali, between 50.and 60 miles S.. of Nagpur, dark red 
sandstones are found, rich in Estheria, and containing remains of 
Plants, Ganoid Fishes, and Reptiles (Brachyops laticeps, Owen). 
These beds Mr. Hislop thinks to be of the same age as those of Nag- 
pur and Chanda. Still further 8. (170 miles from 1 Nagpur), at Kota, 
there are (under thick sandstones) limestones and shales, containing 
fishes of the genera <Zchmodus and Lepidotus, Teleosaurian remains 
Coprolites, fossil Insects, Cypride, and Estherie, with obscure plant- 
remains. These beds are also regarded by the author as equi- 
valent in age to the plant-bearing sandstones of Nagpur ; whilst the 
‘sandstone above them may be equal to the sandstone of the Maha- 
dewas ; and the red clay beneath them may be the same as that of 
Maledi 30 miles off (to the N.E.), where Ceratodus teeth and Co- 
prolites have been found in abundance. 

Mr. Hislop then compared in detail, 1. the fossil flora of the coal- 
fields of New South Wales with that of Central India; 2. the fossil 
plants of Western Bengal with those of Central India ; and 3. the 
fossil fauna of these two regions ; and came to the conclusion that, 
on the whole, they probably represent the Jurassic (or possibly the 


Triassic) period,—at all events some portion of the Lower Mesozoic 
epoch. 


3. “On the Geological Age of the Coal-bearing Rocks of New 

South Wales.” By the Rev. W. B. Clarke, F.G.S. 

_ The author first referred to his report, in 1847, of the occurrence of 
Lepidodendron, Sigillaria, and Stigmaria in the coal-fields of Australia ; 
and advanced proofs of the occurrence of Lepidodendron (Pachy- 
phleus (?), Goeppert) over a region extending from 23° to 37° S. 
lat., and at least 1000 miles long. After some observations on the 
association of Carboniferous and Devonian fossils with the coal-beds - 
of Australia and ‘Tasmania, Mr. Clarke stated that in 1859, at Stony 
Creek, near Maitland, Mr. B. Russell, having sunk two pits in search 
ef coal, found four or five coal-seams lying between beds containing 
Pachydomi, Spiriferi, Orthoceratites, Conularie, &c.; and beneath 
them a shale containing Neggerathia, Glossopteris, Cyclopteris, &c. 
From this and other evidence the author is induced to believe that 
the beds are of paleozoic age, in spite of the “ Jurassic ” appearance 
of the plant-remains. 


4. “On some Reptilian Remains from North-western Bengal.” 
By Prof. T. H. Huxley, F.R.S., Sec.G.S. 

Some bones, found by Mr. Blanford in the uppermost portion of 
the ‘‘ Lower Damuda” group of strata in the Ranigunj coal-field, 
and forwarded to the author by Professor Oldham, have proved to be- 
long to Labyrinthodont Amphibia and Dicyncdont Reptiles, hereby 
affording new and interesting links with the fossil fauna of the 
Karoo-beds of South Africa, and largely increasing the probability 
that the rocks in which they were found are of Triassic, or perhaps 


Permian, age. 
April 10.—Sir R. I. Murchison, V.P.G. = vimtthe cil 
ce; following communications were read :—~ 
. ‘*On the Geology of the Country between Lake miisrick and 


538 Geological Society. 


the Pacific Ocean (between 48° and 55° parallels of latitude), ex- 
plored by the Government Exploring Expedition under the command 
of Captain J. Palliser (1857-60).” By James Hector, M.D. Com- 
municated by Sir R. I. Murchison, V.P.G.S. 

This paper gave the geological results of three years’ exploration 

of the British Territories in North America along the frontier-line 
of the United States, and westward from Lake Superior to the Pacific - 
Ocean. 
- It began by showing that the central portion of North America is 
a great triangular plateau, bounded by the Rocky Mountains, 
Alleghanies, and Laurentian axis, stretching from Canada to the Arctic 
Ocean, and divided into two slopes by a watershed that nearly follows 
the political boundary-line, and throws the drainage to the Gulf of 
Mexico and the Arctic Ocean. The northern part of this plateau 
has a slope, from the Rocky Mountains to the eastern or Laurentian 
axis, of six feet in the mile, but is broken by steppes, which exhibit 
lines of ancient denudation at three different levels: the lowest is 
of freshwater origin; the next belongs to the Drift-deposits ; and the 
highest is the great Prairie-level of undenuded Cretaceous strata, 
This plateau has once been complete to the eastern axis, but is now 
incomplete along its eastern edge, the soft strata having been removed 
in the region of Lake Winipeg. 

The eastern axis sends off a spur that encircles the west shore of 
Lake Superior, and is composed of metamorphic rocks and granite 
of the Laurentian Series. To the west of this follows a belt where 
the floor of the plateau is exposed, consisting of Lower Silurian and 
Devonian rocks. On these rest Cretaceous strata, which prevail all 
the way to the Rocky Mountains, overlain here and there by de- 
tached tertiary basins. 

The Rocky Mountains are composed of Carboniferous and Devo- 
nian limestones, with massive quartzites and conglomerates, followed 
to the west by a granitic tract which occupies the bottom of the 
great valley between the Rocky and the Cascade Mountains. The 
Cascade chain is volcanic, but the volcanos are now inactive; to the 
west of it, along the Pacific coast, Cretaceous and Tertiary strata 
prevail. The description of these rocks was given with considerable 
detail, on account of their containing a lignite which for the first 
time has been determined to be of Cretaceous age. This lignite, 
which is of very superior quality, has been worked for some years 
past by the Hudson Bay Company, and is in great demand for the 
steam-navy of the Pacific station, and for the manufacture of gas. 
Extensive lignite-deposits in the Prairie were also alluded to; and, 
like those above mentioned, were considered to be of Cretaceous age ; 
but, besides these, there are also lignites of the Tertiary period. 

The general conclusion was that the existence of a supply of fuel 
in the Islands of Formosa and Japan, in Vancouver's Island, in the 
Cretaceous strata of the western shores of the Pacific, but principally 
within the British territory, and in the plains along the Saskatchewan, 
will exercise a most important influence in considering the practica- 
bility of a route to our Eastern possessions through the Canadas, 
the Prairies, and British Columbia. 


Intelligence and Miscellaneous Articles. 539 


- 2, “On Elevations and Depressions of the Earth in North 
America.” By Dr. A. Gesner, F.G.S. 

After some observations on the differences between volcanic uplifts 
of the land and the slow upward and downward shiftings produced 
by changes in the position of great parallel areas during long periods 
of time, the author proceeds to enumerate evidences of local eleva- 
tion and subsidence that he has observed along the coast from the 
northern part of Labrador to New Jersey. 

In the south-eastern part of New Jersey, at Nantucket, Martha’s 
Vineyard, and Portland, submergence of ‘the land is proceeding, 
locally at the rate of probably four feet in sixty years. In New 
Brunswick, at St. John’s the land has been elevated; at the Great 
Manan Island and the Great ‘T'antaman Marsh there has been sub- 
sidence. At Bathurst and on the opposite coast of Lower Canada 
the land seems to be rising. In Nova Scotia, near the Bay of Fundy 
and Mines Basin there is subsidence; on the southern side, however, 
there are signs of elevation. The sea rapidly encroaches upon 
Louisberg in Cape Breton; and in Prince Edward’s Island, also, at 
Cascumpec, submergence of the land is taking place. 


LXXIX. Intelligence and Miscellaneous Articles. 


ON THE THEORY OF CYLINDRICAL CONDENSERS. 
BY M. J. M. GAUGAIN. 


HAVE ina former note” called attention to the fact that it is very 
difficult to analyse the phenomena of condensation produced in 
submarine telegraphic cables, the gutta percha which envelopes them 
being only imperfectly non-conducting, so that there is at one and the 
same time propagation by conductibility and condensation. To study 
the latter phenomenon by itself, I substituted for gutta percha di- 
electrics, which isolate much more perfectly ; I employed for this 
purpose gum-lac and air; with gum-lac the absorption is very small, 
with air it is nothing, or altogether imperceptible. 

The laws which I have succeeded in establishing are very simple, 
and may be of some practical utility, since they afford a solution of 
the different questions which relate to electric condensation in sub- 
merged cables; it is, however, from a philosophical point of view that 
they seem to be of the greatest interest, since they confirm in a 
remarkable manner the views of Faraday. This illustrious physicist, 
in amemoir published in 1837 (Experimental Researches, Series XI. 
No. 1320), expressed himself nearly as follows :—‘‘ The power of 
isolating and that of conducting are only two extreme degrees of the 
same property, and ought to be considered as being of the same nature 
in any satisfactory mathematical theory.” Now it will be seen that, 
in the case at least of cylindrical condensers, the laws which regulate 
the propagation of electricity by excitation do not differ from those 
which Ohm has established for propagation by conductibility. The 
general results of my researches may be stated shortly as follows :— 

1. When the internal cylinder is the collector, that is to say, when 
it communicates with the source, and the external cylinder commu- 


* Comptes Rendus, 28th October, 1860. 


540 Intelligence and Miscellaneous Articles. 


nicates with the ground, the excited charge of the external cylinder 
is equal to the evetling charge of the internal cylinder. 

2. When the external cylinder is the collector, the excited charge 
of the internal cylinder is precisely the same as it would have been 
if it had been put in direct communication with the same source. 

3. When the external cylinder is the collector, its charge may be 
considered as consisting of two parts, one of which is equal to the 
excited charge of the internal cylinder, the other representing the 
quantity of electricity which the external cylinder would take up by 
itself under the influence only of the medium in which it is placed. 

The latter law enables us to foresee what would happen in the case 
of a condenser formed of three concentric cylinders, The charge 
which the middle cylinder would take up when put in commu. 
nication with the source, the other two being connected with the 
ground, must be equal to the charge which would be excited in it by 
the two other cylinders. I have found by experiment that this is 
really the case. 

It follows that condensers arranged in a spiral form, may serve to 
collect in a small volume a large quantity of electricity. 

4. If we agree to call by the name of resistance to excitation a 
quantity inversely proportional to the charge received by either 
armature, when the tension of the internal cylinder is maintained 
at unity, and that of the external cylinder at zero, then this resist- 
ance, which I shall call p, is expressed by the formula 


p=hk log Ro 
- 


R and r representing the respective radii of the external and internal 
cylinders, and k being a constant which depends on the inductive 
capacity of the dielectric, and on the length of the cylinder em- 
ployed. 

This formula is remarkable, since it might have been deduced 4 
priori from the ordinary theory of propagation by conductibility. 
Suppose, in fact, that the substance which separates the two cylin- 
drical armatures of the condensers possesses a certain conductibility, 
and Jet us call by the name of resistance to conduciibility, a quantity 
inversely proportional to the amount of clectricity which, in a unit 
of time, traverses the annular space between the two cylinders, the 
tension of the internal cylinder being maintained at unity, that of 
the external cylinder at nothing. ‘This resistance to conductibility 
may be caleulated according to the principles established by Ohm, 
and it will be found that it is expressed by the same formula as the 
resistance to excitation, ‘To pass from one formula to the other, it is 
only necessary to change the meaning of k. We may say therefore 
that the same theory, that namely of Ohm, regulates propagation by 
excitation and propagation by conductibility, at least when we con- 
fine ourselves to the consideration of spaces bounded by concentric 
cylinders. I propose to verify this principle under other circum- 
stances, and especially in the case of spherical condensers.— Comptes 
Rendus, Feb. 18th, 1861. 


Intelligence and Miscellaneous Articles. 541 


ON THE PRODUCTION OF GRAPHITE BY THE DECOMPOSITION OF 
CYANOGEN COMPOUNDS. BY DR. P. PAULT. 

The mother-liquors obtained from the evaporation of a solution of 
the so-called black ash are now commercially worked for caustic 
alkali. These liquors contain the following compounds :.— 

1. Chiefly hydrate of soda, 

2. Some quantity of carbonate of soda. 

3. Several sulphur compounds of sodium: viz. sulphide of sodium, 
hyposulphite of soda, sulphite of soda, and sulphate of soda. 

4, Sulphide of iron held in solution by the sulphide of sodium. 

5. Chloride of sodium. 

6. Several cyanogen compounds of sodium, and especially ferro- 
eyanide of sodium. 

These liquors are evaporated in large cast-iron pots, and in order 
to destroy or oxidize the sulphides of sodium and iron, as also the 
cyanogen compounds, an equivalent quantity of soda-saltpetre is 
added. All the oxidable sulphur compounds, together with the 
small quantity of sulphide of iron, are changed to sulphate of soda 
and peroxide of iron by the nitrate of soda in the boiling hquor, ata 
temperature not below 260° to 270° F. The cyanogen compounds, 
on the other hand, are not decomposed by the nitre until the 
liquor begins to pass from the watery into the dry fusion, and the 
uncombined water of the hydrate of soda has been driven off. When 
the whole mass of alkali (generally about four tons) reaches a low red 
heat, a regular evolution of gas is observed; this is evidently owing 
to the oxygen produced by the decomposition of the nitrate, and to 
the nitrogen from the decomposition of the cyanides; at the same 
time a plentiful liberation of graphite is observed, covering the whole 
surface of the liquor with a bright layer of graphite. ‘This liberation 
of graphite is still more plainly seen if no nitre be added to the liquor 
at first, or only so much as is sufficient to oxidize the sulphur com. 
pounds; but if a few pounds of nitrate of soda be added when the 
water has been driven off, and the mass is allowed to become red-hot, 
a violent reaction takes place, and a large quantity of graphite is set 
free. ‘This sudden liberation of graphite proves that this substance 
cannot be derived from the cast iron of the pot in which the fusion 
is made. So violent is the evolution of gas, that a complete cloud 
of fine particles of caustic soda is carried up into the air, rendering 
it almost impossible to remain in the neighbourhood of the operation. 
In this way all the cyanogen compounds are completely decomposed, 
the iron in the ferrocyanide of sodium becomes peroxide, and in a 
few hours falls to the bottom of the pot. If the right quantity of 
saltpetre has been added, a colourless mass of fused caustic soda 
remains; but if too large an amount of nitre has been added, the 
liquor becomes coloured deep green, owing to the formation of man- 
ganate of soda. It is remarkable that, in the absence of nitrate of 
soda, the cyanogen compounds act reducingly upon the sulphide 
of sodium; this is seen from the fact that a portion of the soda-lye, 
which gives no sulphide reaction with a lead salt, produces a black- 
ening after the caustic alkali has been heated to redness. 

The graphite may be skimmed off the surface of the fused alkali; 


542 Intelligence and Miscellaneous Articles. 


and when washed with water and hydrochloric acid, it appears in 
the form of an extremely fine bright powder. If allowed to swim 
on the top of the almost red-hot fused soda, the graphite is oxidized 
gradually, and after the lapse of about three or four hours it alto- 
gether disappears. Heated in a platinum crucible by itself it is in- 
combustible ; but it generally contains small particles of charcoal 
mixed with it, and these undergo oxidation, 

The temperature at which this evolution of graphite takes place is 
a very low one, compared with that at which graphite is liberated 
from cast iron; for a thin iron wire can scarcely be brought to a 
visible red heat by dipping it into the fused alkali. 

From this peculiar decomposition it would appear that we have 
good reason to assume that the carbon contained in cyanogen is pre- 
sent in the graphite modification ; for if this be not the case, how is 
it that the easily combustible charcoal can withstand the oxidizing 
action of the saltpetre, whilst none of the iron of the ferrocyanide of 
sodium is reduced to the metallic state. 

It has, besides, been lately shown by M. Caron, that the forma- 
tion of steel, 7. e, the combination of iron with carbon in the graphite 
modification, can only take place in presence of cyanogen compounds, 
and that no carbon whatever is taken up by the iron when this metal 
is heated with other carboniferous gases. ‘The mode of production 
of graphite noticed in this communication appears to be an interme- 
diate reaction between that from the carbide of iron and from the 
nitride of carbon. 

As in the process of cementation it is seen that the carbon of the 
cyanogen is taken up by the iron without being set free, so this re- 
action proves that cyanogen can be split up into its constituent parts 
without either of them combining with a third body. 

Despretz asserts that the carbonization of iron is always preceded 
by a combination of this metal with nitrogen, a process which makes 
it porous and more fit for uniting with carbon, The correctness of this 
supposition has, however, become rather doubtful, by Caron’s recentl 
published experiments (Comptes Rendus, Nos. 15 and 24, 1860). 

To conclude, I beg to say some words about the formation of 
native graphite; I do not think that this body has been formed from 
coal or diamond, but I rather believe it has been separated out of 
carbon compounds as graphite, by processes perhaps anaiogous to 
those above described.— Proc. Manchester Phil. Soc., April 16, 1861. 


ON ELECTRICAL PARTIAL DISCHARGES. BY P. RIESS. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 

Professor Rijke has met with a difficulty in the explanation of 
Wheatstone’s experiments on the discharge of a Leyden jar, and has 
himself instituted experiments*, from which it seems that more elec- 
tricity remains on a conductor when it is discharged through a wet 
string than when it is discharged through a metallic wire. 

I do not think that this difficulty exists, nor that these experiments 
have any claim to novelty. ‘'wenty years ago I showed that when 


* Phil. Mag. for May, p, 365. 


Intelligence and Miscellaneous Articles. 543 


a battery is discharged through a column of water, three-eighths of 
the charge remain on the battery, but that two-thirteenths remain 
when the discharge is effected through a metallic wire; and from 
this I concluded that the electricity of the battery is discharged in a 
successive manner (Pogg. Ann. vol. lili. p. 14. ‘‘ Lehre von der Rei- 
bungselectricitat,” § 634). 

Since then I have always assumed that the spark accompanying 
the discharge consists of several sparks ; and the discharge of an elec- 
trified body, of several individual discharges, which I have called par 
tial discharges. By this assumption Wheatstone’s and many other 
electrical experiments have become capable of explanation. 

I am, Gentlemen, 
Yours truly, 
Berlin, May 10, 1861. P. Riess. 


ON THE FREEZING OF WATER AND THE FORMATION OF HAIL. 
BY M, L. DUFOUR. 

When water is preserved from contact with solid bodies by placing 
it ina mixture which has the same density, and which does not form 
aqueous mixtures, its congelation may be materially retarded, Water 
placed in a mixture of chloroform and oil (the best is oil of sweet 
almonds) takes the form of perfect globules, and remains at rest in 
the interior of the mixture. If this mixture be cooled, the water in 
this condition scarcely ever freezes at 0° C.; its temperature sinks 
_ to —6°, —10° before this change takes place. Globules have in this 
way been even reduced to —20° while still liquid. 

The globules either change into globules of ice, or they simply 
freeze on the surface, according to their dimensions and the diminu- 
tion of temperature. They persist in the liquid state with remark- 
able stability. In this mixture of chloroform and oil they may be 
shaken, and foreign bodies introduced, without solidifying ; but soli- 
dification immediately ensues when they are touched with a piece of 
ice. ‘The discharge of a Leyden jar or a galvanic current may tra- 
verse these globules without their solidifying ; but the powerful dis- 
charge of a Ruhmkorff’s coil causes their immediate solidification. 

When an ice-sphericle formed in the mixture of chloroform and 
oil is surrounded by other spheres which still remain liquid, the con- 
gelation of the latter may be effected by bringing them in contact 
with the first. Different effects are obtained according to the tem- 
perature and dimensions of the globules. Sometimes (with small 
globules and low temperatures ) the spheres touched solidify suddenly, 
and remain separate; sometimes (with larger globules and some- 
what higher temperatures) they coalesce more or less completely ; 
they stretch out on each other at the moment of solidification. In 
this way pieces of ice of the most varied shapes may be obtained—irre- 
gular spheres formed of concentric layers (each layer consisting of a 
globule which enveloped the nucleus at the moment of its forma. 
tion), spheres with protuberances, &c. ‘These varied forms would 
have but a subordinate interest, if they did not recall the concentric 
zones and the irregular shapes observed in hailstones. This reseme 
blance is evident in these experiments; and the question naturally 


544, Intelligence and Miscellaneous Articles. 


arises whether hailstones are not formed under similar circumstances. 
In a memoir which I shall publish in the Bibliotheque Universelle, 1 
examine this analogy more closely, and endeavour to show that it is 
not superficial, but extends into numerous details. I attempt to show 
that this particular case of freezing gives a suitable explanation of 
the general phenomena, as well as of the accidental peculiarities of 
hailstones: I attempt to show that these aqueous globules may also 
be cooled below 0° in the atmosphere; that they can then freeze and 
unite just as in the mixture of chloroform and oil, and that the grains 
of ice thus formed, increased by the condensation of atmospheric 
vapour on their surface, may be hailstones.—Comptes Rendus, 
April 15, 1861. 


ON AN APPARATUS FOR EXPERIMENTS ON RESPIRATION AND 
PERSPIRATION IN THE PHYSIOLOGICAL INSTITUTE AT MUNICH, 
BY PROFESSOR PETTENKOFER. 

In order to determine the quantities of carbonic acid and of water 
which are eliminated through the skin and lungs, numerous methods 
have been proposed, and the processes and results of Scharling, 
Vierordt, Valentin and Brunner, Regnault and Reiset, Smith, and 
others, are well known to every physiologist and chemist. The 
objections to all previous methods are of two kinds: first, that the 
accuracy of the method cannot be determined by control experiments 
with known quantities of carbonic acid; and second, that the men 
and animals were compelled to breathe, in these experiments, under 
more or less unusual and burdensome, and therefore unnatural con- 
ditions. ‘The experiments of Bischoff and Voit on the food of car- 
nivora have further shown that the carbonic acid eliminated by the 
lungs and skin, cannot be obtained by taking the difference between 
that administered as food, and that secreted in the urine and feces, 
allowing for the difference in weight of the body; because two un- 
known quantities of carbonic acid and water are eliminated from the 
lungs simultaneously, and in varying quantities. As it was neces- 
sary to determine directly at least one of these magnitudes, the 
author endeavoured to construct an apparatus by which a constant 
current of air could be passed over a man, and the increase of car- 
bonic acid and water of this air determined. 

Pettenkofer’s apparatus consists of a small sheet-iron chamber 
(which will be called the saloon) 8 Bavarian feet in every dimension, 
with an iron door, a light at the top, and windows at the sides. 
The windows were cemented, and the sides and cover riveted 
as air-tight as possible. The door had moveable openings in order 
to ensure access of air at other points besides the joints of the door. 
On the side opposite to the door there are two apertures, one 
below and the other above, which, by means of two tubings, are con- 
nected with a single wide tube outside, in which the air flows towards 
that part of the apparatus which serves as an aspirator. ‘l'his piece 
of the apparatus, which is placed in a different part of the house, con- 
sists of two suction cylinders with valves, which can be uniformly 
worked to the same height of stroke by means of a powerful clock- 
work motion, The weight of the clockwork is continually raised in 


Intelligence and Miscellaneous Articles. 545 


proportion as it sinks, and in this way is obtained a continuous cur- 
rent of air through the doors of the iron room towards the suction 
cylinders. But the air cannot reach the suction cylinder without 
first passing through a continuously acting measuring apparatus. 
For this purpose the author selected a large gas-meter, of such dimen- 
sions that 3000 English cubic feet could be measured with it in an 

hour. 
~ . In order to investigate a portion of the air entering by the aper- 
tures in the door and any accidental leakages in the apparatus, 
as well as of the air flowing towards the gas-meter, and to calcu- 
late from the observed difference in the proportion of water and car- 
bonic acid the quantities which had entered from the apparatus, 
there are two aspirators, each of which simultaneously withdraws an 
equal quantity of air. The water of the air is absorbed by sulphuric 
acid and weighed, and the carbonic acid is determined by allowing 
the air to pass in fine bubbles through a determinate quantity of 
lime-water of known strength, and the strength of the lime-water 
finally determined by means of dilute oxalic acid. 

In order to take a specimen of the air remaining in the saloon, a 
forcing and suction pump is connected with the outlet pipe, by which 
flasks holding 6 or 8 litres may be filled with air, and the quantity 
of carbonic acid determined by means of lime-water. The same 
pump serves to determine at any time the variations in the carbonic 
acid during the progress of an experiment. There is an arrangement 
by which test-quantities of any amount may be taken out without 
causing any loss in measuring the whole current. For this purpose 
a flask is connected air-tight with the pump, and by continuous 
pumping its air is completely replaced by air from the outlet pipe. 
The air pressed out of the flask is not allowed to escape, but is 
passed by means of a caoutchouc tube into the current which goes to 
the gas-meter; of course, in a place where it cannot affect the deter- 
minations of carbonic acid. 

In order that the air-current may take no water from the large gas- 
meter by evaporation, the air before entering the gas-meter first 
passes through an upright cylinder filled with pieces of pumice kept 
moist. 

Where the air issues from this apparatus, there is in the tube a 
psychrometer, in order to measure the temperature and moisture of 
the air which passes into the gas-meter. In the tube which leads to 
the moistening apparatus there is a psychrometer, and several tubes 
for taking out specimens of air, &c. 

The apparatus has been examined since May last in every parti- 
cular, and the author recommends the methods of investigation as in 
every way convenient. It was above all important to prove that the 
carbonic acid disengaged in the saloon could actually be found again 
and determined—a control which has been omitted in all previous 
experiments on respiration. After the author, by numerous experi- 
ments, had investigated all the influences of the apparatus and of 
the methods on the accuracy of the results, he took a stearine candle 
and determined its carbon by elementary analysis. When the suc- 


Phil. Mag. 8. 4. No. 143. Suppl. Vol. 21. 2N 


546 Intelligence and Miscellaneous Articles. 


tion cylinders of the apparatus, and simultaneously the apparatus for 
analysis of the air, were at work, a weighed candle was lighted in 
the saloon from without, and, before the experiment terminated, 
again extinguisked from without and weighed. 

The carbonic acid formed by combustion of the candle must be 
partially contained in the air which had passed through the large 
gas-meter, and partly in that contained inthe saloon. ‘lhe carbonic 
acid in the air which had passed through the gas-meter was deter- 
mined by allowing a continually equal proportion (about 100 cubic 
centims. in a minute) of the current from the saloon to the gas-meter 
to bubble through lime-water, The carbonic acid of the air remain- 
ing in the saloon was determined, after mixing the different layers 
of air well together, by filling two or three vessels of 6 to 8 litres 
capacity, determining by lime-water, and calculating this upon the 
known capacity of the saloon. Itis only after these flasks have been 
filled that the saloon may be entered to take out the candle and 
weigh it. 

Since the air which passed into the gas-meter, and that which 
remains in the saloon, contained not only the carbonic acid formed 
in the experiment, but that already contained in the air as it passed 
into the saloon, the quantity of the carbonic acid of the air entering 
must be subtracted. ‘This is obtained from the experiment where 
the air which enters is withdrawn and investigated in just the same 
manner and the same quantity asthe emergent air. In this way the 
difference in the quantity of carbonic acid inside and outside is de- 
termined; and this ensures the exactitude of the determinations, 
because all constant errors of the method are thereby eliminated. Of 
course all the measurements are made with allowances for the ten- 
sion of aqueous vapour, of temperature, and pressure of the atmo- 
sphere. 

The author adduces some experiments which he made with stea- 
rine candles, and states his reasons for believing that, during an ex- 
periment in which more than four-fifths of the disengaged carbonic 
acid pass into the current between the saloon and the gas-meter, no 
greater errors than at most | or 2 per cent. are to be feared. Inas- 
much as the duration of experiments with men and animals can be 
extended to twelve or twenty-four hours, it is to be hoped that even 
greater accuracy may be attained. 

This is the first apparatus of its kind in which living is possible 
under normal conditions. Men can live in it just as well as in any 
well-ventilated room, and can move about, eat, and drink in the 
ordinary manner. By a moveable window in the door of the saloon, 
food and other articles can be supplied or taken out—just as, ina 
small room, provided the draught in the chimney is in order, a stove- 
door can be opened without admitting smoke. The observer out- 
side the saloon who has charge of the experiment does not by his 
respiration affect the result in the least; for the carbonic acid in the 
air passing into the saloon can be continually checked by one of 
the control apparatus, and can be allowed for.—Journal fiir Prakt. 
Chemie, vol. 1xxxii. p. 40. 


547 


INDEX to VOL. XXI. 


ACETYLENE, researches on, 358. 

Alcohols, polyglyceric, on the, 499. 

Allylene, on the formation and con- 
stitution of, 359. 

Ammonia, on the specific gravity of 
liquid, 364. 

Ampére’s experiment on the repulsion 
of a rectilinear electrical current on 
itself, on, 81, 247, 319. 

Antozone, on the insulation of, 88. 

Arsenic, on the presence of, in the 
beds of rivers, 318. 

Atkinson’s (Dr. E.) chemical notices 
from foreign journals, 120, 292, 
309, 495. 

Atmosphere, solar, on the chemical 
analysis of the, 185. 

Balance-galvanometer, on some re- 
sults im electro-magnetism obtained 
with the, 311. 

Barometers, on the temperature cor- 
rection of siphon-, 206. 

Battery, on a constant copper-carbon, 
80 


Beilstein (M.) on chlorobenzole, 299 ; 
on saligenine, 363. 

Benzole series, observations on the, 
176. | 
Bernoulli (M.) on tungsten and its 

alloys, 292. 

Blair (G.) on some results in electro- 
magnetism, 311. 

Bodies, on the cubical compressibility 
of certain, 447. 

Boiling-point and composition, on the 
relation between, in organic com- 
pounds, 227. 

Books, new :—Todhunter’s History 
of the Progress of the Calculus of 
Variations, 520. 

Brewster (Sir D.) on certain aifections 
of the retina, 20, 


Brodie (Rev. P. B.) on the distribu- 
tion of the corals in the lias, 237. 
Broun (J. A.) on the lunar-diurnal 
variation of magnetic declination at 

the magnetic equator, 384. 

Butlerow (M.) on the action of am- 

- ee gas on dioxymethylene, 

Butyryle, observations on, 501. 

Calcium spectrum, on the, 239. 

Calorimeter, on the construction of a 
new, 462. 

Cambridge Philosophical Society, 
proceedings of the, 469. 

Campbell (D.) on the presence of 
arsenic and antimony in the beds 
of rivers, 318. 

Cannizaro(M. )onhomoanisic acid,360 

Caoutchine, on the properties and 
composition of, 463. 

Capillary attraction, on peculiar forms 
of, 254. 

infiltration through porousrocks, 
researches on, 479. 

Carbonic acid, on a new method of 
obtaining solid, 495. 

Carl (Dr.) on the galvanic polariza- 
tion of buried metal plates, 377. 
Carré (M.) on the production of low 

temperatures, 296. 

Cayley (A.) on the theory of deter- 
minants, 180; on equations cf the 
fifth order, 210, 257; on the parti- 
tions of a close, 424; ona surface 
of the fourth order, 491. 

Challis (Prof.) on a theory of mag- 
netic force, 65, 92, 250; on the 
planet within the orbit of Mercury, 
discovered by M. Lescarbault, 470; 
on theoretical physics, 504. 

Chapman (Prof. E. J.) on the drift- 
deposits of Western Canada, 428, 


548 


Chemical notices from foreign jour- 
nals, 120, 292, 358, 495. 

Chlorobenzole, 299. 

Chowne (Dr. W. D.) on the elastic 
force of aqueous vapour, 225. 

Church (A. H.) on the oxidation of 
nitrobenzole and its homologues, 
176. 

Clairault’s theorem, observations on, 

O00. 

Cockle (J.) on quintics, 90; on trans- 
cendental and algebraic solution, 
379. 

Colour, on the neutralization of, in 
the mixtures of solutions of certain 
salts, 435. 

Colours, compound, on the theory of, 
141. 

Compass, on the deviations of the, on 
board iron-built ships, 531. 

Copper, on the electric conductivity 
of pure, 224. 

Corals, on the distribution of the, in 
the lias, 237. 

Croll (J.) on the repulsion of an elec- 
trical current on itself, 247. 

Crookes (W.) on the opacity of the 
yellow soda-flame to light of its 
own colour, 55; on the lithium 
spectrum, 79; on the existence of 
a new element, 301. 

Currents, on the velocities of, 1, 188. 

Dahlander (G. R.) on the equilibrinm 
of a fluid mass revolving freely 
within a hollow spheroid, 198. 

Daubrée (M.) on capillary infiltration 
through porous substances notwith- 
standing a strong counterpressure 
of vapour, 479. 

Davy (Prof. EK. W.) on further appli- 
cations of the ferrocyanide of pot- 
assium in chemical analysis, 214. 

Debray (M.) on the preparation of 
oxygen, 295. 

Debus (Dr. H.) on the fibrous arrange- 
ment of iron and glass tubes, 238. 

De Morgan (Prof.) on the logic of 
relations, 473. 

Determinants, on the theory of, 180. 

Deville (M.) on the theory of disso- 
ciation, 202; on the preparation of 
oxygen, 295; on the formation of 
some minerals, 496. 

Dianic acid, researches on, 415. 

Dioxymethylene, on the action of am- 
moniacal gas on, 125. 

Dittmar (W.) on a new method of 


INDEX. 


arranging numerical tables, 137; 
on graphical interpolation, 139. 
Donaldson (Rev. Dr.) on the origin 
and proper value of the word “ ar- 

gument,” 469. 

Drew (F.) on the succession of beds 
in the Hastings sand, 309. 

Drion (M.) on a new method of ob- 
taining solid carbonic acid, 495. 
Dufour (M.) on the freezing of water 

and the formation of hail, 543. 

Dupré (Messrs.) on the existence of a 
fourth member of the calcium group 
of metals, 86, 239. 

Electric current, on the repulsion of 
an, on itself, 81, 247, 319. 

currents, on the application of 
the theory of molecular forces to, 
281, 338. 

~——— discharge, on the duration of the 
spark of an, 565, 542. 

endosmose, on, 159. 

Electrical charge, on a new electro- 
meter for measuring the, 452. 

Element, on the existence of a new, 
of the sulphur group, 301. 

Hneseetiti, on the principles of, 274, 

Equations of the fifth order, researches 
on, 90, 210, 257, 348, 379. 

Evans (F.J.) on deviations of the 
compass on iron ships, 531. 

Fairbairn (W.) on the density of steam 
at all temperatures, and the law of ex- 
pansion of superheated steam, 230. 

Faraday (Prof.) on regelation, 146. 

Fermentation, on alcoholic, 120; ob- 
servations on, 361. 

Ferrocyanide of potassium, on new 
applications of, in chemical ana- 
lysis, 214. 

Field (F.) on the neutralization of 
colour in the mixtures of solutions 
of certain salts, 435. 

Fittig (M.) on the oxidation of toluole 
by dilute nitric acid, 362. 

Fizeau (M. H.) on several pheno- 
mena connected with the polariza- 
tion of light, 438. 

Fluor-spar, on the occurrence of ant- 
ozone in, 90. 

Forbes (D.) on the geology of Bolivia 
and Southern Peru, 154. 

Forbes (Dr. J. D.) on Ampére’s expe- 
riment on the repulsion of a recti- 
linear electrical current on itself, 
81, 


INDEX. 


Force, on physical lines of, 161, 281, 
338. 
Freund (M.) on butyryle, 501. 


Galvanic currents, on a standard mea- 
sure of resistance to, 25, 107. 

polarization of buried metal 
plates, on the, 377. 

Gaugain (M.) on the theory of cylin- 
drical conductors, 539. 

Geikie (A.) on the altered rocks of 
ae western and central Highlands, 
306. 

Geological Society, proceedings of 
the, 154, 233, 305, 536. 

Gilbert (Dr. J. H.) on the sources of 
the nitrogen of vegetation, 521. 
Glass tubes, on the fibrous arrange- 

ment of, 238. 

Glennie (J. S. S.) on the principles 
of the science of motion, 41; on 
principles of energetics, 274, 350. 

Glycerine, on some derivatives of, 
209. 

Glycolic acid, on the preparation of, 
360. 

Gore (G.) on ozone, 320. 

Govi (M.) on the polarization of light 
by diffusion, 157. 

Graphite, on the production of, by 
the decomposition of cyanogen 
compounds, 541. 

Gutta percha, on the msulating pro- 
perties of, 75. 

Hail, on the formation of, 543. 

Harkness (Prof. R.) on the geology 
of portions of the Highlands, 308. 

Heat, on a new proposition in the 
theory of, 241. 

Hector (Dr. J.) on the geology of 
the country between Lake Superior 
and the Pacifie Ocean, 537. 

Heintz (Dr.) on the preparation of 
glycolic acid, 360. — 

Helmholtz (M.) on the motion of the 
strings of a violin, 393. 

Hennessy (Prof.) on Clairault’s theo- 
rem, 396. 

Hirst (Dr. T. A.) on ripples, and their 
relation to the velocities of currents, 
1, 188. 

Hofmann (Dr.) on the action of ni- 
trous acid upon nitrophenylene- 
diamine, 457. 

Hopkins (W.) on the construction of 

Huanew calorimeter, 462. 

xley (Prof.) on a uew species of 


549 


Macrauchenia, 156; on Pteraspis 
dunensis, 303. 

Tron tubes, on the fibrous arrange- 
ment of, 238. 

Isoprene, on the properties and com- 
position of, 463. 

Jamieson (T. F.) on the geological 
structure of the South-west High- 
lands, 235. 

Jenkin (F.) on the insulating proper- 
ties of gutta percha, 75. 

Jerrard (G. B.) on quintics, 39, 348. 

Jolly (M.) on the specific gravity of 
liquid ammonia, 364. 

Kekulé (M.) on brominated deriva- 
tives of succinic acid, 124. 

Kirchhoff (Prof.) on the chemical ana- 
lysis of the solar atmosphere, 185 ; 
on a new proposition in the theory 
of heat, 241. 

Kirkby (J. W.) on the Permian rocks 
of the south of Yorkshire, 310. 

Kobell (Prof. F. von) on dianie acid, 
415. 

Kopp (Prof. H.) on the relation be- 
tween boiling-point and composi- 
tion in organic compounds, 227. 

Landolt (M.) on phosphuretted hy- 
drogen, 126, 

Lawes (J. B.) on the sources of the 
nitrogen of vegetation, 521. 

Lea (M. C.) on the optical properties 
of the picrate of manganese, 477. 
Leroux (M.) on the refractive indices 
ot genes at high temperatures, 

296, 

Light, on several phenomena con- 
nected with the polarization of, 
157, 438; on the determination of 
the direction of the vibrations of 
polarized, 321; on the nature of 
the, emitted by heated tourmaline, 
391; on the reflexion of, at the 
boundary of two isotropic trans- 
parent media, 481. 

Liquid expansion, on a law of, 401. 

Liquids, on the laws of absorption of, 
by porous substances, 57, 115; on 
certain laws relating to the boiling- 
points of different, 331; on the 
dispersion of different, by electrical 
action, 452. 

Lithium spectrum, note on the, 79. 
Loir (M.) on a new method of ob- 
taining solid carbonic acid, 495. 
Lowig (Prof.) on a new sulphur com- 


550 


pound, 125; on the action of so- 
dium on oxalic ether, 126. 

Lorenz (L.) on the determination of 
the direction of the vibrations of 
polarized light by means of diffrac- 
tion, 321; on the reflexion of light 
at the boundary of two isotropic 
transparent media, 481. 

Lourenco (M.) on polyglyceric alco- 
hols, 499 

Lowe (E. J.) on a new ozone-box 
and test-slips, 466. 

Lunar tables, on the, 239. 

Macrauchenia, on a new species of, 
156. 

Magnetic declination, on the lunar- 
diurnal variation of, 384. 

force, on a theory of, 65, 92. 

phenomena, on the application 
of the theory of molecular vortices 
to, ]61, 281, 338. 

Magnetism, on theories of, 250. 

Martius (M.) on the platinum metals, 
502. . : 

Matteucci (Prof.) on electric endos- 
mose, 159. 

Matthiessen (Dr. A.) on an alloy 
which may be used asa standard of 
electrical resistance, 107. 

Maxwell (Prof. J. C.) on the theory 
of compound colours, and the rela- 
tions of the colours of the spec- 
trum, 141; on physical lines of 
force, 161, 281, 338. 

Metals, new, 86, 239. 

Miasnikoff (M.) on the preparation 
of acetylene, 359. 

Minerals, on the formation of native, 
496. 

Mitchell (Rev. H.) on the old red 
sandstone of Forfar and Kincar- 
dine, 236. 

Motion, on the principles of the 
science of, 41. 

Murchison (Sir R. I.) on the altered 
rocks of the western and central 
Highlands, 306. 

Nicol (Prof. J.) on the structure of 
the north-west Highlands, 233. 
Nitrobenzole, on the oxidation of, 

176. 

Nitrophenoie acid, 178. 

Nitrophenylenediamine, on the action 
of nitrous acid upon, 457. 

Numbers, prime, on a new theorem 
concerning, 127. 


EN Dt xX. 


Numerical tables, on a new method 
of arranging, 137. 

Oxygen, on the preparation of, 295. 

Ozone, note on, 329, 

fea and test-slips, on a new, 
466. 

Pasteur.(M.) on alcoholic fermenta- 
tion, 120. 

Pauli (Dr. P.) on the production of 
graphite by the decomposition o 
cyanogen compounds, 541. ; 

Pettenkofer (Prof.) on an apparatus 
for experiments on respiration, 544. 

Phosphuretted hydrogen, on inflam- 
mable, 126. 

Physies, theoretical, on, 504. 

Picrate of manganese, on the optical ° 
properties of the, 477. 

Platinum metals, on the cyanides of 
the, 502. 

Playfair (Dr. L.) on a method of 
taking vapour-densities, 398. 

Polyammonias, researches on the, 
457. 

Pontécoulant (M. de) on the lunar 
tables, and the equalities of long 
period due to the action of Venus, 
239. 

Pteraspis dunensis, 303. 

Pugh (Dr. E.) on the sources of the 
nitrogen of vegetation, 521. 

Putrefaction, observations on, 361]. 

Quinties, remarks on, 39, 90, 210. 

Reboul (M.) on some derivatives of 
elycerine, 299. 

Regelation, note on, 146. 

Resistance-thermometer, on a new, 
73. 

Respiration, on an apparatus for ex- 
periments on, 544. 

Retina, on certain affections of the, 20. 

Riess (Prof.) on electrical partial dis- 
charges, 542. 

Rike (Prof. P. L.) on the duration of 
the spark of an electric discharge, 
365. 

Ripples, on, and their relation to the 
velocities of currents, 1, 188. 

Rose (Prof. H.) on the separation of 
tin, 207. 

Rossi (M.) on homocuminie acid, 561. 

Royal Society, proceedings of the, 75, 
141, 224, 384, 457, 521. 

Saligenine, researches on, 363. 

Satellites, on the stability of, in small 
orbits, 263. 


IND EX. 


Saturn's rings, on the theory of, 263, 
508. 

Sawitsch (M.) on acetylene, 358. 

Scheenbein (Prof.) on the insulation 
of antozone, 88. 

Scholz (M.) on a new sulphur com- 
pound, 125. 

Schroeder (M.) on fermentation and 
putrefaction, 361. 

Schiitzenberger (M.) on a new class 
of salts, 497. 

Seelheim (M.) on saligenine, 363. 

Siemens (C. Wm.) on a new resist- 
ance-thermometer, 73. 

(M. W.) on a standard measure 
of resistance to galvanic currents, 
25. 

Siphon-electrometer, on the, 452. 

Smithe (J. D.) on the gravel and 
boulders of the Punjab, 305. 

Soda-flame, on the opacity of the 
yellow, to light of its own colour, 
55. 


Spectrum, on the relations of the 
colours of the, 141. 

Staurotide, ou the formation of, 496. 

Steam, on the density of, at all tem- 
peratures, 230. 

Stewart (B.) on the nature of the 
light emitted by heated tourmaline, 
391. 

Stromeyer (M.) on the estimation of 
tin, 298 

Sucecinic acid, on derivatives of, 124. 

Swan (Prof. W.) on the temperature 
correction of siphon barometers, 
206. 

Syllogism, on the, 473. 

Sylvester (Prof.) on the numbers of 
Bernoulli and Euler, 127; on the 
historical origm of the unsymme- 
trical six-valued functions of six 
letters, 369; on a problem in tac- 
tic, 515. 

Tait (Prof.) on Ampére’s experiment, 
319. 

Tate (T.) on the laws of absorption 
of liquids by porous substances, 57, 
115; on the density of steam at 
all temperatures, and the law of ex- 


5 5 l 


pansion of superheated steam, 230 ; 
on certain peculiar forms of capil- 
lary attraction, 254; on certain 
laws relating to the boiling-points 
of different liquids, 331; on a new 
electrometer for measuring the 
electric charge of a machine, 452. 

Temperature correction of siphon 
barometers, on the, 206. 

Temperatures, on the production of 
low, 296. 

Thermometer, on a new resistance, 73. 

Thomsen (J.) on a constant copper- 
carbon battery, 80. 

Tin, on the separation of, 297. 

Tourmaline, on the nature of the 
light emitted by heated, 319. 

Tungsten and its alloys, researches 
on, 292. 

Vapour-densities, on a method of 
taking, 398. 

Vapours, on the refractive indices of, 
at high temperatures, 296. 

Vaughan (D.) on the stability of sa- 
teilites in small orbits, and the 
theory of Saturn’s rings, 263; on 
phenomena which may be traced 
to the presence of a medium per- 
vading space, 507. 

Vegetation, on the sources of the 
nitrogen of, 521. 

Venus, on the inequalities of long 
period due to the action of, 239. 
Violin, on the motion of the strings 

of a, 393. 

Wanklyn (J. A.) on a method of 
taking vapour-densities, 398. 

Water, on the freezing of, 543. 

Waterston (J. J.) on a law of liquid 
expansion, 401. 

Wertheim (M. G.) on the cubical 
compressibility of certain solid ho- 
mogeneous bodies, 44/7. 

Williams (C. G.) on isoprene an 
caoutchine, 463. 

Woods (Dr. J.) on Sainte-Claire De- 
ville’s theory of dissociation, 2U2. 
Yeast, on the permanent vitality of, 

123. 
Zircon, on the formation of, 496. 


END OF THE TWENTY-FIRST VOLUME. 


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