ie
*

4
‘i

CAS
VANS)

hoe oa

pe

See en
eta. War

Raa
Whe FRB
PPR ed iat
ane

eRe a! . wie

Hh e i a ae Ny aS y\
Haris - TRS : Pekan bea S “
’ we S

h : - ne
wee we wa
ie SUR Re
J MURMUR ee

PAPAL A res Sa Be
‘SWS OS a's

a

THE

LONDON, EDINBURGH, axp DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

Beer Gan BY
LORD KELVIN, LL.D. P.R.S. &e.
GEORGE FRANCIS FITZGERALD, M.A. Sc.D. F.B.S.

AND

WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S.

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

VOL. XXXV.—FIFTH SERIES.
JANUARY—JUNE 1893.

LONDON:
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.

SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.; WHITTAKER AND CO. ;
AND BY ADAM AND CHARUES BLACK ;—T. AND T. CLARK, EDINBURGH ;
SMITIT AND SON, GLASGOW ;--HODGRES, FIGGIS, AND CO., DUBLIN ;—

PUTNAM, NEW YORE ;—-~VEUVE J. BOYVEAU, PARIS ;—

AND ASHER AND CO., BERLIN,

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

“Cur spirent venti, cur terra dehiscat,

Cur mare turgescat, pelago cur tantus amaror,

Cur caput obscura Phoebus ferrugine condat,

Quid toties diros cogat flagrare cometas,

Quid pariat nubes, veniant cur fulmina ccelo,

Quo micet igne Iris, superos quis conciat orbes

Tam vario motu.”

J. B. Pinelli ad Mazonium.

CONTENTS OF VOL. XXXV.

(FIFTH SERIES).

NUMBER CCXIL—JANUARY 1893.

Prof. R. Threlfall on the Electrical Properties of Pure Sub-
stances.—Part I. The Preparation of Pure Nitrogen and
mitempes to Condense it... (Plate d.) 1. ele os td die oe ys

Messrs. Heinrich Rubens and Benj. W. Snow on the Refrac-
tion of Rays of Great Wave-length in Rock-salt, Sylvite,
amr ALONE). bola, soctasbheds oid. wyaiw is wi escel ol ote’ oo 0%

Mr. Walter Baily on the Construction of a Colour Map .

Mr. R. H. M. Bosanquet on Mountain-Sickness ; ; and Power
MEME ERODE MCE oe 3 or 260s =. oh ois.'n, 3; mopiyas cayijeoe Masveuds AER

Dr. William Pole: Further Data on Colour-blindness.—

Prof. F. Y. Edgeworth « on a New Method of treating Corre-
Ee SCS) IN Artis hui a bat miyhre Fi Swicki slew Foesens
Mr. Fernando Sanford on a necessary Modification of Ohm’s

emmy Ae oo Sra ce ik, te eke ge oe nS tees anoles
Messrs. Rimington and Wythe Smith on Experiments in
Electric and Magnetic Fields, Constant and Varying.
Ephedra) eR Ses 2p crus C etme, whic « tate see WBN Y welnias pos ae NS
Notices respecting New Books :-—
Mid esawers Odorographiag.'.). .0\4a%. 0 ss eee oes «
Proceedings of the Geological Society :—
Prof. M. E. Wadsworth on the Geology of the Iron,
_ Gold, and Copper Districts of Michigan............
Mr. H. M. Becher on the Gold-quartz Deposits of
aban (vialay Peninsula) iter. cease ea ols esis
Mr. F. D. Power on the Pambula Gold-deposits ......
An Electrolytic Theory of Dielectrics, by A. P. Chattock
On a Chemical Actinometer, by H. Rigollot Bh Aen ae ae
On the Attraction of two Plates separated by a Dielectric,
eevee silicon Mereynes eg Wa Ses eee ck ee ee ees
Investigation of the Properties of Amorphous Boron, by
Be VOUSSAI \. Suny ae es sek ee vs 5 MS OES Se area ane

Page

1V CONTENTS OF VOL. XXXV.——FIFTH SERIES.

NUMBER CCXIII.—FEBRUARY.

Page
Dr. W. E. Sumpner on the Diffusion of Light ............ 81
Dr. G. Gore on the Relation of Volta Electromotive Force to
Pressure &. 2. ces es oe ee 5s te, rr 97
iB] Galitzine on Radiant Hnergy ........-... .5: 3 eee 113
Mr. 8. U. Pickering on the Diffusion of Substances in
Nolution ..6. 2 Si. se eee kee aed oo er 127
Prof. J. G. MacGregor on Contact-Action and the Conserva-
tion Of Hnerey oo... tea ee sos ee 134
Mr. A. A. Campbell Swinton’s Experiments with Ze
Frequency Electric Discharges .. 52. ..2.. 3c 142
Notices respecting New Books :—
Mr. J. F. Blake’s Annals of British Geology, 1891 . 145

Proceedings of the Geological Society :—
Prof, E. Hull’s Outline of the Geological Features of

Arabia: Petrea and -Palestine.-...... 2.0. «s..05eeee eee 146
Rev. A. Irving on the Base of the Keuper Formation in
Devon’ 2-0. A IC a err 147
Mr. J. H. Cooke on the Marls and Clays of the Maltese
Tslamds: asco oe oaceia oie Wie caleta: «ate eer 148
Prof. T. G. Bonney on the Nufenen-Stock (Lepontine
AN 0) :) A EO EEE 5 148

Prof. T. G. Bonney on some Schistose ‘‘ Greenstones ”
and allied Hornblendic Schists from the Pennine Alps,
as illustrative of the Effects of Pressure-Metamor-
PHISMs © see ee eee oe eee ese ete he 149
Prof. T. G. Bonney on a Secondary Development of
- Biotite and of Hornblende in Crystalline Schists from

the: Binnenthal-......-. i... 8.04 one 150
Mr. J. H. Collins’s Geological Notes on the Bridgewater
: District in Eastern Ontario. . 5. ~°" 120 eee 150

Visible Representation of the By polsde Lines in Plates
traversed by Currents; explanation of Hall’s Phenomenon,
by ©. Hommel... 0.0.5.4. 3 2. oe. 2a er 151
On the Action of Light upon Electrical Discharges m.various
Gases, by I. Breissig..00. 0.0... 2 | 0 151
Notice of a Meteoric Stone seen to fall at Bath, South Dakota,
by A. FE: Foote... 0.0.00 152

NUMBER CCXIV.—MARCH.

Prof. Ludwig Boltzmann on the Equilibrium of Vis Viva-—
Wart WT os fas i. oa wee S's 2 ak es er 153

Mr. Carl Barus on the Fusion Constants of Igneous Rock.—
Part II. The Contraction of Molten Igneous Rock on Passing
from Liquid to Solid: (Plate V.) 2... .... >) ase 173

Dr. J. R. Rydberg on a certain Asymmetry in Prof. Rowland’s
Concave:Gratings.. 00... ah aa ca errr

CONTENTS OF VOL. XXXV.-—FIFTH SERIES. v

Page
Mr. EH. C. C. Baly on the Separation and Striation of Rarefied
Gases under the Influence of the Electric Discharge...... 200
Dr. J. H. Gladstone on some Recent Determinations of
Molecular Refraction and Dispersion ...............+.. 204
Mr. Frederick J. Smith on High Resistances used in con-
nexion with the D’Arsonval Galvanometer ............ 210
Mr. William Sutherland on the Laws of Molecular Force .. 211
Mr. Carl Barus on the Fusion Constants of Igneous Rock.—
Part III. The Thermal Capacity of Igneous Rock, con-
sidered in its Bearing on the Relation of Melting-point to

fpeetemcoy. CelatooVil.)*! M5. seiko Aye wie Se Sg ke Ph 296
Notices respecting New Books :—
Mr. P. Alexander’s Treatise on Thermodynamics ...... 307
Dr. Carl Barus’s Die physikalische Behandlung und die
Messung hoher Temperaturen.............. 0.00% 310
Dr. Ad. Heydweiller’s Hiilfsbuch fiir die Ausfihrung
elekerischer Messumgemi. hh .ckiad la sean ss eee dll

Proceedings of the Geological Society :—
Herr Victor Madsen on Scandinavian Boulders at Cromer 312
Miss C. A. Raisin on the Variolite of the Lleyn, and

assecidted Volcanic Rocks. 2 as . we.) aw ts aay cians wa = 312
Mr. H. Emmons on the Petrography of the Island of
CANDIED Fh che Se euoag Re Cnn Ge Nar ae eatag ge em eer 313
On a New Electrical PRES. by M. Henri Moissan ...... 313
On the Daily Variations of Gravity, by M. Mascart........ 314
Preliminary Note on the Colours of Cloudy Condensation, by
MO eA TSU Speer ck Sh reg oie dS ev andeav's ypale Gh ae basen oe ahem 315

NUMBER CCXV.—APRIL.

Dr. Charles V. Burton on Plane and Spherical Sound-Waves

Sra tmmie; AMPLE Or... sc ths ei sre ip wie ede oe orig, vob or oe 8 = 317
Prof. J. D. Everett on a new and handy Focometer........ 333
Mr. G. H. Bryan on a Hydrodynamical Proof of the Equations

of Motion of a Perforated Solid, with Applications to the

Motion of a Fine Rigid Framework in Circulating Liquid . 338
Prof. G. M. Minchin on the Magnetic Field of a Circular

CTUETRSTAUE "5 Ss scene Oar en ao CG 304
Dr. John Shields on Hydrolysis in Aqueous Salt-Solutions.. 365
Dr. G. Johnstone Stoney: Suggestion as to a possible Source

of the Energy required for the Life of Bacilli, and as to the

DP iicey Ok Ue is IMA WE SIZ whence y c1sis cyeuy m. shnisl sh sini oun #5 sues © 389
On the Magnetization of Iron Rings slit in a Radial Direction,

lose Jak Mie loeiies anil seein te ere rae ne ne ae ee cn 392

Je ORAS UBT RANE ee! Sor Rea ng ean arco ee RIA re AY CEE eens 393
On the Official Testing of Thermometers, by I]. F. Wiebe .. 395

vi CONTENTS OF VOL. XXXV.—FIFTH SERIES.

NUMBER CCXVI.—MAY.
Page

Prof. H. A. Rowland on Gratings in Theory and Practice .. 397
Mr. T. H. Blakesley on the Differential Equation of Electrical

WG Wee OE a ee |e 419
K. Tsuruta on: the Heat of Vaporization of Liquid Hydro-
chleric"Acid™ >. 2200.3 oe ES er vos SO

M. P. Rudski on the Flow of Water ina Straight Pipe .... 439
Prof. J. Perry (assisted by Messrs. J. Graham and C. W. Heath)
on Liquid Fmetion.. (Plate ViT.) ~.2: ..2 2 ee 44]
Miss A. G. Earp-on the Effect of the Replacement of Oxy-
gen by Sulphur on the Boiling- and Melting-points of
Compounds’*30. 27202. 0 oD Pe 458
Notices respecting New Books :—
Mr. R. Lachlan’s Elementary Treatise on Modern Pure
Geometry 220i. se PS 462
Revue Semestrielle des Publications Mathématiques ré-
digée sous les auspices de la Société Mathématique
d’ Amsterdam... ..)..2y2 2s. 0 to. 2 463
Proceedings of the Geological Society :—
Prof. J. W. Judd on Inclusions of Tertiary Granite in
the Gabbro of the Cuilin Hills, Skye ; and on the Pro-
ducts resulting from the Partial Fusion of the Acid

‘by the Basic Rock... 00. 5 SA er 464
Mr. W. 8. Gresley on Anthracite and Bituminous Coal-
beds) cis i os oo tad ee 465

Messrs. Fox-and Teall. on some Coast-Seetions at the
Lizard; and on a Radiolarian Chert from Mullion

island seo. 3 ne EE 466
Mr. T. Roberts on the Geology of the District west of

CaerinaribeMlc .. se. ices = 2's 4530 ie 467
Lieut. G. C. Frederick’s Geological Remarks on certain

Islands in the’ New Hebridés °..-........ - eee 467

Mr. H. W. Monckton on the Occurrence of Boulders
and Pebbles from the Glacial Drift in Gravels south
of the Thames. 2. ....5 2260s... 150s 468
Mr. O. A. Shrubsole on the Plateau-Gravel south of
Meade... dae ees se es a ee ee 468
Mr. Clement Reid on a Fossiliferous Pleistocene Deposit
at Stone, on the Hampshire Coast ...............- 469
On Villari’s Critical Point in Nickel, by Prof. Heydweiller .. 469
On the Interference-Bands of Grating-Spectra on Geiatine, by
DUE ON A. oe sis oes ova aie Bo hd ss Vale Un a 471

CONTENTS OF VOL. XXXV.—FIFTH SERIES. Vil

NUMBER CCXVII.—JUNE.
Page
Lieut. G. Owen Squier on the Electrochemical Effects due :
SMMC IAAT ON Gacy fa tot on Fests a wd vq ieiaas od eieleehei co od vee 473
Dr. ©. V. Burton on the Applicability of Lagrange’s Hqua-
tions of Motion in a General Class of Problems; with
especial reference to the Motion of a Perforated Solid in a
MRE Mere ay os aN) oe VR ois 8 ages aQabte foe wats die d= 490
Mr. A. B. Basset on the Finite Bending of Thin Shells .... 496
Prof. Angstrém on Bolometric Investigations on the Inten-
sity of Radiation by Rarefied Gases under the Influence

<5 Flag rer DISIGI or ae rae a 502
Mr. E. C. Rimington on Luminous Discharges in Electrodeless
WEE TIE ELLEN ecg ne eins Can ere ee Sa 506

Mr. M. S. Pembrey’s Comparative Experiments with the Dry-
and Wet-Bulb Psychrometer and an improved Chemical

TEV EIST TED ESC RG e e eg e wes d e RR Deer 525
Mr. R. E. Hughes on Water as a Catalyst...............- 531
Notices respecting New Books :—

Drs. Bedell and Crehore’s Alternating Currents . .... 534

Prof. 8. W. Holman’s Discussion of the Precision of
Measurements, with Hxamples taken mainly from
Physics and Electrical Engineering................ 535

On the Disengagement of Heat occurring when Electrical
Vibrations are transmitted through Wires, by Dr. I.

Riis cer gas poke. LIS. Sthekoe Wie ahice ie 537
On the Potential of Electrical Discharge, by Prof. Heyd-

NER PE Cotes aad bas bn (Ss alten Wo pease aden a WRRe 62 Da wees 538
On a Property of the Anodes of Geissler’s Tubes, by E.

Sead SEM Tete sis, = Dae lav ain oahawel PH Viv SF ROE VL ee dW ae 538

PLATES.

_ I. Illustrative of Prof. Threlfall’s Paper on the Electrical Properties
of Pure Nitrogen. : )

II. Illustrative of Messrs. Rubens and Snow’s Paper on the Refraction
of Rays of Great Wave-length in Rock-Salt, Syivite, and Fluorite.

IIT. Illustrative of Mr. F. Sanford’s Paper on a necessary Modification
of Ohm’s Law.

IV. Illustrative of Messrs. Rimington and Wythe Smith’s Paper on
Experiments in. Electric. and Magnetic Fields, Constant and
Varying.

V. & VI. Illustrative of Dr. Carl Barus’s Papers on the Fusion Con-
stants of Igneous Rock. .

VIL. Illustrative of Prof. J. Perry’s Paper on Liquid Friction,

THE

LONDON, EDINBURGH, axn DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

SSS eT SSS

[FIFTH SERIES.]

JANUARY 1893.

I. The Electrical Properties of Pure Substances.—Part I. The
Preparation of Pure Nitrogen and attempts to Condense it.
By Professor R. THRELFALL”.

[Plate I.]

a 1886 a paper was published in the Proceedings of the

Royal Society by Professor J. J. Thomson and myself,
“On an Effect produced by the passage of an Electric Dis-
charge through Pure Nitrogen.” The effect in question was
briefly as follows :—When a nitrogen tube provided with a
small mercury or sulphuric-acid gauge is exhausted to a pres-
sure of about 8 millim. of mercury and then sparked with a
discharge too small to heat the tube in a sensible manner, a
diminution of the elastic force of the enclosed gas is observed.
This diminution was found to be independent of the size or
material of the electrodes, of the volume of the tube or the
extent of its surface, but to depend on the kind of discharge
employed, and its duration ; on the temperature and pressure
of the gas in the tube during the process of sparking and
afterwards. Arguing by exclusion, we attributed the diminu-
tion of pressure to a condensation of nitrogen molecules,
similar to the condensation which oxygen undergoes when
converted into ozone.

This property of nitrogen, if established, would be of un-
doubted interest, and consequently in 1889 I undertook a

* Communicated by the Author.

Phil. Mag. 8.5. Vol. 35. No. 212. Jan. 1893. B

I FO a Ot NL A TG I Ry NS A TN NT yee My mm

2 Prof. R. Threlfall on the Electrical

repetition of the experiments with a view to testing our con-
clusions by an extended examination of the phenomena in
question. This investigation has proved a most laborious
task; and it was not until December 1891 that I finally
satisfied myself that the effect was due to the combination of
nitrogen with the mercury of the pressure-gauge under the
influence of the electric discharge, and in the presence, as I
think, of a minute trace of some other substance whose nature
I have not been able to determine.

The experiments to be described leave little doubt that pure
nitrogen at ordinary temperatures does not condense in the
same way that oxygen condenses, whether the discharge be
by means of external electrodes or by means of wires fused
into the tube. Since these experiments form the starting-
point of other researches, I will begin by an account of a
method by which pure nitrogen may be most advantageously
prepared. Singularly enough this apparently simple chemical
problem has not, so far as I know, been solved hitherto. Sias,
in his researches, makes the remark that nitrogen is easily
obtained pure (Bulletin de ? Académie Royale des Sciences de
Belgique, 1860, sér. 2, t. x. p. 254); and this remark may
very possibly have produced misunderstanding—everything
depends on what is meant by the word pure. ‘lhe fundamental
principles in all processes of purification are :—Ilst, that
reagents used to remove any impurity must really keep the
impurity when they have got it, and not liberate it or its
equivalent through any instability of the compounds formed ;
and 2nd, that the reagents themselves must not give rise to
impurities. As an example of a common violation of the first
principle, I will mention the absorption of sulphuretted hydro-
gen, sulphur dioxide, or the oxides of nitrogen, by potash or
soda ; and of the second, the use of imperfectly prepared phos-
phorus pentoxide. Trouble arising from layers of air or
other gases condensed on the surfaces of glass vessels can
only be relieved by arranging the method of production of
the gas required in such a way that the glass surfaces may
remain for weeks or months in contact with the gas under
experiment, otherwise completely purified. If mercury be in
contact with glass in any part of the apparatus, then, as I
believe, it is impossible by ordinary means to be sure that the
glass is ever completely denuded of its primitive layers of gas.
I append a list of some of the varicus ways in which nitrogen
has been prepared for careful work, and shall, I think, be able
to show that all these processes are open to objection, at all
events where a continuous supply of gas is necessary. The
list is short, because nearly all experimenters simply state that

Properties of Pure Substances : Nitrogen.

3

they used pure nitrogen without giving details of its method
of preparation.

Name.
Moor otas,...

Neuman

Olzewski ....

re blew Et:
Lupton

H. Deslandres.
W. Gibbs....

N. W. Fisher,

Regnault ....
Wullner

Huggins

Warburg ....

Reference.
Bull del Acad, de
Belgique, vol. x.
p. 204.

J, fiir prk. Chemie,

[2] xxxvil. p. 342.

Wien. Anzerger,
March 1884.

C. &. xeviii. p. 982.

Cas: J. 18763
Chem. News,
XXxiil. p. 90.

CR. ci, p. 1256.

Ber. x. p. 1887.

Poge. Ann. xvii.
. 187

Pp :
COR} t. xx..p. 975.
Pogg. Ann. cxlvil.

p. 325.

Phil. Trans. 1860.
Ann, der Chem. und

der Phys. 1887,
p. 048.

Method.

By passing purified air over hot
copper turnings and gauze,
which are previously reduced
by hydrogen. Copper oxide at
end of tube (?); ordinary ab-
sorbent reagents to help purify
the gas after leaving the hot
copper.

From chloride-of-lime cubes (made
by Winkler’s method) and
aqueous ammonia (see C, 8S. J.
1887, p. 442).

Hot copper and air.

Hot copper and air.

Air and ammonia over hot copper ;
claims to get pure N with a
short tube.

Hot copper and air; no precaution
mentioned.

Sodium nitrite, ammonium sul-
phate, and potassium dichro-
mate in excess. If there is a
trace of chloride present, im-
purities are introduced.

Uses cuprous chloride as an ab-
sorber of oxygen from air.

Hot copper and air.

Burning phosphorus in air over
mercury and removing traces of
oxygen by incandescent iron
wire.

Purified air over hot reduced
copper.

Hittorf’s method. Dust-free air
over hot white phosphorus, then
over potassium permanganate,
solid potash, and phosphorus
pentoxide. Special drying in
some cases followed by exposure
(Wied. Ann. xl. p. 1) to nascent
sodium obtained by the electro-
lysis of glass.

It is clear that the most popular way of making nitrogen is
to absorb the oxygen from air by means of red-hot copper.
There are a great many objections to this method, however,
even when precautions are taken against the possibility of the

formation of oxides of nitrogen.

In the first place, a satis-

factory method of making connexion to the porcelain tube is
unknown to me; indiarubber stoppers are undesirable in any

~

4. Prof. R. Threlfall on the Electrical

case, and particularly in places where they can become hot.
One never feels certain, moreover, that a red-hot tube, even
of glazed porcelain, is absolutely ‘impermeable to furnace-
gases. If one uses a bath of magnesia this difficulty may
perhaps be overcome, but there remains the difficulty of
making proper connexions.

If hard glass be employed instead a porcelain, then there
is insecurity i in the joints between it and the glass used for
the remainder of the apparatus. Metal tubes present similar
difficulties with regard to the junctions, and are besides more
or less porous at high temperatures. Another grave dis-
advantage is that, whether porcelain or glass tubes be used,
there is “always a chance of a crack occurring, and perhaps
escaping notice.

The reduction ef the copper also presents great difficulty:
it is more difficult to get a strong stream of really pure
hydrogen or carbon monoxide than to get the nitrogen ;
and any sulphur absorbed by the copper is a permanent
disadvantage ; for, as metallurgists know, copper contain-
ing sulphur may be oxidized and reduced many times and
yet at each oxidation some sulphur will burn out. The
reason is, of course, that sulphide of copper heated in air
forms some sulphate of copper as well as sulphur dioxide.
On the next reduction sulphide of copper is re-formed, and
then, on passing air over the mixture, the process of incom-
plete oxidation is repeated. Judging by a discussion which
took place in Section A of the British Association not long
ago, these simple facts are not as widely known as might
have been expected. I know of no reagent which will absorb
sulphur dioxide so as to form an absolutely stable compound,
and which is itself easy to prepare in a state of sufficient
purity to be above suspicion of giving off foreign matters to
the nitrogen. Of course it may be argued that a large
number of vessels containing, say, a solution of caustic potash
might be used, the second retaining the sulphur dioxide given

off from the first, and so on; but this device is obviously
unsuited for a continuous process, where the reagents must
be untouched for weeks or months.

Finally, I gave the process a careful trial, and found it
unsatisfactory “from the causes mentioned ; and, as a matter
of fact, the trouble of preparing hydrogen or carbon monoxide
in a sufficient state of purity to reduce the copper without
contaminating it with sulphur or chlorine is at least as great
as the trouble of preparing nitrogen itself.

With regard to the method of passing air over melted
white phosphor us, the manipulation of phosphorus i is always

Properties of Pure Substances: Nitrogen. 5

troublesome, and I have not been able to find any information
as to whether phosphorus absorbs gases which might be given
off during the process of the removal of oxygen from. air.
Warburg used a solution of potassium permanganate to absorb
the vapour of phosphorus; but I have not been able to obtain
information as to whether such a solution is to be relied on,
in the first place to remove all the phosphorus, and in the
second to give off nothing else during the process. I
understand, from the paper im Wied. Ann. vol. xl. TSOOF peele
that Warbur ‘o, in his later experiments, did not succeed to his
satisfaction in remov ing the last trace of oxygen by this
method, but had to electrolyse the glass of his vacnum-tubes
so as to liberate the sodium in presence of the nitrogen, in
order to get rid of the last traces of oxygen and hydrogen.
This method appears satisfactory if one has at one’s disposal
a sufficient electromotive force, suitable glass, and an infinite
time : the hydrogen appears to be absorbed as by palladium.
Another method over which I spent six months of fruitless
labour is based on the decomposition of ammonium bichromate
by heat. This method is convenient, because if the bichro-
mate could be got to deliver nitrogen of suitable quality,
small quantities of the salt could be decomposed in bulbs
fused on to the vacuum-tubes along with suitable purifying
reagents. Ordinary ammonium bichromate (i. e. that sold as
pure) gives off a good deal of ammonia and oxides of nitrogen
as well as nitrogen itself and water-vapour. This means the
use of a good many purifying reagents, so that the method
loses its advantages of simplicity ; and in addition the oxides
of nitrogen cannot be fixed satisfactorily by any suitable
reagent ‘known to me. I thought, however, that possibly
very pure ammonium bichromate might decompose in a
simpler manner, and consequently went to great trouble to
procure a pure sample, For this purpose I purified a large
quantity of ammonium chloride and sulphate by the method
described by Stas (Bull. de ? Académie Royale de Belgique,
2nd ser. t. x. p. 283), repeating the boiling with nitric acid
more often than Stas found requisite. The purified samples
were used to generate gaseous ammonia (under the influence
of specially prepared marble-lime), which after copious wash-
ing was absorbed by chromic acid. Some samples of this
ammonia were passed over red-hot platinized asbestos with
sufficient pure oxyg gen* to destroy three quarters of the
ammonia, 4NH;+3 ))= 6H, O+2N,, with a view to destroy-
ing any traces of organic ammonium compounds; but the

* The method of procuring pure oxygen will be described in another
connexion.

eis Prof. R. Threlfall on the Electrical

resulting bichromate of ammonium coming from the small
quantity of ammonia which was not destroyed by the oxygen
did not differ in behaviour from the other samples. It may
be noted here that Stas found (loc. cit.) that purified ammonia
has a much less unpleasant smell than ordinary ammonia :
careful trial, however, failed to enable me to detect any differ-
ence between the smell of my purest ammonia and that
obtained by boiling so-called pure solution of ammonia obtained
from the dealers. I conclude that the “ pure ammonia” of
commerce is much purer now-a-days than it was thirty years
ago.

The chromic acid was made from repeatedly crystallized
bichromate of potash, bought as pure, and the sulphuric acid
which is sold for analytical purposes. The resulting chromic
acid was washed free from sulphuric acid by strong nitric acid,
distilled for the purpose. I found incidentally that the addition
of a little chromic acid to the mixture of nitric and sulphuric
acid in the retort appeared to have a good effect in diminish-
ing the quantity of nitrous acid which generally accompanies
“fuming” nitric acid. The washed chromic acid was dried on
tiles in the usual way, and heated with great care and continual
stirring until it partly melted ; but even so it was slightly
decomposed. Of course the greater portion of the nitric acid
had been previously got rid of by heating the chromic acid on
a water-bath in a partly exhausted retort with ground-on
condenser, the latter containing some sticks of potash. The
chromic acid being partially decomposed gave a solution,
which had to be filtered through glass-wool before it was
used to absorb the ammonia. This solution was tested by
distilling, the distillate being tested for nitrites both before
and after reduction with sodium amalgam. The result of
these tests was to show that either the solution contained no
nitro-compounds, or, if so, not more than are contained in the
same quantity of platinum distilled water. The bichromate
of ammonia made from this was recrystallized three times
from platinum distilled water. Some small samples were
crystallized up to six times, but did not differ from the results
of the third crystallization. All these samples, when heated
either in air or in vacuo, gave off nitrous compounds, and
did not behave in any way differently to the sample which
had been bought as pure. I therefore conclude that the
normal decomposition of ammonium bichromate is complex,
and that it is not a good substance to use as a source of
nitrogen.

I will now describe a method of procuring nitrogen which
has not been mentioned hitherto, which lends itself remark-
ably well to a continuous process, and which is almost, but not

Properties of Pure Substances : Nitrogen. 7

quite, free from objection. I refer to the copper-ammonia
and chromous-chloride method of Berthelot and Recoura
(‘ Watts’ Dictionary, new edition, and Ann. de Phys. et de
Chim. s. 6, vol. x. p. 5). When air is exposed to a large sur-
face of copper wet with strong ammonia, the oxygen is for the
most part absorbed. In my experience with the arrange-
ments about to be described, there is only about three per
cent. of oxygen left after the reagents have acted for half an
hour, and only one per cent. after three hours. Since in
practice with my apparatus the air often stands over the
copper for a day or even a week, the absorption is probably
nearly complete. The last traces of oxygen are absorbed by
a strong solution of chromous chloride, which perhaps exer-
cises a stronger absorptive power on oxygen than any other
liquid, and is for this purpose quite easily prepared. As the
method is not so well known as it deserves to be, I give the
following description from Recoura’s paper :—

A large flask is taken, and in it are placed 250 to 300
grammes of granulated redistilled zine with 50 grammes
powdered crystals of potassium bichromate. The bichromate
must be finely powdered ; it should be pounded till it looks
bright yellow. Three hundred cubic centimetres of pure
hydrochloric acid are mixed in a beaker with two hundred
cubic centim. of water, and I have found it advantageous to
heat the mixture almost to boiling. The contents of the
beaker are then poured as quickly as possible into the flask,
and a violent evolution cf hydrogen and steam at once com-
mences. If the flask is too small, some of the liquid will of
course be projected from it. Under the powerfully reducing
influence of the zine and hydrochloric acid, the chromium is
rapidly reduced to the state of green oxide, which then
redissolves to a beautiful blue solution. The whole reaction
only takes about ten minutes or a quarter of an hour. If
the bichromate is not sufficiently finely powdered, a further
quantity of hydrochloric acid may have to be added to com-
plete the reaction, or the mixture may be left (excluding air)
for a few hours. The blue solution contains chromous chlo-
ride, chlorides of zinc and potassium, and possibly various
impurities. The slightest trace of oxygen destroys the perfect
colour of the chromous chloride by converting it into the
green or grey substances investigated by Recoura. On
standing over zinc for some time, however, if not too much
oxidized and slightly acid, the chromium compounds become
again reduced and the fine blue colour reappears. The colour
is as clear and bright and almost exactly of the same shade
as the colour of an ammoniacal solution of cupric hydrate.
Recoura states that a stream of gas containing free oxygen

8 Prof. R. Threlfall on the Electrical

can be completely deprived of the latter by allowing it to
bubble once through a flask containing the blue liquid. To
test this I placed two flasks in series, both containing a few
hundred centimetres of the solution, and fitted with tubes
allowing air to be sucked through both, one after the other.
Though I allowed the air to pass much more briskly than if
I had been actually using the process (say three times faster
than one ordinarily allows the oxygen to pass in an organic
analysis), I did not observe any change in the second flask
till the first had long been quite opaque and had become more
than warm, and then suddenly the contents of the second
flask became attacked. In manipulating the chromous-
chloride solution, it is useful to have a flask of the blue liquid
permanently at hand to purify the carbonic acid or nitrogen
which must be used in the subsequent operations. In many
cases it does not matter whether the gas has a trace of hy-
drogen in it or not; but for my purpose I was not willing to
run any risk of having hydrogen about, and consequently I
never allowed the purifying flask to contain zine.

Having satisfied myself as to the reliability of the chromous
chloride as an absorber of oxygen, I undertook a number of
experiments with the object of discovering, Ist, the most
suitable form in which to use it; 2nd, whether in the process
of absorption any other gas was given off, or any vapour
which could not be safely absorbed. In these experiments
large vessels containing copper and ammonia (arranged in a
manner to be presently explained), and capable of furnishing
a continuous steam of nitrogen mixed with oxygen in pro-
portions which could be varied at will, were used throughout.
The ammonia was removed from the nitrogen by strong sul-
phuric acid that had been heated to boiling and cooled in a
vacuous desiccator. With regard to the best way of using the
chromous chloride, I began with the impression that tubes
filled with the dry salt would be the most convenient, espe-
cially as Recoura shows that small crystals of dry chromous
chloride have an affinity for oxygen which surpasses that of
the solution. I therefore prepared large quantities of the
blue solution, and obtained the crystals from it by the method
recommended by Recoura, which is briefly as follows :—The
blue liquid is mixed with a saturated solution of sodium
acetate, which precipitates echromous acetate in the form of a
dark red powder. This powder is then dissolved in dilute
hydrochloric acid, and the chromous chloride precipitated
from the solution by passing in gaseous hydrochloric acid so
as to gradually increase the strength of the hydrochloric-acid
solution

Properties of Pure Substances: Nitrogen. 9

The crystals are repeatedly washed with strong hydro-
ehloric acid and dried by pressing them into tubes with
Kieselguhr. All these operations require to be performed
in an atmosphere free from oxygen, and consequently are
troublesome. The crystals are of a fine sky-blue colour, and
have a really extraordinary affinity for oxygen. For my
purpose, however, I disliked the use of the sodium acetate,
because I never felt quite sure that I had washed all the
resulting acetic acid out of the crystals. I have no reason to
believe that, even if acetic acid were present during the
absorption of oxygen, any organic compound would be libe-
rated, but in the absence of any information I thought it
better not to run the risk. I therefore turned my attention to
the criginal blue solution. This of course contains chlorides
of zinc and potassium, free hydrochloric acid, hydrogen in
solution, and possibly traces of sulphur compounds coming
from impurity in the potassium dichromate. It is a question,
then, whether during the absorption of oxygen we may not
have chlorine or sulphur compounds liberated. Both the acid
and zine were free from arsenic and antimony, so that I had
no uneasiness about these substances. I first satisfied myself
that chlorine was not given off, by allowing nitrogen with
3 per cent. of oxygen to pass through two flasks of chromous
chloride, and then through copper sulphate to retain traces of
hydrochloric acid, and finally over paper dipped in a solution
of iodide of potassium and starch. Though ten litres of gas
were passed through, I could detect no change in the starch-
paper. Sulphuric acid, when added to the blue liquid, is
partly reduced and hydrogen sulphide is given off; conse-
quently, since potassium bichromate is generally contaminated
with potassium sulphate, which is hard to remove, I had to
test whether any sulphur compounds were evolved. For this
purpose, and with the arrangement of the last experiment, I
passed nitrogen through the liquid and then over filter-paper,
saturated with a slightly acid solution of nitrate of silver, but
no change of colour could be detected. It remained for me
to make sure that in the liquid I intended to use there could
be no volatile impurity (the traces of hydrochloric acid itself
need not be considered, because hydrochloric acid can be
stopped readily by potassium hydrate).

Before discussmg this I must explain my method of pre-
paring the blue liquid, which was as follows :—About ten litres
of the raw product were prepared in several operations and
drawn into one large vessel through a filtering-tube. This
tube contained a length of four inches of compressed glass-
wool, and was closed at its lower end by a perforated platinum

10 - Prof. R. Threlfall on the Electrical

plate whose edges were fused into the tube. The blue liquid
was forced through the plug by a pressure of carbonic acid
made from marble, which had been boiled for a good many
hours at reduced pressure in water before being placed in the
Kipp’s apparatus. This carbonic acid always passed through
a wash-bottle of blue litmus purified in the way to be described
by a preliminary experiment. ‘The filter acted so perfectly
that the liquid passing through it was brilliantly clear and
free from zinc-dust, which I greatly feared. In these preli-
minary operations I was practically forced to make use of some
rubber-stoppers, and this 1s the worst fauit of the method. How-
ever, all the stoppers used were well coated with pure paraffin;
and though they might have given oft some hydrocarbons,
still I was unable to detect any trace of them in the nitrogen
finally obtained. Some rubber-tubing was also employed to
make joints, but the same precautions were taken with it, and
in all cases the sulphur was well cleaned off. The filtered
liquid was finaily got into a retort with a ground-on con-
denser, and was concentrated to one third of its original
volume in a brisk current of carbonic acid. ©

Towards the end of the operation the stream of carbonic
acid was stopped, and a partial vacuum was created in the
retort and condenser by a water-pump, so that the final con-
centration took place under reduced pressure. These pre-
cautions were considered sufficient to remove the hydrogen
dissolved in the liquid as well as any traces of volatile sulphur
compounds resulting from supposed impurities in the potas-
sium bichromate. The resulting liquid was a clear blue
syrup, and was transferred at once to the absorption-apparatus.
Before going into any details as to other precauticns, I will
describe the arrangements adopted for the continuous pre-
paration of the nitrogen by this process. These arrange-
ments will be most easily understood by a reference to the
diagram (PI. I.), though taps and clips are exaggerated for
clearness. g is a pipe projecting through the window of
the laboratory, and terminating close to the wall at a height
of about three metres from the ground. The University
paddock separates the laboratory by nearly a quarter of
a mile from the nearest road on this side, but the road on
the other side lies within 150 yards. The elevation of
the laboratory is 120 feet above sea-level. Consequently
the composition of the air is probably move nearly that of
typical “country air” than of town air. H is a U-tube
with paraffin (M.P. 51° C.) covered cork stoppers, and is
tightly packed with cotton-wool, from which the dust was
blown before the tube was mounted. F is a two-way tap,

Properties of Pure Substances: Nitrogen. it

enabling the large glass vessel to be placed in communication
either with the external air through H, or with the system of
purifying tubes. The large vessel with tap KH is filled with
copper gauze and strip, and communicates by a tube having
a rubber-joint and clip D and tap C with another large
vessel placed 2°4 metres above it (measured from bottom to
bottom). The upper vessel can be put in communication
with a water-pump by a pipe passing through B and having
atapat A. This upper vessel contains strong liquid am-
monia. It will be readily understood that by. working the
taps &e. the ammonia may be drawn into the upper vessel
while air is being admitted to the lower, and may then be
allowed to descend by gravity, and furnish the requisite head
to force the gas through the remainder of the apparatus when
the two-way “tap F is ‘suitably turned. G is an auxiliary tap
for allowing samples of the gas to be drawn off and tested for
oxygen in an ordinary Hempel’s gas-analysis apparatus, not
shown in the diagram. The air, from which the greater part
of the oxygen has been sbsonbed by the copper and ammonia,
now passes into a horizontal tube I about half filled with
strong sulphuric acid, where the greater portion of the
ammonia is absorbed. The management of this tube requires
care or the entrance soon gets stopped up by the formation
of ammonium sulphate. After two years’ work this tube was
replaced by a large glass wash-bottle with ground-in stopper.
J isa tube containing strong sulphuric acid through which
the gas bubbles; / is merely a drawn-out end for facilitating
the acon of the joints of the glass tubes. At K are
two “double ” wash-bottles containing the chromous chloride
Sys and L represents a U-tube with ground-in tap-stoppers
filled with glass beads, and likewise containing chromous
chloride. The stoppers of L and K are weighted with lead
weights to enable them to stand the pressure, and mercury
cups are arranged round the stoppers. M is a tube contain-
ing a solution of caustic potash. N contains nitrate of silver
together with a little silver hydroxide and potassium nitrate,
O contains more potash, and P contains strong sulphuric
acid. @ is half filled with potash in lumps, and half with
soda-lime. KR is a tube into which phosphorus pentoxide
has been distilled so as to present a large surface. 8,a Win-
chester bottle with ground-in stopper, and the wide tube U
both contain phosphorus pentoxide. Originally there was a
mercury-gauge at V, and though this was dispensed with,
the apparatus for eliminating mereury vapour was allowed
to remain because one or two ‘drops of mercury had got into
the tube near V. W is a specially fine tap protected with

12 Prof. R. Threlfall on the Electrical

mercury ; and X is a little phosphorus-pentoxide tube re-
quired to protect the tap, which is lubricated with phosphorus
pentoxide, and which of course requires to be kept at the
proper degree of concentration. Y is a sulphur tube, and at
Z are silver and copper tubes. Beyond Z is seen a tube and
gauge of the type used in experimenting on the nitrogen at
low temperatures. & is a small phosphoric-acid guard-tube,
Wis a sulphur tube, and © and ©® are silver and copper
tubes separated from each other by long tubes of capillary
bore. This system divides at 6, so that it may be put in
communication with a water-pump wd d, a, and e, or a
Geissler pump through 7, where there is another tap not
shown. ‘The taps at F, W, d, and / are fine samples of the
diagonal taps made by the successors of Geissler, of Bonn ;
they have all been reground with ‘ optical” precision, and
are all lubricated (except I) with phosphorus pentoxide and
protected with mercury. ‘lhe weak point in the system is at
the stoppers of L and K, which had to be lubricated with
tallow. In order to satisfy myself of the nature of the
tallow I began by purifying it with animal charcoal, and
finally by keeping it melted for eight hours in a vacuum.
After this the smell was almost gone and the tallow was
applied to the stoppers mentioned. The tap F was lubricated
with vaseline and beeswax also long melted zn vacuo. I
feared that I should introduce hydrocarbons at these points,
but the convenience of using the tallow caused me to try it,
and undertake an examination of the gas in a vacuum-tube
in order to find whether any hydrocarbons were present or
not. The result was that no trace of the ‘ three” bands
could be found, so that the enormous complications which
would have been required in the other event were happily
unnecessary. The stoppers of the large ammonia vessels
were of paraffin-coated rubber. It will be noticed that all
the points where tallow or rubber were used are to the right
of the main purifying system, which includes strong sul-
phuric acid, and the grinding of all the stoppers was so ac-
curate that an almost inappreciable film of tallow was all that
was necessary. It remains to describe the precautions taken
with the various reagents, beginning on the right.

Ammonia.—The examination of the ammonia sold as “ pure
liquid ammonia”’ which I made in connexion with the am-
monium bichromate experiments showed that nothing was to
be gained for the purpose of the main experiment by attempt-
ing any further purification.

Copper.—At different times sheet gauze, wire, and turn-
ings were employed. The purity of the copper does not

Properties of Pure Substances: Nitrogen. 13

seem to be of importance, but it is necessary to get rid of
grease. This must be done in such a way as not to waste too
much copper. In order tu clean the turnings and gauze they
were soldered into a copper tube, and a considerable quantity
of shale benzine was distilled and allowed to condense among
them. This secures that every part shall be wetted. The
process was then continued by gasoline. The gasoline was
distilled over the copper to avoid residues, and was finally
dried out at about 120° for twelve hours, a good stream of
filtered air being drawn over the copper by means of an air-
pump. The same process was gone through with alcohol,
and finally water. The copper was then washed with dilute
chromic acid and digested with strong ammonia for half an
hour. All this trouble was gone to, to avoid wastirg the
turnings, which one has to cut oneself in order to get them
in nice long curls, so that they will stand in the bottle and
not break up at once and go to the bottom. After about a
year’s work it was found necessary to renew the copper and
ammonia—the former having almost disappeared in a yellow
red mud (cuprous oxide ?) which was not further examined—
and the ammonia solution had also partially lost its blue
colour. Copper strip about 1 millim. thick was now used
to replace the gauze and turnings and wire, and was of course
strong enough to stand dipping in nitric and sulphuric acid.
It is, on the whole, more convenient to use copper in strip
than any other form.

Sulphuric Acid.—This was bought as pure for analysis,
and was heated with pure ammonium sulphate for some time
before being used. Its purity was, however, of no great
moment, except in the case of the final drying-tube P.

Chromous Chloride—Already discussed.

Potassium Hydrate-—During the experiments on the de-
composition of ammonium bichromate, I incidentally noticed
that all the samples of petash and soda in my possession
yielded traces of nitrites, either on simple solution or when
distilled with strong sulphuric acid (which was itself free
from this impurity) and the distillate reduced by sodium
amaleam. The samples of potash which were said to have
been purified by solution in alcohol were the worst in this
respect, while some rough lumps of commercial caustic potash
were nearly free from the impurity in question. I found
considerable quantities of nitrites also in samples of potash
procured by exposing clean potassium to moist air. I did
not try with dry air. After a good deal of trouble I was re-
duced to using a solution of a sample of potash in sticks not
specially purified, but which only gave the reaction very

Ae Prof. R. Threlfall on the Electrical

slightly, and was boiled under diminished pressure for two or
three hours before use. The solution still gave a distillate
with sulphuric acid which reacted with starch and iodine,
but after a time so long that it was possible that the exposure
to air during the experiment had been sufficient to supply the
nitrite discovered. In fact a control experiment made with
some ammonia, known to be free from nitrites or nitrates,
yielded a distillate which coloured to nearly the same extent
on standing. ‘The solution was made up to the strength re-
commended for use in organic analysis.

Silver Nitrate.—Crystals of silver nitrate bought as pure
were dissolved in platinum distilled water to make a ten-per-
cent. solution ; to this, when in the tube, a little of the potash
solution was added—so as to form a little silver hydroxide.
This hydroxide darkened gradually in the bright light to
which it was exposed. It was not considered necessary to
investigate the solution for traces of free nitrous compounds,
as the gas on leaving it passed through another potash-tube.

Solid Potash and Potash-Lime.—The above-mentioned
stick potash was used, and the potash-lime was made by
adding a little of the solution to some marble-lime prepared
in the laboratory ; the drying process was carried out in a
clean iron dish.

Phosphorus Pentowide.—This, being the last reagent tra-
versed by the nitrogen, requires to be exceptionally carefully
treated. I began by acting on a hint obtained in 1889 from
Prof. Josiah P. Cook, of Harvard, and endeavoured to pre-
pare a pure sample of the pentoxide by burning phosphorus
in a very strong draught of air, rather than by attempting to
purify the ordinary commercial reagent. For this purpose
an elaborate sheet-iron cylindrical chamber, measuring 3 feet
by 2 feet, was prepared and fitted with suitable contrivances
for carrying out the combustion of several pounds of phos-
phorus. ‘The air-blast was obtained from a Root’s blower
worked by a gas-engine, and the filtered air travelled through
a tin tube about 4 feet long and 7 inches in diameter, filled
with calcium chloride in the state usually described as “ rough
dried.” After many attempts a large quantity of excellent
pentoxide was obtained, which, however, though indefinitely
better than the commercial product, still retained traces of
phosphorus. The tests | employed for the purpose of dis-
covering whether the pentoxide contained free phosphorus or
not were the following :—(1) Dissolving 10 or 15 grammes
weight of the pentoxide in clear distilled water and observing
(a) whether anything remains undissolved, (@) whether, at
the moment of throwing the phosphorus pentoxide on the

Properties of Pure Substances: Nitrogen. 15

water any smell of phosphorus can be detected. (8) is a
good deal more delicate than (a), for I clearly discerned the
smell of phosphorus after the pentoxide had become pure
enough to yield no perceptible particles when thrown into
water. (2) A small porcelain crucible was filled with the
pentoxide to be tested, the lid was replaced, and the crucible
rapidly raised to a dull red heat, or till the pentoxide just
began to distil off. The room in which the operation was
conducted was quite dark except for the fickle light emitted
by the Bunsen flame used in heating the crucible. As soon
as the proper moment arrived the observer adjusted the cru-
cible tongs with one hand and turned out the Bunsen with
the other. The cover of the crucible was then removed. and
by turning on a tap ready to hand a jet of oxygen was caused
to impinge on the phosphorus pentoxide in the crucible: if
any phosphorus is present “ sparkles’? are seen on the sur-
face of the pentoxide ; and if the room is dark and the eyes
of the observer sensitive this is a very good test, but not
quite so good as that by the smell caused by throwing a large
quantity of the pentoxide on water. (3) A few drops of a
solution of chloride of gold in ether were mixed with about
500 cub. centim. of water, so as to make a very dilute solution.
This solution was divided into two parts and occupied two
similar cylinders. To one portion the solution obtained by
throwing about 1 gramme of the pentoxide into 100 cub.
centim. of water was added, and to the other an equal quan-
tity of pure water. The observation, lasting for several days,
consisted in watching the cylinders and noting the reduction
of gold that took place, as evidenced by the rosy purple
colour which the solution assumed. This test is not so deli-
cate as the others, and is valueless unless a control experiment
is made in the manner here described.

As tested by these tests, the phosphorus pentoxide prepared
by myself was never quite free from phosphorus, and I was
therefore obliged to undertake the distillation of the raw
product in a stream of oxygen. ‘This of course involved the
making of the oxygen in a sufficient state of purity. For-
tunately the presence of nitrogen in oxygen used for this
purpose is of no consequence so jong as the amount is not
large, the impurities to be dreaded are hydrocarbons and
chlorine. The oxygen was consequently prepared from po-
tassium chlorate with the usual precautions as for an organic
analysis, being passed through several potash-tubes and wash-
bottles on its way to the gas-holder—a large copper one free
from grease on the taps. J'rom the gas-holder the oxygen
passed through the following system:

16 Prof. R. Threlfall on the Electrical

(1) Solution of potassium hydrate in tube 4 feet long.

*(2) Tube 18 in. long, first half filled with metallic anti-
mony, second half filled with clean silver foil.

(3) U-tube 12 x1 in., solution of silver nitrate.

(4) U-tube 12 x1 in., solid potash.

(5) 2 ditto, salphuric-acid beads.

(6) 1 bottle, phosphorus pentoxide.

(7) 2 U-tubes, ditto.

All the connexions were of glass throughout, but it was
found convenient to use several rubber stoppers coated with
hard paraffin. The distillation of the pentoxide was carried
on in a porcelain tube 2 centimetres in diameter and nearly
a metre long, the connexions being made with glass tubes
pushed into the ends of the porcelain tube, and packed with
glass-wool and some pentoxide. This packing is very firm
and good. The first three quarters of the porcelain tube
were nearly filled with pentoxide, the last quarter contained
platinized porcelain and asbestos, the latter most carefully
purified by boiling in hydrochloric acid and strong heating.
The distillation was carried on in some cases so as to cause
the pentoxide to condense in the tubes and vessels in which
it was to be used, and a considerable quantity was also
collected in a bottle.

The final product passed all the tests I have enumerated,
and was used throughout the nitrogen apparatus, even for
drying the pump, lubricating the taps, &e. Of course a good
many tubes full of pentoxide were distilled, and nearly three
months were consumed in obtaining the final product. If I
had not had the assistance of Mr. J. A. Pollock in this work,
I have an impression that I might be at it still. The com-
mercial pentoxide was used in this work, for the substance
we prepared ourselves was probably good enough for most
purposes as it was. I have sometimes wondered whether ex-
perimenters who have of late used so much pentoxide for
critical work on gases have recognized the necessity of testing
the product obtained by distilling the pentoxide in oxygen.
In my experience, unless the oxygen stream be very strong it
is quite possible to fail to remove the last traces of free
phosphorus.

Sulphur t.—I happened to have some very pure sulphur
which had been prepared for another purpose. It will be

* It was found as the result of several preliminary experiments that
metallic antimony is a rather good absorber of chlorine, and keeps what
it absorbs.

t+ An account of the experiments with sulphur will form a chapter of
this monograph.

Properties of Pure Substances: Nitrogen. li

sufficient here to say that the sulphur was originally precipi-
tated from calcium polysulphides by hydrochloric acid ; it
was laboriously ground and washed, and distilled five times,
and care was taken not to let it take fire. The degree of
purity attained was tested by burning off large quantities in
a burnished platinum dish, and continuing the process till the
residue had disappeared. This product was rather precious,
consequently it was made the most of in the present case by
using it to coat glass beads ; some in powder was also employed
near the entrance of the purifying tubes.

Copper and Silver.—Both bought as pure and deprived of
grease by dipping in appropriate acid solutions.

General Remarks.— During the two years the apparatus
has been in use various accidents, such as the breaking of
pumps &e., have at ditterent times caused some of the re-
agents to get mixed up, and the apparatus has been taken
down and set up again some three or four times; the first
bottles of chromous chloride have also required to be refilled.
The phosphorus pentoxide has never required to be touched.
I wish to draw attention to a remark of Hittorf’s as to the
importance of using tubing free from air-bubbles. On
several occasions I have been much troubled by the minute
leaks which such imperfect tubes give rise to at the joints,
and I have in my possession at least two tubes leaking from
this cause, but so minutely that even when the leak was
localized to within six or seven inches it was impossible to
say exactly where it was. In work of this kind the cleaning
of the tubes is of course of great importance. If the work is
to be done rapidly the great secret is to clean the tube with
alcohol before the jointing or general glass-blowing opera-
tions are carried out on it. ‘The dirty places are almost
always near where the blowpipe-flame has been applied, and
after trying all and every means of cleaning, I have finally
come back to aqua regia caused to boil at the dirty place and
left in the tube for at least ten hours. Certainty of cleaning
and jointing has led me to employ English flint glass ex-
clusively in this work, and I always use the clean flame of an
oxygen-gas blowpipe, which saves time so as to far more than
repay the cost of the oxygen. All the blowing required in
jointing the tubes is done through a compact but efficient
establishment of filtering and phosphoric-acid tubes. The
glass springs so extensively used throughout allow of con-
siderable latitude in the relative movements of parts of the
apparatus, and I have had no cases of spontaneous breaking.
The whole of the glass work has been done by myself, as L
can get no assistance of a suitable kind in Sydney.

Phil. Mag. 8. 5. Vol. 35. No. 212. Jan. 1893. C

os

18 - Prof, R. Threlfall on the Electrical

~ It may possibly be objected that some of the precautions
taken are finnicking, and that (as in the manufacture of the
oxygen) an unnecessary variety of absorptive materials are
used. The reply I should make to such a criticism is that the
complete operation of any one reagent is always to some
small extent hypothetical, and I consider that by varying the
reagents one helps to get rid of the chance of the persistence
of impurities so small in amount as to be beyond the range of
ordinary analysis, 2.e. beyond the point up to which we are
certain of the action of the reagents.

Testing the Gas for Hydrocarbons and Hydrogen.

_ In order to avoid the impurities introduced by the presence
of internal electrodes, a tube was prepared with external
electrodes. It was about 35 centim. long, of which length
20 centim. were made of capillary tube. In order to fill this
with the pure gas, the apparatus was exhausted three times,
as far as the chromous chloride U-tube, each exhaustion re-
quiring seven or eight hours’ work with the Geissler pump,
after a good water-pump had got rid of the greater part of
the gas.

The pressure of the remaining gas was imperceptible by
inspection of the pump-gauge (of which a description will be
given), but the pump continued on each occasion to show a
just appreciable bubble of gas when the mercury flowed into
the barometer-tube. The pumping was done at times separated
from each other by three or four days in order to give the
residual gas from the walls of the vessel time to come off ; of
course this gas was removed as it appeared. he pressure I
should judge was, on each occasion, about of the order of -01
millim. Several bottles of gas were also forced through the
apparatus at the ordinary pressure.

Finally, on Feb. 19, 1891, the tube together with another
for experimental purposes were fused off—the former at about
*1 millim, pressure (the latter will be dealt with later). The
tube had previously been heated till the glass began to soften
and the walls to fall in, and the gas admitted had been for
several days in contact with the phosphorus pentoxide. The
only objection to the external electrode tube is that I have
hitherto failed to produce a line-discharge in it—though of
course Prof. J. J. Thomson’s method (Phil. Mag. vol. xxxii.
1891) would give it in an endless tube without electrodes,
and if the method had been known at the time I should have
employed it. However, I got a bright bluish-white discharge
in the narrow tube (the larger ends being golden), and this

Properties of Pure Substances: Nitrogen. uy)

yielded a fine band-spectrum which has been described often
enough, showing well both in the more and less refrangible
ends. I took as my authority on the typical hydrocarbon
bands those mentioned in the B.A. Report for 1880, p. 226.

Observer. Wave-length.
Angstrom and Thalén . . 5633 at least refran-

gible end.
Pi ges ee ty a p WOOL L

Angstrém and Thalén . . 5164
Peaks fe herby Sf ae} lei’ err, HOLOD

Angstrém and? Thalén elo 2 4736
Weise eet ai ear So

Professors Liveing and Dewar (Proc. Roy. Soc. vol. xxx.)
say that the characteristic spectrum of hydrocarbons is com-
posed (among others) of four bands in the orange, yellow,
green, and olive. ‘These were well seen by me in an olefiant-
gas tube prepared for the purpose without any pretensions to
purity. The cone of a Bunsen flame was also examined, and

I saw the lines (according to my map)

a at 5637 instead of 5634
[Seas (Salat A, 5165 (strongest)
y ,, 4736 ms 4738

1 had a number of commercial tubes and examined these as
a check ; the following is the result :

@ turned up in petroleum and alcohol but not in olefiant gas,
where there was a band at 5197 to 5198. This last band was
strong and was seen in CO,, H, O, turpentine, petroleum, and
eoal-gas, as well as in the clefiant gas. I do not know what
this band is due to, but it did not appear in the nitrogen.
The nitrogen was examined side by side with an alcohol tube
showing « and 8 well; but the former did not show these
bands or any trace of them. The nearest band was at 5240,
and quite too far away for there to be any mistake. The
experiment was also tried with a similar tube and nitrogen at
10 millim. pressure, with a like result. Finally the examina-
tion was repeated at the lowest pressure at which I could get
a brilliant discharge, which was of course far beyond the
limit of discrimination of my pressure-gauge. The result
was the same as before. The red and blue hydrogen lines
were never seen in any of my tubes showing banded spectra.
This analysis is of course dependent partly on the accuracy of
our map, though when once the typical lines were picked up,
their coincidence or not could be determined by direct expe-

C2

20 Prof, R. Threlfall on the Electrical

riment. It was necessary, therefore, to make a map of the
spectrum to suit my spectroscope. The latter was an instrument
with a 5-in. Trouton and Sims circle, and was made by Hilliott
Bros. ; one fine heavy glass prism was used throughout, and
the map refers to it; 1t was always in the position of minimum
deviation for each line observed. The mapping of the spec-
trum was done for me by Mr. J. H. D. Brearley (a student
in the laboratory), who also assisted at this time in all the
spectroscopic work and to whom my thanks are due. The
map was made by a selection of 33 lines drawn from all sorts
of sources, and verified in all sorts of ways, the tables used
being those in the B.A. Reports for 1884, 1885, 1886 ; Row-
land’s map (got in 1889) ; and Rowland’s table, Phil. Mag.
1889. Schellen was also found of some use. Hach line
was set upon ten times; and the prism was adjusted ten
times.

Intermediate lines were now well picked up off Rowland’s
map. Our limit of discrimination was about 2 in the fourth
significant figure of the wave-length, 7. e. I could not decide
with certainty that a line 1 made out to be at, say, 5165 was
not at 5163.

I append a list of the lines used in mapping the spectrum,
not because it is in any way to be regarded as a model selec-
tion, but because I, as a beginner at spectroscopy, should have
been very glad of such a list at the time, had I been able to
find one. I also note the means adopted by us for the iden-
tification of the lines, as it may interest other beginners in
spectroscopy. The lines are not given in the order in which
they were examined, but in order of wave-length.

1.—B. Sun, 6867°796-6867-462. Rowland, Phil. Mag.
June, 1889. Recognized by being near both to a large
iron and to a potassium line.

2.—Li,, 6705°4. From lithium chloride in a Bunsen flame.
Wave-length from B.A. Report, 1884; given by Mascart,
Liveing and Dewar, and Thalen.

3.—C, Sun (hydrogen). Good line recognized by com-
parison with a tube-spectrum of H,O. A=6563°042.
Rowland, Phil. Mag. 1889.

4,—Sun, 6400°2. A good line picked up when the map
was nearly finished from Rowland’s map.

5.—Sun, 6191°7. Same as number 4.

6.—Li,;, 6102. Authority, Mascart.

3.—Iron line, 5930°4. Rowland’s map verified by com-
parison with spark-spectrum of iron. B.A. Report.
Cornu gives 5929-3.

Properties of Pure Substances : Nitrogen. At

8.—D. Halfway between the two lines. Mean, A=5893.
Rowland, Phil. Mag. 1889. Compared with sodium
flame.

9.—Picked up from Chart. A=5709°8.

10.—Barium (vy). From flame-spectrum of Ba (NO3)p.
B.A. Report, 1884. Liveing and Dewar. %=5534:3.
A bright line. ;

i1.— Magnesium, A=5528. Rowland’s map and_ spark-
spectrum.

12.—Thallium (2), \=5349. B.A. Report, 1885. Liveing
and Dewar, and de Boisbaudran. Got from flame-
spectrum.

13.—Iron, 5328:°2. Rowland’s map verified by spark-spec-
trum. A good line.

14.—H. A=5270. Rowland’s map, a big double. Picked
up at first because it was found from Schellen’s map that
it was between two cobalt lines and near an iron line.
These lines were seen in their proper relative places in
the spark-discharge from iron and cobalt. This was one
of the first lines identified.

15.—b,, 5183°798. Rowland, Phil. Mag. Verified by mag-
nesium-spectrum. One of the first lines got.

16.—A=5041-5042. Picked up from Rowland’s map. Veri-
fied by finding from B.A. Report that it was an iron
line and then confirming by spark-spectrum.

17.—vA=4957°6. Picked up and verified as in the last case.
18.—rA=4920°6. Ditto.

19.—F. 2X7=4861:492-4859-929. Rowland’s map confirmed
by vacuum-tube.

20.—Bismuth. »=4752. B.A. Report, Thalen, and Huggins.
From spark-spectrum. Not very good. lHvidence as to
identification, its general relation and appearance.

21.—Bismuth. XA=4724°5. <A very prominent line. EKvi-
dence and authority as in last case.

22.— Bismuth. A=4705. Ditto. These lines cannot be
mistaken.

23.—-Strontium blue line. A=4607. From flame-spectrum.
B.A. Report, 1884. Liveing and Dewar, Thaleén,
Huggins. |

24.—Ceesium 8. A=4597. B.A. Report, 1884; de Bois-
baudran and Lockyer (4592). de Boisbaudran’s value
was taken, rather to my regret. One of the first lines
got. Flame-spectrum.

25.—Cesiuma. A=4555. Liveing and Dewar; B.A. Re-
port, 1884; Lockyer and de Boisbaudran (4560).
Flame-spectrum.

yes _ Prof, R. Threlfall on the /lectrical

26.—Indium blue line. 2=4509°6. Liveing and Dewar
and Thalén, B.A. Report, 1884. Took Liveing and
Dewar’s number. Tlame-spectrum.

27.—Solar spectrum. X=4405. Rowland’s map. _Schel-
len’s map gives it identical with an iron line. Verified
by spark.

28.—Solar spectrum. 2»=4383°6. As in case of last line
(27).

29.—Solar spectrum. Hydrogen violet. 71=4340°5. Row-
land’s map and vacuum-tube.

30.—NSolar spectrum. =4825-982. A fine line. Rowland’s
map and Phil. Mag. 1889. Picked up from map.

31.—Soiar spectrum G. 2~A=4808-023. Rowland’s map and
Phil. Mag. The subject of a misprint in Rowland’s list
in Phil. Mag. 1889. It is an iron line.

32.—Solar spectrum. 2X=4227. A calcium line given in
Schellen’s map. Well seen on Rowland’s map. Could
not verify from flame.

It will be found that the lines mentioned in this list are
well spaced, and a curve drawn to them will enable most of
the other lines to be set upon by calculation. It is obvious
that all sorts of appliances must be to hand in order to verify
the lines in the first instance, as well as a good stock of the
rarer metals and their salts.

Preparation of Pump-Gauge.—All gauges of closed U-type.
Gauge 1 constructed of tube 5 centim. in diameter, and
3 millim. thick in the walls, tested for evenness, &c. Hach
limb about 20 centim. long, one limb closed at the top and
the other open to the pamp. The bend constructed of thick
tubing having a bore of rather less than 1 millimetre in dia-
meter. This gauge was boiled ont in a good Sprengel vacuum
some twenty times, but I never could get rid of the last
minute traces of gas. I have an idea that the last trace of
gas cannot be got rid of—it can only be reduced asymptoti-
cally. However, the gauge was excellent ; it was painted
black, except for a slit down each limb, and was read (with
the precautions mentioned by Reenault) by one of the Cam-
bridge Scientific Instrument Company’s (Poynting’s) eathe-
tometers from about three metres’ distance. This gauge be-
haved admirably, and I used it during the spectroscopic
work ; in some of the preliminary tube-experiments at a low
pressure, however, a joint broke, and the momentum of the
mercury was sufficient to break the closed end of the gauge in
spite of the constricted bend. Under the circumstances, the
gauge being much better than was required, I made No. 2

Properties of Pure Substances : Nitrogen. 23

similar to it, but of only 1 centim. diameter, and having a
finer constriction of thermometer-tube in the bent part. This
tube was not so good as the last, as it was not gas-free, and
a small correction amounting to ‘half a millimetre or so had
usually to be applied on this account. This correction was
determined several times, and a table of readings and correc-
tions made out. There is no uncertainty as to the readings
beyond about -05 millim., a quantity pees insignificant for
our purpose. This oause lasted till 1892 , when I finally
got tired of applying corrections, and made a new and better
gauge on the same lines and of the same dimensions. ‘This
is still in use.

Lube Pressure-Gauge.—A glance at the Plate will show
that this gauge was similar ‘to the one used by Professor
Thomson and myself i in 1885, with the exception that it was
of glass throughout. A tube of about 2 centim. diameter is
bent into a U-shape, the bend being of tube about *5 millim.
in diameter. The limbsare about 5 centim. long. The mer-
cury is introduced so as to stand about halfway up the wide
tubes. ‘The upper ends of the limbs | are connected to each
other, so that the gauge is really a “ring” space, and the
space above the mercury communicates with the experimental
tube by a filamentary glass tube of from one to two metres in
length. When it is desired to observe the change of pressure
in the spark-tube, the connexion between the space over the
free surface of the mercury in the two limbs is interrupted by
fusing a previously narrowed neck into a solid mass. This of
course allows the pressure in the closed limb to retain its
initial value, whatever that may be; while the pressure in the
open limb varies with the pressure in the tube.

The effect of the metre-long filamentary tube is to hinder
the diffusion of mercury vapour into the sparking-tube; and
this in one cr two experiments was also attended to by in-
cluding a tube filled with clean silver foil between the mercury
and filamentary tube. ‘The filamentary tube, however, never
let enough mercury-vapour in to give a mercury- spectrum at
the lowest pressure at which I worked. Of course the mer-
cury in the gauge was carefully boiled several times in order
to cause any considerable quantity of gas that might have
been condensed to be given off before the exper iment began.
These gauges, of which large numbers were made at one time
and another, were very satisfactory, and when observed with
proper precautions by means of the cathetometer, would cer-
tainly betray a difference of pressure of about °05 millim., all
sources of uncertainty being taken into account.

24. Prof. R. Threlfall on the Electrical

Experimental Spark-Tube.—tThe first successful tube was
furnished with external electrodes and sparked between Feb. 24
and March 2, 1891. Detai's are (pressure 8°8 millim.) :—

h m
Feb. 24. Sparked 1 30 Sparks being long and thin, large
resistance in circuit.
Feb. 25. ee tO:
Feb. 28. » 98 0 Ditto. Then 3 hours 15 minutes
with less resistance.

Mar. 2. » 4 0. The least perceptible discharge.

No effect was noticed at any time. The tube was left for
three days in order that the temperature might reach the
exact value it had when the gauge was sealed, and it happened
that this did not occur for three days. There was still no
effect. This tube was sealed from the pump in series with
the spectrum-tube and is still in my possession.

Tube 2.—After experimenting with many tubes mostly of
the form shown in the diagram (fig. 1), with the armed ends
in mercury cups, a satisfactory tube was got on April 21st.

igo.

YI Vi

The difficulty arose from my determination to have the elec-
trodes white hot for several hours by a preliminary sparking at
about ‘1 millim. before the tube was finally filled with gas and
sealed off. The excessive heating of the electrodes generally
broke the glass. During this time I noticed a thing which
was new to me, but which I daresay is well known, viz., the
ease with which the colour of the fiuted spectrum-discharge
may be made to change. Thus on the 20th I found that at a
pressure of less than 1 millim., and with a very intense dis-
charge from a coil giving 12-in. sparks without condenser, I
could cause the golden-coloured discharge to become pinkish
by heating the tube with a bare flame to about 200° C., a
necessary step in the preparation. The spectrum, of course,
merely showed a shift in relative luminosity from the red
towards the blue end. The action was reversed on cooling
the tube. This could be repeated once or twice. However,
with the next filling of gas the experiment did not succeed at
all,no heating of the tube caused any change in the colour of

Properties of Pure Substances: Nitrogen. DS

the discharge ; and in subsequent experiments only variable
results were met with. The tube in question was finally sealed
off at 9°2 millim., and sparked for six hours without effect.
The next day the sparks were made stronger, and sent through
the tube for four hours; still no effect was produced. The
tube then cracked on the next attempt to spark it.

Tube 3.—April 25. Pressure 9-4 millim. In preparing
the tube I noticed what I always noticed afterwards, viz., that
at about 2-3 millim. the discharge begins by being pink, and
then in a minute or two becomes golden, and keeps so. On
turning off the spark and reducing the pressure to about 1
millim., the same effect is observed. J have noticed this effect
in allthe tubes prepared since my attention was first directed
to it. The sparking of this tube was as follows :—

April 25. 4 hours with the effective sparks described
in the former paper. No effect.

April 27. 6 hours ditto. No effect.

April 28. 4 hours. Sparks of various intensity. No
effect.

April 29. 4 hours. Ditto. Ditto.

This tube was sound throughout, and the result was con-
vineing. It then occurred to me that possibly the mercury
used in our gauges might account for the results obtained by
Professor Thomson and myself in 1886. At that time we
used a gauge fused directly on to the discharge-tube, with
perhaps 10 centim. of 2-millim. tubing between the mercury |
surface and the tube, and with globules of condensed mer-
cury hanging to the walls of the connecting-tube almost up
to the discharge-tube itself. I remember that the glow often
extended down to the mercury.

Tube 4.—Made with a side tube containing some very pure
and dry mercury, so as to imitate our older form of tube.
Pressure 8°5 millim. |

June 11. Sparked 3 hours with effective sparks. No
effect.

June 12. Sparked 4 hours with effective sparks. Hxa-
mined on 15th, when-it showed a just perceptible diminution
of pressure.

June 15. Sparked 8 hours. LHffect increased to about 1-2
millim. In order to try whether large sparks would reduce
the effect, as was formerly found to be the case, I increased
the intensity of the discharge, but did not succeed in producing
any increase of pressure during half an hour (except that due
to rise of temperature). The tube was then carefully exa-
mined, and it was found by holding a sheet of white paper

26 Prof. R. Threlfall on the Electrical

behind it that there was a slight appearance of a bronze-
coloured fog in the tube near the mercury-pocket.

June 16. A strong discharge sent through the tube so that
it became warm to the hand, say 40° C.; the discharge was
kept on for three hours.

June 18. The temperature again being the same as when
the tube was sealed, it was noted that the effect appeared to
have increased by about ‘2 miilim. in spite of the strong
discharge. Two “ gallon” Leyden jars were then included
in the circuit provided with an air-gap, and parallel to the
spark-tube. During two hours’ sparking the effect went on
increasing, and the bronze-coloured stain on the glass grew
deeper near the drops of mercury till it became a black
mirror.

This was of course partly due to the volatilization of the
mercury near the drops. The effect had increased to about
7 millim. by the next morning, when the temperatures had
become uniform.

June 19. Sparked, say, 5 hours. Effect on cooling was
now 7°3 millim., indicating that only about 1:2 millim. of gas
was left in the tube.

June 20. The mirror of mercury compound, which had now
become very black about the narrow tube and in the part of
the spark-tube near it, was heated with the Bunsen flame.
After some heating, say at about 250°C., the film began to
crepitate audibly and emit flashes and sparks of blue flame.
The deposit turned brownish as the temperature rose, the
sides became indistinct, and finally the flash and crackling
noise came on and the film vanished, leaving a clear bright
tube. The process was repeated till the mirror of mereury
had been chased all over the tube ; and even then the gauge
only came back far enough to show a_pressure-difference
of 4°2 millim. in the same direction as before—. e. it only
came back by 3°1 millim. The ends of the tube, where the
the electrodes were fused in, were not heated ; and this may
have accounted for the persistency of the diminution of
pressure. In order to test this the tube was removed from
the mercury cups and placed in an extemporized air-bath
made out of a kerosene tin. Several thermometers were
ranged alongside the tube, and the whole apparatus was
covered by an asbestos cloth. The bath was heated by a
Bunsen burner. A good many rather elaborate readings of
temperature and pressure were taken on June 20, the
temperature rising to about 170° C. in the middle of the
tube and to a few degrees less at the ends. These readings
turned out to have no significance, in consequence of a doubt

Se

Properties of Pure Substances : Nitroyen. 27

as to whether the ends of the limbs of the tube into which the
wires were fused were or were not at the same temperature
as the rest of the tube. However, there is no doubt that the
temperature of the ends was eee 150° C., and yet when all
was cold again it was observed that the effect still amounted
to a difference of pressure of 3°4 millim.

Now a compound of mercury and nitrogen, described as
trimercuramine, was obtained by Plantamour (Ann. Chem.
Pharm. x]. p. 115) by passing ammonia gas over mercuric
oxide. This substance is said to explode on heating, and
Plantamour gave it the formula Hg;N, on the strength of its
behaviour with copper oxide in a combustion-tube, though he
did not analyse it. The formula is, however, probably not
very far from being correct. Plantamour does not state the
temperature at which the nitride explodes, but says that if a
little heap of the substance be placed on a card or piece of
paper, and heated over the flame of a spirit-lamp, the explosion
will occur before the temperature is high enough for the paper
to be turned yellow. My compound cer tainly required a
higher temperature than this to start the explosion ; but it
is possible that its being in a nearly vacuous space, and very
much contaminated with free mercury, may have had some-
thing to do with this. Plantamour’s compound exploded with
a white flame, which was bluish red at the edges; the com-
pound I obtained emitted a brilliant bluish-white light on
explosion. ‘There is some evidence from Plantamour’s paper
that a temperature exceeding 200° C. prevents the formation
of the nitride from mercuric oxide and ammonia gas, and that
the best temperature at which to carry out the synthesis is
150° C. These facts appear to point to the conclusion that
mercury nitride is a dissociable compound ; and the substance
I obtained is probably so, as the continuation of the history of
the tube will show. On June 22 the tube was wrapped in a
good deal of copper gauze, and the bundle so made and into
which three thermometers passed was placed in the air-bath.
The burners were regulated so as to give a stationary tempe-
rature, first of 185°C. and then of 196°C. At the former
temperature the gauge appeared to show that some substance
was still undecomposed ; but there is some uncertainty, from
the ratio of the volume of the spark-tube to the gauge-tube not
being exactly known. Lstimating these volume-ratios, how-
ever, as nearly as pessible by means of external measurement,
and applying the necessary corrections, I found that the
pressure ought to be (as shown by the gauge) 5 millim.
greater on the tube side than on the sealed side. The ob-
served pressure-difference was 5:2 millim.—a better agreement

28 Prof. R. Threlfall on the Electrical

than one had any right to expect. The temperature was kept
constant for a quarter of an hour after the observation, in the
hope of detecting any further change, should it take place; but
the readings remained constant. J am therefore inclined to the
belief that the substance dissociates on heating, and is all de-
composed at a temperature of about 190°C. On June 23rd,
when all parts of the apparatus were again at a uniform
temperature, the original effect had almost returned, there now
being a difference of pressure of 3°2 millim. between the tube
and the sealed space; or, in other words, partial recombination
of the nitrogen appeared to have taken place.

Other matters required my attention at this time, and I did
not get an opportunity to continue the study of the tube till
August13. On this day the pressure-difference was 3°7 millim.,
apparently showing that slow recombination had been going
on. On August 13, 14, 15, and 17 the tube was heated each
day up to about 190°, and curves drawn showing the relation
between the pressure and temperature. These curves did not
show a very good agreement, from the uncertainty as to cor-
rections above mentioned ; and I therefore will only state that
the effect of the heating on the 13th was to reduce the pressure
difference to 2 millim., on the 14th to 1:5 millim., on the 15th
to ‘6. On each day the heating took place during five hours
or thereabouts, and the tube was maintained at its highest
temperature for aboutan hour. On August 17th the tube was
exposed to a temperature of 200° C. for six hours, and then
kept at 110° all night; and then, on August 18th, again
heated to 200° C. for five hours. When the tube was cold, on
August 19th, the effect had entirely disappeared, the mercury
standing at the same height in both limbs of the tube. On
August 21st recombination appeared to have taken place to
the extent of ‘5 millim., and then this disappeared again be-
tween August 21st and September 3rd. No further change
having taken place by September 20th, the tube was finally
disconnected, and the following conclusions were provisionally
noted from a consideration of its behaviour.

1. A compound is formed when the electric discharge is
passed over a mixture of mercury and nitrogen at a pressure
of about 8 millim. The action commencing slowly, and in-
creasing in velocity till it reaches a maximum, then decreasing,
but continuing slowly till at least seven-eighths of the nitrogen
is absorbed, the mercury being in excess.

2. The compound formed is brownish at first, but as time
goes on it becomes black, probably owing to a continual
increase in the quantity of mercury deposited with it.

Properties of Pure Substances : Nitrogen. 29

3. The compound decomposes with crepitation at a tem-
perature of about 200° C. (very rough).

4. The compound is probably identical with the trimer-
curaminé of Plantamour.

5. It behaves as a dissociable compound on heating and
cooling, and can finally be entirely decomposed by repeating
the heating and cooling often enough.

6. An attempt to get the dissociation curve with such
accuracy as would allow the application of analysis failed,
through the want of a preliminary determination of the
relative capacity of tube and gauge.

It now became necessary to repeat the experiment under

Fig. 2.

To gauge, 120 cm. of filamentary tube.

B t i

To pump.<—=
peree | < Inlet for gas.

<-- UD §-01 --->

ee we ee a a a a ee ea me

A
3X |

MERCURY LEVEL 3cer
l
Vv

Inside diameter of main tube 1:5 cm. ; thickness of walls 15 cm,

slightly changed conditions, so that new facts might present
themselves and the previous results be controlled. I decided
to make a tube of such a kind that I could begin by sparking
it so that the sparks only passed through nitrogen, and then,
after a sufficient interval of time and at any convenient
opportunity, introduce mercury with a view to observing the
modified action. In order to vary the conditions, the whole
drying apparatus up to the sulphuric-acid tube was pumped
out afresh and filled with gas, which passed through the
reagents very slowly. This precess occupied two days, one
day and a half it took to exhaust the vessels, and half a day

t

30 Prof. R. Threlfall on the Hlectrical

(5 hours) for the gas to flow in. It will be convenient here
to describe the tube employed, though the dimensions given
are taken from a later experiment, which was supposed to be
a repetition of the one in question ; the dimensions of this tube
may therefore be in error by a few per cent., but the actual
dimensions are not of muchimportance. The ends of the tube
dip down into mercury cups (not shown) so as to protect the
part where the wires enter from leakage. The mercury pocket
in the tube which forms the subject of the diagram (fig. 2) is
attached to the spark-tube by means of a capillary tube 14
centim. long.

This capillary tube was the finest piece of thermometer
tubing I actually happened to have by me, and was, as I should
imagine, about*1 millim.indiameter*. In preparing the tube
after the final filling, the inlet at A is fused off, and when
the proper pressure is reached the pump connexion at B
is sealed, and afterwards, in two or three hours’ time, the con-
necting tube of the mercury gauge.

September 10-19. These days were spent in abortive
attempts to get tubes of the pattern described to submit
to having their electrodes white-hot for two or three hours
without fracturing the glass.

September 19. Tube 5, as described, sealed off at 87
millim,. The mercury was put in hot through a side-tube,
but was not boiled zn setu in order to avoid getting vapour
into the spark-tube. In order to avoid the presence of air-
bubbles between the mercury and the glass, the tube at C was at
first about 8 centim. long, and was drawn down to a fine point,
where it was fused off. The apparatus was then filled with
nitrogen and well heated when containing a nitrogen vacuum,
especial care being devoted to the mercury pecket. Nitrogen
was then admitted at more than atmospheric pressure, and
finally the end of the tube was broken off near © and the
mercury run in as quickly as possible from a fine funnel
reaching to the bottom of the pocket. The tube at C was then
sealed, and the mercury warmed again to perhaps 100° C. and
the visible bubbles displaced, the tube being of course vacuous.

Sept. 21. The mercury in the gauge was accurately at the
same height in both limbs. Sparked for five hours with the
best kind of sparks ; no effect.

Sept. 22. Sparked four hours with an air-break in cireuit
just sufficient to stop the spark but not the brush-discharge
across the air-break. It was noticed that luminosity went

* This capillary tube was part of the later arrangements. In the tube
under discussion its place was taken by a tube 2 millim. in diameter and
only about 6 centim. long.

Properties of Pure Substances : Nitrogen. al

down the tube to the mercury, and was much increased by
touching the outside of the tube near the mercury. This dis-
charge, ‘of course, was small compared with the discharge in
the main tube. There was no effect on the gauge.

Sept. 23. Sparked with rather large sparks 6} hours. No
effect. ;

Sept. 24. Sparked strongly, so as to make the tube warm,
for 64 hours. No effect.

Sept. 25. The mercury boiled up into tube. This led to
the gauge showing a real increase of pressure of a little less
than *1 millim.; T attribute this to gas from the sides of the
tube between it and the mercury. Sparked strongly for
52 hours; when all was cold the pressure excess had grown
to about *2 millim., i.e. in a direction contrary to the one
expected.

Sept. 26. Discharge on for 64 hours fairly strong, so as
to warm tube perceptibly. The gauge then showed the same
pressure on each side.

Sept. 27. A wet paper band round that part of the tube
where the mercury was most thickly condensed. Sparked
four hours (?). No effect.

Sept. 28. Ditto 3 hours. No effect.

Sept. 29. Faint sparks for 5 hours ; wet paper band, as
before. No effect.

Oct. 1. Temperature being more rigorously equal, and
gauge carefully tapped, there isa shrinkage of about *1 millim. |
Sparked six hours with faint sparks and wet paper round
tube. No effect

Oct. 2. Strong current on 6 hours. Looking the next
day (Uctober 3rd), a faint yellow tinge was observed round
the mercury drops, and the gauge showed ‘8 millim. difference
of pressure. Sparked hard 6 hours; the mercury was now
obviously attacked, and when examined on October 8rd it was
found that the pressure difference amounted to 3°2 millim.
Sparked 3 hours with full discharge ; this increased the effect
to 6 millim., and in another 44 hours the discharge had become
splendidly golden, the resistance in the tube small, and the tube
was fluorescing strongly (a sign of mercury vapour). Effect
increased to about 7 millim. The experiment was then inter-
rupted by the cracking of the tube.

No opportunity for examining the deposit occurred till
November 16th, z.e. for more than a month. The tube was
then cut into bits, and it was observed that the deposit had
become partly incrusted with some whitish incrustation. On
trying to produce an explosion the experiment failed, and it
was obvious that the film had quite decomposed. It is to be
noted that the mercury was only attacked with difficulty.

oo Prof. R. Threlfall on the Electrical

Tube 6.—Dec. 5, 1891. This is the tube shown in fig. 2.
All drying apparatus exhausted twice; tube prepared by
a steady discharge during December 11th; left till 14th to
test for leaks, when it was found that the whole apparatus
was air-tight. Tube again sparked hard all December 14th
with best pump-vacuum attainable. Electrodes at a bright
red heat for 15 hours ; mercury separated by long tube and
boiled in pocket. Sealed off at about 6 millim. pressure on
December 15th.

Dec. 16. Sparked 2 hours through capillary water resist-
ance ; tube slightly warm. No effect.

Dec. 17. Sparked so as to produce a yellow glow for
3 hours and by small blue sparks for 1 hour. No effect.

Dec. 18. Sparked with fairly strong discharge for 8 hours.
Tube too warm to read: so left till December 3]st, when it
was found that the tube pressure had diminished by *2 millim.
This led to an examination of the tube by hoiding a sheet of
white paper behind it; and it was found that a bronze-coloured
film had formed where mercury had condensed near the top
of the capillary tube. ‘The mercury within the sphere of action
was only the most minute trace. Sparked 3 hours and on.

Dec. 22. Effect about :3 millim. Sparked for about an
hour, and then on careful examination it was found that the
glow was actually passing down the tube to the mercury. It
was clearly of no use to go on with the experiment in this
way, and consequently the mercury was boiled into the tube
and the spark turned on. ‘The effect diminished during the
boiling from °35 millim. to ‘3 millim. Sparked then for
5 hours ; effect increased to 1°2 millim.

Dec. 26. Sparked 4 hours. Effect 2-4 millim.

Dec. 27. Ditto 3 hours. Hffect 4°3 millim.

Dec. 28. Sparked for one hour, when it was noticed that
the tube-resistance had increased and the gauge showed 5°38
millim. of effect ; hence the tube is nearly empty. On first
turning on the spark, the illumination began by being strong -
for about one minute. The strize were well marked, and the
mercury spectrum prominent. After about one minute the
luminosity diminished to that corresponding to faint blue
sparks. In twenty minutes the tube was again hot and fairly
luminous, and continued with luminous sparks and rising tem-
perature for 35 minutes: the gauge showed that the rise of
temperature (?) was producing an increase of pressure. Tube
cooled for one hour, when it was found that the excessive
sparking had at last cracked the tube near the platinum wire,
and that some mercury had been drawn in. The tube was
then cut into bits, and one was heated in a test-tube in a

Properties of Pure Substances: Nitrogen. 33

glycerine bath with the same precautions exactly as one uses
in taking a melting-point. I extract the following account
from my note~book verbatim:—“ I could not detect any change
till about 230° C., at which temperavure quiet decomposition
set in, and was complete and the tube clean at 235°. A con-
siderable portion of the thermometer stem was outside the
bath, though it did not begin to register till above 110°.
Making all allowances, the temperatures might on this account
have been anything less than 5° above those given. The tem-
perature rose very slowly, and the glycerine was kept well
stirred by a crescent-shaped stirrer of zinc. Hxperiments on
other bits of the tube were made by heating them in the bare
flame. In two of these (out of about four) there was a distinct
crepitation, but I did not note any flash, though that the
decomposition when once started ran very rapidly over the
whole mirror was well seen in all the experiments. The deposit
suddenly brightered with a puff of vapour. I could detect no
nitrous smell. The temperature must heve been 200° C. in all
eases. The platinum deposits were enormous, and the elec-
trodes torn up in all directions as described by Hdison.”
These experiments may be considered to settle the question
of the cause of the effect observed by Professor Thomson and
myself in 1885 and 1886. No trace of the effect was ever
found unless the mercury was attacked ; and, contrariwise, the
mercury was never seen to be attacked without the “ effect”
making its appearance. It is curious to note the difference in
the readiness with which the action can be brought about, even
when all the circumstances of the experiments appear to be
identical. It is for this reason that I imagine that the reaction
requires the intervention of minute traces of some third sub-
stance, and the actual amount of these traces differs in different
experiments. When the reaction once commences it goes on
with increasing rapidity till near the end, and apparently
faster the more powerful the discharge. One experiment
appears to indicate that even after the trimercuramine (?) is
decomposed its constituents are in a state of “labile”’ equi-
librium with respect to one another, and combine slightly or
separate according to some set of circumstances which I cannot
assign. It is curious, too, that the dissociation should be so
irreversible. Unless the mercury vapour continually liberated
is removed from the sphere of action—by combination with
the platinum deposit, for instance—I cannot understand the
effect of repeated heating ; and, indeed, I consider that the
suggestion just made is very possibly the true explanation.
The condensation of nitrogen, therefore, at ordinary tem-
peratures has not been observed ; but it is possible that it may

Phil. Mag. 8. 5. Vol. 35. No. 212. Jan. 1893. D

b4 On the Electrical Properties of Pure Substances.

occur at low temperatures. Jor this purpose | prepared

Tube 7, which is figured in the Plate in the position
it occupied before it was sealed off. This tube was prepared
with even more than the usual care. Thus, the cleaning
of the tube occupied two days and the final rinsing was
accomplished by means of some thrice-distilled water from
the platinum and gold still. This water ran into the tube direct
from the still. The electrodes were prepared by sparking
during five hours witha discharge sufficient to make them red-
hot, during which time the tube was thrice filled and exhausted.
The next day the tube was heated twice, and on each occasion
about 500 cub. centim. of gas were passed through it; after
which it was exhausted as far as possible (in an hour), and
then the final charge was allowed to enter. The tube was
sealed off at 8°7 millim. pressure, and then put in salt and
pounded ice and kept at —14° C. by means of frequent stirring
and the aadition of fresh ice and salt. Sparked 2 hours with
effective sparks: no effect. (The effect was looked for the
next day, when the temperatures were equalized, but was not
observed.) |

Jan. 2. Sparked for 2 hours at about —10° C., all kinds of
sparks. No effect.

The filamentary tube was then replaced by a wider one, as
it was observed that the gauge only acted very slowly owing
to the extreme fineness of the filamentary tube. The spark-
tube then required to be pumped out and prepared afresh,
except for the heating of the electrodes, which, however, inci-
dentally took place.

Jan. 4. Sparked 13 hours at —10°C. No effect.

Jan.6. Sparked 7 hours ata mean temperature of — 8° C
various sparks. No effect.

Jan. 7. Observed again, at very uniform temperatures.
Still no effect.

Jan. 12. Ditto.

The conclusion is that no effect is produced on nitrogen, so
far as condensation goes, by sparking it at a temperature of
about —10°C. and at a pressure of 8:2 millim.

s
ce)

Summary of Results.

1. Nitrogen can be prepared by a continuous process in a
state of great purity.

2. Nitrogen so prepared cannot be caused to condense by
any available kind of spark down toa temperature of —10° C
and a pressure of about 8 millim.

3. When mercury is presen:, a compound of mercury and

Refraction of Rays of Great Wave-length. 35

nitrogen is formed. This compound is probably identical »
with the nitride obtained by Plantamour.

4, The rate of formation of this nitride, other things being
the same, is so irregular as to suggest that its formation is due
to the interaction of an otherwise inappreciable trace of some
other substance.

5. This compound is dissociable ; but under the circum-
stances of the experiment the dissociation process is not
entirely reversible, since sufficient heating will permanently
destroy the compound.

6, There are changes in the appearance of the discharge in
nitrogen which can be brought about by very slight variations
of temperature, and possibly of electromotive force, for which,
so far as I know, no explanation is at present forthcoming.

Sydney, August 5, 1892.

II. On the Refraction of Rays of Great Wave-length in
Rock-salt, Sylvite, and Fluorite. By Heinrich RuBens
and Bens. W. Snow™*.

[Plate IL]

N volume xl. of Wiedemann’s Annalen one of the present
authors recently described a method whereby a know-
ledge of the dispersion of rays in the infra-red may be easily
obtained. With the aid of this device the dependence of the
index of refraction upon the wave-length was determined for
sixteen materials ; viz. for nine different samples of glass, for
water, carbon disulphide, xylol, benzol, quartz, rock-salt, and
fluorite. Inasmuch as in this paper is given a minute de-
scription of the methods employed, it will suffice here briefly
to refer to the main features of the method of procedure
followed in the present determination.

The rays from the zirconia burner of Linnemann, after
being reflected from the front and the rear surfaces of a thin
plate of air, enclosed between two parallel glass planes, were
then concentrated upon the slit of a spectrometer, by which
means two beams of light were produced, capable of mutual
interference, so that the otherwise continuous spectrum of the
incandescent zirconia plate was crossed by a series of vertical
interference-bands. The wave-length » of each such dark
band, multiplied by a certain whole number m, always equals
the product of twice the thickness d of the layer of air and
the cosine of the angle of incidence? of the rays. With the aid

* Communicated by the Authors.
D 2

36 HH. Rubens and B. W. Snow on the Refraction of

of the Fraunhofer lines the wave-lengths of the interference-
bands were determined for the visible portion of the spectrum,
and from these data were calculated the order m of each dark
band and the product K=2dcosi. The knowledge of these
two constants proved, then, sufficient to determine also the
wave-lengths of the interference-bands in the infra-red.

The positions of these latter were obtained by allowing the
sensitive filament of a linear bolometer to wander through the
spectrum, and plotting the observed galvanometer-deflexions
as a function of the angular deviation. ‘The interference-
bands are then recognized as minima or maxima in the curve.
In this way, for a series of angular deviations may be deter-
mined the corresponding indices of refraction; that is, a
number of points in the n—2 plane determined, which, when
joined by a smooth curve, give the curve of dispersion for the
material examined.

In the majority of the bodies thus investigated, the limit of
the region in the infra-red capable of being explored was
prescribed by the absorption, which increases rapidly with
increasing waye-lengths. In two cases alone, viz. when
working with rock-salt and with fluorite, were the investiga-
tions discontinued at wave-lengths ~X=5°7m and A=d'3yu
respectively, before the region of strong absorption was
reached. This was rendered necessary by the fact that the
apparatus employed proved to be insufficiently sensitive to
measure the exceedingly feeble energy found in the spectrum
of the zirconia burner at these long waye-lengths.

As a means of continuing the investigation beyond this
point two ways of improvement suggested themselves. At
first we thought it possible to increase the energy of the source
of light, but all endeavours to attain this end proved of no
avail. The use of the electric arc for this purpose was, after
a short but thorough trial, discontinued. Even are lamps of
unusually good regulation, when supplied by the almost per-
fectly constant current of the Berlin Central Station, gave a
radiation too fluctuating to be used in place of the zirconia
light. The regulation of the are by hand was also tried, but
also without success. The use, moreover, of a zirconia burner
of nearly double the dimensions of the former resulted in only
a feeble increase in the energy, while a series of new diffi-
culties was thereby introduced, such as the melting of the

latinum cell, a greater consumption of gas, &. We con-
cluded, therefore, for the further investigation, to retain the
source of light in its original form, and to make better use of
the energy here at hand by increasing as far as possible the
sensitiveness of the measuring apparatus.

—

Rays of Great Wave-length in Rock-salt, Sylvite, §e. 37

The first change toward the accomplishment of this end
was efiected in the substitution of two plane surfaces of larger
dimensions in place of the reflecting plates formerly used.
For this purpose the optical firm of Carl Zeis, of Jena, most
generously provided us with two plates with plane surfaces,
4 centim. square and 1 centim. thick, one of crown glass and
the other of fluorite. The plates were set in metal frames,
and the distance between them regulated by a system of
screws, as in the former case. With the exception of the
extreme edges both plates were ground to a truly plane sur-
face. A rectangular opening in a diaphragm, placed in the
path of the rays, allowed only light to enter the slit of the
spectroscope which had been reflected from the central portion
of the plates. The interference-bands thus produced were
unusually sharp, as can be seen from the pronounced minima
of the curves in figs. 1, 2, and 3 (Plate I1.), which represent
the three different energy-spectra. Hardly need it be men-
tioned that in the following experiments the entire optical
system consisted wholly of rock-salt and fluorite.

The delicacy of the bolometer was increased chiefly by using
a galvanometer of the highest degree of sensitiveness which one
of us had constructed, and which will be described in detail in
a forthcoming paper. The coils of the galvanometer in series
measured 140 ohms resistance. When the period of the
needle was reduced for the single swing to 10 seconds, one
millimetre deflexion on the scale indicated a current of
1:3x10-" ampere. With this degree of astaticism the zero-
point of the needle was perfectly constant.

The bolometer with which the following determinations
were made is described as No. 2 in the previous paper. It
consisted of two strips of platinum, 12 millim. long and
0:05 millim. wide, each having about 80 ohms resistance,
only one of them being exposed to radiation. With the aid
of the new galvanometer we were able to trace a sensitiveness
of 0:000003° C. per millimetre deflexion. A standard candle
one metre distant produced a deflexion of 400 milli.

With the exception of the changes here mentioned all
pieces of apparatus were identical with those formerly de-
scribed. The relative positions, moreover, of the instrument,
as well as the manner and the order in which the operations
were performed, were retained unchanged. We can therefore
pass at once to the results of our observations.

Measurements were made upon the three materials so well
known for their diathermanous properties—rock-salt, sylvite,
and fluorite.

38 H. Rubens and B. W. Snow on the Refraction o7

I. Rock-salt.

We had at our disposal a prism of this mineral having
a triangular base 34} centim. on each side and 43 centim. in
height. Before being used the prism was freshly polished
and its refracting angle redetermined. ‘The observations
with the bolometer gave the energy spectrum represented in
fig. 1, Pl. Il. The positions of the maxima and minima
were corrected, as in the paper cited above, with the aid of
the enveloping curve, whereby the points of contact of the
two curves were used without further modification as the
characieristic points in question. As the theory shows, this
method givesa closer approximation to the quantities required
than the method by construction given in the former paper.
But little weight, however, is to be attached to the superiority
of this modification, as both methods lead to results which are
identical to the fourth decimal place.

Inasmuch as the present investigation was undertaken ex-
pressly for the purpose of extending measurements as far as
possible into the infra-red, we were compelled to use a com-
paratively thick layer of air for reflecting the interfering
beams of light, which brought the interference-bands in the
spectrum very near together. It was quickly found, how-
ever, that even the narrow width of the bolometer and the
impurity of the spectrum, caused by the aberration of the
lenses, placed a limit beyond which the further reduction of
the breadth of the interference-bands could not be carried.
With the feeble dispersion of the materials used, this limit
was practically reached when the visible spectrum was crossed
by seven or eight interference-bands, which gave a value to
the constant K=2d cosz of about 8-54. According to this,
the minimum of the first order, which is the farthest possible
attainable point in the infra-red, has a wave-length A=8-5p.
Then follow the maximum of the second order and the corre-
sponding minimum, which have wave-lengths A=5°7p and
A==4°3u respectively. Although the curvature of the curve
of dispersion in this region is slight, it seems to us, neverthe-
less, desirable to add, for greater accuracy in our measure-
ments, other possible points to the small number already
obtained. In order to attain this end, we found it advan-
tageous to use not only the corrected positions of the maxima
and minima and their corresponding wave-lengths for plotting
the curve of dispersion, but also the points of intersection of
the energy curve G=/(a) (see fig. 1) with the curve of
mean energy R=/(«), since the wave-lengths corresponding
to the abscissee of these points are easily calculated. This

Rays of Great Wave-length in Rock-salt, Sylvite, §c. 39

latter curve might have been observed directly, had the
distance between the plates enclosing the reflecting layer of
air been sufficiently increased. This curve R=/f(a), which
represents the distribution of energy when no interference is
present, can be constructed, however, with sufficient accuracy,
when at each point an ordinate is erected equal to the mean
of the ordinates of the corresponding points of the enveloper,
Pand Q. If the curve G=/(a) is intersected at any point
by the curve R=/(a), then the amplitude for the abscissa of
this point must have the same magnitude which it would have
attained had a superposition of the energy of the two beams
taken place without interference.

The vibratory motion of the two beams whose amplitude
and period are A and T' respectively, may be represented >
the equations

; a
y=Asin Qa 7 x)
Ie =e
Ygz= A sin 2a ( 2 gw i

They unite to form the ray

(K+ postr ect
ca fyiN e an Tg e 1 a a
Bee ETO T x

ra a
=2A sin™© sin 2 (4-2),

It follows from what has been said above that, for the

abscissa of the point of intersection of the two curves R and

G, the amplitude of the beam Y, viz. 2A sin a must equal
+A V2. dis accordingly determined from the equation
sin as =+35 V2,

wmK w 389 Sm (Qn+1)7

ee ee ae 2

where n is any whole number. The wave-length, therefore,

of each point of intersection is given by the equation

_ 4K

~ Qn+1:
A knowledge of the order of the adjacent maxima and
minima gives at once an interpretation to the quantity x. If

40 H. Rubens and B. W. Snow on the Refraction of

the point of intersection in question lies in such a way that
the adjacent minimum (mth order) lies on the side of the
longer wave-lengths, and the adjacent maximum on the side
of the shorter wave-lengths, then »=2m.

- The introduction of these points in the calculation of the
curve of dispersion made it possible for us to conduct the
observations with interference-bands as broad aswerenecessary,
and at the same time to obtain a sufficiently great number of
points to enable us to ascertain the character of the curve of
dispersion with nearly the same degree of accuracy as in those
ee of the spectrum lying but little beyond the reach of
the eye.

At this point mention should be made of a peculiarity of
the energy-curve, which may be observed in the drawing
(fig. 1). The deflexions of the galvanometer, at the point of
the last minimum a,,, not only sink to zero, but even assume
negative values. The cause of this singularity, which also
appears to a smaller degree in the energy-curve of fluorite, is
to be found in the fact that the second unilluminated arm of
the bolometer, which was placed in the apparatus within a
casing of hard-rubber, notwithstanding this covering received
upon its surface a greater amount of energy than the first
arm, which was exposed to the direct radiation. The plausi-
bility of this explanation is increased when we remember that
the covered resistance is then at a portion of the spectrum
in which the mean energy is 50 times greater than in the
neighbourhood of the minimum ay, and that ebonite is not
opaque to thermal radiation of great wave-length.

In the following Table are found the results of the observed
indices of refraction and wave-lengths. The first column,
entitled “ Name,” gives the quality of the characteristic point
in question, as Fraunhofer line, minimum (a), maximum (5),

‘or point of intersection (c) of the curves G and R; the second

column contains the angle of deviation « as measured on tue
graduated circle ; the third contains the index of refraction n,
calculated from the refracting angle @ and the angle of
deviation « according to the formula

eee
2
=—$—=— -
ing
the fourth column contains finally the wave-length which is
calculated from the order m of the interference-band and the
constant K=2dcos?. The curve of dispersion plotted from

the data of this Table is found in fig. 4,a.

Rays of Great Wave-length in Rock-salt, Sylvite, Sc. 41

TABLE I.

Refracting Angle of the Rock-salt Prism, 6=60° 2’.
K=8°307p ; a, is 11th Order.

Name. at, Ne Xr.
titan 4 p.

ae @ 37 15607 0-434
pe a 5g 15531 0-485
eee... | 7 15441 0-589
7 a 40 47 15404 0:656
a... 29 15370 0-755
a 222 15358 0-790
we. 164 15347 0-831
ER A... 114 15337 0:876
po... 7 15329 0-923
ts oe oe 4 15321 0-978
(a 39 58 15313 1-035
eile. n: 544 15305 1107
oe... al 15299 1186
Lao ATR 15293 1-277
sine A4 15286 1:384
ae Al 15280 1511
oe... 38 15275 1-660
(cee 35 15270 1-845
7 32 15264 2-076
Dee i. 28 15257 2:372
Annas Selesinciste-r's 223 1:5247 PATA
oe . 18 15239 3-022
eee 133 15230 3:320
oie oe 7 15217 3:690
(ag ee 2 15208 4:150
a... 38 56 . 15197 A745
i ee 49 15184 5-540
Des... 373 15163 | 6-647
cn 4 15138 | 8:307

It is well known that Professor Langley*, by a method
wholly different from the one here described, was able to
follow the dispersion in rock-salt to a wave-length A=5-du.
He found, in these experiments, that the curve of dispersion
from about X=2yp on followed very nearly a straight line.
Owing to the fact that even with the elaborate means at
hand he was unable to extend measurements by his method
farther than this in the direction of the long wave-lengths, he
concluded to extend this straight line throughout the still
more distant region of the infra-red in which his observations
were taken.

Many theoretical objections are at once suggested by so
extensive an exterpolation. Among these criticisms may be

* Ann. de Chim. et de Phys. [6] ix. p., 483 (1886).

42 HH. Rubens and B. W. Snow on the Refraction of

mentioned one in particular, that, from a definite wave-
length on, the indices of refraction would assume negative
values, which points to an utter impossibility. There re-
mained, however, the possibility that within the limits of
Professor Langley’s measurements of energy, the straight line
exterpolation gave results which were at least a first approxi-
mation to the true value. A glance at the curve (fig. 4, a)
shows, on the other hand, that in reality this is not the case.
Indeed it is true that our own curve of dispersion tends
toward a straight line until a point is reached almost as distant
as A=5u; but at \=5y the curve begins gradually to lessen
its inclination to the horizontal axis of wave-lengths ; and at
N= 8yu the effect of this curvature is so considerable that a
straight line exterpolation carried from A=5u on to this
point would introduce an error in the determination of wave-
length not less than lp. es

In the following Table a comparison is made- between our
results and those of Professor Langley. It is to be noticed
that his curve, as far as this is plotted from his observations,
agrees fairly well with our own, but that his values given by
exterpolation differ widely from those observed by us, and
that their difference increases as the wave-lengths become
longer. There are also added here for completeness the data
obtained from the previous paper. That an easier com-
parison may be made with Langley’s figures, the wave-lengths
selected increase by multiples of Ap>=0°589u.

TaseE If,
3 :
7 i) ube a zs
Wave-length. cancion (uuiene: i rane pret ey
Be

1, X,,=0°589 | 15442 | 1:5441 1-5441 00001
2 — tie) Lbebl | 1-5300 1°5301 0
Se ion 1 O22 1:5269 15272 1)
4. d,=2856 | 15254 | @|° 1-253 15256 —0:0002
5. A, = 2945 | 15248 \ gs 15241 1-5240 +6°0003
6. ,=8'5384 | 15227 Sy 1°5227 15226 1
ke tla)» Sl -ozi5 |” 15214 1-5212 3
8. A,=4712 | 15201 1-5202 1°5200 1
SNe oS0l-: 1 5186 ) 1:5189 1:5188 —0:0002
10. 4,=5°890 | 151724 3 ie 15177 5
11. 4,=6-480 | 15158 | ¢ 1:5166 8
12. Ap=7070 | 15144 \'S 15157 18
13. Ap = 7°66 15129 | 2 15148 ten
14. ’p=S25.- | 15115 J > 1:5138 28

a i

Rays of Great Wave-length in Rock-salt, Sylvite, §c. 43

The values, therefore, attributed by Professor Langley* to
the wave-lengths in that region of the spectrum lying be-
tween A=( and A=5y are undoubtedly correct. Beyond
this limit, however, at least as far as X=8r3y, the values
assumed are too small, but it is not impossible that when still
greater wave-lengths are reached the sign of the error may
change. ‘The results, nevertheless, of his observations remain
of the greatest interest, since it will be easily possible to apply
a correction to the wave-lengths as soon as the dispersion
in rock-salt can be followed to sufficiently small indices of
refraction.

Sylvite.

The behaviour of rock-salt is in every respect similar to
that of the mineral sylvite, to which it stands in close chemical
relation. There was placed at our disposal a prism of this
material, 14 millim. at the base and 20 millim. in height.
The surfaces of this prism were so well polished that the
refracting angle could be determined to within 0°5 minute.

In fig. 2 the observed galvanometer-defiexions are plotted
as functions of the angular deviation of the arm of the bolo-
meter. Hrom this curve is computed the table of dispersion
in the manner described above. Corresponding to this is
plotted the curve of dispersion (fig. 4, b).

Tasxe IIT.
Refracting Angle of the Prism of Sylvite, 6=59° 54’.
K=8:022 3 a, is 10th Order.

|

Name. | a. N. r. Name. a n. r.
J ae ee REY 2 | URE aE aS ore S|
| pe
Oh jul : Q 4 “&

Hy ...| 387 30 1:5048 0:434 OR phe a1) 14766 1:458
a es ee 36 55 14981 0:486 UR xacase 23 | 14761 1:603
eee ste 133] 1:4800 0589 Dig asec 34 594) 1:4755 1-781
Crees 35 57 | 14868 | 0-656 Ge terae 564| 1:4749 | 2-005
Gy icles ol 1:4829 0:802 Greta ss 53 1:4742 2°291
Dips ac 32 14819 0°845 Gi Nitec 48 1-473: 2-673
Gi. Zi 1:4809 0°893 Op Seas 43 14722 3°209
(Di Seem 234 | 1:4802 0:944 CML 404} 14717 3561
Di donniss 20 1:4795 1:003 Gigineee sn 38 1:4712 4011
ee 164| 14789 | 1-070 || c, ...... 362) 1:-4708.| 4577
Oks winis«' 13 14782 1:145 ORR gi 32 14701 5345
Orettens 10 1:4776 1:234 Che tee 28 1-4693 6:412
ae 73| 14771 | 1387 || a, ..| 22 | 14681] 8022

* Langley, Sill. Journ. [8] xxxi. pp. 1-22, 1886; further [3] cai
pp. 88-106, 1886, and [3] xxxviil. pp. 421-440; Phil. Mag. xxvi. p. 505,
1888. The same is true of t he paper of Angstrém, Ofversigt af Kongl.
Vet.-Akad, Forhandl. ix. p. 549, 1889, and vii. p. 851, 1890, and W.
Hi. Julius, Are? Néert, i, pp. 310-384, 1888.

44 H. Rubens and B. W. Snow on the Refraction of

A study of this curve shows that the dispersion in sylvite,
which in the visible spectrum is only slightly inferior to that
in rock-salt, decreases in a similar manner but far more rapidly
than in the latter mineral, so that at wave-length A=8y the
dispersion is only about one third of the corresponding
dispersion in rock-salt.

Notwithstanding the great durability of this material, and
its permanence in moist air as well as its almost perfect trans-
parency to thermal radiations, the exceedingly rapid decrease
in the dispersive power of sylvite renders this substance not
so well adapted for experiments involving the use of prisms
as rock-salt, whose surfaces are only with difficulty kept
perfect. In the construction of condensing lenses this
difficulty does not occur.

Fluorite.

The prism here examined is the same one which was used
in the former investigation. The value of the refracting
angle was redetermined and was found to agree very closely
with the observations previously made.

For a long time we tried in vain to measure beyond wave-
length X=3'5 pw, the energy-spectrum produced by the fluorite
prism. The results of the previous observations show the
cause of our failure to be due to the fact that, after a region
of comparatively feeble dispersion, the dispersive power of
fluorite increases and the energy in this portion of the spec-
trum becomes proportionally weaker. In order to make
further advances, we were finally compelled to open wider
the slit of the spectrometer at those places where the radiant
energy sank below a measurable quantity. The repetition of
this device enabled us to reach a wave-length in the infra-red
greater than X=8y. In the curve shown in fig. 3, which
represents the observed distribution of energy produced by
the fluorite prism, the slit was twice opened ; the first time
from 0:1 millim. to 0°4 millim. when the arm of the bolometer
was at a deviation «=380° 10’, and a second time from 0:4
millim. to 1:0 millim. at an angle of deviation «=28° 50’.
By this means the deflexions of the galvanometer were
increased fourfold and tenfold respectively. Owing to the
greatly increased dispersion and the corresponding increase
in the breadth of the mterference-bands, this change in the
width of the slit did not materially interfere with the sharp-
ness of the bands in this region of the spectrum. Inasmuch
as only one side of the slit was movable, a correction had to be
applied to the reading of the arm of the bolometer when the
slit was opened. :

The distribution of energy, as shown in fig. 3, gives a curve
whose character is wholly different from the representation of

Rays of Great Wave-length in Rock-salt, Sylvite, §c. 45

the energy-spectra produced by rock-salt or sylvite, given
in figs. 1 and 2. While in these latter the breadth of the
interference-bands increases only slowly as the extreme infra-
red is reached, amounting finally to hardly more than double
the smallest value, the breadth of these bands varies in the
energy-spectrum, as given by the fluorite prism, from
5 minutes to more than 24 degrees. Corresponding to this
peculiar characteristic in the energy-spectrum of fluorite, the
quality of the dispersion in this mineral is quite different from
that of the materials previously considered.

In the following Table, which contains these data, the indices
of refraction are given only to three decimal places. As a
result of the very considerable breadth of the interference-
bands, it is impossible to locate the position of the cha-
racteristic points with the precision attainable in other cases.

TABLE LY.

Refracting Angle of the Fluorite Prism, 6=59° 593’.
K=8:070,; a, is 10th Order.

Name. a. Ne Ar. Name. a nN. d.
ay) ‘ie Qt le?
Bly ees!) 32-5 1:43898 0:434. Getenne: 30 59 1:4267 1-466
de ered ol 52 1:43872 | 0°485 CU ass 554 | 1:4260 1613
Dee Be 36 1:4340 0-589 Oe 51 1:4250 1-792
Cie. 29 1:4325 0:656 Ca 46 1:4240 2-019
Cerin. 19 1:4307 0:807 OF ee 33 14224 | 2-303
Dats. iW 1:4303 O;850) iP aiicess: 29 1:4205 2°689
Open iia 142; 1:4299 0-896 Oana ire 14174 | 3:225
On ese 12 1:4294 0:950 Cie cee 29 46 14117 4°035
Ga easis 10 1:4290 1:009 Ouran 29 1-408 4°62
i ee 8 1:4286 1-076 Oh eipons 4 1:403 5°38
Grosses-| 6 14281 L152 OR ihe 28 30 1°396 6:46
Bit ate 4 14277 AO RE ae 8 eel oe 1:378 8:07
Gros 2 14272 | 1:345
|

The curve of dispersion, shown in fig. 4, ¢, exhibits more
graphically than this table the peculiar character of the dis-
persion. From this it is seen that the dispersive power of
fivorite decreases as far as A=2 w and then gradually increases,
reaching at X=8y a value only slightly inferior to the value
of the dispersion in the red.

Compared with rock-salt and syivite, the dispersion of
fluorite in the visible spectrum is exceedingly small and
unusually great in the infra-red; so that this material is
peculiarly well adapted to the production of prismatic heat-
spectra, an advantage which is still further increased by the
ease with which it can be worked and by the permanence of
its surface in the air.

Physical Laboratory, University of Berlin,

June 1892,

lia a

ILI. Notes on the Construction of a Colour Map.
By WAuTER Batty, M.A.*

iL is my paper on this subject, read before the Physical

Society on April 8 last}, in discussing the method of
plotting out the curve giving the mixtures of two spectrum
colours, I stated that points in the curve lying in the ab-
normal or imaginary regions could not be determined by
experiment. This I now find is a mistake.

Let 8, and 8, be spectrum colours, of which the mixtures
are to be represented by points on the curve. The part of
the curve lying in the imaginary and abnormal regions is
obtained by subtracting light of one colour from light of the
other colour, and equating the resulting colour to the mixture
(if I may use the expression) obtained by subtracting white
from some other spectrum colour 8S.

We have

MS, —mS.=S—aw.

This equation does not represent any possible physical ex-
periment, but it may be transformed, without altering the
value of any of the quantities, into

S) + Ngo = Ri + aw.

This last equation means :—Make a colour-patch of 8 and
S,, and a colour-patch of 8; and W, and vary the quantities
of 8), S:, and W until the two patches are similar in colour,
and then measure the quantity of white. A line drawn to
the left from the position of 8, and proportional in length to
the quantity of white, will define the position of the required
point in the curve.

2. In the map the region on the right of the line of spec-
trum colours is occupied by all the colours obtained by mixing
spectrum colours and white. I suggest that this should be
called the Spectral Region. The equation. for determining
points on the mixture curves in the Spectral Region is

nS + NoSo= S +auW.

The region to the left of the abnormal and imaginary
regions is occupied by colours complementary to those in the
Spectral Region. I suggest that this should be called the
Complementary Region. The equation for determining points

* Communicated by the Physical Society: read October 28, 1892.
t+ Phil. Mag. June 1892, p. 496.

Mountain-Sickness ; and Power and Endurance. AZ
on the mixture curves in the Complementary Region is
Ss =e nS, + Noe =cW.

The equation for determining points on the mixture curves
in the Imaginary and Abnormal! Regions has just been shown
to be (for one part of the curve)

s + Nye = N94 + aW,
and it is obvious that for the other part it will be
S -- nS, Vise + aW.

8. In defining a colour as compounded of a spectrum
colour and white, we have to determine both quality and
quantity of the white light.

A colour may be defined by three spectrum colours by
means of the equation

29; + Ngdo=nz383+aW,
or of the equation
N94 + Nee + N33 =avW.

The colour is that obtained when a patch formed in ac-
cordance with one side of the equation is made identical with
a patch formed in accordance with the other. In this case
quantity of white need not be defined, but quality must be
defined.

If a colour be defined by four spectrum colours the defini-
tion is independent of any convention as to the quality of
white light. Let 8,, S:, 83, 8, be four spectrum colours
whose waye-lengths are in oer of magnitude, then the
equation

19, +7393 = Ngdeot+ 484

defines a certain colour, which can be obtained by making a
patch of S, and $3 identical in colour with one of S, and 8,

TV. Mountain-Sickness ; and Power and Endurance.
By R. H. M. Bosanquet, /.A.S.*

HE account of mountain-sickness at great altitudes,
given in Mr. Whymper’s work, ‘Travels amongst the
Great Andes of the Equator,’ is of great interest. On reading
it, it appeared to me to suggest a simple explanation of the
occurrence of mountain-sickness under the circumstances

* Communicated by the Author,

48 Mr. R. H. M. Bosanquet on Mountain-Sickness ;

narrated, an explanation consistent with all the facts, inclu-
ding the immunity enjoyed by Mr. Perring (p.51). Ithought
the matter too plain for publication. But the appearance of
Mr. Dent’s article in the ‘ Nineteenth Century’ (Oct. 1892),
“Can Mount Everest be ascended?” shows that my point of
view has escaped notice. This appears at once from the
remark at p. 611: “ Men of large vital capacity, with large
bones and full-blooded, are the best suited [for the ascent of
the highest mountains].’? So far as mountain-sickness of the
great-altitude type is concerned, this is certainly not true
without qualification : the case of Mr. Perring above alluded
to is in point.

The body may be compared to a steam-engine and boiler,
the food-arrangements being paralleled by a mechanical stoker,
such that the supply of fuel can be fed into the reservoir of
the stoker in lump quantities, as food is fed into the stomach
at meals. The digestion and other internal arrangements,
which we may speak of as the “internal feed,” pass this on
into the place of combustion just as a mechanical stoker does
fuel. When food is regularly taken, the internal feed will
supply the combustion within the body at a more or less con-
stant rate, not depending on any voluntary action at the
moment, but depending on the constitution, on the average
amount of food taken at meals, and probably on the efficiency
or wastefulness of the internal feed.

The rate of the internal feed must vary enormously in
different persons. In men “of large vital capacity, ...and
full-blooded,” it will generally be very much larger than in
persons of small vital capacity.

Now we can easily suppose an internal feed so copious as
to approach, in its requirement of oxygen for its proper
combustion, the possible supply afforded by the breathing
mechanism. And my suggestion is simply that in eases of
great-altitude mountain-sickness, such as Mr. Whymper
relates, the diminution of the air-supply reaches a point at
which there is not enough oxygen for the consumption of the
fuel continually brought forward by the internal feed. Of
course, so long as this is the case, disturbance of the system
is to be expected from the accumulation of the reducing
(oxygen-devouring) substances furnished by the internal
feed to the blood. Under these circumstances, food would
probably not be taken for a time; the internal feed would
after a time be reduced ; and an equilibrium of the system set
up again founded on a reduced food consumption. And this
is precisely wuat happened, according to Mr. Whymper’s
account.

‘and Power and Endurance. 49

On the other hand, Mr. Perring, “rather a debilitated man,
and distinctly less robust than ourselves” (p. 51), escaped the
sickness. According to my view, the food-supply his system
was dealing with was not in excess of what could easily be
consumed by the air he breathed, even at the reduced
density.

According to this view, while the artificial supply of oxygen
advocated by some investigators should be able to give relief,
if the oxygen could be got to its work, yet the obvious course
is to attack the other element; and by a judicious preliminary
course of moderate starvation, combined with light work, to
endeavour to bring the system into the required condition of
reduced fuel consumption—in fact into the condition at which
it arrived in Mr. Whymper’s case, through the painful path
of the attack of mountain-sickness.

So far I have spoken of what may be ealled “ great-alti-
tude ” mountain-sickness. As to the more ordinary form, I
am sorry to say I was at one time a sufferer. Hxperience
enabled me to overcome it by adopting a slow uniform mea-
sured pace. But, after the disappearance of the agility of
youth, for some seasons I always suffered in my first expedi-
tions, even at quite moderate elevations. And I have no
doubt whatever that it was due to the system being over-
tasked ; that is to say, when I was endeavouring to do some-
thing like, say, ;4; of a horse-power for a time far longer
than I was capable of, I collapsed, probably not being capable
of doing more than, say, 3!, of a horse-power for any con-
siderable time, at all events when out of training.

So far I have avoided going into numerical details, as they
are not necessary for the general explanation, and they open
up an exceedingly wide subject. But I propose now to deal
shortly with certain relations of the external work which can
be performed by men; this is conveniently reckoned in terms
of ‘ horse-power.”’

One “‘horse-power” is commonly defined as 550 footpounds
per second, without qualification. When recently horses were
replaced by electric motors on certain tramways, it was gene-
rally considered a surprise that motors of about 35 H.P., as
above defined, were required to replace the horses. ‘The
explanation is that the 550 footpounds per second definition
was based on the average effort that horses could exert for a
considerable time. ‘The output of power of a horse on such
occas’ons as drawing a load up a sharp hill must be quite ten
times a nominal horse-power. And the machine is required
to be able to replace the greatest effort of which, say, 3 horses
are capable.

Phil. Mag. 8. 5. Vol. 35. No. 212. Jan. 1893. K

50 Mr. R. H. M. Bosanquet on Mountain-Sickness ;

Similarly, consider a man weighing 12 stone. According
to a well-known mountaineering datum, he may lift his wel ght
1000 feet per hour for many hours. Under. these cireum-
stances he is doing about +4, of a nominal horse-power.

Certain experiments on the treadmill gave § horse-power
external work, maintained: for 34 hours. soe

But any ordinary person can do-a whole horse-power, if the
time of the effort be short enough. Take a man weighing
12 stone=168 lb. If he raise his weight a little over 3 feet
per second, he is doing a horse-power of work. (For 550/168
= 3°27, or a little more than 34.) Now any ordinary person
who can run upstairs two steps at a time can do this easily
for a few seconds, and an active person for longer, but the
duration of the effort will not easily exceed a certain fraction of
a minute.

Further, active people can do 2 horse-power, running
upstairs at the rate of 64 feet of ascent per second, for a very
few seconds.

It appears, therefore, that the power a man is capable of
exerting depends on the duration of the effort.

The following (p. 51) are a few data I have selected as the
basis for a numerical law.

The law adopted is that the time of duration of effort (or
the “ endurance’’) varies inversely as the cube of the power
exerted, supposed uniform. Or, conversely, that the power
which can be exerted for a given time varies inversely as the
cube root of the time (or of the “ endurance’’).

Of course the numbers here given can only be rough
approximations to an average; and we need not be surprised
if we find wide divergences in isolated cases.

While the correspondence of the calculated times with the
estimates is not in all cases close, the discrepancies are in
opposite directions. Further, any considerable change in the
assumed law would tend to make the calculated numbers
impossible in the one direction or the other. Thus, if we took
the fourth power instead of the cube, it would make the tasks
at the bottom easier, and that at the top impossible or nearly
so, and vice versa if we took the square instead of the cube.

The treadmill datum has been taken as the starting-point,
the calculated endurances of the other cases being derived by
multiplying 34 hours by the cubes of the inverse ratios
of H.P.

It must be noted that we do not know the average weight
of Leslie Stephen’s party. I have assumed that this was
12 stone. If not, a correction will be required. It will be
seen that their actual endurance appears greatly to exceed

oe

and Power and Endurance.

ae

ae

. | on | Estimated
© . Nature of Data. Exact. H.P. ae Cee | ieee sich Sut eras.
a | | |
Mountaineer’s rule of 1000 feet per hour. Esti- | | O85 We | 1]h gm 10h
mated endurance, say 10 hours ....... Seas 4 |
Leslie Stephen : Dom from Randa. 10,000 feet 105 ce 5h 54s | Sh
NOL co), LKOTTNTS a ( Jem ess Beet 0 oie ole yea ane a be: a
Datum from treadmill, quoted from Smith by | | =
Frankland (Chem. Journ. 1868, p. “a = + 33> (datum). 35°
Reduced by me to English units ........ |
1 H.P. exerted by ascending at rate of 3:27 feet 1 9456 _ Fraction of
per second fo some fraction of a minute ee | minute.
2 H.P. exerted by mena at rate of 64 feet 9 28.8 Few seconds.
per second for few seconds.............. iG hows |

ie ee iy eae NS 2 is nae Vink eer teem bei ie ia ee kes Pe, cea Ie hale eS aly Ae ee

52 Dr. W. Pole on Colour-Blindness.

that indicated by the law for the power developed. If the
average weight were much less the discrepancy would be
lessened. But I think I remember seeing Leslie Stephen
described somewhere as “the fleetest-footed of all the Alpine
brotherhood ;” so that probably his party might be expected
to show an endurance in excess of the average, at a high
speed of ascent.

The bearing of these considerations on the use of such an
expression as “horse-power ” is important. However con-
venient it may be asa short name for 550 ft.lbs. per sec., it is
clear that no specification of ft.lbs. per sec. can really repre-
sent the work of any animal, unless the endurance, or the
time for which that power can be maintained, is also specified,
and the law connecting the two is known.

V. Further Data on Colour-blindness.—No. ILI.
By Dr. Wiuttam Poe, F.R.S.*

Professor von Hetmuoutz’s Handbook of Physiological
Optics.

F all the names that could be mentioned as authorities
on the subject. of colour-blindness, probably that of
von Helmholtz stands the highest, not only from the asso-
ciation of his name with that of Young in the most popular
theory of colour-vision, but more especially on account of his
monumental Handbuch der Phystologischen Optik, which has
acquired a classical celebrity. This work appeared at inter-
vals from 1856 to 1866 ; but scientific knowledge advances
much in a quarter of a century, and the learned author is
conferring a great boon on the public by giving them a new
edition, thoroughly revised and brought up to date. To
make it more accessible it is published in separate “ Liefer-
ungen,” of which seven have appeared, comprising 560
closely printed large octavo pages.

I have been surprised to find how little this new edition is
known in Hngland ; and as the part treating of colour-
blindness is already out, it would be culpable, in offering
data on this subject, to omit reference to it, particularly as
one of the special objects of this Magazine has always been
to call the attention of the English-reading scientific world
to important foreign publications. The subject mentioned
forms, indeed, but a minute item in the whole treatise ; but

* Communicated by the Author.

Dr. W. Pole on ColourBlindness. oe

“ex. pede Herculem,’ and I may claim a more extensive
discipleship under the great master in another branch of his
labours. .

The description of colour-blindness which Helmholtz gave
in the old edition is so well known that it is only necessary
to reter to a few passages bearing on our comparisons with
the new one. The author stated (p. 294) that the patients
saw in the spectrum only two colours, which they for the
most part called blue and yellow, and he mentioned experi-
ments on a patient tried by himself, which proved that for
this person’s eyesight all colours could be compounded by
mixtures of yellow and blue. He then explained how, on
Grassmann’s principles of colour mixtures, ‘‘ for an eye which
acknowledges trichromic matches, but which confuses red
with green, it follows that all the hues which it especially
distinguishes may be compounded of two other colours some-
thing like (etwa) yellow and blue.” . |

The author, however, in further explanation, pointed out
why he believed that yellow and blue might not. be the
colour-sensations really experienced. He said, p. 297 :—

In the Young hypothesis the colour invisible to the colour-
blind eye could naturally be only one of the fundamental colours,

Red-blindness would thus be explained on Young’s hypo-
thesis by a paralysis of the red-perceiving nerves ..... and it
follows from this that the red-blind perceive only green, violet,
and their mixture, blue.

He also (p. 299) mentioned another class, in regard to
whom “it might be conjectured (kann man vermuthen) that
their defect lay in an insensitiveness of the green-perceiving
nerves.” These passages, it will be seen, contain the essence
of the original application of Young’s theory to dichromic
vision, which became so popular.

We now turn to the new edition; and as it is matter of
common knowledge that, in the interval of time since the
previous publication, the applicability of the hypothesis re-
ferred to has been seriously questioned, we look with interest
to what is said now on the matter.

We may take it up at page 362, where we find a mathe-
matical investigation by geometry and algebra, to show that
if two colours, R and G, appear alike to the colour-blind,
there may be found another colour which, though visible to
the normal eye, is invisible to them. All this is just as it
stands in the old edition ; but now we come to the first
change of importance. The author, at the end of the investi-
gation, adds a new passage as follows :

54 Dr. W. Pole on Colour-Blindness.

But it is not hereby excluded that this wanting colour might
-also be wanting to. the normal eye, and its weight = 0. That
would mean that two of the fundamental sensations of the normal
eye would, to the colour-blind person, be excited to equal strength
by all exciting causes. In fact, it has recently become probable
that the solution of the enigma is to be sought in this direction.
The older attempts to explain colour-blindness proceeded from
the first-named assumption, that one of the fundamental sensa-
tions was wanting to dichromic eyes. I myself have adopted
this in the first edition of this hand-book*. ins}

_ As Helmholtz is not a person to use language incon-
siderately in such a case as this, we may gather much
information from this short passage. In the first place he
makes it clear that the original hypothesis was not in-
tended as a positive and definite explanation. It was only an
“attempt to explain,” and it is now characterized as “alt ”
(old), a word which, as I understand it, does not here mean
simply early in time, but carries with it the idea of “aged,”
“ancient,” “antique,” ‘stale,’ something superseded by
“new.” The expression often recurs with clearly this
meaning. Then the explanation of colour-blindness is called
an “enigma’”’ ; it is still obscure, and wanting “ solution.”
_And thirdly, the passage states that in consequence of some
recent events a new solution has become probable in a
certain direction. The recent events alluded to have been
clearly the more complete evidence acquired as to the facts
of dichromic vision ; and the new solution, which indeed is
already indicated, will be better explained by and by. _

It is difficult to construe all this otherwise than as intimating
that the author does not now attach much weight to the
former explanation, and we shall find, farther on, abundant
confirmation of this interpretation.

He, however, thinks it right to reprint the part which
-contains the “ tilteren Hrklirungsversuche,” but he adds now
the following new saving clause (p. 366). |

Nevertheless (¢mmerhin), as it appears doubtful what sensations
of the normal eye correspond to the two colour sensations of the
dichromic patients, Donders has recommended that, according to

* The important original passages are as follows :—

“Das wurde heissen, dass zwei der Grundempfindungen des normalen
Auges dem Farbenblinden durch alle Reizmittel gleich stark erregt
wurden. In der That ist es neuerdings wahrscheinlich geworden, dass
in dieser Richtung die Lésung des Riithsels zu suchen ist.

“ Die alteren Erklirungsversuche der Farbenblindheit gingen von der
erstgenannten Annahme aus, dass den dichromatischen Augen eine der
Grundempfindungen fehlte. Ich habe dies in der ersten Auflage dieses
Handbuchs selbst angenommen,” .

Dr. W. Pole on Colour-Blindness. Da

the customary expression of painters, the colour corresponding to
the red or less retrangible halt of the spectrum should be called
the warm colour, and that of the blue half the cold colour; and we
will do so in what follows.

At pages 367-8 he remarks on the distinction of the
classes of “ red-blind ” and “ green-blind,” but more positive
opinions are given later.

At pages 368 and 369 we come upon the “ new ”’ explana-
tion of colour-blindness already alluded to. The idea of this
appears to have arisen with Helmholtz himself at a very
early period. In 1860 Edmund Rose pointed out the diffi-
culty of Young’s original explanation, stating that after
eareful examination of 59 colour-blind patients, he found it
irreconcilable with the facts observed. In 1867, when the
last portions of Helmholtz’s work appeared, he noticed Rose’s
experiments, admitting as an alternative suggestion (p. 848),
that “in the case of the congenital colour-blind it might well
be imagined that the activity of the nerve-fibres might not
be removed, but that the intensity curves of the three kinds
of light-sensitive elements might change, whereby a much
greater variability in the effect of objective colours on the
eye might enter” *,

Leber, in 1873, expanded the idea and put it into a practical
form. The great difficulty had been the continually increasing
evidence that the warm sensation of the colour-blind corre-
sponded with the normal yellow, and not with red or green
as the Young explanation would require ; and Leber pointed
out that if, instead of abolishing the red or the green
element, the two were assumed, by changes in their intensity
curves, to coincide, forming yellow, the whole difficulty
would vanish. This explanation was afterwards repeated by

. Fick, and at a later time, 1886, reproduced by Konig in his
communication to the British Association.

Helmholtz takes this up in his new edition apparently with
approval, and much matter will be found bearing on it in
pages 368 and following, and again at page 376. He thinks
that if the green curve has gone over to the red, it will
produce the sensations of the “ green-blind”; but if the red
curve has gone over to the green, it will produce those of
the “ red-blind,” there being, however, less frequent inter-
mediate degrees between the two extremes.

In pages 372 to 374 he applies the same explanation (as
Fick had done) to the colour phenomena of the normal

* The new explanation is always ascribed to Leber; this clear antici-

pation of it by Helmholtz seems hitherto to have escaped attention, even
by Dr. Konig,

56 Dr. W. Pole on Colour-Blindness.

retina, and alludes to the analogy between these and colour-
blindness. . :

- Helmholtz thinks it right to devote considerable space
(pages 376 to 382) to the discussion of the theory of Hering.
He considers it a modification of Young’s theory, giving a
long description of it, illustrated by mathematical formule,
and he says it will explain the facts of colour combinations as
well as, but not better than, Young’s theory. Then follows
much controversial, matter, founded on arguments and state-
ments by Hering, but very little of which affects the question
of colour-blindness.

The most important novelty in Helmholtz’s second edition
is contained in section 21, on The Intensity of the Sensation of
Light. This section is a long one, extending over nearly 100
pages ; and a large portion of it, 2. e. from pages 401 to 473,
is entirely new. It contains a most elaborate essay on
“ Helligkeit,’ a word for which we have no perfect equi-
valent, but which is generally rendered hy “brightness”
or “luminosity.” The matter is principally devoted to the
relations between “ Helligkeit”’ and colour, which appear to
be exceedingly complicated and difficult ; so much so, indeed,
that Helmholtz, with the modesty that so often accompanies
great knowledge, expresses distrust of his power to. deal
satisfactorily with them. 3
_ Fortunately, however, we have no occasion to speak of these
relations, further than as they are connected with an entirely
new determination of the three fundamental colowr-sensations,
by a method in which “ Helligkeit” (which for this purpose
I translate as “luminosity”’) takes a part. This investigation
may be said to begin on page 444, with a dissertation, “On
the relations between Sensitiveness to Colour and Sensitive-
ness to Luminosity.” The author raises the question how far
observations on the spectral colours, having these elements in
view, will bear on the nature of the three physiological colour-
sensations, and having satisfied himself on this point he
undertakes the investigation.

I can only give (and it would not be right to do more) the
barest outline of this interesting but difficult and complicated
problem. It adopts in the first place the view of the funda-
mental sensations applied shortly before by Kénig and Die-
tericl in attempting a similar inquiry. They had analysed
the spectral hues by a great mass of experiments, using three
“ Hlemental colours” R, G, V, taken from the two ends
and the middle of the spectrum, by combinations of which
every other spectral hue could be produced. These, on the

Dr. W. Pole on Colour-Blindness. 57

old plan, would have been called the primary colours ; but
here they were only considered as preliminary elements ; the
new fundamental colours, say w, y, and z, being dependent on
them and connected with them by linear equations : thus

e=a,.R+b,.G4+¢.V,
y=a,.R+b,.G+¢, .V, ,
z=a3;.R+b;.G+e;.V.

The nine coefficients having to be hereafter determined,
making, in each line,

at+tb+e=l1.

To arrive at these constants appears the cruz of the problem,
it being necessary for this purpose to enter into the investi-
gation regarding the colour and luminosity relations before
referred to. ‘The quantities dH,, dE, and dH; are taken to
represent the magnitudes of the differential perceptions for
the elementary observations, and dE is the magnitude of the
difference in the colour resulting therefrom. This latter
quantity had to be expressed in terms of x, y, and z, and for
this purpose the following formula was arrived at (p. 453) :—

oh a/( ak wy +(2 dy = =) Lic eld ae
ko V3 ean Vy GN) Xd aN 2 aN ee aan)

,

where \ = wave-length, 6\ = a certain mean error, and ka
constant found by multiplied observations. This equation
has to do with the sensitiveness to colour.

With the aid of the constants, having given an observation
of the values of R, G, and V, at any wave-length, the values
of #2, y, and z may also be found, and the constants must be
such that dH, determined by the above equation, shall be
equal, or nearly so, at all points of the spectrum.

Having got this constant value of dH, it has then to be
compared with the equation for dH arrived at in a different
way, from dH,, dy, and ds, viz.

Qi hi nel A/ a

where ¢ is a certain very small fraction, also arrived at by
observation. This second value of dE has to do with the
sensitiveness to luminosity. And if the two values are
equal or nearly so, the calculation may be considered justified.

ines uns ih 2 .
* Probably this is a misprint for—. The book unfortunately contains

several typographical errors,

58 Dr. W. Pole on Colour-Blindness.

The most suitable constants were found to be, in round
numbers, |
x=0°'80.R—0°35 .G+0°55 .V,
y=0°26.R+035 .G+0°39 .V,
2=0:25.R+0:125.G+0°625. VY,

where R, G, and V represent the quantities of each elemental
colour in a given spectral hue. _

To carry out the calculations, an immense number of obser-
vations were collected on the various spectral colours (some
50 on each hue), determining the proportions of R, G, and V
in each colour. For example: at w.l. 520, the green hue
was found to be made up of

A:62 of R+8:45 of G+1°:10 of V;

then, applying the above equations to these figures, the pro-
portions of the three fundamental colours contained in this
hue of the spectrum were found to be

1:37 of #+4°51 of y+2°90 of 2.
Or in 100 parts of the green,
| 15 of #+51 of y+ 384 of <.

This being done for many points along the spectrum, and
the comparisons being satisfactory, the fundamental colours
can be laid down in a triangle, and their relations with the
spectrum shown in a geometrical form. The results will be
found in the tables on pages 454 and 455 and in the diagram
on page 457,

The three newly-found fundamental colours are, generally
speaking, red, green, and blue; but all very much more
highly saturated than anything in the spectrum.

:

The Red, x, is a highly saturated carmine-red, more tending
to blue than the extreme red of the spectrum.

The Green, y, is a yellow-green about w.l. 560, somewhat
greener than the complement to violet, and nearly corre-
sponding to the green of vegetation.

The Blue, z, is about w.l. 482, corresponding to ultra-
marine.

The author states that the fundamental red and blue cor-
respond with Hering’s anticipations (Vermuthungen) ; and I
may be allowed to say that the former agrees with my deter-
mination of my own wanting colour in 1856, before any
one suspected the existence of an extra-spectral fundamental.

The following short table, which I have made out from the
diagrams, tables, and formulee, will show, in a simple manner,

Dr. W. Pole on Celour-Blindness. - 59

the percentages of the “ Urfarben,” 2, y, and z, contained in
some of the chief hues of the spectrum.

Wave-

‘lengths. ce y: i
ee i ends «hi 61 6) A Se
MOAN PE e005. .6s e052: eee OOO a Ve Ete 00) 28
kee eee 580 36 30 thle hoo
Shida) | 22 2h eemRee ee 520 i) D1 34
ln. 480 31 29 40
RA OICUMER aac. av aec tenner: end. 539) 25 40
Tits a re aio 830 ul nae

If we apply to these quantities the principle that a mixture
of equal proportions of the three fundamental colours will
make white, we may form an idea of the enormous vrade of
saturation of the ideal fundamental colours, compared with
that of the spectral hues. For example, spectral red will
contain 42 parts of w, 1 part of y, and 57 of white; spectral
yellow will contain 11 parts of w, 14 of y, and 75 of white;
spectral blue will contain 2 parts of a, 11 parts of z, and 87
parts of white. This is a somewhat astounding idea; but
a glance at the diagram on page 407 will show it is what the
author intends.

The author points out that all simple colours excite the
three nerve-elements simultaneously, and with only moderate
distinctions of intensity ; facts for which there are analogous
phenomena in the known photochemical effects of photo-
graphy.

This brief account gives a very vague idea of the skill
and labour that has been embodied in the work referred to;
and, considering the entire novelty and difficulty of the
attempt, the acuteness of the logical reasoning required, and
the complicated nature of the relations involved, I should
venture to say it may be pointed to as one of the most striking
examples of the application of high mathematics to physio-
logical research.

— But it may be asked, What immediate connexion has this
with Colour-blindness ? . The author has himself answered the

60 - Dr. W. Pole on Colour-Blindness.

question by immediately going on, page 408, to a further
investigation, entitled “ Comparison with Dichromic Eyes.”

He begins with the remark that the fundamental colours
he has found do not coincide with those which K6nig and
Dieterici had deduced from the comparison of colour-blind
eyes with normal ones, and which he had himself quoted in
former parts of this work. They had arrived at pretty nearly
the same hues of red and blue, but their third fundamental,
green, differed materially, and the intensities were very
different in all.

Helmholtz takes some pains to explain and comment on
ihis, showing that the discrepancy is due to the attempt made
by Konig and Dieterici to apply the “old” assumption that
dichromic vision was simply caused by the absence of one
of the fundamental excitements of the trichromie eye. He
mentions that this assumption originated with Young, and
was, at an earlier period, accepted by most of the adapters of
the theory, including himself and Hering, as well as Konig
and Dieterici, and he thereby gives a good defence for their
zealous endeavours, but at the same time he leaves no doubt
that this assumption has vitiated their results.

As a further proof of this he cites (p. 461) the determina-
tion by Konig and Dieterici of the colours wanting to the
red and green blind respectively, according to the funda-
mental colours chosen by them ; and he shows that when the
newly found fundamentals are substituted, such a determina-
tion leads to irrational results, giving negative values ; whereas
(p. 460) Young’s hypothesis only allows positive values of
the physiologically possible colours.

Considering therefore, apparently, the old assumption as
now proved intractable, he goes on to explain that a more
general hypothesis respecting the existence of dichromatism
may be found, in which the necessity ceases that the missing
colour should be one of the fundamentals *.

* The following are the original words :—‘‘ Die hier gefundenen Grund-
farben stimmen nicht mit denen iiberein, welche die Hrn. A. Kénig und
C. Dieterici aus der Vergleichung farbenblinder Augen mit normal-
sichtigen hergeleitet haben. Nur die besondere, von Th. Young ausge-
gwangene und von den meisten Bearbeitern der Theorie, auch von mir
selbst, von E. Hering, A. Konig, und C. Dieterici friher angenommene
Erklarungsweise, dass bei den Dichromaten einfach eine der Grund-
erregungen des trichromatischen Auges nicht zu Stande komme, tritt in
Widerspruch mit dem bezeichneten Ergebniss.

“ Aber es ist eine allgemeinere Hypothese tiber das Wesen der Dichro-
masie moglich, bei welcher die Nothwendigkeit aufhort, dass die fehlende
Farbe eine der Grundfarben sei, und doch die Regel festgehalten wird
dass alle Farbenpaare, welche fur das normale trichromatische Auge
gleich aussehen, auch fiir das dichromatische gleich aussehend bleiben.”

Dr. W. Pole on Colour-Blindness. 61

He first shows the possibility of this by a simple example.
Suppose, he says, that the rays which ordinarily excite the
green sensation do not excite the green sensitive nerves, but
do continue to excite the red and blue ones. The eye would
become dichromie, and according to the old explanation would
see only red and blue. But these two sensations will not be
the same as the trichromic red and blue, in which the green
element forms part; and further, it is possible that the
green nerves, though not excited by the green rays, might
retain their former excitability by the red and blue ones,—in
which case the dichromic colours would be a certain kind of
yellow and blue.

The author then explains (pages 458 to 461) his “Adlge-
meinere Form der Dichronvasie.” First, by algebraical reasoning.
If 2, y, and z represent the three fundamental colour-sensations
in the normal eye, and X, Y, Z the three in the dichromic
eve, then, as all matches for the former are also good for the
latter, X, Y, Z must be linear functions of w, y, z, and the
following equations are arrived at, namely :-—

O=aX+BY+yZ.
Xp U + poy + p32.
Y= qe t+ Qey + 932
L=aX+bY.

The result being that the whole colour value of the dichromic
eye appears as a mixture, in variable proportion, of two
definite compound colours, X and Y.

Another explanation is given by geometry, in which the
author uses a more comprehensive mode than the ordinary
plane diagrams. He adopts Lambert’s plan of geomecry of
three dimensions. ‘The values of the three trichromic funda-
mentals wv, y, z, are used as rectangular coordinates, by which
may be formed an imaginary parallelopipedon (like a brick
whose three dimensions 9 x 44 x 3 will represent w, y, and z
respectively) : then the extreme corner most distant from the
origin of the coordinates will represent the place of the com-
pounded colour ; the length of the diagonal line drawn _be-
tween these two points will represent the quantity of the colour,
and its direction will represent the hue. Planes may be also
drawn intersecting the figure, which will represent the ordi-
nary plane colour-diagrams, and will serve as the bases of
‘Lambert pyramids,” containing all the colours physiologi-
cally possible. It is shown that, under the conditions of
dichromatism, the resulting planes will each be uniformly

62 Dr. W. Pole on Colour-Blindness.

coloured, and the trichromic variety of hues will no longer
exist.

This more general theory of dichromatism appears, so far as
I can understand it, to amount to the view that while the two
dichromic hues must be in some way derived from the three
fundamental colours of normal vision, there is no necessary
condition as to the manner of their derivation, or as to what
they shall be*.

The author, further, in regard to his new theory, calls
attention to a point of considerable importance. One of the
greatest stones of stumbling for years past has been the
division, consequent on the “old” explanation, of dichromic
patients into the two theoretically distinct classes of “ red-
blind”? and “ green-blind.” It is obvious that this division
naturally disappears when the old explanation is abandoned ;
but Helmholtz takes pains to show geometrically that his new
theory gives no place for such a division. And he, moreover,
expresses the opinion that such a division does not seem to
have been fully justified by observation.

He adds, ‘‘ By this it is also shown that the want of corre-
spondence between the absent colour of the dichromic system
and one of the fundamental colours found by us, does not in-
volve any insoluble contradiction f.

It is not my business to offer any comments on the views
I have endeavoured (imperfectly I fear) to call attention to ;
I have only to repeat the reference to the original for fuller
information regarding them. But even though there should
be differences of opinion on minor points, there can be
none as to the character of the work or the position of its
author among the great men of the age.

Atheneum Club, $.W., December, 1892.

* Only it would seem that as the dichromic eye now loses nothing,
but uses the whole of the three fundamentals and no more, and as
their sum makes normal white, then the total sum of the dichromic
vision must make normal white also, and the two hues, X and Y, will
be complementary.—W. P.

t On account of the great importance of these two expressions of
opinion, I subjoin Helmholtz’s own words (page 461) :—“In unseren
Betrachtungen ist keinerlei Beschrankung fiir die Lage der Schnitt-
punktes gegeben. Daher fallt bei dieser Verallgemeinerung der Theorie
der Dichromasie auch die Trennung in zwei scharf getrennte Klassen,
Griinblinde und Rothblinde, weg, welche ja auch den Beobachtungen
gegentiber nicht ganz gesichert erscheint.

“Damit ist auch nachgewiesen, dass der Mangel an Ueberstimmung
zwischen der fehlenden Farbe der dichromatischen Systeme und je einer
der von aus gefundenen Grundfarben keinen unléslichen Widerspruch
einschliesst.” : .

E 63oc

VI. A New Method of treating Correlated Averages.

By Professor F. Y. Epcuworta, M.A., D.C.L.*
oo following is a simpler method of solving one of the

problems treated in a former paper relating to correlated
averagest. Taking the case of three variables for conve-
nience of enunciation, let us put for the exponent (of the
expression for the probability that any particular values of
the variables will be associated)

R= aa? + by? + cz" + 2fyz + 2gaz + 2hay.
And let it be required to determine the coefficients a, b, ¢, &e.
The most probable values of y and z corresponding to any
assigned value of x, say w’, are deduced from the equations
by +fethe’ =0,
: Lezt+fy+tgu =0.
The values of y and z determined from these equations may
indeed diverge widely from the particular values corresponding
in any one specimen to vw’. But if we take a number of
specimens, it becomes more true ft that
bSy+fSz+hda’=0,
eSze +/Sy + 9a’ =0.

Dividing each equation by the sum of the assigned values

+2’, we have
ee +/Pi3 +4=0,

CPs t+fpitg=0 5
where pj2, p13 Mean (as in the former paper) the coefficients
of correlation pertaining to each couple of organs (Mr.
Galton’s 7).

By similarly assegneng values of y and of z, and observing
the associated values of the other variables, we obtain six
(in general n(n—1)) equations for the sought coefficients
a, b,...g, 4; which, being rearranged, are as follows :—

Prttp3g+t h=0,
pitt g+po3h=0 ;
230+ baa sh
— protpaft h=0;
puctprft g=9,
poset ftppg=0.

* Communicated by the Author.
Tt Phil. Mag. August 1892.
} Cf loc. cit, p. 191 et seg.

64 A New Method of Treating Correlated Averages.

A solution of this system is afforded by putting a, b, ¢ each
proportional to one of the principal minors, and f, q, h each
to a certain one of the other three minors, of the following
determinant :—

JL P12) P3is
| P12) 1 P235
r+] P3i P2395 1, :

For call the three minors formed by omitting successively
each constituent in the first row a, h, g. By a well-known
theorem ™*, if each of these minors is multiplied by the corre-
sponding constituent in the rows other than the first, the sum
of these products=0.

That is Pritt h+ po23g¢=0

P31 + po3h + g=0
Thus the first two of the above-written six equations are
satisfied. By parity of reasoning, if we put, for 0, the princi-
pal minor b, for c, ec, and, for 7, the minor f, obtained by
omitting the row and column containing (either) p3, the
remaining four equations are satisfied. ‘The proposed system
of proportional values is therefore a solution. And since the
equations are simple, it is the solution.

We have thus obtained by a simpler method than before
the solution of the problemy: given the values of some of
the variables, what are the most probable values of the other
variables? For the proportionate values of the coefficients
a, b,...g, h having been ascertained, we have only to sub-
stitute in R the given values of one or more variables, e. g.
z'; and for the most probable values of the remaining vari-
ables we have the equations

erage,

But we have not obtained a solution of the second problem f:
given the values of some of the variables, what is the law of
dispersion for the remaining ones? For in order to solve
this problem we require the absolute values of the coefficients.
I do not see how to obtain these, except by the method before
adopted, viz., obtaining the integrals of the expression

J ea? + by? + cz? + Bfyz+ 2gxz+ 2hary)

with respect to all but two, and all but one, of the variables.
Balliol College, Oxford.

* Salmon, ‘ Higher ‘Algebra,’ lesson iv. article 27.
+ Generalizing the statement given in the former paper, p. 190.
{ Generalizing the statement given in the former paper, p. 190.

[El
_ VII. A necessary Modification of Ohim’s Law.
By FERNANDO SANFORD*.

[Plate III]

URING the past year I have been engaged in some

investigations which seem to call in question the validity
of Ohm’s law, by showing that the resistance of a metallic
conductor varies with the nature of the dielectric in its field
of force. For the purpose of determining if this be the
case, I have made a large number of measurements of the
resistance of a copper wire in various dielectrics, and have
found that in several cases the change of resistance, both in
liquid and gaseous dielectrics, is very marked.

The apparatus used consists of a copper tube about four
feet long and one inch in internal diameter, closed with
copper plates at the end, and having a copper wire 1 miilim.
in diameter stretched through its centre and fastened by
means of a binding-screw to the centre of one end plate,
while it passes through an insulating-plug in the centre of the
other end plate. The tube is provided with stopcocks at the
ends for filling and emptying, and with an opening in the
side for inserting a thermometer. The current, which was
always between the extremes of five and eight milliamperes,
was passed one way through the tube and back through the
wire, so that the whole dielectric in its field could be changed
at will. The measurements were made by means of a Wheat-
stone’s bridge with arms of i : 1000, and a sensitive galvano-
meter. A change of resistance of 0°1 ohm in the box, which
corresponded to ‘0001 ohm in the tube and wire, produced
a very noticeable deflexion of the galvanometer-needle. The
measurements were accordingly estimated with a fair degree
of accuracy to ‘00001 ohm.

The resistance of the tube and wire was measured in air at
different temperatures through a range of about ten degrees
Centigrade, and a curve was plotted, using the temperatures
as abscissee and the resistances as ordinates. This curve did
not depart appreciably from a straight line. The dielectric
to be tested was then poured into the tube, a set of measure-
ments was made in it through the same range of temperatures,
the dielectric drawn out, the tube cleaned and dried, and a
new set of measurements made in air. This was repeated
several times, until it was certain that after each change of
dielectrics the resistance returned to the same value which it
had previously shown in the same dielectric. In the case of
air and petroleum this comparison was carried on for a month,
the dielectrics in the meantime being changed five times, and

* Communicated by the Author.
Phil. Mag. 8. 5. Vol. 35. No. 212. Jan. 1893. K

66 Mr. F. Sanford on a necessary

the apparatus being allowed to stand untouched for two weeks
to make sure that none of the constants were changing, and
in the whole series not a single measurement in either dielec-
tric fell upon or beyond the curve made for the other dielectric
(see Pl. III. fig. 1). The resistance of the wire in petroleum
was shown to be about ‘00006 ohm less than in air; and as the
whole resistance of the tube and wire averaged about °0335
ohm, this difference corresponded to about ‘18 of one per cent.
of the whole resistance.

Regarding the conductivity of the wire in air as unity, its
conductivity in the liquid dielectrics tested was as follows :—

Petroleum . a 5 al OES

Mixture of carbon bisulphide and turpentine > 10009
Carbon bisulphide, uncertain, apparently . . I+

Wood alcohol "9998
Benzine. 5. fk ws ce oe ot
Wood alcohol and benzine ... . . . «sumeeo
Absolute aleohol . .. .-.. %. + « «oe
Wood alcohol and petroleum . . .. =. . ‘9973
Distilled water, uncertain, apparently . . . I—

It will be seen that when two dielectrics which do not seem
to mix with each other were used together the resistance of
the wire was greatly increased, as in the case of wood alcohol
and benzine, and wood alcohol and petroleum. That these
liquids do diffuse into each other was shown by measuring the
index of refraction of the two components before and after
they had stood in contact with each other, and in every case
a change was observed.

A similar change of resistance was noticed when the tube
contained different gaseous dielectrics. This was first observed
when the burning gas used in the laboratory was allowed to
enter the tube. This gas was made from gasoline by a
machine on the ground, and consisted of the vapour of gaso-
line mixed with air. <A series of measurements was made in
this gas and in air, the measurements in air being made both
before and after those made in the gas. Of the seventeen
measurements with the wire in the gas, only one was as
much as ‘00001 ohm from the curve drawn, while the nearest
distance of any gas measurement to the air-curve was ‘00004
ohm, and the average distance of the gas points from the
air-curve was ‘000058 ohm. From these measurements the
resistance of the wire in gasoline burning gas was 1:0017
times its resistance in air (see fig. 2).

The other vapours used were those of volatile liquids, a
small quantity of the liquid being poured into the tube and
allowed to evaporate. Taking, as before, the conductivity of

Modification of Ohm’s Law. 67

the wire in air as unity, the conductivities in the vapours
tested were approximately as follows :—

Peeeryapolre me ee eee ee RE OOOLS
SiMoraiorn vapour ss) sso ae. «99830
Peeoleme burminowease f.0 7.0.6 al Sire ys «1799820
Palphuric ether vapour’. . 2... . 2) «7% ‘99750
Carbon bisulphide vapour, approximately . . 1
_ Rarefied air, less than VARS atte 1

Some of the phenomena observed made it seem probable
that only that part of the dielectric in direct contact with the
wire was concerned in this change of resistance. For example,
when the petroleum was poured out of the tube and a measure-
ment made before it had drained off and evaporated, the
resistance observed was the same as when the tube was filled,
with petroleum, and it was only after the tube bad been care-
fully drained out and dried that the resistance returned to its
former value in air. In the case of sulphuric ether vapour
this phenomenon was very marked. It was only after the.
tube had been washed out with alcohol one or more times, and
had: been dried out by drawing a current of air through it for
several hours, that the resistance returned to its former value.

I am now engaged in investigating the same phenomenon,
using a silver wire of the same size as the copper wire used
in last year’s experiments. In general, the difference in
resistance with the dielectrics above mentioned is less marked
than in the case of the copper wire formerly used, but it
is still noticeable. As in the case of the copper wire, the
greatest variation yet noticed was when the tube was filled
with sulphuric ether vapour, but with the silver wire the re-
sistance is decreased in the ether vapour, while with the copper
wire it was increased, The same difficulty in removing the
effect of the ether vapour also appears with the silver wire,
in which case it was only after repeated washings with alcohol
that the resistance of the wire returned to its former value.

Ihave thus far been unable to find with what other properties
of the dielectrics these phenomena are correlated, but it seems
clear that hereafter Ohm’s Law will have to be so modified as
to take account of the dielectric surrounding a conductor, as
well as the nature and temperature of the conductor itself.

The measurements upon which the above conclusions are
based are given in full in a paper entitled “Some Observa~
tions upon the Conductivity of a Copper Wire in various
Dielectrics,” which is now being published by the Leland
Stanford Jr. University.

Palo Alto, California,
October 26, 1892.

lies aul

VIII. Experiments in Electric and Magnetic Fields, Constant
and Varying. By Messrs. Rimmxeron and WYTHE SMITH. *
. [Plate IV. |

f hes object the authors have in bringing these phenomena
before the Society is not to establish any new theory,
nor to show imperfections in present theories, but to exhibit
experiments which help the actions taking place in a dielec-
tric under stress to be more easily grasped.
The experiments are divided into two sets :—

(1) Performed in electric fields.
(2) Performed in varying magnetic fields.

Although these two fields cannot exist separately, their
effects are isolated.

Set 1. Constant Electric Field.

A constant electric field was produced by two charged
metal disks + and —, each of which was stuck on the out-
side of a glass plate (Plate IV. fig. 1). The object of the glass
plates was to prevent brush discharges between objects placed
in the field and the plates.

Fig. 1, a, 6 represents a partially exhausted electrodeless
tube, placed in the uniform electric field. In the position
shown, the tube is at a uniform potential. Now let it rotate
in the direction of the arrow ; the potential of a will fall and
that of 6 rise until the P.D. between the ends is sufficient to
break down the tube. There will then be a convection-
current equalizing the potential, during the continuance of
which the tube will glow. On rotating still further a similar
action will take place.

The effect of these actions is to produce a double fan-shaped
set of images, as shown in fig. 2. The number of images in
the fan depends on the intensity of the field.

This phenomenon is intensified by constricting the middle
part of the tube.

In designing the tubes for these experiments, care was
taken to have the point where they were connected to the
pump in such a position that there was no tendency for dis-
charge to take place at these points when in use. The tubes
used in this experiment are shown in fig. 3 (a, 6, c, and d).
The stem was used to connect them to the whirling motor.

The surfaces of these tubes should be fairly clean and dry,
and it is advisable with a new tube, or one left unused for some
time, to excite it between the knobs of an influence-machine.

In the double fan-shaped set of images (see fig. 4, a) one

* Communicated by the Physical Society : read November 25, 1892.

Experiments in Electric and Magnetic Fields. 69

end will be seen to be brighter than the other, the current
passing from the dull end to the bright end. |

Not only is this effect visible with a straight tube, but on
rotating an exhausted bulb in the field a stationary luminous
region will be seen (see fig. 4, b).

Varying Electric Field.

Instead of rotating the tube a similar effect is produced by
varying the field in which the tube is placed.

The tube should be placed with its longer axis in the direc-
tion of the lines of force. The plates in this case may either
be charged and discharged by an influence-machine and dis-
chargers, the latter sparking, or by an induction-coil, with or
without sparking.

When an induction-coil is used, very long tubes will glow
when brought near.

Set 2. Magnetic Field.

The authors were of the opinion that, by taking advantage
of the action of the Geissler tube, one might show Hertzian
phenomena to fairly large audiences. ‘They therefore substi-
tuted a Geissler tube for the spark-gap in the resonator.

This was very successful with a Leyden-jar oscillator (fig. 5).
The oscillator and resonator consisted of two similar small
Leyden jars for capacity, and a single convolution of thick ~
copper wire for the conductor-circuit. The Geissler tube was
placed as a shunt to part of the conductor-circuit of the
resonator (see fig. 5).

But although they designed special tubes, they were unable
to get good results with the ordinary forms of Hertz oscil-
lator and resonator.

They next made a resonator of the following form:—

Two metal plates, a and b (fig. 6), give capacity, and the
wire self-induction. An electrodeless exhausted tube was
placed as dielectric between the plates. When a fairly large
Hertz oscillator was used, this tube glowed brightly, even
when taken to considerable distances.

Glow produced in varying Magnetic frelds.

Instead of, as in the last set of experiments, having a
secondary composed partly of a metallic conductor and partly of
a vacuum-tube, the whole circuit may be composed of rarefied
gas. It is evident that, in order to generate a current in such
a circuit, a large induced H.M.F. would be required ; this
would necessitate either a very strong magnetic field, or one
which changed very rapidly. The former was out of the
question, the latter was obtained by taking advantage of

70 Messrs. Rimington and Smith on Electric and

the phenomenon of oscillatory discharge in the following
manner :—

P (fig. 7), a primary consisting of a very few turns of
gutta-percha covered wire, was placed in a Leyden-jar circuit,
as shown. As a secondary an exhausted bulb, or annular
tube, was placed near P. ;

On sparks passing at D, a bright ring of light appeared in
the secondary.

In the actual experiments a metallic secondary, 8, was also
wound with P and exactly similar to it. On short-circuiting
S, the induced current in this circuit will weaken the mag-
netic field so as to completely extinguish the Geissler
secondary.

If S is connected to a third coil this coil will behave in a
similar manner to P, with weaker effects; P and S in this
case form a one to one transformer.

The wire of the coil P is itself luminous when 8 is open ;
short-circuiting S will stop this effect.

(Since the authors started their researches some of these
latter experiments have been shown by Prof. Thomson.)

APPENDIX.
Theory of a Vacuum-tube in a varying Electrie Freld.

‘When an electrodeless vacuum-tube is placed axially
between two plates, and a potential difference established
between them, the tube forms part of the dielectric between
the plates, and some of the lines of induction pass through
the tube. Now a rarefied gas is a very weak dielectric, and
readily gives way under the electric stress; a convection-
current flowing through the tube (during which time the
gas in the tube behaves as if it were a conductor) *.

This results in the ends of the tube becoming charged,
or lines of induction from the plates terminate on the ends
of the tube, there being no lines in the tube itself (see fig. 8).
The whole of the tube will also be at the same potential.

When the plates are discharged, the lines of induction
passing from the plates to the ends of the tube will now pass
through the tube; the rarefied gas will again break down
under the electric stress, and a convection-current will pass

* Of course the tube will not conduct after the manner of a copper
wire, but rather like a quantity of pith balls between two conducting
plates.

+ By the term “ends” is meant the msde surface of the glass at the
ends of the tube.

Magnetic Fields, Constant and Varying. 71

through the tube until the charges at the ends neutralize
each other.

If the change in the electric field take place rapidly
enough, the convection-current will produce sufficient dis-
turbance of the molecules to cause luminosity.

Theory of a Vacuum-tube rotating in a constant Electric

Field.

Consider the tube in a constant field in position ab (fig. 9).
There will be a — charge at “a” anda + one at “6”, and
the tube will behave as a nonconductor. We shall in fact
have conditions similar to those in fig. 10, where “¢” and

Fig. 9. Fig. 10.

a
a “3s G, Venis
cz

a,
3 y g
a =
+ O O 7
,
5 = O,
a vA 2

“qd” are two insulated conductors, which have been previously
connected together by a conductor, and which correspond to
the ends of the tube.

Imagine now “c” and “d” to be moved to positions ¢
and d,; they will now be no longer at the same potential,
and, if connected together, a current will flow from @, to ¢,
again equalizing their potentials.

72 Experiments in Electric and Magnetic Fields.

The same will happen to the tube if it move during rotation
from position ab to a,b,;; and, when the potential difference
between its ends attains a sufficient magnitude, the dielectric
of rarefied gas will break down, a convection-current flow
from 6, to a,, and the tube for the instant will behave like a
conductor. During this instant of breaking down the tube
will glow. After this the tube will behave like a noncon-
ductor, the ends being at the same potential until the tube
rotating moves into position a2 b,, and, if the potential ditter-
ence between a, and a, is equal to that between a and ay, and
the same for the 6’s, the tube will glow for an instant at
position ay by.

In the same way it will glow in the positions a3 63, a4 b.,
&e., if continuously rotated in the direction of the arrow. The
points a3 a, &¢., bs b, &e. are such that the potential difference
between each consecutive two is approximately the same. As
the glow takes place at the end of each alteration of the
potential difference, it is obvious that the double fan-like set
of images obtained will not be symmetrical with respect to
the plates, but will be displaced in the direction of rotation
by about one image.

he number of images in a single revolution will be pro-
‘portional to the potential difference between the plates, but
will not depend on the speed of rotation, provided that speed
exceed a certain limit. The effect of increasing the speed is,
however, to apparently increase the number ofa images ; since
those of one revolution do not fall in exactly the same
positions as those of the preceding one, and the images of
several revolutions are seen aE saison on account of
persistence of vision.

Ii scharge through Coil surrounding exhausted Bulb.

When a Leyden jar is discharged through a coil of wire,
the varying magnetic induction due to the discharge-current
will cause an H.M.F’. to-act in the dielectric inside and outside
the ring in a series of concentric circles. Let » be the radius
of the coil: consider a circular path in the dielectric of radius
aless than vr. If the magnetic induction passing through the
coil were uniformly distributed, the number of lines pas sing
through the path x would be proportional to its area or to 2”,
and the H.M.F. per unit of length along it to x divided ie its

7)
pets ae
circumference or to rae i.e.to a. Hence the electric stress

along a circular path z in the dielectric is greater the larger a,

Of course the actual distribution of the magnetic induction is

not uniform, but increases as we pass from the centre to the

Notices respecting New Books. 3 13

circumference: this will of course make the electric stress

Increase more rapidly than x. When the dielectric is a
rarefied gas it is not broken down until the electric stress

exceeds a certain value: hence the discharge takes the form
of a luminous ring in the outside of the bulb. By increasing
the sparking-distance in discharging the Leyden jar the
magnetic induction is increased, making the electric stress

greater and broadening the ring.

The breadth of the ring also depends on the degree of

exhaustion of the bulb, as the value of the electric stress
requisite to break down the rarefied gas depends on the
degree of rarefaction. In the case of an annular exhausted
tube placed outside the coil the luminous ring will be nearest
to ihe inner side of the tube: since when « is greater than 1,
the H.M.F. per unit of length is less the greater x, on account
of the lines of magnetic induction outside the coil being in
the opposite direction through the path « to those inside
the coil.

IX. Notices respecting New Books.

Odorographia: a Natural History of Raw Materials and Drugs used
in the Perfume Industry. By J.C. Sawer, /.L.S. London:
Gurney and Jackson. 1892.

N this work by Mr. Sawer we have another illustration of the
intimate relation existing between science and industry which is
such a striking feature in the educational movement of the time.
No book has yet appeared in which the ground covered by the
present author has been traversed by any writer who has brought
such qualifications to bear upon the subject, and we have as a
result a volume which may fairly be commended as unique in its
way, and which will prove a boon to all interested in the chemistry,
natural history, and technology of the numerous materials used in
perfumery.

A very brief description of the contents will suffice to show how
thoroughly the subject has been handled. In the first chapter,
devoted to musk, we have an account of civet and ambereris, and
a list of all the animals and plants which eive this odour, together
with a description of the artificial musk recently introduced by
Baur, and obtained by the nitration of certain coal-tar hydrocarbon
derivatives. ‘The second chapter, on the odour of roses, is a very
long one, and deals first with the true “ otto of rose” manufactured
in Bulgaria and elsewhere, the chemistry and technology of which
are given in considerable detail, and illustrated by figures of the
apparatus used anda map of the Bulgarian rose-farm district. An
account of rose culture in France is also given, and a description
of other odoriferous substances resembling rose, such as pelar-
gonium, and artificial rose perfumes, such as ammonium salicylate,

74 Geological Society :—

methylbenzylenic ether, phenyl paratoluate, citronellic aldehyde,
&¢. The actual methods of extracting the oil of rose by macera-
tion, enfleurage, and by the use of various solvents, are fully
discussed and illustrated by figures. The “citrine odours” are
described in the third chapter. These comprise the oils of orange,
lemon, lime, shaddock, and bergamot; incidentally sylvestrine is
referred to, and the oils of neroli, citronella, and lemon-grass
(Andropogon citratus, DeCand.) receive adequate consideration.
Jasmine, jonquil, and hyacinth are treated of in the fourth chapter,
the odour of violet in the fifth, ylangylang &c. in the sixth, and
the ‘‘ odour of the hayfields” in the seventh. In this last chapter
we find an account of coumarin, both natural and synthetical.
The eighth chapter, on vanilla, claims over 30 pages, and is
remarkably complete from every point of view. In the ninth
chapter the bitter almond, cherry laurel, and heliotrope are treated
of; in the tenth chapter, cinnamon, cassia, and clove; in the
eleventh, benzoin, storax, and the balsams; and in the twelfth,
opoponax, bdellum, myrrh, &c. Lign-aloes, patchouli, and related
perfumes are described in the thirteenth chapter; santal and
cedar in the fourteenth; camphor in the fifteenth; cajeput,
lavender, and rosemary in the sixteenth and concluding chapter.

There can be no doubt, from this epitome, that Mr. Sawer has
succeeded in carrying out the idea set forth in the preface, wherein
he states :—‘* An endeavour has here been made to coilect together
into one Manual the information which has hitherto been only
obtainable by reference to an immense number of works and
journals, English and foreign, in many cases inaccessible to readers
interested in the subject.”

It is not only as a technical work, however, that the present
volume demands notice in this Magazine. Although professedly
addressed to technologists, its subject-matter appeals both to
botanists and chemists; and the latter will be surprised to find
what a large and interesting field of work is before them for inves-
tigating the constitution of the numerous odorous compounds
furnished by the vegetable kingdom or synthesized in the labora-
tory and factory. New outlets for tar-products may be looked for
in the direction of the perfume industry ; and in bringing together
all that is known in connexion with the subject, Mr. Sawer has done
good service to a somewhat neglected branch of applied science.

X. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from vol. xxxiy. p. 385.]
November 9th, 1892.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.
HE following communications were read :—

1, «A Sketch of the Geology of the Iron, Gold, and Copper
Districts of Michigan.” By Prof. M. K. Wadsworth, Ph.D.,A.M., F.G:S.

After an enumeration of the divisions of the Azoic and Palsozoic

Gold-quartz Deposits of Pahang. 75

systems of the Upper and Lower Peninsulas of Michigan, the author
describes the mechanically and chemically formed Azoic rocks, and
those produced by igneous agency, adding a table which shows his
scheme of classification of rocks, and explaining it.

The divisions of the Azoic system are then described in order,
beginning with the oldest—the Cascade Formation, which consists
of gneissose granites or gneisses, basic eruptives and_ schists,
jaspilites and associated iron ores, and granites.

The rocks of the succeeding Republic formation are given as
nearly as possible in the order of their ages, commencing with the
oldest :—Conglomerate, breccia and conglomeratic schist, quartzite,
dolomite, jaspilite and associated iron ores, argillite and schist,
granite and felsite, diabase, diorite and porodite, and porphyrite.
The author gives a full account of the character, composition, and
mode of occurrence of jaspilite, and discusses the origin of this rock
and its associated ores, which ke at one time considered eruptive ;
but new evidence discovered by the State Survey and the United
States Survey leads him to believe that he will have to abandon
that view entirely.

In the newest Azoic formation, the Holyoke formation, the
following rocks are met with :—Conglomerate, breccia and con-
glomeratic schist, quartzite, dolomite, argillite, greywacke and
schist, granite and felsite(?), diabase, diorite, porodite, peridotite,
serpentine, and melaphyre or picrite. The conglomerates of the
Holyoke formation contain numerous pebbles of the jaspilites of the
underlying Republic formation ; a description of the Holyoke rocks
is given, and special points in connexion with them are discussed.

The author next treats of the chemical deposits of the Azoic
system, gives a provisional scheme of classification of ores, and
discusses the origin of ore deposits.

The rocks of the Paleozoic system are next described, and it is
maintained that the eastern sandstone of Lower Silurian age
underlies the copper-bearing or Keweenawan rocks. ‘The veins and
copper deposits are described in detail, and the paper concludes
with some miscellaneous analyses and descriptions, as well as a list
of minerals found in Michigan.

2. “The Gold-quartz Deposits of Pahang (Malay Peninsula).”
By H. M. Becher, Esq., F.G.S.

The gold-quartz deposits of Pahang traverse an extensive series
of slates, sandstones, and dark-coloured limestones, sometimes more
or less metamorphosed, and probably of Paleozoic age, occupying
the low-lying hill-country on the eastern side of the central granitic
mountain-range. The prevailing dip of the strata is eastward.

In some places the auriferous rock penetrates adjacent intrusive
syenites, but has not been traced in connexion with the main granitic
‘massif’ which is generally considered to be the matrix of the
cassiterite found in the ‘ Straits’ alluvial Tin-fields.

The gold occurs in lodes and irregular formations, which, how-
ever, are not distinguished from one another by any hard-and-fast

76 Intelligence and Miscellaneoiss Articles.

line; the difference depends on the size, shape, and continuity of
the quartz veins, though even the lodes seldom maintain their regu-
larity for more than a few score feet. The quartz often occurs in
very narrow veins intersecting one another to form what may be
called ‘ stockworks.’ It is probably from these minute veins that
the alluvial gold is derived. In the Raub mine numcrous rich
veinlets occur in a certain zone where the whole slate-rock is charged
with iron pyrites, probably auriferous. Many ‘stockworks’ are
intimately associated with dykes or intrusions of a rock which may
be called trachyte-porphyry, and these igneous rocks are decomposed
where prominently associated with aurifer ous quartz.

3. The Pambula Gold-deposits.” By F. D. Power, Esq., F.G.S.

The Pambula Gold-field is situated in the parish of Yowaka,
County of Auckland, in the South-eastern corner of New South Wales.

The lodes are different from ordinary auriferous deposits, inas-
much as the material filling the ore-channels does not differ greatly
in appearance from the ‘country ’ rock, and is but slightly miner-
alized. The ‘country’ rock is ‘pyrophyllite schist,’ associated
with ‘felspar-porphyry,’ sometimes turning into ‘ quartz-porphyry,’
the whole being tilted at a high angle. The bedding and cleayage-
planes appear to be coincident. The rock forms lenticles both micro-
scopic and macroscopic. Some of the lodes are accompanied by a
quartz ‘indicator’ which contains little or no gold in itself, the
precious metal being found in the shattered ‘country’ rock of its foot-
wall. On the footwall-side this shattered zone gradually merges
into the ordinary ‘country’ rock. The cause of the parallelism of
the auriferous lodes, the mountain-ranges, and the seacoast is dis-

cussed, and it is pointed out that the gold does not occur in large
grains.

XI. Intelligence and Miscellaneous Articles.
AN ELECTROLYTIC THEORY OF DIELECTRICS.

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

INCE writing the paper on dielectrics which you published in
your last issue, it has occurred to me that the calculation of ¢
from tenacity and dielectric strength might be made directly,
instead of in terms of specific inductive capacity and Young's
modulus. Perhaps it may be well to point this out.
Disruptive discharge occurs when the mechanical force on a

molecule is equal to 2 = Td’; andas the force applied electrically is

12
equal to ¢ x alsa: it follows that
s

dV max. = Td? °

g

From this g for glass = 3 x10~"'—a number which is probably

Intelligence and Miscellaneous Articles. 77

rather too small, for two reasons: firstly, because flaws reduce T

more than =a (as I explained in the paper); and, secondly,
s
because the measured value of T' depends on the cohesion between

tas depends on that between
s

the least-paired particles, whereas
those which are most paired.
With liquids the second of these causes of error will be more
marked than with solids, because the pairing in them is-so much
more pronounced; so that although the measured values of T for
liquids are probably much lower than for solids, the true values for

electrical stress are likely to be the same for both, or even higher

ae ae
for liquids. It is therefore significant that Eee is so nearly the
s

same in the three substances, glass, water, and oil, for which I
measured it; for constancy in the values of g and T involves, of
course, constancy in the values of dV max. (to within the limits
of variation of d). ds
IT am, Gentlemen,
University College, Bristol, Your obedient servant,

December 15, 1892. A. P. CHATtocg.

—=

ON A CHEMICAL ACTINOMETER. BY H. RIGOLLOT.

This apparatus consists of two plates of oxidized copper im-
mersed in water containing +,!;> of chloride, iodide, or bromide of
sodium. One of the plates is exposed to the rays of light, the
other is protected from the~action either by surrounding it with
parchment or paper, or by placing it directly behind the first plate
at a distance of about a millimetre.

The action of the light is instantaneous and disappears when the
illumination is destroyed.

The sensitiveness of an element decreases rapidly at first and
then becomes virtually constant.

The electromotive force of a given actinometer varies with the
colour of the light which acts upon it.

M. RigolJot has investigated the electromotive force in the
different parts of the spectrum, and gives the curves obtained by
taking as abscissee the lengths of waves, and as ordinates the
divisions read off on the galvanometer-scale. These curves show
that the actinometer with copper plates is most sensitive in the
red portion of the spectrum, that is in the region most luminous
for the eye. In this respect it differs from actinometers with
silver compounds, which are more especially sensitive to the most
refrangible rays.

If, after having traversed the spectrum from red to violet, the
sysvem of plates is again exposed in all parts of the spectrum but
proceeding from violet to red, the curves retain the same form,
and the increase of sensitiveness for red rays observed by
M. Becquerel (Lumiere, vol. ii, page 188) for iodized plates which

78 Intelligence and Miscellaneous Articles.

have been previously exposed to the most refrangible rays, does
not seem here to take place.

M. Rigollot used his actinometer to investigate the light diffused
by the northern region of the sky at different times of the day. He
gives the curve obtained on September 17, 1889, on the terrace of
the Physical Laboratory of the Faculty of Science at Lyons with a
clear sky. This shows a maximum illumination towards half-past
twelve; the curve is virtually symmetrical with respect to this
maximum for different times of day.

The author has investigated if, as M. Egoroff has found for
iodized plates, the intensity of the current is inversely proportional
to the square of the distance from the source to the apparatus.
_ This law holds approximately with Drummond’s light as source,
that is to say with a feeble light, but with sunlight the intensity
increases nore rapidly than the intensity of the current.

As the indications of the instrument are proportional to the
illumination for faint light, it may be used with advantage in
certain cases, such as examining the luminosity of the sky in
diffused light.—Journal de Physique, November 1892; from
Annales de Chimie et Physique, vol. xxii. p. 567, 1891.

ON THE ATTRACTION OF TWO PLATES SEPARATED BY A
DIELECTRIC. BY M. JULIEN LEFEVRE.

I have measured the attraction of two electrified plates sepa-
rated by a dielectric not in close contact with them, and have
verified that it is al by the following formula :—

rio

where Fis the attraction of the i plates at the distance e+e’ in
air; F the attraction at the same distance when a plane insulating
plate of thickness ¢ has been placed between the plates; ¢' is then
the suin of the thicknesses of air on either side of this plate; & is
the dielectric constant of the plate.

I used two horizontal plates, and a sensitive balance to the
beam of which was hung at one end a scale-pan; the movable
plate of the electrical apparatus, which is 12 centim. in diameter,
is suspended at the other end by an insulating stem. This plate
is surrounded by a guard-ring provided with a kind of cover, which
is only perforated by a hole to allow the rod to pass.

The fixed plate, which is 19 centim. in diameter, is placed below
the former and rests on an insulating support with levelling-
screws, so that the distance e+e’ can be varied. Three insulating
rods pass through this plate and support the dielectric. On either
side of this are layers of air as thin as possible; it must, however,
be possible for the movable plate to make small oscillations.

The source of electricity is a Ruhmkorft’s coil worked by six
Bunsen’s elements. One of the poles communicates with the
fixed plate, and with the inner coating of a jar the capacity of

Intelligence and Miscellaneous Artzcles. 79

which is, according to circumstances, 70 to 150 times greater than
that of the condenser formed by the two plates. The other pole,
the external armature of the jar, the movable plate, and the beam
of the balance are put to earth.

The whole apparatus except the scale-pan is placed in a cage the
air of which is dried.

The plates of sulphur and of paraffin are obtained by melting
in a mould, the bottom of which is carefully levelled. The thick-
ness of the plate is measured by a two-ended screw and a catheto-
meter. The distance between the two plates is also measured by a
cathetometer.

The dielectric is placed in the cage some days befove the experi-
ment so as to get rid of all traces of electricity.

The balance being somewhat too lightly tared, and all parts
being put to earth, I counterpoise by a weight p. I then electrify
the fixed plate, and counterbalance again with a weight P. I put
this plate to earth and counterpoise again by a weight p’: then

tap (ae.
F=P—*3.

The attraction EF’ is determined in like manner by three operations.

I work in the same way with liquids, measuring FE’ first, and then
F so as to avoid evaporation. The thickness of air e’ undergoes in
this case a slight correction, which consists in replacing the thick-
ness of the layer of air forming the bottom of the vessel containing
the liquid by the equivalent thickness of air.

In each experiment I calculate the ratio a and then the cor-

rected ratio Re # (1S i
1 Gaee
From (1) we should have pip,

The following table, in which e and ¢’ are expressed in centi-

metres, F and F i in milligrammes, shows that the values of VR
agree with the values of 4 which I have obtained by means of
Coulomb’s balance (Comptes Rendus, Nov. 16, 1891).

The formula (1) is therefore correct ; and particularly in the

case in which ¢’ can be disregarded, we have r = -

| Dielectric. é. e', E 1 = R VR. | &

Paraffin, No.1 ......) 2°20 | 0-70 | 39°5 | 17:25] 2:29 | 353] 1:88 | 2

~ Spiny a eobies ) 0-66 | 40°5 | 14 2°89 | 438 | 2:09 | ,,

5 No. 2c 3°37 | 061 | 805 | 9 3:39 | 4:51 | 2:12] ,,

eines 9 OOS 2S8De) i2ol eee eee 210.1.
Sulphur Eeiaanaaccine | 356 | 0°54 | 485 | 9°75) 4:97 | 7:27 | 2-70 | 26
IONMIGON, S5.,c0iccn desis 2:04 | 0°32 | 72°75| 18°75} 3:88 | 5:39 | 232 | 23
Carbon bisulphide...) 2°60 | 1:09 | 22 oe | 28 | er) Le |
Oil of turpentine .... 2°77 | 0-79 | 26:25) 18 2:02 | 249] 1:58 | 15]
| Petroleum ............ 2-98 | 071] 1950) 8 | 243] 388] 1:84 | 1:91
| |

80 Intelligence and Miscellaneous Articles.

i may, in conclusion, observe that the attraction of two plates
lends itself perfectly to the measurement of dielectric constants ;
it is simple, rapid, and only requires a sensitive balance, and is
preferable to all methods now in use.—Journal de Physique, June
1892.

INVESTIGATION OF THE PROPERTIES OF AMORPHOUS RORON.
BY H. MOISSAN.

Pure amorphous boron, obtained by reducing borie anhydride by
means of magnesium, is a bright chestnut-brown dirty powder, of
specific gravity 2-45. ven in the electric arc it cannot be melted ;
heated for a long time to 1500° it agglomerates, but not to any
great extent. The electrical conductivity is small; the specific
resistance ~=801 megohms.

Heated in the air, amorphous boron takes fire at 700°, and burns
with production of sparks. It burns in oxygen with a brilliant
lustre; with sulphur also it unites at 610°, with incandescence,
boron sulphide being formed: Borcn takes fire in chlorine at 410°;
it burns with bright incandescence, forming chloride; bromine acts
in an analogous manner.

Amorphous boron combines with metalloids more readily than
with metals. At a high temperature it combines, however, with
magnesium, iron, and aluminium, and more readily still with
silver and platinum.

Very concentrated nitric acid readily acts on amorphous boron
and with ignition. Sulphuric acid is reduced to sulphurous ;
phosphorus is separated from phosphoric acid at 800°, arsenic
from arsenic acid, and iodine from iodic acid.

Boron is a powerful reducing agent, exceeding carbon and
silicon in this respect, for at a red heat it can withdraw oxygen
from carbonic oxide and from silica. it can readily reduce a
number of metallic oxides; CuO, SnO, PbO, SbO,, and 5i,0,,
even on moderate heating, part with their oxygen to boron, with
incandescence. Lead peroxide detonates violently when rubbed
with boron in a mortar; and a mixture of sulphur, nitre, and boron
detonates under a red heat like gunpowder.

Amorphcas boron also has a reducing action on a great number
of salts; the sulphates of potassium and sodium, as well as those
of calcium and barium, are reduced by boron to sulphides as by
carbon. Silver is separated in beautiful crystals from solutions
of silver nitrate; and from solutions of palladium, platinum, and
gold the corresponding metals.

Boron unites directly with nitrogen only at very high tempe-.
ratures. .

Amorphous boron shows thus in its chemical relations remark-
able analogies with carbon.— Comptes Rendus, vol. exiy. p. 607.

THE
LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FIFTH SERIES.]

FEBRUARY 1898.

XII. The Diffusion of Light. By W. EH. Sumpnur, D.Se.*

| ee information appears te have been published about

the diffusing power of unpolished surfaces. The sub-
ject has been studied by optical measurements by Zollner and
others, chiefly for astronomical purposes ; and the radiation
from such surfaces has also been investigated with appa-
ratus designed for measuring radiant heat. But the in-
fluence of such diffusion in increasing the illumination of
rooms and open spaces, although well known, does not appear
to be appreciated to the extent that its importance deserves 3
and a few numerical determinations of the coefficients of
reflexion, absorption, and transmission of diffusing surfaces
may prove of interest.

Terms in light are used vaguely, and it will not be deemed
out of place to define those which will be here needed. By
the reflecting power of a surface is meant the ratio of the
amount of light reflected by it to the total amount of light
incident upon it. The zddwmenation of a surface is the amount
of incident light per unit area of the surface. The unit
quantity of light is the flux of radiation per second across a
unit area of a sphere of unit radius at whose centre a unit
light (of one candle) is placed. The amount of light radiated
by a source of & candle-power, within a solid angle Q, is kQ,
and the total quantity of light emitted by it is Ark. The
brightness of a diffusing surface is its candle-power per unit

* Communicated by the Physical Society: read Dec. 9, 1892.
Phil. Mag. 8. 5. Vol. 35. No. 213. Feb. 1893. G

82 Dr. W. E. Sumpner on the Diffusion of Light.

area in the direction normal to the surface. The illumination
produced at a point by a surface of brightness B, subtending
a (small) solid angle Q at the point, is BO, and if a surface,
containing this point, have its normal inclined at an angle ¢
to the axis of Q, the illumination of this second surface due
to the first is BO cos ¢.

If B is the brightness of a surface rendered luminous by
reflexion, if 7 is its (diffused) reflecting-power, and if I is
the illumination of the surface, then

cB=7l. 2.

This relation follows from the assumption of the law of
cosines, viz. that the candle-power (per unit area) of a bright
surface is Bcos ¢ in a direction making an angle ¢@ with the
normal. The right-hand member of (1) is by definition
equal to the whole light reflected from unit area of the sur-
face, and must be equal to the integral of B cos ¢ dQ for all
directions on one side of the surface. The value of the
integral is easily seen to be 7B.

The brightness of a body, as just defined, is directly pro-
portional to the illumination of the image of the body on the
retina of the eye, and the word may thus be quite justly used
in the ordinary physiological sense of the term. Similarly
the law of cosines, just alluded to, is merely another way of
expressing the fact that the sensation of the brightness of a
diffusing surface is the same from whatever direction this
surface may be viewed. For the amount of hght received
by the eye, and concentrated on the image on the retina, is
simply the product of the area of the pupil of the eye and
the illumination at the surface of the eye due to the bright
object. Tbe former tactor is constant for different directions
of view, and the latter must vary as the solid angle subtended
by the object at the eye, since the area of the image on the
retina is a measure of this solid angle. The illumination at
a point at which a surface of brightness B subtends a solid
angle © is not necessarily BO for all inclinations of © to the
surface, unless the law of cosines is fulfilled; and, if this law
is fulfilled, it follows that the illumination of the image of
this surface on the retina of the eye is constant at all dis-
tances and inclinations. The eye is a good judge, and is
indeed the only judge, of quick variations in brightness, and
the cosine law is always applicable to diffusing surfaces, the
appearance of which does not alter as the eye moves past
them. Any divergence from this law is negligible so far as
its influence on illumination is concerned. 7

If @ is the quantity of light radiated per second by the

Dr. W. E. Sumpner on the Diffusion of Tight. 83

light-sources within a room, and if Q’ is the total amount of
light falling on the walls,

OO ee 2)

For of the quantity Q’, a portion 7Q’ must be reflected, and
the rest absorbed, and the rate at which light is absorbed by
the walls must be equal to the rate at which it is produced.
The average illumination I! of the walls of the room must
hence be related to I, the i/lumination due to the direct action
of the lights, by the equation

Bes aS ee ee et)
eee — 9) 101 and 1 4="90).1/=2 I, so that the

illumination due to the walls of the room may become far
more important than that caused by the direct rays of the
hghts.

The truth of this relation may be also seen as follows :—
The light Q falling on the walls is partially reflected, and a
quantity 7(@ is sent back into the room. This light falls on
the walls again and a portion 7 xQ is reflected a second
time. The total quantity of light Q! falling on the walls
owing to successive reflexions is given by the equation* ,

OO AO ae =. =7 2.

Or, again, as the illumination I,’ of the walls at any point P
is made up of a portion I, due to the direct rays of the lights,
together with a part caused by radiation from the walls, we
have

L/ =I, + | Bos dQ, eh Sond nara as

where B is the brightness of the walls, and @ is the inclina-
tion of the solid angle dO, to the normal to the surface at the
point P. Assuming that the brightness is the same all over
the bounding surtace of the room, the value of the integral is
readily seen to be mB, and this, as already shown, is equal
to nl’, where I’ is the average illumination of the walls.

When the bounding surface of a room or enclosure consists
of portions whose reflective powers are different, the average
reflective power may be taken as

1, = De iieest &e. S00 Ue ‘ . (5)

* Since writing this paper I have discovered that this relation has
been already pointed out by Mascart [see Palaz, Trazté de Photométrie
Industrielle, p. 268).

G 2

84 Dr. W. E. Sumpner on the Diffusion of Light.

where A is the total area of the bounding surface, of which a
portion A, has a reflective power equal to 7;, and a second
portion A, a reflective power 7, &e. This relation is very
approximately true for ordinary rooms, and may be shown to
be quite accurate for a spherical enclosure.

For let P and Q be any two points of a sphere of centre C
and radius 7 (fig. 1). Then PQ=2r cos ¢, where ¢ is the angle
which the chord makes with the radius through either P or
Q. Also, with the same notation as before, we have

dA cos¢@

PIP? y

where dA is an element of area at Q of brightness B,
and subtending a solid angle dA cos¢/PQ? at P. Now
PQ’=4?r? cos*$ and tB=71’, where I’ is the illumination of
the area dA: hence

os 1
I, =I,+gasindA=1,+ 7 )IndA, . ©)

iby = if + | Beos¢

A being the total area of the spherical surface. The integral
is constant whatever the position of the point P, and what-
ever the character of the reflecting surface of the sphere.
Thus if any complete [or if any portion of a] spherical sur-
face be illuminated in any manner I, by the direct rays of a
combination of light sources, the actual illumination I,’ will
exceed I, by a constant amount all over the sphere, owing to
the reflective action of the surface. Also, if the original dis-
tribution be uniform all over the sphere, I,=I, a constant,
I,’ will also be constant, =I’, and

/ :
=I +5 Jad = I+ tal’,

where :
ndA
13 (7)

Dr. W. E. Sumpner on the Diffusion of Light. 85

Taking as an average case for rooms a reflecting power of
70 per cent. for the ceiling, 40 per cent. for the walls, and
20 per cent. for the floor, the average value of 9 is a little
over 40 per cent., and the increase of illumination by re-
flexion becomes as much as 70 per cent. If the walls and
ceiling of a room be well whitewashed, the average reflecting
power will not fall far short of 80 per cent.; and in such
ceases the illumination due to diffused reflexion is four times
as important as that caused by the direct action of the lights
in the room. A further great advantage, resulting from the
use of good diffusing surfaces, arises from the fact that the
illumination they cause is, in most cases, very approximately
constant all over the room, and does not cast shadows.

Tt is to be noted that when a reflecting surface is coloured,
its average reflecting power does not properly represent the
character of the increase of illumination caused by it. A
room whose walls are covered with red paper whose average
reflecting power is 40 per cent., may quite possibly have the
red light in the room increased five times owing to the action
of the walls. Suppose, for instance, that the reflective power
of the paper for red light is 80 per cent., and for other kinds
of light only 10 per cent., the average reflecting power will
not exceed 40 per cent., yet the red light will be increased
five times, while other kinds of light will not be increased to
any perceptible extent.

Measurements of [eflective Power.

The surface, whose reflective power was required, was
attached to a Jarge screen of black velvet placed at one end
O of a 3-metre photometer-bench OL (see fig. 2), so as to

Fig. 2,

be perpendicular to its length. Two lights were used, one
being a Methven two- candle. gas standard, placed at L, and

86 Dr. W. E. Sumpner on the Diffusion of Light.

the other a glow-lamp run generally at about 20 candle-
power, placed at P,;. A Lummer-Brodhun photometer was
slid along the bench to a point P, at which the illumination
due to reflexion from the surface OR was equal to that due
to the Methven standard at L. At first the lamp P, was
permanently situated a little to one side of the bench, and
the rays from it in the direction of the photometer P, were
screened off. Subsequently the points P, and P, were made
to coincide, the lamp being fixed to the same slider as the
photometer and suitably screened from it and from the eyes
of the observer. In some experiments the distance OL was
kept fixed and the position of balance OP was determined
for each surface tested. In other cases both OP and OL
were varied.
Let :—

A = area of diffusing surface on screen OR (centre at O).
D,, O, = solid angles subtended by A at P,, P. respectively.
21, #2 = distances OP,, OP, respectively.

y = distance P.L.
K = candle-power of the glow-lamp at Pj.

k = candle-power of Methven standard at L.

Then :-—

The quantity of light falling on the area A is KQ,,

the average illumination of A is KQ,/A,

the average brightness is n7KO,,/7-A, by (1),

the illumination at P, is 7KO,0,/7A, ©

and also the illumination at P, is k/y? ;

whence
ey ie eee Se
10,07 K Af?? —

provided the dimensions of A are small compared with «, or
2. When this is not the case, the equation (8) is not suffi-
ciently correct, and a more accurate formula may be obtained
as follows, by taking note of the inclination of the rays to
the surfaces.

The illumination of the surface at the point R due to the
lamp at P, can be easily shown to be K cos? ¢,/2,2, where ¢,
is the angle between RP, and OL, the line of centres of the
bench. The bmghtness B of the surface at R is therefore
nK cos*d,/72z,? by equation (1). An element of area dA at
R subtends at P, a solid angle dO, equal to cos*¢.dA/z,2,
and the illumination at P, due to this element is BdO,=
7K cos’ $; cos*p2dA/7#?22" on any area placed perpendicular
to RP.. As the photometer screen is perpendicular to the

Dr. W. E. Sumpner on the Diffusion of Light. 87

bench and not to RP., we must multiply this expression by
cos, to get the effective illumination due to the element
dA. Finally we have for the total illumination the integral :—

= al CORO COSMO Ly i. see (9)
in which the angles ¢,, ¢ are related by the equation

xv tan ¢;=2, tan do.
When the area A is circular, with O as its centre, this
integral reduces to

I= = COs® Hid S107 O55)... 4. , CLO)
1

The value of this integral can be readily evaluated, but it does
not lead to a convenient formula, and as it was found prac-
tically preferable to fix the lamp to the same slider as the
photometer, and at the same distance from the screen OR,

we may put
$1 = b2= 9;

and (10) then reduces te
KZ ,
l=n-3 zL1 —cos’¢ |, e ° ° 2 SS) (11)

in which ¢ is the semiangle of the cone with base A and
height x.

This expression is rendered more convenient for purposes
of calculation by taking advantage of the fact that A/zx’, or
tan’d, is a small quantity. By neglecting tan*d compared
with unity we obtain

2 iL

5 [1—cos’] = x’
where i Hi

TH
X= +1°754+ 413— 3, bag. 3) SBR ee EE)

and in most cases it will be found that the third term in this
expression is negligibly small compared with the sum of the
other two.

The value of I found in (11) may be equated to k/y? when
the photometer is in the position of balance, and on doing so,
we find for 7 the value

cnikes
faa IK x
which reduces to (8) when 2 is large.

ee te Pete a tS)

88 Dr. W. E. Sumpner on the Diffusion of Light.

This equation was used for the great majority of the re-
flexion tests. With feebly diffusing surfaces such as black
cloth, the distance z had to be so much reduced that the area
A subtended a greater angle at the photometer screen than
the aperture of the photometer itself. In such cases the
angle @ in (11) was calculated from the solid angle sub-
tended by the aperture of the photometer at the centre of
the photometer screen. With diffusing surfaces which
appeared to shine slightly under the action of light the
effect of regular reflexion had to be separated from that of
diffused reflexion, by experiments made with the same
surface for different values of x In such cases, which
will be alluded to subsequently, the true reflecting-power
is not given by formula (13). The areas A of the reflecting
surfaces used in the experiments were never circular, as
assumed in the above proof, but as they were always ap-
proximately square, with the central portion at O (fig. 2),
any error in (12) and (13) arising in this way must be quite
negligible. The ratio £/K of the two lights was frequently
tested in the course of the experiments and was found very
constant during every set of tests.

The results obtained are given in the accompanying table.
In the majority of cases the numbers given are approximate
only, as there seemed no object in aiming at great accuracy.
The first four surfaces referred to in the table, viz., thick
white blotting-paper, white (rough) cartridge-paper, tracing-
paper, and tracing-cloth, were, however, carefully tested,
and the numbers obtained represent the mean of many
observations.

TasLeE J.—Reflecting- Powers.

per cent. per cent.

White blotting-paper_......... 82 Plane deal (clean) ......... 40 to 50
White cartridge-paper ......... 80 (dirty) <2yecseseeneee 20
PDracing-ClOb j..t.2+-6 260 ocuases 30 Yellow cardboard <2-2222-5--ae 30
Dracins- paper. so-<1.-s-4.<psu-sc 22 Parchment (one thickness) ... 22
Ordinary foolscap ............... 70 (two thicknesses) ... a
Newspapers Ae aaa 50 to 70 Yellow painted wall (dirty) ..
Tissue-paper (one thickness) ... 40 »» (Clean) . nae

(two thicknesses) . 5d Black cloth........cccsssseseeerees 12
Yellow wall- Papel i osce.2: cane ees 40 Black velvet .......cscseeee 0-4
LCST OCR eri ne ae or 25
Dark brown paper ...........6645 13
Deep chocolate paper ...,...... 4

Zoéllner found white surfaces to reflect from 70 to 78 per
cent. of the light incident upon them. The numbers given
at the head of the above table are slightly higher. They,
however, agree very well with results which have been pub-

Dr. W. E. Sumpner on the Diffusion of Light. 89

lished with regard to the diffuse reflexion of radiant heat,
since 82 per cent. is generally given as the reflective power
of white substances *

The degree of consistency of the results may be judged
as follows :—In a series of 10 determinations of the reflec-
tive power of white blotting-paper, made with values of &
{see fig. 2), varying from 40 cm. to 82 cm., the mean
reflecting power was found to be 82°4 per cent., and the
average error of a single determination from the mean was
1-4. With surfaces of lower reflecting-power (such as
tracing-cloth) the numbers obtained in “successive experl-
ments were more consistent. The value of » for white
blotting-paper was checked by comparing it directly with
that of a piece of common mirror. The Methven standard
at L (see fig. 2) was replaced by the mirror, arranged so
as to reflect the light from the glow-lamp along the line of
the bench. ‘The reflective power of the white blotting-paper
placed on the screen OR was found to be 98°5 per cent. of
that of the mirror. The value of 7 for the mirror, for normal
rays, was separately determined and found to be 82 per cent.,
and hence y for the blotting-paper comes out as 80°8 per
cent.

Several of the numbers in the above table were confirmed
by comparative measurements, using white paper asa standard
reflector, the Methven standard at L (fig. 2) being replaced
by a surface of white paper exposed to the rays of the glow-
lamp at P. The reflective power of one of the walls tested
was measured in diffuse daylight by exposing the aperture of
a photometer to the radiation of the wall, and balancing the
illumination against that of a standard candle. The part of
the wall affecting the photometer was then covered with a
sheet of white blotting-paper, and the ratio of the two illumi-
nations at once gave the ratio of the reflecting-powers.

Measurement of Absorption.

The absorbing-powers of some of the preceding substances
were determined by measuring the candle-power of the light
from a glow-lamp, first when ‘this was uncovered, and after-
wards when it was surrounded with a cylinder of the paper
under test. The cylinders were short, being just longer than
the height of the lamp, and were closed at top and bottom
with caps of the same paper, so that the lamp was completely

* See Jamin et Bouty, Tome Troisiéme, p. 149. Results by MM:
Goddard, De la Provostaye et Desains.

90 Dr. W. E. Sumpner on the Diffusion of Light.

enveloped by the paper tested. The ratio of the diminution
of candle-power to the original candle-power gave the appa-
rent absorption of the paper. If the candle-power in some
particular case was found to diminish 30 per cent., it would
have been erroneous to conclude that the envelope absorbed
as much as 30 per cent. of the light incident upon it, or that
70 per cent. was transmitted. If the reflecting, absorbing,
and transmitting powers of a material be respectively denoted
by 7, a, and 7, there must exist between these quantities the

relation ntatr=l.

Also if Q be the quantity ef light given out per second by
the light-source within the envelope, the quantity of light
incident per second upon the surface of the envelope will,
owing to internal reflexion, be increased to Q’, where

Q’(1—7)=Q;

the quantities ef light absorbed and transmitted will respect-

ively be
a()’ and 7Q’,

and the ratios these quantities bear to Q will similarly be

ot T
pare and r=:
the sum of course being unity.

If the light-source can be assumed to radiate equally in all
directions, the ratio of its candle-power, after putting on the
envelope, to the original candle-power will not be + but
t/(1—%). The influence of internal reflexion is to increase
both the absorption and the transmission, and unless it is taken
into account large errors may be made in estimating the
coefficients. A very simple way of showing the effect of
internal reflexion consists in surrounding a glow-lamp with
a white paper cylinder, open at the top, and adjusting a pho-
tometer screen till the illumination caused by it is balanced
against that of some standard source of light. If now a piece
ot white paper be placed on the top of the cylinder, so as to
shut in the vertical rays of the lamp, the candle-power in the
horizontal direction will be found to increase considerably.
In some of the tests, in order to avoid error caused by non-
uniform radiation of the lamp, this was first surrounded with
an envelope of tracing-cloth, or blotting-paper, and the com-
bination used as the light-source. If 4, be its candle-power
in this condition, and if 4, be the observed candle-power
after completely surrounding it with an envelope of the sub-

Dr. W. E. Sumpner on the Diffusion of Light. 91

stance to be tested, the apparent absorption of this material

dd >” ky — ke
Sa ak gee ar ol)
and the true absorption coefficient « is given by
ky—k
a=(l—4)—, - spice pana eee (UD)
0

where 7 is the previously found reflexion coefficient.

When an inner envelope is used to produce a light which
radiates equally well in all directions, it is necessary for the
outer envelope to be large compared with it, since otherwise
the formula for the increase of illumination due to internal
reflexion cannot be applied.

The following table gives the values of the absorbing
coefficients, expressed as percentages, for the four substances
at the head of Table I., from which the corresponding values
of m used in applying (15) have been taken.

TABLE II,

Apparent Absorption. Real Absorption.

White Blotting-paper ......... 77 per cent. 13°8 per cent.
White Cartridge-paper ...... 61 Mi 12:2 (,
Mraeine—Clobla i202 .-je.. foe ee sae 23 - 15:0 -
RACINE =PAPCL ciaecveneeeeveees 9 70

Three large glass globes, made for arc-lamps, were also
tested. As the reflective powers of the globes could not
easily be found, only the apparent absorption was measured.
One globe was of opal glass (almost transparent), and the
ratio of apparent absorption was 15 per cent. A second
globe was of ground glass and absorbed 42 per cent. The
remaining one was of opal glass, too opaque to allow any
bright object placed within it to be distinguished. This
absorbed 39 per cent.

Measurements of Transmitting-Power.

The amount of light transmitted through the surfaces
above mentioned was measured in a very similar manner to
that in which their reflective powers were determined ; the

92 Dr. W. EB. Sumpner on the Diffusion of Laght.

only difference being that the glow-lamp at P, (see fig. 2)

was moved to the opposite side of the surface as in fig. 3.
OR represents the screen of paper, pinned on a wooden

frame, and placed perpendicular to the optical bench P;L. The

Fig. 5.

OR —OP — itz lia

glow-lamp was at P,, the photometer at P,, and the Methven
standard at L. The distances OP,, OP, were arranged to be
equal, and balance obtained by moving L along the bench.
On referring to equations (8) to (13) and the arguments
used in establishing them, it will be seen that they are all
applicable to the case now considered if only we substitute 7,
the transmitting-power, for 7.

When, however, tests were made with the paper surfaces
already referred to, it was soon found that the numbers
calculated from expression (13),

X=Y,. 0

were not constant for the same substance. They differed
from each other far more than could be accounted for by
errors of experiment; thus, the values found for 7 by this
formula were too high, and frequently exceeded 100 per cent.
For any given surface the values were found to increase pro-
gressively with the value of « used in the tests. The reason
for this is easily seen when it is remembered that equations
(8) to (13) are only true on the assumption that the surfaces
considered are purely diffusive, and do not alter in appearance
as the eye changes its point of view. When light is trans-
mitted through a semitransparent substance such as tracing-
paper, or tracing-cloth, the brightest part of the surface is
always on the line joining the eye to the light, and visibly
moves over the surface as the point of view ischanged. The

set Ne

Dr. W. EH. Sumpner on the Diffusion of Light. 93

easiest way to represent these facts is to assume that, of the
light transmitted, a portion 7, passes through without change
of direction, Paul that the rest 7, is diffused in accordance
with the cosine law. The case is analogous with a reflecting
surface such as white enamelled iron, which reflects a portion
m, of the incident light in accordance with the regular law
of reflexion, and diffuses another portion 7, according to the
law of cosines. On referring to equations (8) to (11) it will
be noticed that they are still true for the illumination due to
diffusion if we substitute for 7 either tT. or n, (according as
we are considering transmission (fig. 3) or reflexion (fig. 2)
respectively). The additional illumination at the photometer
due to regular, z. e. direct, transmission (transparency) is

K
Ui Qa)” : (17)
and a similar expression holds for regular reflexion if we
substitute 7, for 7}.

The whole illumination must, as before, be equal to k/y?, and
by (11), (12), and (17) we have

K Kees tk
Tae Te 0 = 5 ° ° (18)

whence the value of Y in (16) is equal to
Y=7,+ eee: aoheeco ual soence 19)

and a similar expression holds for reflexion if we replace 7,
and 7, by , and 7, respectively. The true values for the
transmitting and reflecting coefficients are

rantt, |

20
n=m™+, |’ oy

and the reason the values found for Y were too high, and
became greater and greater as x increased, was simply that
the values used for X (see 12) were always greater than 4,
and increased rapidly with «.

By plotting the numbers found for Y with the corresponding
values of X, a straight line is obtained from which the values
represented by the symbols in (20) can all be determined.
The straightness of these lines, and the verification of the
fundamental formula

nt+atT=l1,

94 Dr. W. E. Sumpner on the Diffusion of Light.

affords a good criterion of the extent to which the principles
and the formule, referred to in this paper, can be relied
upon.

"The following Tables IIT., [V., and V. contain the results
of three sets of tests on the transmitting-jower of blotting-
paper and tracing-cloth, and on the reflecting-power of
tracing-cloth. The values of Y,,. are calculated with the
aid of (12) and (16) from the observed valnesof «andy. All
the dimensions are given in centimetre-units. In the accom-
panying sheet of curves the values of Y,,, are plotted as
ordinates, with the corresponding values of X as abscisse.
From the straight line most nearly representing the connexion
between the points the values of Y,,,, have been obtained,
and are given in the tables. From this straight line also the
true value of the transmitting (or reflective) power can be
found by finding the value of the ordinate when X=4. The
intercept on the axis of Y shows the portion of the light which
is diffused.

Tasie L1].—Transmitting-Power of Blotting-paper.

A=980, K=26. £=2 r=92. Y,.1,=650527R/*

Pesos es | 60 50 40 45 AD 60

yi Were neal: ge tO 84. 1046 187. 154 |
X Bee | 136 9-8 70 weer;
ee | ibd . 182 - 112. 19-0... (142s
av wae Os | 157° 481-979" yea 4 ae

TaBLE 1V.—Transmitting-Power of Tracing-cloth.

A=980, K=931. s=2 r=544. Yi). =410+418-4X/4.

haces S028 cnow .) WOW 894. 105:6°> 953. 17 eae 46-1 |
SORE | 6 ose 50M NS6 Pra" 22°30 19-4- > 15 ee 8°25

BUOY bs Oe tere SO a7. OGSHIG 107 915 Sli -ias

os Gta Sion 5 60'6 40-9272 AS 106 940-- 7802 sa

ide)
Qn

Dr. W. EB. Sumpner on the Diffusion of Light.

Taste V.—Reflecting-Power of Tracing-cloth (shiny side).
A=1300. K=12. £=2. 9=85°7. Yate, =80°9+4'8X/4.

J Pee 56 55 623 598 475 445
ee OLA | 977, 1202. 85. 755
BO ii! ee S10 Ae tO4y 7-22 655
ee... Wee Set lee AS 2) 896 S86
Me eresates: | 408 «418 4k 484896 88-7

200

150

100,

0 5 10 15 20

Several sets of tests were taken. Some of these are repre-
sented by the sheet of curves shown in fig. 4. Y is the
percentage of the incident light which the surface apparently
reflects or transmits, assuming that it is all diffused, and is
calculated from equation (16). The true values ef the co-
efficients are obtained from the curves by applying equations
(19) and (20). The numerical details of the observations are
of no special interest, and the essential results may be sum-
marized as follows :—

96 Dr. W. E. Sumpner on the Diffusion of Light.
TasLe V1I.—Reflective Powers.
Regular. Diffased. Total.
7): No: 1).

——— —— ———_____ |, ——__—_

ee a oeeemae

Blottme=paperzts.c.0.se22 34sec | 0 per cent.| 82 percent. | 82 per cent.

if

Cartridge-paper ~.2..----.5.25- 8) S SO 2 80 = |
Tracing-cloth (shiny side) .... 48 ,, | RO case fee |
» (cough side)...| 2-7 ,, B168 | BY ay cial
Tracing-paper .............06... D2. ss 19:3. | DEO
TasBLeE VIi.—Transmissive Powers.
Direct. | Diffused. Totaly:
Tae Tix ze
Blotime-papetices...0-------- 2-7 per cent. | 6:5 per cent. | 92 per cent.
Cartridge-paper .........0. a ee 87, a
|
racine =e Opies: cece aneaner | 13°4 5 41-0 % | Sas oe
|
Tracimeopapetesc:-..0--.267- | 29°8 os 46:2 A 76:0 3

We may now collect the coeflicients 7, a, 7, determined by
the foregoing independent methods, and compare their sum

with unity. TABLE VIII

0. a. T. nt+eatr.
Blutting-paper ...... 82 per cent. | 13°8 per cent.| 9:2 per cent.| 105-0 per cent.
Cartridge-paper ...| 80 ___,, 22a. | CU ee 1034.5,
Tracing-cloth ...... Sper, | 150 3 54:4 te 1044 — ,,
Tracing-paper ...... v7 aaa (fe TOD a 1050 ae

The numbers in the last column differ from the true value
of 100 per cent. to a greater extent than can fairly be accounted
for by the limits of experimental error. They are all over 100;
and this was the case, not only for the tests here given, but
also for every one of many sets of tests taken. The small dis-
crepancy would be accounted for by assuming that the law of
cosines is not exactly fulfilled. A very slight departure from
this law would be amply sufficient to expiain the results.

Suppose the candle-power of a unit area of a diffusing
surface in the direction of the normal is B, and in any

Relation of Volta Electromotive Force to Pressure $c. 97

direction ¢ is B (cos )!+«,
It is then easy to show that the total amount of light given
out per unit area is equal to

Bia

-
(es
+9
In all the above experiments the actual measurements have
referred to the light receding from the diffusing substance at
inclinations all practically normal to its surface. The quantity
B has been measured, the total light has been calculated as

a B, and has been overestimated in the ratio 1 +5: Ie

To account for an error of 5 per cent., the quantity e« need
only be 0-1. The brightness of the surface (in the physio-
logical sense) would, when viewed at an inclination @¢, be
proportional to

B (cos g)'t*/cos f, or B (cos d)*.
This quantity is practically constant (if e=0°1) until @
becomes very large. Its value is ‘994 for 6=20° and :974
for @¢=40°, and the change in the brightness of the surface
would hardly be perceptible to the eye.

This correction applies to the coefficients 7, and T.; it does
not affect the values of 7, #, or tT, In some of the first tests
of reflecting-power the inclination of the light-rays to the
surface was considerably less than 90 degrees, and the values
of 7 obtained were less than those given above. ‘These tests
confirm the idea that the cosine law is not strictly fulfilled,
but they were not accurate enough to be conclusive.

The above measurements were all made in the Optical
Laboratory of the Central Institution, and the writer has had
the benefit of the assistance of some of the students of that
College in re-testing and confirming the results given in the
foregoing tables.

XM. Relation of Volta Hlectromotive Force to Pressure §e.
By Dr. G. Gore, P.A.S.*

aan years ago I made several experimental
attempts to discover a difference of molecular state of
the upper and lower ends of a vertical column of solution of
cupric sulphate:—I1st. By suddenly reversing the ends of a
utta-percha tube, about 6 feet high and 6 inches diameter,
filled with the liquid, by swinging the tube in a vertical
* Communicated by the Author.
Note. Compare Wild’s experiment (Wiedemann’s Galvanismus, 1872,
vol. i.p. 776; Pogg. Ann. 1865, vol. exxv. p. 119).

Phil. Mag. 8. 5. Vol. 35. No. 213. Feb. 1898. H

98 Dr. G. Gore on the Relation of Volta

plane upon a transverse horizontal axis at its centre, the ends
of the tube being formed of two similar plates of electrolytic
copper connected with a galvanometer ; and 2nd, by simul-
taneously raising and lowering two similar disks of copper 1m
a tall column of such solution, the disks being attached to the
galvanometer and suspended from the two ends of a cord
passed over a pulley. These attempts, however, were not
successful owing to disturbing influences at the surfaces of
the plates, and to the employment of an insufficiently sensitive
galvanometer. Recently I have renewed the experiments in a
somewhat different form, and have succeeded in obtaining de-
finite though small effects; only minute ones were anticipated.

The arrangement usually employed was as Fig. 1.
follows:—A single glass tube (or several), about
3 metres long and 1 centim. bore, securely
fixed upon a board, was fitted with corks and
two wire electrodes of the same kind of metal
at its two ends, and filled within *5 centim. with
an electrolyte (see fig. 1). It was then placed
horizontal, so that the bubkle of air receded
into the branch of the tube; the two elec-
trodes were then connected with a Thomson’s
reflecting-galvanometer of 3040 ohms resist-
ance, and the tube allowed to remain undis-
turbed until all sign of current or of variation
of current ceased. It was then placed vertical,
and as soon as a steady permanent deflexion
occurred its direction and amount was noted ;
the tube was then placed either horizontal until
all current ceased, or at once placed vertical
with its ends reversed, and the amount of
maximum steady deflexion again recorded.

In many cases five such tubes were fixed
upou the board and connected in series, the
upper electrode of one to the lower of the
next one, in order to multiply the effect, and as
many of them charged with an electrolyte and
connected with the galvanometer as was desired.

The electrodes were fixed in the corks by
means of melted shellac, and the corks were
saturated with melted paraffin. By employing
suitable metals and electrolytes, making each
pair of electrodes of metal cut from imme-
diately contiguous parts of the same piece, and
including in each instance a wire coil of 50,000
ohms resistance in the circuit, the fluctuations Sag B

TV

VAIL EAMTATH ANU ROHOV UCT TH

Wt ls
Aaa

cul

Electromotive Force to Pressure §c. 99

of the current were reduced to a minimum, and the needles
usually settled at or near zero in about 5 or 10 minutes
after closing the circuit with the tubes in a horizontal position.
No perceptible amount of interference was caused by the
small difference of temperature, usually equal to about 1°°5 C.
of the upper and lower parts of the experiment room. All
the experiments were repeated two or three times in order to
ensure reliable results.

The solutions employed were all of them made with dis-
tilled water, and were in nearly all cases dilute; the exact
strength used, however, was not a matter of much importance.
Those of the halogens usually contained about 3°29 grains of
chlorine, 7°41 grains of bromine, or 11:25 grains of iodine in
18 ounces of water. Those of the acids contained about
D9 grains of absolute acid in 40 ounces of water ; and those
of neutral salts or of alkalies contained about 300 grains of
the substance to that amount of water. The electrodes of
cadmium, zinc, aluminium, tin, lead, and copper were formed
of thick wire; and those of nickel, iron, silver, gold, and
platinum were thin wires. The following Tables give the
particulars and the results.

TABLE I,

Hffect of Varying the Hlectrolyte only.
With Electrodes of Zn.

aS Substances. Grains per oz. noe Saas
122 (3) Re eee 164 9) 8° A
C135 ea Bi) f 0
3. CPCI ..22%.: 1848:°3 2 50° A
4, Br+KbBr ......... OT+ ,, . 28715
5. ST ed ed 62+ ., ” 12° ”
6. (CHE oO) > 4 sat. soln.+9°4 4 Ooh
fee |, Br--K Bro i..5. 00. 6drops+ ,, i Very variable.
(Sg pl Ges Ss (Ge 3 grains+ ,, 5 20° 4
9 | 5 (( ©) [gene <hr Sam 68 5 0°
10 HBr dlolclatatafetetelatal avers ‘92 ” 9
tal: FSO; tree scene's 16 » 5
12 HINO), Pee Sate: 1e2 An ”
13 EUCIO, Baers. 6 Sess “75 cs a3
14 HBrO, erefulninje'uinin wists ? ” ”
15 ELLIO) cxteneceates 2:5 2 3 |
16. Acetic Acid ...... 21 “i ”
Wie ce artaricg © «nee: 37 ‘ 7
18. Oxalicw Wai era if . Ke
19. | HClO,+ KOIO, .. 1-0+7°5 3 20° 4
20. HCl+Am(Cl..... “65+7°5 5 ee eat! nots

100

No. of

Expt. Substanees. Grains per 02.
Ess) LRU Somer ecnec toes 75
vy RY, Gay 5 ek | 5
Pes K Bee e a: 53
PA | KOI os... | 5
7-13 aa fee © 51 8 a ee 2°5
26.8) 4? KV ORAS 525k T5
Zils | RIN a ech a. sais. és
DS Salt IC Ogee ee Pe: -
3 sa al (a Us} Cee aoa #
BOr Ol Ki OeO preven... 5
3l. Sh On oe ae a
39, eK Masiegees «| :
pss Mien Wel (GE | Cl sere ema 5
O42 | RECO. 2 ok. 3
35. (Reet atesthse. ss
ais (ie (| Le ae 75
BYE (SY Br on eS ee
38. Te De ee ae eee =
PS ee ee C1 (0 | es 4
AQ) | DN INO.7 os. coos. e0s: 7
le TSEC Cyan aie one | :
AD) Na COs is... Se. 33
AS til AN AOD? 5 ci ccen nes 5
44, IMCLEL Os arene as
ADs 4) han Oiee 2ist hee 75
AGS | PATER ose occ ee ¥3
AG. 3) sam. crue -
4S >"|-AaneSO 7 > vies
49. AmSesquicarb. ... ie
i baie Weta irl 2 ( See eee $3
DN | PAWL oe teccce 75
Livia lie 5: 3 age ARS ee -
Diba sal geal ence be van ge S
54; -+| Ba2BrO, | .....222. sf
BS: Th BaZN On| se... d8e. 5
Die MIE eres wceteae ra)
Dc Hl EOIN coe. actos Me
ie igae! Bi 041 0) ISS oe Sa T5
Sys es bal FO) a Se eae ae 795
GO. UM ESO Frees so 2: -
TIGR E11 C1 a Ses Semen a 75
ad ar AEN 0. na ae 3.
Cob Ars) Ces ae oes e
2 ee es DSS) eed eae 75
65. | Distilled water ...| 32 oz.

Dr. G. Gore on the Relation of Volta
Table I. (continued).

No. of
Tubes.

Amount of
Deflexion.

TT —— ————————_ .

wt

Electromotive Force to Pressure &c. 101

TABLE II.

Effect of Varying the Electrodes and Liquids.
With Electrodes of various Metals.

me. Substances. Grains per oz. eas Tiee
66. | Al with Cl+KCl.| d sat. soln. +94 4 20° A
67. » », Br+KBr.) 6 drops ota 3 302 a5
68. |CdwithC1+KCl.|4sat.som.494/ 4 | 20° 4
69. » » Br+KBr. 6drops’ + ,, Hs 202":
70. 3) os DEKE s..| 3igrains + ,, 302";
71. | SnwithCl+KCl. | } sat. soln. +9-4 1 10° |
72. » » Br+KBr.| 6drops + ,, x 0°
73. | Pb with C1+KCL| d sat. soln. +9-4 1 oe
74. pec l|On.. 75 grains. 3 0°
75. | Fe with Cl+ KCl, 3 sat. soln. +9°4 1 20° A
76. Co ? 9) =F b} 9) =F 9? »” 35° bP)
(Gk Ni 99 99 + 99 99 Te 39 59 50° oe)
78. Cu +) 99 + 99 99 ata 9 50° 99
79. » >» Br+KBr.| 6drops 4+ ,, et 0°
80. |Ag ,, Cl+KCl.| d sat. soln. + ,, 1 0°
Oe &,, KC... .~. 1D 5 0°
82. |Au ,, Cl1+KCl.| § sat soln. +9-4 1 30°
83. Pt 99 39 == 9) >) i 9 19 99 ‘)
84. » » Br+KBr.| Gdrops + ,, 5 0°
SPM 55,7 FOL orcas 16 4 i,
Somming 1, KCIO, 75 2 -
87. ” ” KHSO, 99 5 ”
&8. 9 9 KHO 9 ) ”

TaseE ITI.
Hiquivalent Solutions.

No. of : No. of Amount of

ae Substances. Grains per 02. Tales. Dereon:
89. | Cdwith Cl+KCl.| -18 gr. + 8° gr. 2 12°
90. ” ” Br+KBr.| °37 ein oy ” 28°
91. ” ” T+KI ...| 62 pe ies a 2 10°

In experiments Nos. 17, 18, 20, 66, 67, and 70, evolution
of gas and disturbances of the current occurred; and in
Nos. 71, 72, and 73 the quantity of water employed was only

18 ounces.

102 Dr. G. Gore on the Relation of Volta

In every case of production of current, provided the two
electrodes were neutral whilst in the horizontal position, and
were allowed to remain sufficiently long in each of the vertical
ones, the two opposite currents produced were equal in
amount. In all the cases in which a sudden change from
the horizontal position (and a neutral state) to the vertical
one was attended by production of a current, the maximum
amount of deflexion of the needles usually occurred in about
three minutes ; but if in any case, whilst the tube was vertical,
its ends were suddenly reversed, the reversal of the deflexion
required a longer period of time to attain its maximum.

Degree of Permanence of the Currents.

With the object of ascertaining whether the currents were
temporary or permanent, two of the tubes were fitted with
zinc electrodes and a solution of NaClOs of the usual strength
(see exp. 389) made with distilled water, which had been
deprived of air by boiling. After having become neutral in
the horizontal position, they were placed vertical and gave
the following results :—

TABLE LV.
Influence of Time.
Laue Of | Minutes. Deflexions. |, Minutes.| Deflexions.|| Minutes.| Deflexions,
experiment.
fe) je) °
(\- Ast. 10 } 10th. 30 75th. 30 }
| 2nd. 20 ,, 15th. se 90th. ae
92.
die) Sd. 25, | webth: eile 105th. le
| 4th. 30 ,, 45th, 25 ,, 120th. 7.
\| 5th. shan | 60th. ee 16 hours. yA
l

By subsequently placing the tubes horizontal to become
neutral, and then erecting them again, the deflexion was 25°}.
The results show that the action was of a comparatively per-
manent character, and that the currents were not due to
dissolved air.

Influence of Strength of Solution.

In this case zine electrodes and two solutions of the same
substance of different degrees of concentration were employed.

Electromotive Force to Pressure Sc. 1038

The upper and lower ends of the tubes were wrapped in
cotton-wool. The following are the particulars of the ex-
periments :—

Number of

os: : Number of | Amount of

experiment. SESE AGe, | CUES [De . Tubes. Deflexion.
93. KCW a. +0 2 8
94. 5 Ee 40:0 ” 12 ,,

These results show that the amount of deflexion was in-
creased fifty per cent. by employing a solution of ten times
the degree of concentration (compare alsu experiments Nos. 3
and 5 with 6 and 8). The catton-wool had no apparent effect
upon the amount of deflexion, thus showing that the unequal
temperature of the upper and lower parts of the room had no
perceptible effect.

Period of Time required for Reversal.

With zinc electrodes in the solution of KC1O; (exp. 24)
and three tubes, the period required to attain the maximum
effect after a complete reversal was 4°5 minutes, and was the
same after standing vertical 15 hours. |

With zinc electrodes in the solution of Na,SO, (exp. 41)
and three tubes the time required to completely reverse was
10 minutes, and in the solution of KCl (exp. 21) it was
15 minutes.

With cadmium in the same solution of KCl it was 13
minutes, and after standing vertical 18 hours it was again
13 minutes.

The degree of fixity of the state produced varied, therefore,
both with different liquids and with different metals, but not
with lapse of time.

Degree of Electromotive Force of the Current.

This was measured by the method of balance with two
thermoelectric couples of iron and German-silver wires, the
junctions of which were immersed in melted paraftiin at
120° C., the outer ends of the wires being at 20°C. With
zinc electrodes in two tubes and the solution of four grains of
KCl per ounce of water, giving a deflexion of 8 degrees, as
in exp. 93, the electromotive force was equal to ‘00072 volt.
Wild (see note, ante) attempted to find the variation of

104 Dr. G. Gore on the Relation of Volta

electromotive force of amalgamated zinc in a solution of zine
sulphate by increase of pressure of about two thirds of an atmo-
sphere, and observed that it was in any case less than one
400,000th of that of one Daniell’s cell, = about ‘0000028 volt
(compare exp. 63). He apparently failed to discover the
phenomenon of the current by not happening to select a
suitable electrolyte.

General Results.

On examining Tables I., II., III., and IV. various facts
may be observed :—Ist. Currents were produced by using a
large variety of metals as electrodes, and by employing various
kinds of electrolytes. 2nd. The results varied both with the
kind of liquid and with that of metal. 3rd. In every one of the
ceases in which the liquid employed was a diluted acid alone no
current was observed, and the addition of a salt to the acid
appeared to have no effect unless the salt alone gave a current
(compare exps. 19, 20, 24, 45). 4th. Out. of 91 experi-
ments 41 gave perceptible currents ; probably in many other
cases currents were produced, but were too feeble to be
detected. 5th. Out of the 41 cases in which a current
occurred, in 39 it was in an upward direction and in 2
downward. 6th. The current continued many hours without
sensible diminution. 7th. In every case the current was
extremely small, and required a few minutes to attain its
maximum amount. 8th. It was much smaller with a dilute
solution than with a concentrated one. 9th. The largest
current occurred with zinc in a solution of Cl and KCI, prob-
ably in consequence of the great chemical energy of the
combination and the small amount of resistance. 10th. By
adding to a solution of Cl some KCl, or to one of Br some
KBr, a larger current was obtained than with either liquid
singly, probably in consequence of diminution of resistance.
11th. Sclutions of iodides frequently gave smaller currents
than those of bromides, and bromides less than chlorides ;
there are, however, numerous exceptions to this statement.
And 12th. Vibration of the lower electrode by means of a
tuning-fork had no apparent effect upon the maximum
current.

Influence of Equal Pressure at the two Electrodes.

In order to ascertain whether the current was produced
during the absence of any difference of pressure at the two
electrodes, I employed one of the usual tubes, 3 metres high,
having a porous biscuit-ware diaphragm ;% inch thick near

Electromotive Force to Pressure &c. 105

its lower end, offering such a degree of Fig. 2.
hindrance as to almost entirely prevent
the flow of the liquid, whilst allowing
the electric current to pass, and provided
with a bent glass tube at its lower end
to receive the lower electrode (see fig. 2).
In order to prevent any diminution of
pressure at the upper electrode an open
branch-tube was provided, as shown ;
and to obviate any increase of pressure
at the lower one, a minute nick in the
side of the lower cork allowed any of the
liquid which had passed through to over-
flow: only one drop of the liquid, how-
ever, was forced through by the pressure
in about one hour. Sufficient hindrance
to the passage of the liquid was obtained
by coating the whole of each end of the
diaphragm with varnish, except a minute
portion of the surface about 1 millim.
diameter. A perfectly clean diaphragm
was employed in each case, and it was
soaked in the liquid previous to use.
Only a single tube with zine electrodes
was employed in each experiment.

Two experiments were made, one with
a solution of 18°7 grains of chlorate of
potassium and the other with 18°7 grains
of nitrate of strontium per ounce of pre-
boiled water, and although the circuit
was complete no current was produced
by placing the tube vertical in either case (compare exps. 24
and 57). These results prove that the current was not
produced during the absence of difference of pressure.

este eee:

VOU EE Ee et

LUCA VELARDE UV CUT TEACUP TOU TT Ty a

CULATED TUDE CETTE ETE EET EU

eT

li

Influence of Difference of Pressure without Difference of
Altitude.

In order to test whether difference of pressure alone was
sufficient to produce a current, the following arrangement was
employed (see fig. 8). A, pressure-tube containing mercury ;
B, very thick tube of indiarubber ; C, glass tube witha branch
containing a zinc-wire electrode securely fixed in it by means
of a cork and shellac ; D, porous-ware diaphragm 3 inch long
and 4 inch diameter fixed inacork ; H, a second branch-tube
containing the other similar electrode. The diaphragm was
sufficiently impervious to allow not more than one drop of the

106 Dr. G. Gore on the Relation of Volta

electrolyte to pass per hour whilst under the pressure of a
vertical column of 380 inches of mercury. The electrolyte

Fig. 3.

XS

G;

was a solution of 18°7 grains of chlorate of sodium per ounce
of water, and was allowed to completely saturate a perfectly
clean diaphragm previous to the experiment being made.
The entire arrangement was fixed upon a board.

After placing the tube A horizontal until the two electrodes
became neutral it was quickly raised to the vertical position:
a current and deflexion of 10 degrees was gradually produced
in about three minutes. This current was permanent, but
gradually diminished to 6 degrees on removing the pressure.
Several trials were made, and in each case the electrode which
was under pressure was positive to the other. By repeating
the experiments with a pressure of 52 inches height of mer-
cury, a defiexion of 12 degrees was obtained. The experi-
ments were repeated with the apparatus modified by haying a
glass tube about 3 metres long fixed to the end H and filled
with the electrolyte, with the second electrode transferred to
its distant end: whether this glass tube was horizontal or
vertical, the effects of varying the mercurial pressure were
substantially the same as in the previous experiments. These
results show that difference of pressure alone was sufficient to

Electromotive Force to Pressure Sc. 107

produce the currents. In all these experiments, and in the
previous ones in which a diaphragm was employed (see fig. 2),
the latter manifestly diminished the amount of the current.

Influence of Thernelectric Action.

It might be supposed that the stronger pressure at the
lower electrode, by giving rise to greater chemical heat, is
attended by a thermoelectric current from that electrode to
the electrolyte ; and this view is apparently supported by the
circumstances :—Ist, where the chemical energy is greatest
the current is usually the strongest ; 2nd, the full strength
of the current is developed gradually ; and, 3rd, the current
is a continuous one. But it does not agree with the fact,
established by numerous and varied experiments, that whilst
heat usually makes metals more electropositive in solutions of
alkaline salts and alkalies, it makes them more negative in those
of acid salts and acids (see “‘ The Thermoelectric Properties
of Liquids,” Proc. Roy. Soc. 1878, vol. xxvii. p. 513). If heat
therefore was the cause, downward currents would have
occurred in the latter group of liquids, instead of which no
currents occurred in dilute acids, and upward ones were pro-
duced in solutions of acid salts.

In order to finally settle this point, I made the following
experiments :—Two vertical metal wires, 2 inches long, coated
with shellac over about an inch of their length at about half
an inch from their ends, were immersed three-fourths of an
inch in two portions of the electrolyte contained in two small
glass beakers placed about 3 inches asunder, the two portions
of liquid being connected together by a piece of clean linen
tape previously soaked in the solution and laid upon a strip
of sheet-glass connecting the edges of the two vessels ; each
beaker contained a thermometer, and the wires were connected
with the usual galvanometer. After the needles of the gal-
vanometer had settled at zero, heat was applied to one of the
beakers until the temperature of the liquid had risen about 3
or 4 Centigrade degrees, and the effect was then noted.

With zine and the solution of KHSO, of exp. 29, no per-
ceptible current occurred, but in that of NaClO; of exp. 39
a deflexion of 20° was produced, the warm metal being nega-
tive. With platinum in the KHSQ, solution, and in that of
KHO, no current was perceptible (compare exps. 87, 88).
These results together with those previously mentioned clearly
prove that the currents obtained were not due to thermo-
electric action.

108 Dr. G. Gore on the Relation of Volta

General Remarks and Conclusions.

The currents were manifestly occasioned by difference of
pressure at the upper and lower electrodes, and apparently
by that circumstance alone. They were not due to the unequal
temperatures of the room or to heat evolved by the pressure
at the lower electrode, nor to air or impurities dissolved in the
water, nor to bubbles of gas &. adhering to the electrodes,
nor to greater conduction resistance of the electrolyte in a
downward than in an upward direction, nor to difference of
altitude of the electrodes except so far as it affected the
difference of pressure; nor were the deflexions caused by
mechanical disturbances of the galvanometer or by any
magnetic substance near it. They were also not produced by
thermoelectric action due to greater chemical heat at the
lower electrode. In all the cases in which a diaphragm was
employed, the electric current due to pressure was not per-
ceptibly affected by any current produced by flow of the
electrolyte through the partition ; the considerable conduction
resistance of the septum, however, largely reduced the quantity
of the current due to pressure.

The results of the experiments in general indicate that the
upper and lower ends of a column of an electrolyte are not in ex-
actly the same physical or chemical state ; that a fixed difference
of condition of the liquid and metal was gradually produced
when the tube was placed vertical, and that this condition re-
quired several minutes in order to attain its maximum. ‘That
both the metal and the liquid are altered by the pressure is
shown, not only by the fact that a change of either affects the
amount (and in some cases also the direction) of the current,
but also by the circumstance that the period of time required to
reverse the condition, and the current, by reversing the tube
varies with a change of metal as well as of liquid. These cir-
cumstances are interesting, and indicate the gradual produc-
tion by pressure of a state of mechanical stress of the lower
electrode and of the liquid near it; and as action and reaction
are always equal and opposite, the state of stress of the metal
must be attended by one of counter stress of the liquid. The
same states of stress might of course be produced by means
of a hydraulic press, a lever, &., or by centrifugal action
during rapid whirling of the tube. As the increase of pressure
and stress at the lower electrode was followed by the production
of a permanent electric current, it must also have been followed
by increased energy of chemical union of the metal and liquid

a
”

Ellectromotive Force to Pressure &c. 109

and an increase of electromotive force at that electrode ; the
three kinds of pressure—mechanical, chemical, and electrical—
varying directly together. The greater mechanical pressure
at the lower electrode enabled the liquid and metal to
chemically unite with greater energy, and thus permitted that
electrode to become electropositive to the other. The fact
that the strongest currents were usually obtained by the use
of the most energetic chemical substances further support the
view that the phenomenon is partly chemical, and it is well
known that certain substances will only chemically combine
whilst kept under pressure together.

In all the cases in which the more positive metals, such as
zine, were employed, both the electrodes were visibly corroded ;
as, however, the electric current was excessively minute, only
an extremely small proportion of this chemical action was
inseparably associated with it; and as the currents were not
due to ordinary chemical heat, any examination of the com-
parative losses of weight of the two electrodes by corrosion
would probably have been of but little value.

The phenomena suggest some abstruse questions,— What is
the most hidden cause of the current? Only a very funda-
mental cause could have produced so large a proportion as
95 per cent. of currents in one uniform direction. The
original cause must lie in some change of the potential motion
of the molecules ; some kind of molecular energy must have
been lost in order to produce the currents. The immediate
cause was probably a small proportion of the potential energy
of the motion of the superficial molecules which must have
been transformed into current during chemical union of the
metal and liquid, the other and far greater portion being
directly changed into chemical heat. The questions why one
portion is directly converted into electric current and another
into heat, and why so largely into heat, I have not examined
(compare Proc. Roy. Soc. 1884, vol. xxxvi. p- 8381; also
M. B. Raoult, Ann. de Chim. et de Phys. 1867, pp. 137-193).

We know that work is done during the act of putting on
the pressure, and that this work may increase the energy of
molecular motion; in addition to the energy communicated
to the arrangement in this way, constant pressure may pro-
duce constant current if there is a continual yielding of the
molecules to it; but as only motion can produce motion, and
as unchanging pressure isa purely statical phenomenon, if
there is no such yielding unvarying pressure cannot be a real
cause of continuous current. We know also that the properties
of substances and the molecular motions to which those

110 Dr. G. Gore on the Relation of Volta

properties are due vary with every change of mechanical
pressure. If, therefore, pressure alters the direction or the
velocity of molecular motion, it may act as a permitting con-
dition so as to enable some of the unceasing motion of the
molecules to expend itself in producing a permanent current,
like such motion does in a voltaic cell; and this appears to
be a reasonable explanation. Contraction of total volume by
chemical union, being a yielding to pressure, may contribute
to the result in the present case.

As the production of current was conditional upon deference
of pressure at the two electrodes, it must have been as much
dependent upon the pressure and the state of molecular motion
at one electrode as upon that at the other. And as we know
that volta electromotive force is very intimately connected
with velocity of the molecules, and that the two appear to
vary directly together (see ‘“‘ A General Relation of Electro-
motive Force to Equivalent Volume and Molecular Velocity,”
Proc. Birm. Phil. Soc. 1892, vol. vil. pp. 63-188; The
Electrical Review, vol. xxx. pp. 693, 722, 755, 786; and
Phil. Mag. Sept. 1892, p. 307), it is probable that the greater
degree of pressure at the lower electrode permits some of the
molecules of liquid and metal to strike each other with greater
velocity than at the upper one. It is worthy of notice that pres-
sure has the same effect as dilution of the electrolyte, &e. upon
volta electromotive force (zbzd.) ; as dilution and pressure each
separately increases volta electromotive force, and as dilution
is apparently attended by an increase of velocity of the mole-
cules, it is reasonable to conclude that pressure is probably
attended by a similar effect. It would be interesting to in-
vestigate the relations of the current to the compressibility and
elasticity of metals and electrolytes. The present results
indicate that electromotive force may be due to unequal mole-
cular pressure.

Whatever may be the manner in which the molecular
motions are affected by pressure, whether by altering their
direction or their velocity, the experiments of this research
show that they are influenced in essentially the same way in
39 out of 41 instances, and it is evident that only some very
fundamental cause could produce such a uniform effect. The
fact that nearly all the currents are in one direction suggests
that the real cause of electromotive force itself can only be
about one stage more fundamental than the cause of the
currents. In all cases the currents obtained were results, not
only of a difference of electromotive force between the lower
metal and liquid and the upper ones, but primarily of the

Electromotive Force to Pressure &e. Lie

influence of pressure upon the electric potential of the metal
alone and upon that of the liquid alone at each electrode.

It is probable that an investigation of the effect of pressure
upon the electric potential of the metal alone and upon that
of the electrolyte alone would yield more uniform results
than that of its effect upon the electromotive force of the two
substances in mutual contact, because the conditions would then
be more simple ; but as the effect upon the potential produced
by a single compression would be extremely small, a series of
compressions, with the effects of them accumulated by means
of an electric condenser as in an influence machine, would be
necessary in order to render the effect manifest. Such a
research would probably show that pressure increases the
positive potential of positive substances and the negative
potential of negative ones. As pressure increases electro-
motive force it must increase the two kinds of electric potential
which constitute that force; thus in a case where a current
occurs with a closed circuit, the two potentials are always pro-
duced if the circuit is open. The facts also that the largest
currents in the present research usually occurred with the
most positive metals and the most negative electrolytes (see
exps. 3 and 6), and the smallest frequently, though not in-
variably, happened with the most positive electrolytes (see
exps. 33, 34, 42, 43, 49, 50), support this hypothesis. Some
of the cases in which no appreciable current was produced,
or in which reverse ones occurred, might have been due to
the pressure increasing the electropositive potential of the
liquid as fast as, or faster than, that of the metal.

Although some effect of the atomic or molecular weights
of the substances employed upon the direction or magnitude
of the currents must have occurred, none was observed (see
Table III.) ; many additional experiments would probably be
necessary to properly examine this question. I have not
been able to suggest any explanation of the circumstance that
diluted acids did not in any case produce a current ; nor have
I been able to investigate in what manner the pressure may
have affected the direction of motion of the molecules of the
combining substances, but possibly some information might
be obtained by examining the influence of pressure upon the
thermal spectra of the substances and comparing the results
with those obtained in this research. As the properties and
molecular motions of substances vary with every change of
temperature, it is probable that the electromotive force pro-
duced by unequal mechanical pressure would vary with the
temperature of the metal and electrolyte.

112 Relation of Volta Electromotive Force to Pressure §c.

Liffect of Pressure upon Voltaic Couples.

In all the foregoing experiments the investigation was
limited to the influence of pressure upon the electromotive
force generated by a single kind of metal and a single kind of
liquid, and did not include its influence upon that of ordinary
voltaic couples composed of pairs of metals or pairs of liquids ;
it is evident, however, that the latter are only compound cases
of the former. Gibault has already experimentally examined
the effect of a pressure of 100 atmospheres on several kinds of
voltaic cells, and obtained the following amounts of electro-
motive force in volts :—Daniell’s cell (20 per cent. ZnSO,)
+:0005 ; (27°56 per cent. ZnSO,)+°'0002 ; Warren De la
Rue cells (1:0 per cent. ZnCl,)+°0007; (40°0 per cent.
ZnCl.) —:0005 ; Volta’s cells —:06; Bunsen’s —-04; Gas
battery +0°8 (Comptes Rendus, 1891, vol. cxiil. p. 465; The
Hlectrician, 1891, vol. xxvii. p. 711). Owing to the greater
complexity of the conditions in these experiments, the pro-
portion of cases giving reverse effects was 30 per cent., or six
times larger than in those with single metals in the present
research.

In all such experiments with voltaic cells, we have to con-
sider not only the effect of pressure at the positive metal, but
also that at the negative one. The results obtained in the
present research show that the direction of the current which
oceurs with zine and other positive metals is the same as that
with gold and platinum ; so that the effect of pressure upon
the negative metal of a voltaic couple would probably be in
nearly all cases to produce a greater or less amount of counter
electromotive force, which would either diminish or reverse
the effect due to the positive one. The amount or balance of
effect, therefore, obtained with a voltaic couple would usually
be very much less than that with a single kind of metal ; this
conclusion is confirmed by the results of Gibault’s experiments,
in which the amounts of electromotive force obtained by a
pressure of 100 atmospheres were very much less than those
usually obtained in my experiments by a difference of pressure
of only about 2 or 3 atmospheres. As the pressure alone
attending the height of the liquid of a voltaic cell affects the
electromotive force, it necessarily follows that the energy of
such a cell is affected by gravity and varies with the altitude
and geographical position of the cell.

Pe Pts]

XIV. On Radiant Energy. By B. GaLtrzine*.

§ 1. Introduction.
TARTING with the far-reaching ideas of Faraday, Max-

wellf has developed his theory of dielectrics, in which,
by the identification of light with electrical vibrations, he
comes to the conclusion that a ray of light must exert a
certain pressure in the direction of its propagation, this pres-
sure being numerically equal to the energy contained in each
unit of its volume. One half of this energy is present in the
electric, and the other half in electromagnetic, form.

By an entirely different line of argument, derived from an
application of the second law of thermodynamics, Bartoli t
has arrived at the same result. His paper is extremely inter-
esting, and the method by which he proves the eaistence of
the pressure of light is free from objections, at any rate in
the form given to it by Boltzmann§ in a more recent paper.
But the process by which he calculates the numerical value
of this pressure P appears to me to be wrong. Bartoli
imagines a perfectly reflecting empty sphere of radius R, with
a perfectly non-refleciing (black) sphere of very small radius
yr atits centre. Let Q be the quantity of energy which falls
on each unit of surface of the outer sphere in unit time.
Then if the radius of this sphere be decreased by 6R, accord-
ing to Bartoli the inner sphere receives an amount of heat
g=2Q/V .47R?. dR, where V is the velocity of propagation
of light. In this expression 2Q/V is the energy contained in
unit of volume. Whether the energy can be expressed so
simply or not, is not evident without further explanation.

For the case of a cylinder, & times the energy which is

v
received by any normal section of the cylinder does noé repre-
sent the energy contained in unit volume, as we shall see later.
Boltzmann || has already pointed out that Bartoli does not
appear to have considered the effect of rays with oblique
incidence.
Bartoli goes on to say that, since the inner sphere

has increased its energy by an amount g, the work done

* Translated from Wiedemann’s Annalen, vol. xlvii. pp. 479-495
(November 1892), by James L. Howard, D.Sc.

+ ‘Electricity and Magnetism,” vol. i. p. 144; vol. ii. p. 3983 (2nd edit.).

t Sopra it movimenti prodotti dalla luce e dal calore e sopra i radio-
metro di Crookes (Florence. Le Monnier, 1876). Also Nuov. Crm. [3] xv.
pp. 193-202 (1884) ; Exner’s Repertoriwm, xxi. pp. 198-207 (1885).

§ Wied. Ann. xxii. p. 33 (1884).

|| Tom. ett. p. 35.
Phil. Mag. 8. 5. Vol. 35. No. 213, Feb. 1893. I

114 B. Galitzine on Radiant Energy.

against the pressure of light, viz. P .47R?. dR, must be equal
to this, and hence
2Q
a

This conclusion appears to me to be wrong, although the -
result obtained by a different method of reasoning differs
from Bartoli’s formula only by a constant factor. Our
system consists of the inner black sphere and the space
between the two spheres, which also possesses a portion of
the energy*. On reducing the outer sphere work is done ;
not because the energy of the absolutely black body is thereby
increased—for all the energy gained by the inner sphere is
taken from the space between the spheres—but because the
whole energy of the system passes from a lower to a higher
temperature.

Boltzmann f has also attacked the same question. Let H
be the heat radiated from unit surface in unit time (Boltzmann
denotes it by ¢(t)); then he finds for the pressure P of light
against a perfectly reflecting wall the expression

dE
pa7 ft |r dt — EB],

diy

p=7 [r) ae av],

T being the absolute temperature. He writes the constant of
integration equal to zero. This formula enables us to caleu-
late the pressure P numerically for any assumed law of
radiation. The method by which Boltzmann obtains his
formula is quite a legitimate one, but I differ from him as to
the value of the numerical factor. The subject may be treated
in a more simple manner, as I shall proceed to show.

In conclusion | may draw attention to a paper by Lebedewf,
who has made a very interesting application of the Maxwell-
Bartoli theory, by comparing ‘the force of repulsion due to
radiation with universal gravitation §.

§ 2. Deduction of the Formula for the Pressure of
Light P.

Imagine an empty cylinder AB, of length h, whose walls

or

* Cf. Thomson, Phil. Mag. ce p- 386 (1855).
: Wied, Ann. xly. p-. 292 (1892 | Tomancit.
§ Cf. also Kolacek, Wied. Pies XXX1x. “Pp. 254 (1880).

B. Galitzine on Radiant Energy. 115

and base B, are perfect reflectors, and in which B can be
displaced after the manner of a piston. A is an absolutely
h

black body~ which may be re-

placed, when necessary, by a . |
perfectly reflecting wall. A te
For simplicity, let the area of

the cross section of the cylinder be unity.

Let us denote by ¢ the emissivity of our black body, i. e.
the quantity of heat which unit surface of it radiates out in a
normal direction every second. In a direction making an
angle @ with the normal to the surface the emissivity will
be smaller, namely ecos¢. To obtain the total quantity of
heat E radiated from a unit of surface each second we require
to evaluate the following integral*:—

1/2
B=2me| COMM SING Adi me, 5 . «1 (i)
0

in which both e and E are functions of the absolute tempe-
rature T only f.

Now let us calculate the quantity of energy e in unit
volume of our cylinder when the black surface A is at tempe-
rature T. First of all imagine the cylinder to extend to
infinity on the right, and let e denote the energy contained
in unit volume in this case.

We have obviously
Ge Ee Sg OM ws oh ac atgye ev Cop)

If the surface sent out all its energy EH in a normal direc-
tion, we should have

C= Vv’

or |
oe 2H,

.

But in reality a quantity of heat 2aesindcosd¢dd is
radiated at an angle lying between ¢ and ¢+d¢. The
velocity Vg with which this energy is propagated in a direc-
tion parallel to the axis of the cylinder is, according to the
laws of reflexion, equal to Vcos¢. The amount of energy
in unit volume will thus be greater, and we shall have, as
soon as equilibrium is established,

72 sin b cos ie to
6. =2ire a ee gti) Te i ;
\ Vo ¢ ND NE

* Cf. Wiillner, Lehrbuch der Experimental-Physik, iii. p. 238 (4th
edition, 1885).
+ Cf. Kirchhoff, Poge. Ann. cix. p. 275 (1860).
; 12

116 B. Galitzine on Radiant Energy.

or, from (2), fe
é= as 3 eo 5. «id ae c (3)

e is likewise a function of T only (Kirchhoff). E denotes the
amount of energy which crosses any section of the cylinder
in a given direction during unit of time. In order, therefore,
to obtain the amount of energy contained in unit of volume,
we must multiply the quantity E, not by 2/V, but by 4/V.
(CF. Introduction.)

If P is the pressure exerted on the base B, we have

TAvide
P=1 7 pet é.

First Proof.

Let the piston B be in contact with A, and keep A at
temperature T. Now let the piston B be moved as slowly as
possible through a distance h. The amount of heat Q im-
parted to the system, assuming the masses of A &c. to be
infinitely small, is given by

Q=eh+ Ph.
All quantities of heat are expressed in mechanical units.

If, now, we gradually reduce the temperature of A to zero,
all the energy will be transferred from the cylinder to other
bodies. When this has been done, let B be pushed back again
to A without expenditure of work. The process is reversible,
and as A’s mass is infinitely small the second law of thermo-
dynamics gives us the following equation:—

T T
h de
e+P Tagt
T ={ T aT, (4)

or

pide
pat|, ae, . ees

which was to be proved.
This formula differs, however, from that of Boltzmann by a
constant factor. For, substituting for e¢ its value from (8),

P=7[T| aan et-¥); ae

0

B. Galitzine on Radiant Energy. 117

whereas, according to Boltzmann,

T Tl dH
P=7(T) 7p l—E |. oe (64)

0

Second Proof.

Start with B at a distance A from A, and let A have tem-
perature T. Let us take T and / us independent variables.

Consider, now, how much heat dQ must be given to the
system when T increases by an amount dT, and i by dh. The
work done in this case is Pdh, and

dQ=d(he)+Pdh ;

de
dQ=(e+P)dh +h om aT.

or
The increase of entropy dS is therefore

_ dQ _e+P h de
It follows from this, since according to the second law dS

must be a perfect differential, and since e is a function of T
only, that

Alb ee e ‘° e ° ° ® ° (7)

This equation is an immediate consequence of equation (4),
from which it may be obtained by differentiation.
On integrating equation (7) we obtain

P=1] 0 + | par],

0

P=1(G+ | pS a (8
= + | oa |-e. pe ee eri St)

To make this formula agree with (5) we must put the con-
stant C, equal to zero, which appears perfectly legitimate.
We shall indeed see later that Pis proportional toe. If, then,
for infinitely small values of T, e is proportional to any power
of T, say e=AT”, the assumption C,=0 is clearly equivalent
to the condition n>1.

Third Proof—Yhis proof rests upon the consideration of a
complicated cyclical process, which is the same in principle
as that of Boltzmann. I have merely introduced a slight
alteration, and drawn further conclusions from the equation
which expresses the first law of thermodynamics.

Suppose the piston B to be at A. Move B through a
distance /,, the temperature of A being always kept at Ty.

or

118 B. Galitzine on Radiant Energy.
Let the heat required be Q;. Then, as in the first case,
QO = = exh, + P Ay.

e, and P, denote respectively the energy contained in unit
volume, and the light or heat pressure, at temperature T).

Now let A be replaced by a perfectly reflecting wall, and
let the piston B be moved further away to a distance hg. In
this process an amount of work + will be done, but as the
operation is an adiabatic one the temperature must gradually
decrease from T, to T>.

hy
“=| Pdh. . . 4
WE
The principle of conservation of energy gives us
ho
aun —eaha= | Pdh; ... . ee
hy

or, for an infinitely small displacement,
—d(ech)=P dh, . “o) Raa)

This having been done, we can again replace the reflecting
wall A by a perfectly black sur face, and either (1) oradually
reduce this surface to zero temperature, and then, without
doing any work, push the piston B back to A; or (2) keep
the black surface at constant temperature T, and then bring
back the piston B to A against the constant pressure P, (this
latter being Boltzmann’s operation). The last process neces-
sary to complete the cycle is the heating of A to temperature
T,; this requires no energy, as its mass is infinitely small.
In both cases the cycle of operations is reversible. Applying
formula (4), the second law of thermodynamics gives us the
following set of equations:—

ée:+P, oe: “1 de éo+P, aah de
. n=l pgp he=he| ee Li

From these we obtain

éo+P,
ae

ae
aye

€y
hy—

i —,—-h, =0,

or

e+P
a( 7 h )=0,

d(eh) + Pdh+hdP — fe (e+ P)dT=0;

or, having regard to (10a),

B. Galitzine on Radiant Energy. 119

de SAF)
ior ls PAL
thus leading us back to equation (7) again.
Equation (10a) enables us to find a relation between T and
h for adiabatic processes. As e, and therefore P, are functions
of T alone, it follows from (10a) that

1° eae
ae es uy Seca.» ix, 28 ne ley)

or from (7),

[de ee ree
dT
We can also obtain these formule: by a comparison of the
two integrals in equation (11). These give

Pinder, bo)
{nf Tapa | =0,

an)" Ee ea)
0

Td ak
or AN Te Ner Le
OT ae de
dt

In order to evaluate the expressions in equations (5) and
(13), we should require to know the relation between radiating
power and absolute temperature. But if a direct relation
between P and e could be found by any means, it would enable
us to obtain directly the unknown law of radiation by inte-
erating equation (7). As I have said before, 1 do not consider
Bartoli’s argument to be tenable. I have not succeeded in dis-
covering a relation between P and e from purely mechanical
considerations. Maxwell also, according to his own confession,
was equally unsuccessful*. But the relation sought for may
be deduced from the principles of the electr omagnetic theory
of light, and indeed by a simple application ‘of Maxwell’s
fundamental conceptions to our case, as Boltzmann} was the
first to show. I should like to give a slightly different proof
of Boltzmann’s relation, however.

* Maxwell, ‘ Electricity and Magnetism,’ vol. i. p. 154 (2nd edit.).
+ Wied. Ann. xxii. p. 291 (1884).

120 B. Galitzine on Radiant Energy.

We know that a ray of light exerts a certain pressure
along its line of propagation, which is numerically equal to the
quantity of energy contained in unit of volume of theray. If
the beam is completely reflected the pressure is twice as great.

A 5

(s4a

Suppose for greater generality s is the area of the radiating
surface A, and consider those rays which are emitted with
inclination @ to its normal. According to the laws of re-
flexion these will meet the other base B of our strazght
cylinder at the same angle, as is diagrammatically represented
in the figure. The quantity of energy radiated at the angle
d is
dH=27e sing cospdd s.

We can assume all these rays to have the same direction.
They exert on ab or a'l/, which are perpendicular to their
direction of propagation, a certain pressure dp’, this being
equal to dH/abV.

As ab=s cos ¢, we have

277€

dp = ve sin d dd.

To every element of a/b! there is a corresponding element
of B, which is greater in the ratio of cos¢@ tol, and there-
fore the force acting on each unit of surface of B is cos¢
times smaller than dp’. Besides this, the force acts in a
direction making an angle @ with the normal to B. It
follows that the pressure exerted on B is

dp = dp! cos? $.

If B is a perfect reflector we must double the above ex-

pression in order to obtain the total pressure, and integrate

for all values of @ between 0 and = Hence

72 (lr
P= 2. vA, cos*¢ sin ddd,

or, from (3),
Pete. 6. re

Formula (14) expresses the required relation.

B. Galitzine on Radiant Energy. 121

We see, then, that P is proportional to e. If we substitute
for P in formula (7), and then for e in equations (1) and (3),
we find

de __ 4e
or di ay?
Elias eames oo. ee Go)

This is exactly Stefan’s* law of radiation, which is thus
deduced directly from the principles of thermodynamics and
the electromagnetic theory of light, as Boltzmann has already
indicated.

We have also

Bee erah etree st) 4, OGD ERG)
a formula of which further use will be made in the following
sections.

Hquation (14) makes it possible for us to establish a more
simple relation between A and T. From (13)

,ot__t
or Ah ae

if
Nes (Cy. ape ° e . ° ° ° ° (17)

C, is determined by the initial conditions of the experiment.

It will be observed, then, that in adiabatic and reversible
processes, such as we have just considered, the temperature
varies inversely as the cube root of the volume.

§ 3. The Meaning of Absolute Temperature.

The energy contained in unit volume of our radiation-
cylinder depends directly on the sum of all the electrical
vibrations emitted at temperature T from the perfectly black
surface, these being specified not by their wave-length, which
is variable according to the nature of the external medium,
but by their period or the number of vibrations per second, 2.
If T=0 we must have alson=0. But ifT begins to increase
new swings are constantly being added, and to every tem-
perature there correspends a certain maximum rate of vibration
Mmax, Which the black body is capable of emitting at that
temperature. Plainly mmax 1s a function of T.

FOCI. A icepah ARAM oD)

Let us suppose we are dealing with only one ray (the
whole energy in unit volume will be obtained by integration

* Wien. Ber, Ixxix. p. 423 (1879).

122 _B. Galitzine on Radiant Energy.

with respect to @). If we start with the general equations of
the electromagnetic field the electric force F, at a point,
which corresponds to any given time of swing, must be a
periodic function of the time. Let the corresponding ampli-
tude be a,. Ii the force were constant we should have for
the energy contained in unit volume

1
= 3 AE, ° ° ° ° ° ° (19)

k being the dielectric constant of the external medium.

But in our case F is variable. To every F, there corre-
sponds a particular dielectric constant k,, but the energy in
unit volume for these particular swings is clearly proportional
to a. Since k may be put equal to unity for all swings in
vacuo, the total energy per unit volume (e) is obtained as a
sum of the following form,

e=const. 3 a?,

the summation being extended to all vibrations which the
body is capable of emitting at the temperature T.

a? is a function of T and n.
e@=fT,n). . 19.8 re)

The function / depends directly on the distribution of
energy in the normal spectrum, the term “spectrum” in-
cluding all possible rates of vibration.

If the energy is distributed in a continuous manner
throughout the spectrum, the above summation becomes an
integral.

Let @(n)dn denote the probability of occurrence of waves
whose rate of vibration lies between n and n+dn, then

N»,=(T)

e=eonst. | F(a, Dod@mdn. . eee

For a perfectly black body which exercises no selective
absorption, d(n) is constant, but we ay leave equation (21)
in its more general form. From ( (15), (1), and (8) it follows
that

Dis const." Dd(n)dn: ) (eee
0

The expression under the integral sign is a quantity which
is proportional to the square of the Pomnesipon tis electrical
displacement.

We thus obtain the following result. The absolute tem-

B. Galitzine on Radiant Energy. 123

perature depends directly on the sum total of all electrical
displacements, and the fourth power of the absolute tempera-
ture is directly proportional to the sum of the squares of all
the electrical displacements, these latter being calculated for
vacuum.

The equation (22) enables us to solve another problem. If
we differentiate it with respect to T,, we have

n,,=(T)
Tt ; dw
T? = const. [ | b(n)dri + f(%myL) b(n) ap:

If the function f is known, that is if we know completely
the distribution of energy in the spectrum, we are led to an
equation of the form

Sete
Sr El, 7),

from which the unknown function @ can be determined.

The converse problem untortunately cannot be solved ; that
is to say, a knowledge of the function o tells us nothing con-
cerning the distribution of energy in the spectrum, because
o/(n, T)/OT cannot be equated to zero*,

§ 4. Relation between the Radiating Power and the Surrounding
Medium.

Let us now imagine our radiation-cylinder to contain some

* Cf. on this subject the following references :—Draprr, Phil. Mag.
[3] xxx. p. 340 (1847): KnoBiaucu, Pogg. Ann. Ixx. pp. 205, 337
(1847) : Jaques, Inaugural Dissertation Johns Hopkins University
(Baltimore, J. Wilson & Son, 1879); Bevrbl. ii. p. 865 (1879): Sreran,
Wien. Ber. Ixxix. p. 423 (1879): Crova, Ann. de Chim. et de Phys. [5]
xix. pp. 472-550 (1880): Laneiey, Comptes Rendus, xcii. p. 701 (1881);
xcil. p. 140 (1881), and later papers: DEsains, Comptes Rendus, xciv.
p- 1144 (1882); xcv. p. 485 (1882); xevil. pp. 689, 732 (1883): LrecuEr,
Wied. Ann. xvi. p. 477 (1882): CHrIsTANSEN, Wied. Ann. xix. p. 267
(1883) : SCHLEIERMACHER, Wied. Ann. xxvi. p. 287 (1885): BorroMLEy,
Beibl. x. p. 569 (1886): H. Weser, Wied. Ann. xxxil. p. 255 (1887) ;
Math.-naturw. Mitth, aus den Sitzungsber. d. Berl. Akad. xxxix. pp. 933,
565 (1888); Berbl. xiv. p. 897 (1890): KovEstigerHy, Wied. Anz.
xxx. p. 699 (1887); Ast. Nachr. Nr. 2805, p. 329 (1887) ; Abh. der ungar.
Akad. der Wiss. xii. Ny. 11; Math. u. naturw. Ber. aus Unyarn, iv. p. 9
(1887) ; v. p. 20 (1887); vil. p. 24 (1889); Berd. xii. p. 346 (1888) ; xiv.
p- 116 (1890): W. MicuEtson, Journ. d. russ. phys.-chem. Ges. |4] xix.
p. 79 (1887); [6] xxi. p. 87 (1889) ; Journ. de Phys. [2] vi. p. 467 (1887) ;
Beibl. xiv. p. 277 (1890): EmpEn, Wied. Ann. xxxvi. p. 214 (1889):
GRaAETZ, Wied. Ann, xxxvi. p. 867 (1889): Lord Rayteicu, Phil. Mag.
xxvii. p. 460 (1889): Ferrer, Sill. Journ, [8] xxxix. p. 187 (1890) ;
BLeibl. xiv. p. 981 (1890): Epier, Wied. Ann. xl. p. 5381 (1890): Vioiie,
Comptes Rendus, cxiv. p. 734 (1892) ; Journ. de Phys. [8] 1. p. 298 (1892).

124 B. Galitzine on Radiant Energy.

diathermanous body whose dielectric constant for swings of
frequency nis k, As the temperature remains the same,
the range of frequencies is the same as before, namely, from
n=0 ton, =o(T).

Hquation (19) shows that the energy transferred across
any section of the cylinder will be £, times greater than before,
for swings of frequency n, because the external medium takes
part in the vibratory movement. Also, since the velocity of
propagation V, of these particular waves is smaller than in
vacuum, the energy present in each unit of volume will be
increased k,V/V,-fold ; and if e, is the total energy per unit
volume we have, as in § 3,

— é
Ny»=aXT)

a= const. | kaa fn, TYG (n) dn, . a ees}
0 n

the constant having the same value as in equation (21), which
may be looked upon as a special case of the more general
equation (23).

If we neglect the effect of dispersion of the different waves
we can write down the mean values k and V; instead of kn
and Vn, and we thus obtain

or, having regard to equations (1) and (3),
Are, V Arre

from which
, i ke.

This is exactly Clausius’s law of radiation*, since, according
to the electromagnetic theory of light, provided we neglect
dispersion, we are perfectly justified in taking the square of
the mean index of refraction as equal to the dielectric constant.
Clausius’s law of radiation appears, then, to be a necessary
consequence of Maxwell’s fundataental conceptions.

§ 5. Meaning of the Second Law of Thermodynamics.

The above investigation of the radiant energy in a cylinder
enables us to understand more clearly the meaning of the
second law. In the course of the third proof of the formula

* Clausius, ‘Mechanical Theory of Heat, p. 314, § 10 (Macmillan,
1879); Bartoli, N. Com. [8] vi. pp. 265-276 (1880); Bezbl. iv. p. 889
(1880).

B. Galitzine on Radiant Energy. 125

for the pressure of light we arrived at equation (10a). In
that case the operation considered was an adiabatic one, and
consisted in giving to a new portion of space, or let us say a
new volume of zether dh, a quantity of energy

dq=e dh.

This transfer of energy to a new mass of ether is accom-
panied, as we have seen, by a certain expenditure of work
Pdh. We have, then, two correlative phenomena, and in the
limit, for infinitely small displacement, only 4 of the energy
transferred can be converted into external work. We have,
indeed, from (14),

dt

as
dq ee

The previous investigations enable us to calculate the same
ratio. for adiabatic displacements of finite magnitude; and
this ratio is only a function of the initial and finai temperatures.

From the same equation (10a) it follows that, if we wish
to concentrate a certain quantity of energy into a smaller
mass of ether, this can only be done by the expenditure of
external work, the first law being obeyed throughout the
process. In this lies the closer explanation of the second law.

From equations (10) and (9) we find, for finite displace-
ments,

eyhy —ehy=T= U,— Uz. ° ° ° ° . (24)

is and U, denote the quantities of energy in the cylinder at
the beginning and end of the operation.
From equations (14), (16), and (17) it follows that

N= SOC EI! me 2 AL (95)

Insert this in equation (24) and note that 30C,3 may be
determined from the initial conditions ; we have

T= a
1

The available work is directly proportional to the fall in
temperature (Second Law). Itis only in the case of T,=0, i.e.
when the given quantity of energy U, is distributed over an
infinitely great mass of ether (since according to (17) T=0
only when h=oo ), that the whole energy can be transformed
into externa] work.

In conclusion, let us compare the quantities of energy

126 B. Galitzine on Radiant Energy.

present at the beginning and end of a reverséble adiabatic
operation. These give

ee
Ue ah,
Substituting from (25) and (17),
1
Ben i.
Agus
Who

As fh represents the volume (v) of the sther over which
the given quantity of energy is distributed, the above equa-
tion may be written

U “> = constant.

This is a statement which is probably capable of further
extension. It expresses the fact that in adiabatic and re-
versible processes the quantity of disposible energy is inversely
proportional to the cube root of the volume throughout which
the energy is distributed. The statement does not involve
the absolute temperature, but it really expresses the same
principle as the second law of thermodynamics.

§ 6. Summary of Results.

1. Bartoli’s proof is not admissible in ail its details.

2. The application of the second law of thermodynamics
enables us to calculate the pressure of light, as well as the
changes of temperature in adiabatic and reversible operations
(Boltzmann).

3. The fourth power of the absolute temperature is directly
proportional to the sum of squares of all the electric dis-
placements.

4. Clausius’ law of radiation is an immediate consequence
of Maxwell’s fundamental conceptions.

5. The transfer of energy to new masses of ether is accom-
panied by the expenditure of work in the case of reversible
operations.

6. In the case of adiabatic and reversible processes the
amount of disposible energy is inversely proportional to the
cube root of the volume throughout which this energy is
distributed.

ae

pereliay” i-

XV. Some Experiments on the Diffusion of Substances in
Solution. By SPENCER UMFREVILLE PickgRING, W.A.,
Os

TEXHE following determinations of the comparative rates of
diffusion of various non-electrolytes were intended to be
preliminary to a more extended investigation, but, as I do not
see my way at present to continue the work, I think it well
to put on record those results which have so far been obtained.
Osmotic pressure is held to be due simply to the gaseous
impact of the dissolved substance, and is theretore proportional
to the number of molcules per unit volume, the temperature
being constant. Now, by Graham’s law, the rate of diffusion
of a gas should be, ceteris paribus, inversely as the square root
of its density, or of its molecular weight. Hence, at a given
temperature and pressure the product of the molecular
weight, m, by the square of the rate of diffusion, v, should be
a constant. ‘lhe relative values for v in the case of different
bodies might be determined by sunple diffusion-experiments
if these could be conducted under perfect conditions: namely,
the diffusing liquid remaining of a constant strength through-
out, and the water into which diffusion is taking place
remaining uncontaminated with the substance. ‘The present
results seem to show, either that the above supposition as to
osmotic pressure is incorrect, or that the conditions obtainable
in diffusion-experiments are very far from obtaining to ideal
perfection ; for the values deduced for mv? are by no means
constant, even in those cases where the substances behave
normally as to their osmotic pressure, i.e. where the solutions of
equal molecular strength give the same osmotic pressure, this
latter being measured by the depression exercised by them on
the freezing-point of the water in which they are dissolved.
The method adopted was that termed by Graham jar-
diffusion. The solutions under examination were placed in
an open jar inside a large vessel of water, and the amount of
substance which had ditfused out of the former in a given
time was ascertained by determining the strength of the
remaining solution. The inner jars were beakers of a cylin-
crical form with ground flanges: they were ground also on
the bottom, and rested on inverted ground-glass saucers
placed in the centre of the large outer glass jars. Before
being filled, each jar was placed in position and adjusted so

* Communicated by the Author.

128 Mr. 8. U. Pickering on the Diffusion

that the mouth of the inner jar should be exactly level. The
jars were marked so that they could be replaced in the proper
position after being filled. When filled they were closed by
glass plates with rods attached to them, and then lowered
inside the larger jars which had previously been filled with
water. The glass plates were then removed very slowly and
earefully. At the end of the time allowed for diffusion the
plates were replaced on the jars, the latter were removed from
the water and the strength of their contents determined. Both
the large and small jars were filled two days before the latter
were placed inside the former, in order that the temperature
of the cellar in which the determinations were made might be
attained; and after the inner jars had been placed in position
a further period of five hours was allowed before the glass
plates were removed, so that any disturbance of temperature
which had occurred in placing them in position might subsice.

The capacity of the inner jars was 480 cubic centim., their
internal diameter was 70 millim., and their internal height
125 millim. About three dozen of them were made, and of
these the twelve which were found to be most uniform in size
were used in the determinations. The extreme ditterence in
the capacity of the largest and smallest of these twelve was
3°3 per cent., and the extreme difference of their superficies
at the mouth was 3°8 per cent. ‘The outer jars contained
12,000 cubic centim. of water, or twenty-five times the
volume of the inner jars. The mouths of the jars were about
midway between the surface and bottom of the water in the
inner Jars.

The strength of the solutions remaining in the jars at the
end of the experiments was determined by means of their
freezing-points. ‘The solutions taken to start with were made
up by weighing. The freezing-points of these, and also of
weaker solutions obtained from them by dilution, were deter-
mined, and from these results the strength of any solution
having a given freezing-point could be calculated. In order
to minimize any errors due to possible irregularities of the
freezing-points when plotted against composition, the solutions
of known strengths, of which the freezing-points were deter-
mined, were selected so as to approach as nearly as possible
to the strength of the solution left in the diffusion-jar.

The strength of the solutions taken was, as a rule, about
0:3 molecule to every 100 molecules of water, showing a
depression of the freezing-point of water amounting to about
0°:3 ; about one third of the dissolved substance had diffused
out by the end of the determination, the decrease in the

mR

of Substances in Solution. 129

freezing-point measured being thus about 0° 1. The water
into which the diffusion had taken place would at the end of
the experiment contain only about 4 molecules of the sub-
stance to every 100,000 H,O. ‘These proportions had neces-
sarily to be modified in several instances, and in such cases it
was assumed that, in accordance with Graham’s results (in
upport of which some of the present results may also be
adduced), the rate of diffusion varied directly as the number
of molecules present in a given volume of solution, or, more
roughly, in a given weight of water.

The determinations were made in two separate series,
marked (1) and (2) respectively in Table I., which contains
the results. In the first series the temperature varied from
12°1 to 15°3, the time allowed being probably 18 days,
the record of the exact time having been unfortunately lost :
in the second series the temperature was 16°:0 to 18°:2, and
the time was 25 days. Various steps were taken to estimate
the magnitude of the probable errors. In the first place, the
error due to any disturbance occurring in removing and
replacing the glass plate from the inner jar was found to be
inappreciable. A blank experiment in which these opera-
tions were performed showed that the solution of cane-sugar
which the inner jar contained gave exactly the same freezing-
point before and after the operations, 2. e. within the
estimation-figure of the thermometric reading, which was
0:05 millim. or 0°:0005. Secondly, in the first series dupli-
cate determinations were made with each of the substances
cane-sugar, acetic acid, and urea: the differences in the freezing-

oints of the solutions obtained in each pair were ‘O01L1°,
"0062°, and -0026° respectively, mean 0:00338°, or about 3 per
cent. of the actual decrease measured, a quantity fully
accounted for by the difference in size of the jars. Three per
cent. in the actual decrease, however, represents only 1:24
per cent. in the proportional decrease (or actual decrease
— mean freezing-point), which is the quantity which is
taken to represent the rate of diffusion v; and an error of
1°24 per cent. here will represent an error of 2°4 per cent. on
the values of the supposed constant mv’. Thirdly, glycerine
solutions of the same strength were used in both series, and
so also were cane-sugar solutions of nearly the same strength :
the relative values for mz? in the two series were 1 ; 2°586 in
the case of glycerine, and I : 2°567 in the case of cane-sugar,
the difference between the two ratios amounting to only 0°3
per cent.

The results of the diffusion-experiments are given in

Phil. Mag. 8. 5. Vol. 85, No. 218, Feb. 1893. Ix

130 Mr. 8S. U. Pickering on the Diffusion

Table I., the supplementary freezing-points necessary for the
calculation of the strengths of the final solutions being given
in Table Il. (In the case of cane-sugar and acetic acid the
determinations used for this purpose have already been
published, Berichte d. deutsch. chem. Gesell. xxiv. p. 3329.)

The values in the table refer to the weight of anhydrous
substance, the water of crystallization, whenever present,
having been allowed for. This water, in the case of alloxan,
was found to be 3H,O; whereas in the cases of gallic acid,
tannin, and raffinose, 1, 2, and 5H,0 were taken as being
respectively present. The proportional decrease of freezing-
point or strength of the solution is the fraction which the
actual decrease is of the mean freezing-point or strength.
The molecular weight m’ is deduced from the freezing-points
in accordance with van’t Hoff’s formula

mean strength x 18°9

nm =
mean f.-p.

The values, it will be seen, agree fairly well in most cases
with the theoretical molecular weights.

The sugars as well as the tannin and dextrin were ob-
tained from Messrs. Trommsdorf. The dextrin, however, was
doubtless very far from being pure (indeed pure dextrin
has never yet been obtained), and very little weight can
be attached to the results obtained with it. The sample
of amylodextrin I owe to the courtesy of Mr. Horace
Brown: unfortunately, however, the solution used deposited
some of the substance during the experiments in the insoluble
form, and hence the results with it are very doubtful; for not
only is the mean strength of the solution uncertain, but the
amount which had diffused out is also uncertain; for this had
to be estimated in the diffusate, a large quantity of it being
evaporated to a small bulk so as to “obtain a depression of
freezing-point sues for measurement ; while, to correct
for solids dissolved from the dish by the liquid during its
evaporation, a similar volume of water was evaporated in the
same manner. The calculated molecular weight of the amylo-
dextrin was obtained from the freezing-point of the initial

solution, and of that entered in Table II. The values which

these gave were 2519°4 and 2452°8 respectively. The resnlts
with gallic acid are equally uncertain for a similar reason, the
solution taken having been too strong, and having deposited
crystals during the course of the expe riment,

In the case of pyrogallol the liquid used to make the solu-

of Substances in Solution. 131

tion, and also that into which it diffused, was a very weak
solution of sulphuric acid of which the freezing-point was
0°-0441. This prevented all but a trace of oxidation of the
pyrogallol. The tannin used was probably not pure; but the
difference in the calcuiated molecular weights deduced from
the determinations in the two series is due to the solutions
used being of different strengths, and to the fact that the
molecular depression of the freezing-point diminishes rapidly
as the strength of the solution increases. The depressions, I
may mention, appear to show some marked irregularity ; for
when the four determinations (the two in Table I. at the
initial strength, and the first two in Table II.) are plotted out,
they do not all lie on any simple curve, either the detent:

nation at 12 parts to 100 giving much too small a value, or
that at 16 parts too large” a value. Another speciinen of
tannin was examined as to the freezing-points, and the results,
~which are the last four given in Table II., show the same
peculiarity. This sample, however, gave throughout smaller
values than that used in the diffusion-experiments, and the
three stronger solutions of it deposited some tannin as well as
ice in the freezing-point determination. The first sample did
not do so.

In order to make the results of the first. series more easily
comparable with those of the second, the values for mv?
obtained in the former have been multiplied by 2°577(=2),
in accordance with the results obtained with glycerine and
cane-sugar, as mentioned above. The values for mv’ are, as
will be seen, very far from being constant. They vary from
16-09 with pyrogallol (omitting the doubtful result with gallic
acid) to 46°81 with the weakest solution of cane-sugar; a
variation of some 200 per cent., which cannot be in any way
explained by the purely experimental error, since this, as has
been mentioned, does not exceed 2 to 38 per cent. When we
take the molecular weight deduced from the osmotic pressure
(freezing-point) itself, m’, instead of the theoretical molecular
weight, the constancy is in most cases scarcely improved;
and, indeed, in those three cases where these calculated mo-
lecular weights do not agree with the simple theoretical
weight, the values for m/v? are made much less nearly con-
stant, and attain the enormous proportions of from 72 to 260.
This tends to show that there is a want of agreement between
the values calculated for mv? from the depression of the
freezing-point and the rate of diffusion,

K 2

806-1
600-1
COLT
601-T
061-1
GPL
890-T
GLT-0
986-0
961-0
TSP-0
S¢0-T
661-1
G80-1
666-1
610-1
690-1
090-T
990-1
980-1

“doc *1OW

88-08

86.86

TL- bP

66-18

60-08

19-18

V0-68 =EP-61
68-691

16-9 L=10-L¢
T1-096

T9-TL

LG-F1
8P-IG=VE-8
€L-16=69-01
GE-LT
€9-16=68:8
G6-LT
88-LT=F6-9
96-06 =06-1
9T-L1=99-9

— — | —_————

20, Ub

GP.GE |
09-16

18-99

69-85

60-68

8E-PE

0¢-€¢ =” 00-81
98-86

06-68 = 8P-ST
P8-68

€0-08

09-61

G0-66=2 G6:8
61-82=” F6-01
60-9T
G6-06=7 &1-8
90-8T

66:9
86-8

10-81 =
09-16=
0E:LIT=ZGL.9

“UL

P0-86P | «8-609 cG9G. 690-6 66L-L LGL.9 | 928-8 TL66- 9660: | G9EE-— | GI8G-— | 198E-—
66 89E | x6-IV& PP8s- 889-1 €8¢-G | 681-b | LLE.9 6008. 9880. |GV6G.-— | GOSG-—— | 88E6.—
66-968 be POLE. S10-1 GEL-6 | 666-6 | ZhSE OLOE- 6890. | 98S1-— | S6@I-— | LL8T-—
18-866 F 6ETE- T08-T LELG | LEBb | 8g9.9 L8T&- LOOT. | 8PEE-— | PL8G-— | 188E.-—
6P-028 " P90E- 999-6 G96-TL | GET-OL | 862-81 6PTE: G6GG- =| 9GOL-— | Sh6S.— | LOTS.—
GS-1 6 1VE PLIE- V16-G 169-81 | PL9-CL | 88G.1é BEEE> GELE | SOGT-I—| €E66.— | 6108.1 —
§-968 4 6S6T- GILT LOL-G | 6PT-G | 996.9 9961: 0¢90. | 9068-— | 1864.— | 189. —
T-861 | x6@-LEé 9666. P80: 996-61 | P16-f1 | 066-ST 6606. LLGO» | PGET-— | G8IT-— | S9FT-—
9-61GT | x6G-18& G9IG- Ol0-1 GLO LOL-P LLG T9ST- €Il0. | #6L0-— | 8990-— | 1810-.—
T-9806 | xPG-82E CEcs. 006-8 668-6 80-8 | FOL-IT 6668. ¢¢z0- | LPLO-— | 0290-— | PL80.—
G8:OLL |x PGCE SPOE. GLL-GL | OLL-1¥ | 6OF-SE | SPL.8P LOGE. O€Ge- |OL00.I—| ShZ8-— | SLLT-[—
66-161 69-69T 9616. Pie. 6ST-T | 006-0 | g0P-T 86EP- 9FF0- | PIOI-— | 9880-—- |} “"""
SP-6ET P9-6P1 CPPS. TL9- PPL-G | 80P-6 | 6L10-€ GOES: 9480. | 61LE-— | 166€-— | LPI —
TP-981 PL-AVT BLL. 00g: 008-E | 0S¢-T | 090.2 L8G¢- 0F90- | PLFG— | PLIG-— | P183-—
GG-GET | OL-SEL GLE. Lgl. 090-6 | 169-L | 83P.% O89E- GPO. |€18%-— | 1SEc-— | p6EgE-—
v8-96 81-6 PVG6G: SEP. TLP-T bG6G-1 189-1 90LE- LLLO. | TL8é-— | €8h2-— | 096E-—
G6-16 s GEPP. LLL- 6GL-T | €9¢-L | OPTS Téep- S9GT- | 6296-— | Sh8-— | SIhP.—
91-16 61-16 6S16- 61S. 188-L | 129-L | OPT. 6816. 8901. | 006E-— | 098E-— | PSPP.—
81-69 G6-6 PS9E- O&é. £06+ Sel. 890-1 SPOS: GGOI- | F886-— | 8SEG.— | OLPE.—
T0-8¢ 98-6¢ 8886. Tes. LL6. TI8- GPL G6TE- LION. | S8T&.— | SL0%.— 6698. —

wade y i “‘oseex00p a te ie ae es “sasva.oop ies SS e Bae
WOAT jeoy jeaoy |‘osvorooq | ‘uvop | ‘Teun | ‘penimy jeuoy |osvetooq | ‘uvoy | ‘yeung | ‘Teyy

poyepnoRg| -e100y], || -todorg -10dorg

“qysio MA Le[NoaTOW AMEE *SUOIYNIOG 94} Jo squrod-surzo0A iT

1948 MA JO NOT OF S91Bq—'suOIyNTOg Jo yysueayg

"SUOIJVULLUIO}O(T OY} JO S}[NSoyY—'] AIAVy,

puoc os (2) scouLyesy
mes (G) — asogTe Ty,
reese (z) ‘“
seuss (gz) &
roses (g) &
esses (BZ) “
“ees (7) cedns-oueg
reese (z) “s
Hee (qT) uraUey,

“* (z) ungxopopéury
se eeee (Z)

oer

UlYyxo(q
(Z) poe ore
“"(T) plow OLLB4.U8 7,

eveee (J)

UCXO]LV

(Z) joresoars

Py) pouetd
Hees (g) «s

“"" (7) aura0dT49,
meee CT) Peetal

eaeeee

(1) plow ooo yw

‘vouRysqng

a |

On the Diffusion of Substances in Solution. 133

Taste II.—Supplementary Freezing-point Determinations.

Parts to Parts to
Substance, 100 of F.-p. Substance. 100 of | F.-p.
Water. Water.
Tartaric acid...... 2152 | —-2966 | Dextrin oo... 97-484 | — -6208
2G) oe 1425 | —-2000 ASHEN va PEA AeE AAS, 47-943 | —1:1082
Glycerine ......... 1-453 | —-3023 || Tannin ............ 2557 | — 0440
GHOSE... scc0s 4-670 | —:2463 ih Deh Late ae 12°310 | -- -1221
Pyrogallol.......... 1603 | —°2228 say LIE Aiea SPE aves 15°804 | — ‘1110
Gallic acid... 0667 | —-0697 Fy MA ode es 10184 | — -O844
Sel isieis0 slenisic 07133 | —-0180 ah sete epee 4°983 | — -0542
Raflinose ......3.. 0-640 | —:2669 3h AK Cae: 2-473 | — -0342
Amylodextrin ...| 7940 | —-0609

The “molecular’’ depression, which, on the theory of

osmotic pressure, will be proportional to mv’, must, when we
take the molecular weights calculated from it (m’), be an
absolute constant, whereas the values for this same quantity
(m’v”), when deduced from the diffusion-experiments, and
when these same molecular weights are used, are far from
being constant; moreover, while the ‘theoretical’? mole. |
cular weights give the values of mv’ in the diffusion expe-
riments with dextrin, amylodextrin, and tannin as being
similar to those with the other substances investigated, they
will, when used for calculating the molecular depression, give
values from 4 to ith only of thuse obtained with the other
substances investigated. These values are given in the last
column of the table: molec. dep. = (mean dep. x m) + (mean
strength x 17:96).

The fact that the results with dextrin, amylodextrin, and
tannin are of doubtful accuracy must, it is true, weaken the
strength of any conclusions based on them. But, on the
other hand, the fact that they do not give exceptional values
for mv” renders it probable that they are not very inaccurate ;
and, moreover, the exceptional values which they give for
mv are not out of harmony with the results with the other
substances ; for the sugars, where the molecular weights are
large, give values which are considerably larger than those
given by the other substances examined. There seems indeed
to be a general tendency for m/v? to increase with the mole-
cular weight of the substance diffusing: thus, with the first
seven substances entered in the table we have molecular

134 .Prof. J. G. MacGregor on Contact-Action

weights from 60 to 150, and the value of mv" is generally
about 20: with the last three substances in the. tabie,
where the molecular weights are high, 314 to 430 (taking
the calculated values mm’), m’v? is much larger, namely over
30; while dextrin, tannin, and amylodextrin show still larger,
and, taken in their order, increasing molecular weights, and
also larger and increasing values for m’‘v*. Thus it would
appear that with higher molecular weights the rate of diffusion
is abnormally large.

The exceptionally large values for mv? in the case of the
weakest solution of cane-sugar is remarkable, but in the
absence of a duplicate determination it is well not to lay
much stress upon it.

XVI. Contact-Action and the Conservation of Energy.
By Prof. J. G. MacGrecor, M..4., Se.D.*

(EVERAL years ago Prof. O. J. Lodge, in a series of
papers published in this Magazinet, proposed new
definitions of work done and energy, and claimed (1) that
by their aid he had deduced from the third law of motion
and the hypothesis of universal contact-action alone, a law
(which he called the law) of the conservation of energy ;
(2) that the law thus deduced was an extension of, and fully
as axiomatic as, the law ordinarily enunciated under the same
name ; (3) that action ata distance might be shown to be
incompatible with Newton’s third law, or the law of the con-
servation of energy, or both; and (4) that energy cannot be
transferred without being transformed, or transformed without
being transferred. ‘These claims, though primd facie so
extraordinary as necessarily to have drawn attention, have
never, so far as | am aware, been seriously challenged, and it
is, perhaps, somewhat late in the day to challenge them now;
but the remarkable progress which has recently been made
in the application of contact-action theories, seems to make
it desirable that they should be subjected to examination.

(1) Lhe Deduetion of the Conservation of Energy.

In the first version of the argument by which this deduction
is made t, Prof. Lodge seems to me (a) to assume the ordinary
law of the conservation of energy in addition to the third law

_ * Communicated by the Author.
+ Phil. Mag. [5] vols. viii. (1879) p. 277, xi. (1881) pp. 36 & 529, xix.

(1885) p. 482.

+ Ibid. vol. viii, (1879) p. 278.

and the Conservation of Energy. 1385

of motion and contact-action, and (0) to deduce, not a law of
the conservation of energy, but of its conservation during
transference merely.

Paje T he unacknowledged assumption is made in the “ de-
finition ” of energy :—‘ Whenever work is done upon a body,
an effect is produced in it which is found to increase the
working-power of that body (by an amount not greater than
the work done) ; hence this effect is called energy, and it is
measured by ‘he quantity of work done in producing it.
Whenever work is done by a body, 27. e. anti-work done on it,
its working-power is found to be diminished (to at least the
extent of the work done), and it is said to have lost energy —
the energy lost being measured, as before, by the anti-work
done in destroying it.” ‘The words ‘‘is found ” indicate an
appeal to experience. We may readily recognize what it is,
if we note that the increment or decrement of w orking-power
which is produced in a body on or by which work has been
done, may be kinetic or potential, and that, as Prof. Lodge
says*, “for a body to possess kinetic energy you must have
not merely motion, you must have a guarantee of persistence
of motion, the body must possess inertia,” and “ for a body to
possess potential energy we must have two things—the exer-
tion of a force, together with a guarantee that that force shall
be exerted over a certain distance ; 2. e. a continuance of the
force even after motion is permitted.” If, then, these two
guarantees be expressed quantitatively, so as to ensure fh
equality of the change of working-power to the work done,
they will form a statement of the experience to which
appeal is made. When so expressed, the former is seen to be
Newton’s second law of motion, and the latter the axiom that
the work done by the mutual forces between the parts of a
material system during any change of its configuration de-
pends only on the initial and final configurations. If these
guarantees cannot be deduced from the third law and universal
contact- -action, they are thus unacknowledged assumptions
in the argument under consideration,

We may assume that Prot. Lodge will not hold it to be
possible to make this deduction in the case of the latter of
the two assumptions mentioned. He does hold, however,
that Newton’s second and third laws of motion are ditterent
aspects of one law t, and he may therefore regard the first of
the two guarantees mentioned above as not forming an addi-
tional assumption in his argument. I have not access to ‘ The
Engineer’ of 1885, in which he says his argument in support

* Phil, Mag. [5] vol. xix. (1885) p. 4865.
+ Ibid. vol, xix. (1885) p, 488,

136 Prof. J. G. MacGregor on Contact-Action

of this view is published. But in the edition of his book on
Klementary Mechanics which bears the date 1892, he reaches
this conclusion in the following way (p. 56) :—“ It [ Newton’s
third law] is deducible from the first law of motion (see Max-
well, ‘ Matter and Motion’), for if the forces exerted by two
parts of the same body on each other were not equal and
opposite, they would not be in equilibrium ; and consequently
two parts of the same body might, by their mutual action,
cause it to move with increasing velocity for ever, the possi-
bility of which the first law denies. We have already shown
that the first law is a special case of the second, and now we
have deduced the third from the first; hence all are really
included in the second, which is therefore excessively im-
portant.” ‘That the first law is a special case of the second
ts obvious ; but that the third is deducible from the first in
the above way I have elsewhere * endeavoured to disprove.
It is not necessary to repeat the discussion here ; for it will
probably be sufficient to point out that the equality and oppo-
sition of the action and reaction of two parts of the same body
do not constitute the third law of motion, that law asserting
the equality and opposition of the action and reaction between
two bodies, to each of which the first law applies. That this
criticism is sound becomes especially obvious if we reflect
that the laws of motion, as fundamental hypotheses of dy-
namics, must be held to apply to particles, not to extended
bodies ; and the above argument is clearly inapplicable to a
particle.

The unacknowledged assumptions are thus not deducible, at
least have not been deduced, from those admittedly used.
Now the law of the conservation of energy, as ordinarily
enunciated, may be deduced from these-two assumptions alone.
Hence, in the argument under consideration, Prof. Lodge
assumes the ordinary law of the conservation of energy in
addition to the third law of motion and universal contact-
action.

(6) The following is the conclusion which he draws :—
““Trence the energy gained by the first body is equal to the
energy lost by the second; or, on the whole, energy is
neither produced nor destroyed, but is simply transferred from
the second body to the first.” This states only that energy
is conserved during transference, and says nothing as to its
fate after transference to the first body, and during residence

* In an Address on the fundamental hypotheses of Dynamics, read at
the last Meeting of the Royal Society of Canada, and to be published in
vol, x. of its Transactions. See abstract in ‘Science,’ vol. xx. (1892)
page

and the Conservation of Energy. 137

in it. The law deduced is thus not a law of the conservation,
but of the transference of energy. Obviously, with the
assumptions which seem to me to have been employed, the
complete law of conservation might have been deduced. But
the conservation of energy during residence in the body could
not have been proved without the explicit employment of the
two assumptions involved in the definition of energy.

In a second yersion* of the above argument, Newton’s
third law and contact-action are the only assumptions made ;
but the conclusion drawn is not a law of the conservation of
energy in the sense of working-power. The definition of
energy in this argument is quite different from that of the
earlier paper :— “ Hnergy is that which a body loses when it
does work ; and it is to be measured as numerically equal to
the work done.”” There is here no reference to working-
power. loss of energy is simply a synonym for work done
by, and gain of energy for work done on. The conservation
of energy which Prof. Lodge claims to have deduced is there-
fore the conservation of the work done on two bodies during
mutual action, whichis of the same nature as the conservation
of their momentum, and is quite consistent with the non-
conservation of their working-power.

(2) Generality and Axiomatic Character of
Prof. Lodge’s Law.

It will be obvious that, as Prof. Lodge’s definition of energy
is different from the ordinary definition, his law of conserva-
tion cannot be the same as that ordinarily enunciated under
the same name. He says himself it is “ probably a slight
(very slight) extension” of the ordinary law f. We have
seen, however, that in deducing it he assumes the ordinary
law, the third law ef motion and universal contact-action. It
is therefore merely the form which the ordinary law takes
in the particular case of contact-action with equal reaction.

This conclusion is borne out by a consideration of the
definition of energy quoted above. Work done and the
working-power of a body having been so defined ¢ as to make

* Phil. Mag. [5] vol. xix. (1885) p. 483.

+ Ibid. vol. xi. (1881) p. 533.

t “ Whenever a body exerting a force moves in the sense of the force it
exerts, it is said to do work; and whenever a body exerting a force
moves in the sense opposite to that of the force it exerts, it is said to have
work done upon it, or to do anti-work, the quantity of the work being
measured in each case by the product of the force into the distance moved
through in its own direction.” ‘The working-power of a body is mea-
sured ‘by the average force it can exert, multiplied by the range or distance
through which it can exert it.” Ibid. vol. viii. (1879) p. 278.

138 Prof. J. G. MacGregor on Contaet- Action

their denotation identical with their ordinary denotation, pro-
vided the third law of motion hold, energy is detined quali-
tatively as being the working-power = a body, and quanti-
tatively as being measured by “the work done in producing it.

The ordinary definition of energy is working-power simply,
whether that power be possessed by a body or a system, its
measure being the work the body or system can do. Prof,

Lodge’s energy will therefore be identical with energy in the
ordinary sense only in cases in which his work done and his
werking-power are identical with ordinary work done and
ordinary working-power, and in which the working-power of
a system is the sum of the working-powers of the bodies of
which it consists. Now this latter condition requires that the
actions between the bodies of the system shall occur only at
constant distance. Tor if the actions might occur at variable
distance, a part of the working-power of the system would be
potential working-power which could not be said to be pos-
sessed by the bodies singly. The former condition is satisfied
if the third law of motion hold. Hence Prof. Lodge has so
defined energy as to make its denotation identical with the
ordinary denotation only in cases of action with equal reaction
at constant distance.

Prof. Lodge asserts also that his law is “ fully as axiomatic
as’ the ordinary law*. Mere assertion, however, cannot
make two propositions equally axiomatic. They must be
proved to be so. And the test is very simple. If they are
applicable with equal generality in the investigation of dyna-
mical phenomena, they are equally axiomatic ; if not, they are
not. Now, if there be actions in nature which are not actions

“at constant distance, Prof. Lodge’s law is not applicable to

them, while the ordinar y lawis. Even if it be admitted that
all actions in nature are contact-actions, there are many
groups of phenomena which, in the present state of our
knowledge of them, cannot be investigated on the hypothesis
of contact-action. The early staves. of their investigation
must be conducted by the aid of the fiction of action at a
distance ; and in such stages Prof. Lodge’s law is not applic-
able, while the ordinary law is. Hence Prof. Lodge’s law
is not so general in its applicability as the ordinary law.

(3) Deduction of Contact-Action.

In Prof. Lodge’s argument to prove the incompatibility of
action at a distance with the third law of motion and the law
of the conservation of energy 7, he seeems to me neither to

* Phil. Mag. [5] vol. xi. (1881) p. 533.
t Ibid. vol. x1. (1881) p. 36.

and the Conservation of Energy.

assume a law of the conservation of working-power.
deduce contact-action.

The energy of which he assumes the conservation is (
in the same way as in the second version of his deduction wu
the law of conservation :—A body ‘is said”? to have lost or
gained an amount of energy numerically equal to the work
done by or on it respectively. There is no reference to
working-power. What he assumes, therefore, is the conser-
vation of the work done on two bodies during their mutual
action.

The conclusion drawn is that “ the two bodies must move
over precisely the same distance in the same sense,” which is
action at constant distance, not contact-action. Nor does
the assertion that they are “practically ” the same make it
contact-action.

It is obvious, however, that if the conclusion reached above
is sound, viz., that Prof. Lodge’s law of the conservation of
energy is the ordinary law expressed for the particular case
of action with equal reaction at constant distance, action at
variable distance must be incompatible with it and the third
law of motion.

The argument to show action at a distance to be incom-
patible with the law of the conservation of energy alone is as
follows *:—“‘ If it were possible for two bodies exerting stress —
on one another to move over unequal distances, then it would
be possible to obtain work without the anti-work, and thus
to get a new source of energy (technically called the per-

etual motion) ; but, asa fact of experience, it is not possible.”
Clearly, in the case supposed, there would be a new source of
energy as defined by Prof. Lodge. But a new source of
energy as thus defined does not imply the perpetual motion.
For in such a case there would be working-power which
could not be called energy according to the definition; and
the ordinary law of the conservation of energy tells us that,
provided the stress supposed to act were independent of the
velocities of the bodies acted upon, the change produced
during the motion in this portion of the working-power of
the system would be such as to render the perpetual motion
impossible.

No attempt is made, in the papers cited above, to show
action at a distance to be incompatible with Newton’s third
law of motion alone, although it is asserted t that the incom-
patibility may be proved.

* Phil. Mag. [5] vol. viii. (1879) p.
+ Ibid. vol. Xi. (1881) p. 36.

140 Prof. J. G. MacGregor on Contact- Action

(4) Transference and Transformation of Energy.

Prof. Lodge’s argument to show that, on the assumption
of contact-action, “‘energy cannot be transferred without
being transformed,” is as follows *:—‘ When a body possess-
ing potential energy does work, its ‘range’ f necessarily
diminishes, while the motion of the body on which the work
is done increases. Qn the other hand, when a moving body
does work its motion diminishes, and the body which resists
the motion, since it yields over a certain distance, gains po-
tential energy.” It seems to me that these sentences would
be equally accurate if we were to subject them to “ double
decomposition,” after which process they would read thus :—
When a body possessing potential energy does work its range
necessarily diminishes, while the body on which work is done,
since it yields over a certain distance, gains potential energy.
On the other hand, when a moving body does work its motion
diminishes, while the motion of the body on which the work
is done increases.—A statement which would in general be
more complete than either, would be obtained by combining
the two. For if one body exert on another a certain force
through a certain distance the same work is done on it,
whether the former body lose kinetic or potential energy in
doing the work; while the effect produced in the latter body
will in general be a change both in its motion and its state
of strain, z.e. both in its kinetic and its potential energy.
Thus, whether the former lose kinetic or potential energy, or
both, the latter will, in general, gain both, or transference of
energy will, in general, involve partial but not complete
transformation.

Prof. Lodge cites the air-gun as an instance of the trans-
formation of potential into kinetic energy during transference.
If we extract the bullet and plug up the muzzle it will serve
equally well as an instance of the transference of potential
energy without transformation. For if we now pull the
trigger, the compressed air will do work on the air in the
barrel. The “range” of the former will diminish, that of
the latter will increase. As an instance of the transformation
of kinetic into potential energy during transference, he selects
the case of a bullet fired against a spring and caught by it.
But if the spring have inertia, the energy acquired by it
through the work done by the bullet must be partly kinetie,
and in such a case, therefore, the transformation is only
partial. Such instances, however, must be defective as illus-

* Phil. Mag. [5] vol. xix. (1885) p. 486.
+ That is ‘ the distance through which it can exert force.”

and the Conservation. of Energy. 141

trations, because the air, the spring, the bullet, which are
treated as simple bodies, must be regarded as complex systems
between the parts of which transferences of energy are oc-
curring. When we make a more intimate study of such
instances from the point of view of contact-action, we must,
as Prof. Lodge points out, regard bodies as consisting of
particles connected by a medium possessing some property of
the nature of elasticity. If we assume the particles to be
rigid they can, of course, have kinetic energy only. If the
medium be assumed to have no inertia, its elements can have
potential energy only. Hence if both assumptions be made,
transference of energy between the particles and the medium
must involve complete transformation, while transference |
from element to element of the medium must occur
without transformation. If, however, both the particles and
the medium be assumed to have both inertia and elasticity,
the transference of energy will, in general, it seems to me,
involve only partial transformation, whether it occur between
the elements of the medium or between the particles and the
medium. When, therefore, Prof. Lodge states that “a bullet
fired upwards gradually transfers its undissipated energy to
the gravitation medium, transforming it at the same time into
potential,” he seems to me to assume that the bullet is rigid
and that the medium is without inertia.

Prof. Lodge states finally that “ energy cannot be trans-
formed without being transferred,’ but he gives no demon-
stration of this proposition. I find it difficult to reconcile
with this statement one of his illustrations:—“ A perfectly
elastic bounding hall has all its energy transformed into
potential at the middle of every period of contact with the
obstacle from which it rebounds.’ Immediately after con-
tact has ceased all its energy is kinetic, for apparently vibra-
tions are excluded by hypothesis. The energy has thus been
completely transformed without transference from the ball.
It may, of course, be held that the ball must be regarded as
a system of particles connected by an elastic medium. But
in that case, what has been said of the ball, as a whole, is true
of the particles in contact with the obstacle, if they are as-
sumed to be elastic, or, if not, of the elements of the medium
in contact with them, provided the medium be assumed to
have inertia. After the middle of the period of contact, they
do work on the elements of the medium beyond them. No
work is done on them. They, therefore, lose energy and
gain none. Yet after contact is over they possess kinetic
energy. Whence has it come, if not through transformation
of their own potential energy ? That energy cannot be trans-

142 Mr. A. A. C. Swinton on

formed without being transferred must, of course, be true if
bodies consist of particles with inertia but without elasticity,
and if the medium connecting them possess elasticity but
notinertia. Indeed, on these assumptions we may go farther
and say it cannot be transformed without being transferred
either trom particles to medium, or from medium to particles.
If, however, either or both be assumed to have both pro-
perties, the proposition seems to me to be erroneous, and
certainly requires proof.

In concluding the discussion of this subject Prof. Lodge
says:— All I have stated is that change of form is necessary
and universal whenever energy is transferred.” If this is all
the statements under discussion are to be taken to mean they
may be admitted at once, on the assumption of contact-action.
But this version of the statements quoted above seems to me
to be a new statement altogether. or, expressed in terms of
energy, it says merely that when one body does work on
another through the exertion of contact-force the potential

con)
energies of both bodies in general undergo change.

Dalhousie College, Halifax, N.S.,
Dec. 30th, 1892.

XVII. Haperiments with High Frequency Electric Discharges.
By A. A. CAMPBELL SWINTON *.

‘HE writer has succeeded in passing through his body
from hand to hand sufficient electricity to bring the
filament of an ordinary 5-candle power 100-volt incandescent
lamp very nearly to full incandescence, or to bring the fila-
ment of a 32-candle power 100-volt lamp to full redness.
Practically no sensation was experienced.

The apparatus employed consisted of a large “ Apps”
induction-coil capable of giving 10-inch sparks, supplied with
current through the ordinary vibrating contact-breaker, and
a resistance consisting of eight 50-candle-power lamps in
parallel, from a 105-volt continuous-current supply. The
total energy in the primary, excluding what was lost in the
resistance and contact-breaker, was about 3850 watts, or not far
off half an electric horse-power. To the positive and negative
terminals of the secondary of the induction-coil were connected
respectively the inside and outside coatings of three half-
gallon Leyden jars, connected in parallel. The disruptive
discharge of these jars across an air-gap of about a quarter of
an inch excited the primary of a simple form of high-fre-
quency coil similar to those employed by Mr. Tesla and

* Communicated by the Author.

— High Frequency Electric Discharges. 143

Prof. Elihu Thompson. The secondary of this coil consisted
of 500. turns of No. 26 S8.W.G. cotton-covered wire wound
on a paper tube. Outside this paper tube was a glass tube,
upon which the primary, consisting of 10 turns of three
No. 16 guttapercha-covered wires, in parallel, was wound.
The whole coil was immersed in resin oil contained in a
wooden trough. ‘The ends of the secondary were connected
through small glass tubes, also filled with oil, to brass balls.

On approaching the hand to one of the balls forming the
terminals of the oil-coil, sparks shot out from the brush dis-
charge which surrounds it. Ifthe spark is taken on the skin
a sharp prick is felt, but on approaching the terminal or
touching it with a piece of metal grasped in the hand, or after
grasping the terminal itself, practically no appreciable sensa-
tion is felt. If the terminal is grasped in this manner with
the right hand, sparks will shoot out from the left hand or
indeed from any portion of the body, if brought into proxi-
mity with another person, a piece of metal, the gas- or water-
pipes, or any conducting body. In the experiment referred
to the incandescent lamp was hung by one terminal on a
wire connected to earth, and connexion was made between
the other lamp terminal and the coil through the two arms
and body by the right hand being brought into contact with
one terminal of the oil-coil, and a piece of metal grasped in
the left hand being approached to the free terminal of the
lamp. At the first approach the bulb of the lamp became
filled with phosphorescent light, but, on reducing the distance
between the metal in the left hand and the free lamp ter-
minal, sparks shot out between them and the filament at once
became incandescent—the incandescence increasing very
nearly to the full normal amount when the piece of metal
and the lamp terminal were finally brought into contact.

To produce a similar incandescence of the filament with
continuous or alternating currents of ordmary frequency
would require about one fifth of an ampere, and at first sight
it would seem that this quantity of current must pass through
the arms and body of the operator.

It has been generally assumed that with high-frequency
currents the current is rendered harmless by reason of the
high frequency—in fact, that high frequency renders harmless
to the human body currents of a strength that would be
dangerous and painful, if not fatal, were the frequency lower.
The writer is inclined to think that another explanation is
possible, and that the true fact is, not that high frequency
renders harmless a given strength of current that with ordinary
frequency would be harmful, but that with high frequency
it is possible to obtain effects with exceedingly small currents,

144. Keperiments with High Frequency Electric Discharges.

that with continuous and ordinary alternating currents can
only be obtained by the use of much larger currents.

This hypothesis 1s probably applicable to many other high-
frequency effects, but as applied to the above-mentioned
experiment it is simply this:—The lamp-filament having a
certain definite resistance, with continuous or ordinary alter-
nating currents which pass uniformly or nearly so through
the section of the filament, a certain amperage of current is
necessary to produce the number of watts required to raise
the filament to incandescence. With the high-frequency
currents, on the other hand, as is well understood, the current
travels chiefly on the outer surface of the filament, little or
none passing through the central portion. The current is in
fact merely skin-deep. The virtual resistance is therefore
very high, as only an extremely small portion of the sectional
area of the filament acts as a conductor. There is an ample
sufficiency of volts, and though the current is very minute
there is a sufficient expenditure of watts to raise the filament
to incandescence. ‘The lamp, in fact, ceases to be a 100-volt
lamp and becomes, it may well be, a 100,000-volt lamp. As
confirming this hypothesis, it should be mentioned that while
the filament was incandescent sparks passed between the lamp
terminals, which were at some distance apart, this being evi-
dence that there was a difference of potential amounting
at least to thousands of volts between the two ends of the
filament.

Returning to the experiments, several other curious results
were obtained. If, instead of connecting the lamp to the coil
through the human frame, a wire was used, the filament
became much brighter than in the previous experiment; in
fact, it gave considerably more than its normal candle-power.
From this it was evident that the human body offered con-
siderable opposition of some description to the passage of the
electricity. In order to form some idea of the amount of
this opposition, the body was again inserted in the circuit
between the coil and the lamp, as previously, and the thumbs
of the two hands brought near together. Sparks about one
quarter of an inch in Jengih were found to pass between them,
evidencing that the two hands of the operator hada difference
of potential between them apparently equal to some thousands
of volts. When the sparks passed between the hands, or when
the wrists were brought into contact, so as to short-circuit, as
it were, to some extent the resistance of the arms and bedy,
the filament became very appreciably brighter. It should be
mentioned that when the sparks were allowed to pass be-
tween the hands very perceptible shocks were felt in the

wrists.

Notices respecting New Books. 145

Another experiment was to connect one lamp terminal ‘by a
wire to the coil, connect the other lamp terminal to earth, and
short-circuit the lamp through the body by grasping the coil
terminal with one hand and a piece of metal connected to
earth with the other. The effect of so doing was to reduce
the incandescence of the filament to rather less than one half
its normal amount, half of the available current going appa-
rently through the lamp, the other half through the body.

With the lamp terminal connected to the coil, it was found
unnecessary to connect the other lamp terminal to earth to
produce incandescence, all that was necessary being to touch
this lamp terminal with a piece of metal held in the hand.
That the incandescence of the filament produced under these
conditions was due to the electrostatic capacity of the operator
and not to his forming a connexion to earth, was evidenced
by the fact that it made no perceptible difference whether he
stood on the floor or on an insulated stool.

In all the above experiments the second terminal of the oil-
coil was free and not counected to anything. It was, how-
ever, found that the effect of a second operator touching this
terminal, or of connecting it by wire to earth, was to diminish
the incandescence of the lamp-filament. It was also found
that the filament incandesced toa greater degree of brightness
when connected as above between one terminal of the coil and
earth, than when it was directly connected between the two
terminals of the coil, but that, while the operator experienced
practically no sensation when his body was inserted between
one terminal and earth, the sensation was very severe—in fact,
quite unbearable—when the body was inserted between the
two terminals. The above seem to show that capacity has
much to do with the results obtained, and that the phy-
siological effects of electric currents are not necessarily
_ proportional to their heating-power.

It should also be mentioned that in some of the experiments
there was a decided tendency for the filament to vibrate in
unison with the contact-breaker of the induction-coil. In
fact, in some cases the amplitude of vibration was sufficient to
cause the end of the filament to beat against the glass of the
lamp bulb.

XVIII. Notices respecting New Books.
Annals of British Geology, 1891. By J. F. Buaxs, M.4., F.GS,
8vo. Pages viii & 404. Dulau and Co., London, 1892.
ie a review of the former volume (for 1890) in the Philosophical
Magazine for March 1892, the plan of these “Annals ” was fully
described. It has been followed in the present volume, except

Phil. Mag. 8. 5. Vol. 35. No. 213. Feb, 1893. L

146 Geological Society :—

that :—no notice is taken of papers merely read before Societies,
but not published in the year concerned,—the abstracts and Prof.
Blake’s notes thereon have been submitted to the authors, and
those which have been received back are marked with anasterisk —
and a new feature is “ the introduction of illustrations of all new
British species, and of other important novelties.”

On this last point we may observe that “the will may be taken
for the deed”; but that, though inadequate in very many instances
to define the characters of the intended fossils, the amateur out-
lines may serve as useful indications, to some extent, where the
descriptive memoirs cannot be got at. The two maps (pls. i. and
ii.), though roughly executed, seem to be more available for their
intended purpose.

As the asterisk placed before the No. of an Article indicates
that the abstract has been seen and corrected by the Author or
Editor of its memoir, we may notice that fifteen articles are indi-
cated in the Table of Corrections as being entitled to these asterisks,
as well as the very many (the majority) of the abstracts standing
in the text with those marks. Important corrections appear (from
the List of Corrigenda) to have been fortunately made by the
authors in some of these abstracts after the printing.

The “ Personal Notes” of the former yolume are now limited to
eritical footnotes. These are always suggestive, and not unfre-
quently decidedly useful.

Some of the articles are, relatively, of considerable length ; for
instance no. 6 (Murray and Renard) has 17 pages; no. 324 (A. 5.
Woodward) 7 pages; no. 334 (R. B. Newton) 9 pages. The
*‘ Personal Items” about the Staff and Officers of the Societies
and Institutions are discontinued. The two Indexes (of Authors and
Periodicals) are given, and one of new names. If the geographical
and the geological points were indexed, we think advantages would
accrue; and we venture to suggest that the cost of the plates
might be saved to that end in the next volume.

The masterly Gf not also masterful) manner in which the
numerous memoirs are treated is well sustained, and tends always
to indicate their interest, and often to advance their usefulness.
Evidently no pains have been spared by the enthusiastic author in
earnestly carrying out his plan of diffusing a correct knowledge of
current British Geology, and of the work of British Geologists,
among all who are interested in the Science.

XIX. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[ Continued from p. 76.]
November 23rd, 1892.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.
(ye following communications were read :—

. “Outline of the Geclogical Features of Arabia Petreea and
Palestine.” By Prof. Edward Hull, LL.D., F.R.S., F.G.S.

The region may be considered as physically divisible into five

The Base of the Keuper Formation in Devon. 147

sections, viz. :—(i) The mountainous part of the Sinaitic Peninsula ;
(ai) the table-land of Badiet-el-Tih and Central Palestine; (iii) the
Jordan-Arabah valley ; (iv) the table-land of Edom, Moab, and the
voleanic district of Jaulaén and Haurdan; and (v) the maritime plain
bordering the Mediterranean.

The most ancient rocks (of Archzean age) are found in the southern
portion of the region; they consist of gneissose and schistose masses
penetrated by numerous intrusive igneous rocks. They are succeeded
by the Lower Carboniferous beds of the Sinaitic peninsula and
Moabite table-land, consisting of bluish limestone with fossils, which
have their counterparts chiefly in the Carboniferous Limestone of
Belgium, and of a purple and reddish sandstone (called by the
author ‘the Desert Sandstone,’ to distinguish it from the Nubian
Sandstone of Cretaceous age), lying below the limestone. The Nubian
Sandstone, separated from the Carboniferous by an enormous hiatus
in the succession of the formations, is probably of Neocomian or
Cenomanian age, and is succeeded by white and grey marls, and
limestones with flint, with fossils of Turonian and Senonian ages.
The Middle Eocene (Nummulitic Limestone) beds appear to follow
on those of Cretaceous age without a discordance; but there is a real
hiatus notwithstanding the apparent conformity, as shown by the
complete change of fauna. In Philistia a calcareous sandstone in
which no fossils have been observed is referred to the Upper Eocene;
for the Miocene period was a continental one, when faulting and
flexuring was taking place, and the main physical features were
developed—e. g., the formation of the Jordan-Arabah depression is
referable to this period. .

In Pliocene times a general depression of land took place to about
200-300 feet below the present sea-level, and littoral deposits were
formed on the coasts and in the valleys. To this period belong the
higher terraces of the Jordan-Arabah valley. The Pliocene deposits
consist of shelly gravels. Later terraces were formed at the epoch
of the glaciation of the Lebanon Mountains, when the rainfall was
excessive in Palestine and Arabia. |

The volcanoes of the Jaulan, Hauran, and Arabian Desert are
considered to have been in active operation during the Miocene,
Pliocene, and Pluvial periods; but the date of their final extinction
has not been satisfactorily determined.

2. “The Base of the Keuper Formation in Devon.” By the Rev.
A. Irving, B.A., D.Sc., F.G.S.

In a paper published in the February number of the volume of
the Quarterly Journal for the current year, the author definitely
accepted the breccia which is clearly marked on the left bank of the
Sid at Sidmouth as the base of the Keuper, but he had not then
satisfactory data for determining a similar basement-line in the
country between the valleys of the Sid and Otter, where the
Keuper is repeated by the great Chit-rock Fault. Since then he
has received information from the Rev. Dr. Dixon of Aylesbeare,
mentioning the occurrence of breccia at several points on the east
side of the Otter, and has subsequently visited the district, and with

148 Geological Society :—

Dr. Dixon traced the breccia (the true base of the Keuper) along
the left bank of the Otter, which for many miles seems to mark the
western limit of the Keuper in Devonshire. —

- As results, (i) the paleontological difficulty which the occurrence
of Hyperodapedon east of Ottermouth presented is now removed ;
(ii) the statement made in the last paragraph on p. 71 of the
author’s paper in the February number of the Quarterly Journal
needs some modification ; (iii) the geological maps of the Devon
area require considerable revision; (iv) data are furnished which
enable us to estimate the thickness of the Upper Bunter at not
more than about 100 feet; and (v) points of interest in the physio-
graphy of the country are indicated.

3. “The Marls and Clays of the Maltese Islands.” By John H.
Cooke, Esq., F.G.S.

_ The following deposits (in ascending order) occur in the Maltese
Islands :—I. Limestone, II. Globigerina-limestone, III. Clays,
IV. Greensands, V. Upper Coralline Limestone. The Marls and
Clays forming the subject of this communication are No. III. of
this list. They lie conformably upon the Globigerina-limestone, and
so obscure is the line of demarcation between the two, and so striking
the similarity of their fossils, that the Clay may be considered as an
argillaceous division of the formation upon which it rests. The
upper part of the Globigerina-limestone is referred to the Horner-
schichten of the Vienna basin, and the Clay to the Schlier. The
separation between the clay and the greensands is sometimes, though
not always, complete, and occasionally the greensands are absent,
and the coralline limestone rests directly on the clay. The thick-
ness assigned to the clay by Dr. Murray (20 feet) is probably not
far wide of the mark. A description of the lithological characters
of the deposits of the clay division, based on microscopic evidence,
is given. They consist largely of tests of foraminifera and minute
fragments of minerals, and contain nodules of ochreous clay. A list
of fossils of the clays is appended, including an addition of 31 species
of foraminifera to the 122 contained in Dr. Murray’s list.

December 7th.—W. H. Hudleston, Esq., M.A., F.BS.,
President, in the Chair.

The following communications were read :—

- 1. “Note on the Nufenen-stock (Lepontine Alps).” By Prof. T.
G. Bonney, D.Sc., LL.D., F.B.S., V.P.GS.

In 1889 the author was obliged to leave some work incomplete in
this rather out-of-the-way portion of the Lepontine Alps. In the
summer of 1891 he returned thither in company with Mr. J. Eccles,
F.G.S., and the present note is supplementary to the former paper.
The Nufenen-stock was traversed from north to south, and a return
section made roughly along the eastern bank of the Gries Glacier.
Gneiss abounds on the north side of the Nufenen Pass, followed by
rauchwacke and some Jurassic rock. On the flank of the mountain
are small outcrops of rauchwacke and of the so-called ‘ Disthene-

Schistose ‘Greenstones’ from the Pennine Alps. 149

schists’ (both badly exposed), followed by much Dark-mica schist,
often centaining black garnets. Higher up is a considerable mass of
Jurassic rock with the ‘knots’ and ‘ prisms’ which have been mis-
taken for garnets and staurolites, but Dark-mica schists set in again
before the summit is reached. They continue down the southern
flank of the peak ; but rather north of the lowest part of the water-
shed, between Switzerland and Italy, the ‘ Disthene-schist’ is again
found, followed by a fair-sized mass of rauchwacke.

The return section gave a similar association in reverse order ;
and both confirmed the conclusions expressed by the author in 1890
as tothe absence of garnets and staurolites from Jurassic rocks (with
belemnites &c.), and the great break between these or the under-
lying rauchwacke (where it occurs) and the crystalline schists, in
which garnets often abound, of the Lepontine Alps. The crystal-
line schists and the Mesozoic rocks are thrown into a series of very
sharp folds, which, locally, presents at first sight the appearance of
interstratification.

2. “On some Schistose ‘ Greenstones’ and allied Hornblendic
Schists from the Pennine Alps, as illustrative of the Effects of
Pressure-Metamorphism.” By Prof. T. G. Bonney, D.Sc., LL.D.,
ehess, V ob.G.8.

The author describes the results of study in the field and with
the microscope of (a) some thin dykes in the cale-schist group, much
modified by pressure ; (0) some larger masses of green schist which
appear to be closely associated with the dykes; (c) some other
pressure-modified greenstone dykes of greater thickness than the
first. ‘he specimens were obtained, for the most part, either near
Saas Fee or in the Binnenthal.

These results, in his opinion, justified the following conclu-
slons :—

(1) That basic intrusive rocks, presumably once dolerites or basalts,
can be converted into foliated, possibly even slightly banded, schists,
in which no recognizable trace of the original structure remains.

(2) That in an early (possibly the first) stage of the process the
primary constituents of the rock-mass are crushed or sheared, and
thus their fragments frequently assume a somewhat ‘streaky’ order;
that is to say, the rock passes more or less into the ‘ mylonitic’
condition.

(3) That next (probably owing to the action of water under
great pressure) certain of the constituents are decomposed or
dissolved.

(4) That, in consequence of this, when the pressure is sufliciently
diminished, a new group of minerals is formed (though in some cases
original fragments may serve as nuclei),

(5) That of the more important constituents hornblende is the
first to form, closely followed, if not accompanied, by epidote; next
comes biotite (the growth of which often suggests that by this time
the pressure is ceasing tio be definite in direction), and lastly a water-
clear mineral, probably a felspar, perhaps sometimes quartz.

150 Geological Society.

(6) That in all these cases the hornblende occurs either in very
elongated prisms or in actual needles.

The author brings forward a number of other instances to show
that this form of hornblende may be regarded as indicative of
dynamometamorphism; so that rocks where that mineral is more
granular in shape (cases where actinolite or tremolite appears as
a mere fringe being excepted) have not been subjected to this
process.

3. “On a Secondary Development of Biotite and of Hornblende
in Crystalline Schists from the Binnenthal.” By Prof. T. G. Bonney,
iSc., TiiD., FRS., Vales:

Both the rocks described in this communication come from the
Binnenthal, and were obtained by Mr. J. Kecles, F.G.8., in the
summer of 1891. They belong to the Dark-mica schists described
by the author in former papers, and have been greatly affected by
pressure. In each a mineral above the usual size has been subse-
quently developed. In the rock from near Binn this mineral is
a biotite ; the dimensions of one crystal, irregular in outline and
having its basal cleavage roughly perpendicular to the lines indica-
tive of pressure, are about ‘175 x ‘03 inch. The other mineral, from
the peak of the Hohsandhorn, is a rather irregularly formed horn-
blende, the crystals (which lie in various directions) beng sometimes
more than half an inch long. The exterior often is closely asso-
ciated with little flakes of biotite. The author discusses the bearing
of this fact, and the circumstances which may have favoured the
formation of minerals, so far as his experience goes, of an exceptional
size.

Some remarks also are made on the relation of these structures
developed in the Alpine schists to the various movements by which

those rocks have been affected, and on the general question of pressure

as an agent of metamorphism.

4, “ Geological Notes on the Bridgewater District in Eastern
Ontario.” By J. H. Collins, Esq., F.G.S.

The plateau of the Bridgewater district consists chiefly of gneiss
and mica-schist, with subordinate beds of white marble, quartz-
conglomerate and quartzite, and some veins of ‘ giant-granite.’ The
general dip of the gneissose series is eastward.

The author notes the effect of frost in splitting off flakes of the
eneissose rocks and conglomerates, especially on the bare glaciated
surfaces, and suggests that many of the smaller and shallower
lakelets may have originated by this process.

The conglomerates are described as gneisses and mica-schists, with
subordinate pebble-beds. .

The occurrence of gold in quartz-veins near Flinders and at Madoc
is noted; and amongst other economic products are the micas of the
eranites, asbestiform actinolite, and marble. The author discusses

the mode of origin of the granite, marble, and actinolite-rock.

ol |

~~ XX. Intelligence and Miscellaneous Articles.

VISIBLE REPRESENTATION OF THE EQUIPOTENTIAL LINES IN
PLATES TRAVERSED BY CURRENTS ; EXPLANATION OF HALL’S
PHENOMENON. BY E. LOMMEL. (Preliminary Notice.)

Moen consideration shows that the equipotential lines at right
angles to the lines of flow in a plate are at the same time the
magnetic lines of force belonging to the flow. If iron filings are
strewed on the plate with a sufficiently strong current, they
arrange themselves to form a beautiful image of the equipotential
lines.

If the plate is brought mto a magnetic field. these magnetic
lines of force alter their position, and therefore also the lines of
force which necessarily are at right angles to them. In this lies
the simple explanation of Hall’s phenomenon.—Wiedemann’s
Annalen, No. 12, 1892.

ew

ON THE ACTION OF LIGHT UPON ELECTRICAL DISCHARGES IN
VARIOUS GASES. BY F. BREISSIG.

As source of light the author used a gas-flame. As he had the
intention of determining the influence of the visible rays in
electrical discharges, he tried to find a gas in which this action is
as great as possible, but he came to the conclusion that the
difference between various gases in this respect is too small to
lead to the preference of any one in particular.

M. Breissig uses Hallwachs’ form of the luminous discharge with
a somewhat different arrangement. Opposite the source of heht
is placed an amalgamated zinc plate, and in front of it a wire
gauze, also amalgamated, of galvanized iron, both being insulated.
The zine plate was kept at constant potential by a Daniell’s battery
of 80 elements, while the wire gauze was connected with one
quadrant pair of an electrometer. ‘The potential was measured of
the quantity of electricity passing from the zine plate to the wire
gauze owing to illumination.

A decrease of sensitiveness of the plate with the duration of
the illumination was observed, as Hallwachs and Righi had also
observed for other sources of light; moreover, an increase was
observed in all the gases investigated as the pressure diminished.
In opposition to the observations of others, the author found a
feebler discharge in carbonic acid than in air; the deflexions are
reduced to about one half: this phenomenon is due to the fact
that in his experiments the rays of a spectral region are used
differing from that of other observers, and the action of the
various parts of the spectrum on many gases may be different.
With cool gas a feebler action is observed if the gas has already
been illuminated. '

The discharges in some vapours were stronger than in all the
gases examined, especially in air half saturated with alcohol vapour.
The following table gives in round numbers the results observed
by the author.

V2 Intelligence and Miscellaneous Articles.

Discharge.
ae es
Normal Diminished
pressure. pressure.
Atmosphericair . . . . 10 18-22 —
ORV CEM wn yebigelae® is. he 14 20
VOC CM gee seo sok eof 8 16
Carbonic acid Covey ie 6 14
Coal-gas . . ee a 12
Sulphuretted Hydrogen 3 3
Air containing
vapour of ee
Aleoholi:;').0 °°... «20° 80-40 | aon
GCN cece, Mees Of hs) ea ok 20-30 sae a
Marpembinte ss yo te et 6
BenzGles. nye eine 2 2'4 10-20
Petroleum spirit . ... 10
XV NON ae ee ca ee aN 6

In this the mean strength of the discharge in dry atmospheric
air is taken at 10—Inaugural Dissertation, Bonn, 1881; Beeblatter
der Physik, vol. xvii. p. 60.

NOTICE OF A METEORIC STONE SEEN TO FALL AT BATH,
SOUTH DAKOTA. BY A. EK. FOOTE.

On the 29th day of August, 1892, about 4 o’clock in the afternoon,
while Mr. Lawrence Freeman and his son were stacking upon his
farm two miles south of Bath, they were alarmed by a series of
heavy explosions. On looking up they saw a meteoric stone flying
through the air followed by a cloud of smoke. Its course was

easily traced to the point where it fell within about twenty rods
from where they were standing. The stone penetrated the
hardened prairie to a depth of about sixteen inches, and when
reached it was found to be so warm that gloves had to be used in
handling it. Three small pieces of an ounce or two each had
apparently been blown off by the explosions, but the stone still
weighed 462 lb. One of these small pieces was found by some
men not fax distant, and was broken up and distributed among
them. The explosions were plainly heard by a large number of
people at Bath, two miles away, and at Aberdeen, nine miles away,
it sounded like distant cannonading. The exterior of the stone
presents the usual smooth black crust. The interior is quite close-
grained, resembling in texture the stones from Mécs. The iron is
abundantly disseminated through the mass ; and although the grains
are small, they are easily distinguished and separated on pulverizing.

Preliminary tests made by Mr. Amos P. Brown, of the Minera-
logical Department of the University of Pennsylvania, prove the
presence of nickel and cobalt in considerable quantity. Silliman’ 8
Journal, January 1893. a

THE

LONDON, EDINBURGH, axn DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

a

[FIFTH SERIES.]

MAR CH 1893.

XX1. On the Equilibrium of Vis Viva.—Part III.
By Prof. Lupwig BottzMann*.

IT think that a problem of such primary importance in
molecular science ought to be scrutinized and examined on every
side, so that as many persons as possible may be enabled to follow
the demonstration. Maxwell, Scientific Papers, il. p. 713.

§ 1. On the Variables which reduce the expression for the
Vis Viva to a Sum of Squares.

AXWELL? was the first to establish the formula for

the distribution of vis viva among monatomic gas
molecules, which he regarded as perfectly hard spheres of
similar or dissimilar form (mass and radius). He also worked
out the case in which the molecules are considered as rigid
bodies with three different moments of inertia, and he found
that for such a gas the ratio of specific heats must be 12.
Since, however, this ratio has the value 1:4 for the best
known simple gases, he concluded that the mechanical analogy
is at variance with known facts on this subjectt. It is
remarkable that Maxwell, who was successful in presenting
the solution of the problem with such almost inconceivable

* Communicated by the Author, from the Sitzwngsberichte der mathe-
matisch-phystkalischen Classe der konighch-bayerischen Akademie der
Wissenschaften (Munich), vol. xxii. part 3. Translated by James L.
Howard, D.Sc.

+ “Illustrations of the Dynamical Theory of Gases,’ Phil. Mag.
January and June 1860, Sci. Pap. i. p. 877.

t Maxwell, Sci. Pap. 1. p. 409.

Phil. Mag. 8. 5. Vol. 35. No. 214. March 1898. M

154 Prof. Ludwig Boltzmann on the

ease, both in the case of spheres and of bodies which possess
no axis of rotation, did not then think of considering the allied
and almost similar case, namely that of the various perfectly
smooth and rigid solids of revolution which differ from the
spherical form. He would then have obtained exactly the
desired value 1°4 for the ratio of specific heats.

The proof which Maxwell gave at that time for his law of
distribution of kinetic energy was afterwards shown by him-
self to be insufficient ; and in a second paper* he gave an
exact proof that the distribution of vis viva found previously
was a possible one, 7. e. that when once set up among the
molecules of the gas it would not be altered by their impact.

This proof as well as Maxwell’s law itself is capable of
considerable extension, and he pointed out its very close con-
nexion with a far more general theorem which applies to any
system in which any forces operatet. In the attempt to
make this latter theorem still more general, however, Max-
well{ committed an error in assuming that by choosing
suitable coordinates the expression tor the ws viva could
always be made to contain only the squares of the momenta,
this assumption being, as Lord Kelvin has shown §, in general
incorrect. But the mistake may be easily corrected by a
slight modification of Maxwell’s conclusions. To demon-
strate this let us turn to Maxwell’s paper just quoted above,
and write with him (Sci. Pap. ii. p. 720) 6, b, b3...6, for
generalized coordinates, and a, a)... d, as the corresponding
momenta. We must then stop at Maxwell’s equation (42)
(1. c. p. 724), and so write for the vis viva

T=43[11]a,?+ [12 Ja, Ug.+e-

All Maxwell’s conclusions as far as equation (29) inclusive
are perfectly accurate. In order to correct the further con-
clusions we might write the following deduction in place of
that of Maxwell, from that point onward. Let us suppose «
to be a linear function of the momentum a, and thus write

k=n
an= D CaM.
p=

Then we can always choose the coefficients ¢ so that (1) their

* Phil. Mag. [4] vol. xxxv. (1868); Sci. Pap. ii. p. 26.

+ Boltzmann, Wienzr Sttzwngsberichte, vols. lviil., ixiii., Lxvi., Ixxii ,
Dexty., Lxxy,

t “On Boltzmann’s Theorem on the Average Distribution of Energy,”
Camb. Phil. Trans. xii. part 3 (1878); Sci. Pap. ii. p. 713.

§ ‘Nature,’ 15th August, 1891.

Tquilebrium of Vis Viva. 155
determinant © is equal to unity, that is

Cy C19 2 8 e@

and (2) the doubled kinetic energy takes the form
TS eee

i

In this investigation the coefficients c and w are functions
of the generalized coordinates b,...b, but the «’s cannot in
general be regarded as momenta which belong to any system
of generalized coordinates whatever. I will therefore call
them “ momentoids” in order to prevent confusion.

The angular velocities about the three principal axes of

inertia of a solid in the most general case of rotation furnish
an example.
_ I shall denote by 4, that portion of the whole vis viva
which belongs to the momentoid a, Since @=1, we have
day, ddg...ddn=d,, dé,...de,. Jet us insert the variable T
in place of a, on the jeft and of «, on the right, then

il i
7 dT dag da3...da, = at Ue WER 45 ete
da, da,

Dividing by dT and observing that

2g ellie,
dor aa, aie lyed?

we obtain

EZ day daz «.. Aa, = as daty das... day.
1 jemi
From Maxwell’s equation (28) (/.c. p. 721) we find for
the number of systems whose generalized coordinates lie
between the limits 6, and 0,+db,...6, and b,+db,, and
whose momentoids lie between # and #+da ....a, and
a,+da, («, being determined from the equation of tis viva)
the value
NC
palel
If we now proceed with the integration exactly as Maxwell
does, we arrive at his equation (45), which is thus perfectly
correct.
By calculating the probability that the ws viva dpm,¢,?
M 2

AION ee clan ats Galen

156 Prof. Ludwig Boltzmann on the

belonging to the momentoid a, lies between the values /, and
k,+dk,, we again arrive exactly at Maxwell’s expression (51)
(ae p. 425 ).

The expressions (52) and (53) (Ul. ¢. p. 726) of Maxwell’s
paper thus represent the mean and maximum values of the
vis viva belonging to any momentoid. Instead of the law of
Maxwell that the mean vis viva has the same value for every
coordinate, we now obtain the law that the mean value of the
vis viva belonging to all momentoids is the same.

Since the number of momentoids is always the same as that
of the degrees of freedom, the law given by Maxwell at the
commencement of his paper (/. ¢. p. 716) still remains true,
viz. that the mean kinetic energies of two given parts of the
system are in the ratio of their respective degrees of freedom.
The kinetic energy T; of any portion whatever may therefore
contain the products of different »;’s, the terms p;, being the
momenta of the general coordinates of that portion. But T;,
must not contain the product of a term p; and another mo-
mentum which is not included among the terms p;,. Asa
special case, the law will apply without any moditication to
so-called polyatomic molecules of a gas, whose condition is
expressible by generalized coordinates.

T - i=n ;
As 2 o is equal to > a; eh in all cases, my proof of the
1=1
second law* will still be correct, provided that by g, we un-
derstand, not the momenta belonging to the coordinates pz,
but the momentoids.

ON THE SPECIAL CASES SUGGESTED By Lorp KELVIN AS
TEST-CASES.

§ 2. Motion of a Material Point in a Plane.

I believe that with these modifications Maxwell’s proof of
the laws enunciated in the previous paragraphs is a satisfactory
one; but in addition I have already given another proof from
a quite different point of viewf. I believe therefore that its
truth as a law of analytical mechanics can hardly be called
into question{. As I myself arrived at my theorem only

* Borchard-Kronecker’s Jowrnail, vol. c. p. 201 (1885).

7+ “On the Equilibrium of Heat between Polyatomic Gas-molecules.
Part I. Motion of the Atoms in the Molecules,” Wien. Sitz.-Ber. vol. iii.
9th March, 1871. “Some General Theorems on Equilibrium of Heat,”
ebid. 13th April, 1871. In the latter paper J first made use of generalized
coordinates.

{ It is an entirely different question, whether such systems present a
suffidently close analogy with hot bodies. This question cannot be
discussed here; cf, however, Beibi. v. p. 408 (1881).

Equilibrium of Vis Viva. 157

after a laborious consideration of many special cases*, I can
appreciate the value of continually testing general theorems
by means of special examples, and will therefore take up one
of the particular cases suggested as a test-case by Lord Kelvin,
namely the one he mentions last ; because it is the simplest,
and because I respect the sentence of De Morgan, quoted once
by Prof. Tait, to the effect that “formule, if too long, are
often not read.” |

Let a material point of unit mass move in the plane of a, y.
Let 2, y be its coordinates, qg its velocity, u,v the components
of the velocity in the directions of the axes of coordinates,
and @ the angle which the direction of motion makes with
the positive direction of the axis of abscissa, the angle being
counted from 0 to 27. Suppose the potential V to be any
function of the coordinates. We assume that the motion
neither becomes infinite nor asymptotically approaches a fixed
limit ; and that all possible sets of values of a, y, and @ which
are consistent with the equation of vs vera are obtained with
any required degree of approximation, provided the motion
continues for a sufficiently long time T.

Let us take a ¢-coordinate perpendicular to the plane of
x, y, and define any condition of the moving point by marking
off as z-coordinate over the point where it happens to be, the
angle @ which its velocity makes with the positive direction of
abscisse. We shall call the point of space with the coordi-
nates x, y, 9 the point which characterizes the condition of
the moving body, or briefly the instantaneous condition-point.

We can then define our assumption thus :—In the course
of an interval of time T the condition-point occupies all
positions in a finite cylinder (the condition-cylinder) which
has a height 27 in the direction of the axis of z. The
condition-point passes suddenly from the base to the summit
of this cylinder, and vice versa ; with this exception its motion
is continuous.

Suppose the moving point to be at the point w, y at any
time ¢, and let its velocity make an angle @ with the axis of
abscissee and have the components wv, v. The condition-point
at time ¢ will then be a point A of space with coordinates
w, y, 0.

After the lapse of a very short time 6¢, that is at time ¢+ 6¢,
let the moving point be at w’,y’. Let @’ be the angle between
the direction of motion and the axis of abscissee, and uw’, v’ the

* “On the Equilibrium of Vis Viva,” Wren. Sitz.-Ber. vol. lviii. 8th
October 1868.— ‘Solution of a Mechanical Problem,” ¢ded. 17th December,
1868.—“ Some General Theoren:s on Equilibrium of Heat” (end of part 2)
(d. c.).-- Remarks on some Problems in the Mechanical Theory of Heat,”
Wien. Sitz.-Ber, vol. lxxv. 11th January, 1877 (end of part 3).

158 Prof. Ludwig Boltzmann on the

components of the velocity resolved along the coordinate
AXES.

We may denote the position of the condition-point at time
t+8¢ by A’. A’ will be called the point corresponding to A.
If we consider o¢ as constant, every point within the condition-
cylinder will possess its corresponding point. Always, when
at any time the condition-point has occupied any point of
space, it will, after a time d¢ has elapsed, pass to the corre-
sponding point ; and vice versd, the moving body can never
reach the corresponding point except by having passed
through the point to which it corresponds at a time 6o¢
previously. 7

We have then

w=c+q cos @. dt, Me
w=uté.dt, v'=v+7. 6,

(1)

in which €=— o 7=— = are the components of the force

acting on the moving particle, and are therefore functions of

aandy. Further,

ru
6’ =arctg —
uw

which gives, on substituting the above values,
6’ =6+(n.cos 0—¢ sin @) - + = ee)

Now let us construct an infinitely small rectangular
parallelopiped dxdyd@, of which one edge is situated at the
point A. Let the fraction of the whole time T during which
the condition-point lies within the parallelopiped be dt. This
is the time during which the three variables 2, y, 9 will be
included between the values w and «+dz, y and y+dy, and
9 and 6+d@. We may then write in all cases

dt=/(«,y,@)dzdyd0. -. -. 1 =) Samia}

Now construct at each point of the parallelopiped dz dy d@
the corresponding point, and hence obtain the parallelopiped
dx’ dy’ d@'. That fraction of the time T during which the
condition-point les within dw’ dy’ dé’ is, according to equa-
tion (3),

dt! = f(a’, y', 0) da! dy! dé’.

Sinee, however, according to our definition of the conditicn-
point, every time it enters the parallelopiped dz dy d@ it must
after an interval d¢ enter dz’ dy’ d@', and since the interyal

Hquilibrium of Vis Viva. 159

between the exits from the two parallelopipeds is also exactly
dt, it follows that the condition-point must enter both paral-
lelopipeds the same number of times and must remain for the
same time in each. This gives dt/=dt, or

Ke, y’, &) da’ dy! d =f (x, y, 0) dx dy dé.
But we have

/ / /
dizi dy! dd = oY, Oy, OY dex dy dd.
OF OF OF
Ov Oy 00

As 6¢ is constant, and g?= const. —2V, equations (1) and
(2) give

/ / ,
a = 148050." 80 —14qsind. 7
{
OF == (Ecos 0+ sin a=

If we neglect the terms of order 627, the functional deter-
minant reduces to
On OV) OO.
OL nay SBOrH 2

da! dy’! dW’ = dx dy dé,

from which also f(a’, y’, 0’)=/(a, y, 0). As wecan pass from
the parallelopiped de a d@ to its corresponding one, and from
this latter to its corresponding one, and so on, it follows that
(&, y, 9) is always constant, and therefore that dt=C da dy dé.
This result agrees perfectly with that found in my paper pre-
viously quoted, on the ‘‘ Solution of a Mechanical Problem.”
Lord Kelvin denotes by N d@ dr the number of times during
the interval T that the moving particle traverses an element
of surface, whose length in the direction of motion is ds and
whose breadth perpendicular to this direction is dy, in such a
manner that 0 lies between tlie values @ and 6+d0@. As the
moving point always remains for a time ds/g in the element
of surtace, the fraction of T during which the moving point
is situated in drds and has at the same time a direction of
motion between 0 and 0+ d@, is

and consequently

SN dr ds dé.
q

160 Prof. Ludwig Boltzmann on the

But we have just seen that. this time is
C dr ds dé,

from which it follows that N=Cg. WN is therefore quite
independent of the angle 6, and not only Lord Kelvin’s
coefficient A, but-also A, and all the coefficients following
vanish. |

I can hardly doubt that Lord Kelvin will be satisfied with

this result of his test-case.

§ 3. On the Distribution of Kinetic Energy among
Kelvin’s Doublets.

The other cases suggested by Lord Kelvin relate to a
theorem which is closely connected with the problem just
considered, but not by any means identical with it, nor even
a special case of it; namely, the question of the equilibrium
of heat in the case of polyatomic gaseous molecules. It can
easily be shown that in this problem there exists one particular
distribution of vs viva which is not altered either by internal
motion of the molecules or by impacts.

Let 91, P2;-++*Pn be the generalized coordinates by which
the positions of all constituents of a molecule are determined
relatively to its centre of mass, the rotation of the molecule
being included. Let 41, G2,--.n be the corresponding mo-
menta, T the total vis viva of the molecule, V the potential-
function of its internal forces, w, v, w the components of the
velocity of its centre of mass, and finally A and & constants ;
then the distribution of vis viva referred to is that in which
the number of molecules per unit volume, for values of the
variables uw, U, W, P15 Pay++*Pn> G1» Yay +++ Yn between the limits
wu, and uj+duy,..+Gn and gn+dgn, is equal to

eee Oy its 220 G as

If there are several kinds of molecules present the constant «,
but not A, must have the same value for each.

The verification of this result in the special case imagined
by Lord Kelvin is so simple that I shall not consider it here.
But the other proof, that the distribution of kinetic energy
given by the above formula is the only possible one, can only
be established indirectly by the assumption that a certain
particular function must, if altered, be necessarily increased by
collisions. As this function is very closely connected on the
one hand with the quantity designated by Clausius as entropy*,
and on the other hand with the probability of occurrence of

* Wien, Sitz.-Ber. Bd. lxxvi. (1877), Bd. Ixxviii. (1878).

Equilibrium of Vis Viva. 161

the state referred to, the second law of thermodynamics
appears from it te be purely a law of probability.

It appears to me to be a matter of interest (wide Motto) to
examine this latter proof for the case of the molecule provided
with elastic springs as imagined by Lord Kelvin, and which,
following his example, we shall call a “doublet.” By a
doublet let us understand the combination of two material
points with masses m and m’’, which attract each other with
a force proportional to their distance apart. m’ (the nucleus)
is never acted upon by any other force. The masses m (shells)
of any two doublets impinge on each other like elastic
spheres whenever they come within a distance D” of each
other. Besides these, suppose simple atoms of mass m’ to be
present, which collide with each other if they approach nearer
than distance D’, and with the shells if they come within dis-
tance D from them. We shall always write, for the sake of
brevity, ‘ shell” instead of centre of the shell, and “‘ nucleus”
instead of centre of the nucleus. Let 2, y, < be the coordi-
nates of the nucleus of a doublet referred to « system of rect-
angular coordinates the origin of which is at the centre of the
shell and the axes of which have fixed directions ; let a’, v’”, w’’
be the absolute components of the velocity of the nucleus, and
ul, v, 1 the same components taken relatively to the shell ;
let g, h, k be the components of the velocity of the centre of
gravity of the doublet, u, v, w those of the shell, and a, v4, w,
those of a single atom. Finally, suppose y(a, y, 2, ut, v, W,
g, h, k) dv...dk to be the number of doublets per unit of
volume for values of the variables #...k at the time ¢ lying
between the limits « and w+dw#...k and k+dk, and let
T (uray Ury W1) Cu, dv, dw, be the Srna kes of single soe | in unit
of volume whose velocity-components uj, 71, w, lie between
the limits ,

u, and uj+du,, rv, and v,4+dv,, w, and w,+dwy.

Then the expression the value of which can only be dimi-
nished by impacts, and which for brevity we call the entropy,
is

es \xlog x da hin dk+\ flog f du, dv; dw),

in which the integration extends over all possible values of
the variables. The first term of the expression EH can be
obtained in the following manner. We write down the value
of log yx for ev ery claw alee contained in the unit of volume;
2. e. we insert in log y for all the variables those values w Teck
it takes for the doublet under consideration. Then we add
together all the values of logy so obtained. In order to

162 Prof. Ludwig Boltzmann on the

express this symbolically we may denote the sum by > log x.
In a similar manner the second term gives us } log /, the
summation being extended to all the single atoms in a unit of
volume.

In order to prove that E can only diminish, let us first find
the change produced in the value of {logy simply by the
relative motion of nucleus and shell in the doublets, assuming
no collisions to take place. In this case gy, h, and & would
obviously remain constant. On the other hand, we should
have at any time ¢,

x=Asin(at+B), w=Aacos (at+B),
and at time ¢=(,
#=AsinB, t%t)=Aacos B.
If we consider all doublets for which A and B are ineluded
within specified infinitely close limits, then
da di=da,dyj=AadAdb » 2 ie
and similarly for the y- and z-axes,
dy dv=dy) dv), dzdw=dza dw 20. 2)
It can easily be shown that the equation
dx dy dz dit dv dw = day dy dz dit dv, AW
also holds good if the nucleus and shell have any other central
motion whatever. (Cf. my investigation of the equilibrium
of heat in the case of polyatomic gaseous molecules, previously
referred to.) If no collisions were to take place the doublets,
whose variables at time t=0 lay between the limits xz) and
Xo t+dx...ky and ky +dky, would have their variables at time ¢
between the limits # and e+dza...k and k+dk. Let us
therefore consider for a moment the variable ¢ as explicitly
expressed in the function x, in order not to exclude the pos-
sibility of a variation of y with time. We have then as the
number of the former doublets,
X(2-- Wo, g, h, k, O)day..dk=yy day... dk
and of the latter
Veh tide. cdie=wde «Ake.

Hence we have
Xo Axo erie dk=y dx a6 dk,

and from (4) and (5)
Xo =X;
from which it follows that
Xo log Xo, day)..dk =x logy dx..dk.

— Equilibrium of Vis Viva. 163

The integration of this last equation over all possible values
of the variables involved in it shows us at once that the
quantity = log y suffers no alteration by internal motion of
the doublets, and the same will be true, of course, for any
central motion. All that now remains is to determine the
effect of the collisions.

Let us now introduce instead of u, v, Ww, 9, h, k, the absolute
velocities a, v,w, uw’, wv”, w’. Since
Malt

(m +m!) g=mu +m usu! =u,

it follows that.
dg du=du du".

If we write for the number of doublets in unit. volume,
whose variables x, y, z, wu", v", w", u, v, w, lie between the limits
xand e+da...wandw+dw, the value F (a, y, z, ul v", w",
u, v, w) dx ...dw, where

,
mut nu’ \

F= (eget ee)
x Ys%) m +m" JP
then

> logx=|F log F da...dw= log F,

in which the summation again extends to all the doublets
contained in the unit of volume. Now denote by 6,3 loy F
the increase in & log F produced during time 6é by the impact
of doublets on each other, by 6,2 log f the increase in & log f
during the same time, produced by the impact of single atoms
on each other, and by 6,,(3 log F+% log f) the corresponding
increase of the quantity in brackets, produced by the impact
of doublets and single molecules.

To calculate 6,.(2 log F +2 log /f) we must sort out, from
all the impacts between a shell and a single atom in unit
volume during time o¢, those collisions for which the velocity-
components of the shell at the moment of the collision (and
likewise before) lie between the limits w and u+du, v and
v+dv, w and w+duw, the velocity-components of the nucleus
being between w!' and w" +-du!', vo" and vu" + dv", w!’ and w" + dw",
the coordinates of the nucleus relatively to the shell being
between w and «+d, y and y+dy,z and z+dz; further, the
velocity-components of the common centre of gravity of the
shell and the single atom are to lie botween p and p+dp, q¢
and g+dq,7r and r+ dr, and the direction of the line of centres
of the impinging atoms at the moment of impact are to lie
within an infinitely narrow cone placed in a definite direction
in space and having an infinitely small angle dX. The velocity-
components of the single atom at the instant when the impact

164 Prof. Ludwig Boltzmann on the

begins are then
_m+m— m m+tm =m

.— — — 1 = — Vv
1 m! P mi? 1 mi q 73
I
m+m m
Wy, — ay — —U. e (6)
VID m

For the number of impacts which take place in unit volume
during time 6t, under the conditions specified above, we find
without difficulty the value

dn=D?. F(a, y, z, ul", v", w", u, v, w) f (a, M1, U1)
x Vedax... dw" du dv dw du, dv, dw, dr 6.

In this expression V is the relative velocity of the two
atoms at the moment of collision, and e the cosine of the acute
angle between the line of motion and the line of centres.
If we introduce instead of w, v,, w, the variables p, q, 7, from
equation (6) we find

1) 3

dn=D* Ff, es Veda...dw!" du dv dw dp dq dr dn &E,
in which the suffix 1 denotes that the values of the variables
as given in equations (6) are to be substituted in the function.

In each of the impacts just specified a shell loses velocity-
components uw, v, w, and hence in all the dn impacts = log F
will be diminished by dn log F.

After each of the impacts considered let the velocity-
components of the shell be between w! and u! +dw', vandv'+dv',
wand w'+dw!. In order that shells may be formed with
these new velocities {log F must be increased by dn log FE’,
where the affix denotes that the variables 2... w", ul, v', w!
are to be substituted in the function F. We assume that the
collisions are instantaneous, in which case the variables z... aw"!
are unaltered by the impacts. The total increase of Y log F
by reason of the impacts considered is, therefore,

dn (log F’—log F).
In like manner we find that Slog 7 receives an increase
dn (log fy’— log f;)

during time 6é from the same impacts, the affix and suffix
meaning that the following values of the velocity-components
of the impinging single atom after impact are to be substi-
tuted in the function /.

Equilibrium of Vis Viva. 165
aoe mi Denier ; m+m! m
u,!= — — 7) o/= ——v
- pene ele E a all
!
m+m m
!
oo L——w. . 7
i an! m! @)

The total increase of Slog F+ 2 log/ by all impacts of the
type specified is, therefore, dn (log F’ + log /"; —logF —log f\).
From this we shall obtain the total increase previously
designated by 6,,(2log F+ log /) if we integrate over all
values of the variables whose differentials are contained in dn*.

This integration may be performed by means of a special
device. In conjunction with the above terms which are
furnished by the “ specified ” impacts, let us take the terms
furnished by the “ opposite’ impacts, and thus divide the
whole of the collisions into pairs.

We shall consider an impact to be “ opposite” to any
‘“ specified ’’ one when the condition of the colliding atoms at
the end of either is exactly the same as their condition at the
commencement of the other one. ‘The centres of the colliding
atoms must, however, be interchanged of course, since they
approach each other before impact. The remaining variables
a...w' will be included between the same limits for both
impacts. In the accompanying figures the largest circle repre-
sents a shell, the smallest a nucleus, and the intermediate one
a single atom; the arrows drawn through their centres represent

* If we assume that the second of the impinging atoms is not a single
atom, but a shell, we arrive by exactly analogous reasoning at a similar
equation

28,3 log F= \dn (log F’+log F,’—log F —log F,),

in which “cia

By SF (@, Yyy My Ma'', Py ') Wi") Uy M, W).

BY SE y, yy 2 Uy") P15 W's Uy’, |, &')-
U,V, Wy, and w,', v,',w,’ are the velocity-components of the second shell
before and after the impact, and must be expressed by equations of
similar form to (6) and (7). %4, Y%, %, %'', v,’, w,"' are the remaining
quantities by which the position of the second doublet at the moment of
the impact is determined. Finally,

dn=D'? FF, Vedz... dw" du dv dw dx,... dw,'' dp dq dr dy &t.
By similar processes of reasoning we should find

23,3 log f= {dn (log. f’+log f;'—log f— log /)

dn=D"ff, Ve du dv dw dp dq dr ad &t.

and

The meanings of the quantities in these equations will be clear without
further explanation.

166 Prof. Ludwig Boltzmann on the

the velocities. Figs. 1 and 2 show the configurations before
and after an impact respectively, while figs. 8 and 4 give the
Fig. 1. Fig. 2.

— Tr:
4 O°
g. o.- tL 12.

Fig. 3
2 4 a
ones :

configurations before and after the corresponding “‘ opposite ”
impact respectively. Arrows numbered alike have always
equal lengths and make the same angle with the line of centres.

For all collisions which are “ opposite” to those previously
considered, the velocity-components of the impinging shell at
the commencement of the impact lie between the limits

wand ul +du', v' and vo +d, w! and w! + dw!
and at the end of the impact they le between
wu and u+du, vand v+dv, w and w4 dw.

The same holds good for the impinging single atom in
which the motion of the centre of gravity, the magnitude of
the relative velocity and its inclination to the line of centres
have the same values for the opposite impact as for that
originally considered. In each opposite impact a shell loses
velocity-components w’, v’, w', and a single atom loses
uy', vy!, w'; on the other hand, a shell gains u, v, w, and a
single atom uy, %, wy. If dn! is the number of collisions per
unit volume in time 6¢ which are opposite to those previously
considered, the term = log F +2 log/ is increased by them to
the extent of

dn! (log F + log f; —log F’—log 7).
The total increase in the value of this expression due to the
specified and opposite impacts together is
(log F + log f,—log F’—log f\!)(dn—dn’).

If we integrate this expression for all values of the variables

whose differentials are contained in dw and du, we obtain

Equilibrium of Vis Viva. 167

261o(>% log F + % log tT); because we count every Impact twice ;

once as a“ specified,” and the second time as an “ opposite,”

impact. As V,e¢, and dd are not changed by the impact, we

have

Pes Oa a are Veda... du! du! du! dw! dp dq dr dv 6t.
It can easily “ shown (most simply by a geometrical

proof ) that du’ dv' dw'=du dv dw, and hence

§,(S log F+ Z log f) = z { (log F’ + log f/ — log F—log f)

1\3
x (Ff, — F'7') ee VeD?du dv dw dp dq dr dz...du" dr. (8)

Similarly it can be shown that
§,3 log F = 281) (log F! + log F\!—log F —log F,)(FF,—F'Fy')
x Ve D'?dz...dw"dx,... dw," du dv dw dp dq dr dn,

8,3 log f= 284\(log /' + log f,'—log f—log ft) (SAS)
NeW dududwmdpagd: AN. 2 5.) . (9)

in which the variables are the same as in the footnote on
page 165.

We shall confine our attention to the consideration of the
stationary condition, in which F and / are at all times the
same functions of the variables contained in them. In this
case no causes except those already considered can effect
changes in 2 log F and 2 log /; and the total change in H
during the time 6¢ is therefore

dH=6, (Slog F+ > log /)+6,2 log F+8, 3 log /.

Since everything (and therefore EL) remains unaltered, 6H
must be zero. But in the integrals of equations (8) and (9)
the two factors in brackets have necessarily opposite signs,
while the remaining quantities are essentially positive. The
expression to be integrated is therefore necessarily negative,
and the sum of the integrals of which 6H is composed can
only vanish if at each impact

eye Ee ——ay i «ss . CLO)

Let us now consider the most simple case, namely, that in
which the shelis always pass each other without i impinging,
and similarly with the single atoms ; but between a shell and
a single atom let there be “alw ays an impact if they approach
within distance D of each other. We have then only the
first of the equations (10), but it holds good for every possible

168 Prof. Ludwig Boltzmann on the
impact. If we put the velocity of a single atom
Vu +o +07

equal to ¢,, then /, is clearly a function of ¢, but F may be
expressed as a function of the following six variables: —(1) the
two velocities c and c” of shell and nucleus, (2) their distance
apart p (measured from centre to centre), (3) the angles « and
a'’ which the directions of c and c" make with the line p, the
latter being supposed drawn from shell to nucleus, and (4) the
angle 8 between the plane containing p and c and that con-
taining p and c”. | .

Now imagine a collision to take place, and denote the
values of these variables at the moment immediately before
the impact by letters without an affix, their values just after
the impact being distinguished by the affix. We can so
choose the direction of the line of centres at the moment of
impact and the direction of cq, that c, «, and @ take any re-
quired values c’, a’,and 8’, provided these latter furnish a real
value c,' of the variable ¢, after impact. This value will be
determined by the equation of vis viva

me? +me?=m'e2 +me.

The values of the variables c’, p, and x” will not be altered
by the impact. The first of the equations (10) can therefore
be written in the form

Fc", a, p,c,e, B) - fala) =F, al, p, eya!, Sa

xf, / (x /ot4 (ce) )

This equation must be satisfied by all possible values of the
variables ¢c', a", p, c, a, 8, c, a, B', and ¢,; from which it
follows easily that

Filer) =A. e—K'ey? KF = AewKme?,

in which A, and / are simple constants, while A may contain
the variables ¢", p, and @”.

It is therefore evident that the mean kinetic energies of a
shell and a single atom are equal, and that Maxwell’s law of
distribution of velocities between shells and single atoms is
satisfied, without assuming the existence of impacts of shells on
each other, or of single atoms on each other. These assumptions
do not alter the distribution of vis vzva in the slightest degree,
however, because the values of /; and F found above satisfy
identically the other relations demanded by the equations (10).
On the other hand, the condition that the nuclei should never

- come into collisions of any kind does not prevent the law from

Equlbrium of Vis Viva. 169

applying even to them ; but the proof of this is much more
difficult. For, if such collisions existed, it would follow that
F would depend upon c” in exactly the same manner as it
depends upon ¢, and there we should be forced to stop. In
this case we must consider more closely the internal motion
of the doublet.

We can next prove without difficulty that in the distribu-
tion of velocities just found the values of c, a, 8 are altered
on the average in exactly the same manner and degree by
each impact as by its opposite one, for every set of values of
c', p', and #". If, then, certain forms of central motion are
suddenly destroyed by a collision, the same forms are pro-
duced again elsewhere equally often by other collisions, and
consequently the same law of distribution of central motions
would exist even if all impacts were suddeniy to cease.

It is remarkable that just for the simple case imagined by
Lord Kelvin, in which the central force is taken proportional
to p, the calculation is exceedingly long. In order not entirely
to forget the sentence of De Morgan, previously quoted, I will

b e e
assume some other law, e.g. ap + o°? or, indeed, any one in

which the angle between two consecutive apsidal lines bears no
rational proportion to 7.
The total energy of a doublet is

Pe et, oe. (LL)

where @ is the potential-function. The doubled velocity of
the relative motion of shell and nucleus in the plane of their
central motion is

K=p V¢ sin? a +c” sin? a” —2cc" sin a sin a" cos B, . (12)

and the velocity of the centre of gravity of the doublet mul-
tiplied by m+m"' is
G= V m2? + m!?d? + 2mm''ce"(cosacos a! + sin asin! cos 8) (18)
and its component perpendicularly to the plane of central
motion is
3 ce" sin a sin #" sin B (14)
— We sin? até? sin? a! — Qc" sin asin a cos B

The number of doublets in unit of volume for which

K, L, G, H lie between the limits
Kand K+dK, L and L+dL, G and G+dG, H and H+dH,
Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893. N

170 Prof. Ludwig Boltzmann on the
may be written
®(K, L, G, H) dK dL dG dH.

The number of these doublets for which p lies between p
and p+dp is
dp Podp dp
®,. dK dL dGdH .—+ —=Vdk dL dG .dH—,

Oo
Pl

dt

1
a peri-centre to an apo-centre; this latter is, therefore, a given

functionof K,L,G, H; andV=@ / ‘ = is likewise a function

in which o= Sy , and |" ze is the time which elapses from
p

/ 1

of these four variables. Let us limit our attention to those
doublets for which (1) the last apsidal line of the central
orbit makes an angle lying between ¢ and e+ de with a straight
line drawn in the plane of the orbit parallel to a fixed plane;
(2) two planes, one normal to the central orbit and including
the direction of motion of the centre of gravity, and the other
parallel to a fixed straight line , make angles between w and
@+dw with each other; and (3) the direction of motion of the
centre of gravity lies within a cone of given direction of axis
and of infinitely small angie dA. We have then to multiply
by de dw dd/167°, and the number of doublets in unit volume
which fulfil.these conditions is

1 7

If we denote by g and g+dg, h and h+dh, k and k+dk,
the limits between which the velocity-components of the
centre of gravity of the doublets must lie (the coordinate axes
being rectangular and fixed), then

G?dG dx=dg dh dk.

Now keep g, h, and & constant, and place at the centre of the
shell a system cf rectangular coordinates whose z-axis is in
the direction of G; denote the coordinates and velocity-com-
ponents of the nucleus relatively to this system by 2, y, 2,
Uy, Vj, W, respectively, and transform these six variables in

, L, H, p, e,@. We then introduce a second system of co-
ordinates, referred to which the coordinates and velocities of
the shell are 2, Yo, 22, Ug, Ve, We, respectively. The z-axis of
this second system is to be taken normal to the plane of the
central motion, and its z-axis in the section of the plane of

Equilibrium of Vis Viva. 171
central motion and the old zy-plane. We have then
H=Gsin 08,
90—@ being the angle between the two axes of z; therefore,
since G is constant,

dH=G cos 6 dé.

Winally, let us denote by the angle between the two
w-axes, seeing that it only differs from the angle previously so
designated by a quantity which we are at present regarding
as constant. In this case

sg=w, cos Osin w + y; cos 8 cos w + 2; Sin O,

We =U, Cos Osin w + v, cos 8 cos @ + w, sin 8,
and these two expressions must both vanish, inasmuch as the
xy plane is that of the central motion. By means of these

two equations we can introduce @ and @ in place of z, and w,,
when #, 7; % and vy, are constants, and we thus obtain

oy le de.

dz, dw, = (yu — 20) —

Further
Xy= #1, COSM—Y; SIN @,

Yo SInO=2,sin wo +4, COS @,

with similar equations for 2, v2, u, v. From these it follows
that

YU — Ly = sin O (yyto— Xyvq) = K sin 9,
and, if 0 and » are contants,
day dy, sin @=da,dy,; dugdvsin 0=du, dv,
from which :
diy dy, dz, du, dv, dw,=K cos 8 daydys dug dv, dO dw.
Now let us denote, as before, by o and 7 the component
velocities of the relative motion of shell and nucleus in the

direction of p and normal to this direction, respectively ;
then for constant values of w, and y,

do dr=duydvy

K=pr, L=h a qn (0? +7”) + h(p)
, 7 © 2(m+m') p

nl!
dKkdL= emit oe do dr,

where [iy is the energy ‘ee anal of the centre of gravity, and

172 On the Equilibrium of Vis Viva.

is now constant. Finally, let the angle between p and the
last apsidal line be yr, then

a=pcos(etp), Y2=p sin(e +),
in which ¥ is a function of p, K, and L ; both the latter are
now constant, and therefore

pdpde= day dy2.
Collecting all these equations ee find that

da, dy, dz, du, dv, dw,= a ae isd ae dK dL dH dp do de ;

and it will immediately “ seen ae if coordinates and
velocities without suffix or affix refer ae any random set of
fixed coordinate axes, we must have likewise

dx dy dz du dv dw= ee dK dl dH dp dw de.

Introducing this in equation an es remembering that for
constant values of wu, v, and w,

mils
Lis oe dv" dw",
we find (m+m
1 mt WW

Jo Topol
167° (m+m")* KG, Kad dy dzdu dy dw du! dv’ dw

for the number of doublets in unit of volume for which the
variables w...w’” lie between z and x+dw...w" and w”+dw."
But we have previously found for this number the expression

F . dex dy dz du dv dw du! de! dw",

and we then saw that F must be of the form Ae—*”, in which
A is a function of ¢",p, and «” ouly. It follows then, if we
write

K= NB Ye IES PO)

that B must be on the one hand a function of e”, p,and a”
only, and on the otker hand a function of K, L, G,and H
only. B must therefore be a function of these latter variables
which i is quite independent of c, «, and 8, and only a function
ore oranda <

If we put B=/(K, L, G, H), then this function must be
independent of ¢, «, and 8, for all values of c” and #”. Sub-
stitute for the variables K, L, G, H their values from 11, 12,
13, and 14, and make c’=0 at first. Then

K=pcesina, L=}mc’+¢(p), G=me, H=0.
2
B=/(posin 2,“ +$(p), me, 0).

The Fusion Constants of Igneous Rock. 173

As this expression is independent of ¢ and & the function f
does not contain the quantity K, and it only involves L and
G in the form 2mL—G’. We can best express this by
writing the function with variable 2mL—G?, instead of
L, G, when it becomes B=/(2mL—G?,H). If we introduce
again into this expression the general values given in equations
11 to 14, we see that the two variables in the function are
quite independent of each other if c, a, 8 are to have all
possible values. And since B is constant for all values of ¢, a,
and £8, it is so for ail values of 2mlL—G? and H, and is
therefore absolutely constant. The distribution of ws viva is
therefore obtained.

XXIL. The Fusion Constants of Igneous Rock.—Part II. The
Contraction of Molten Igneous Rock* on Passing from
Liquid to Solid. By Cart Barusf.

[Plate V. |

INTRODUCTORY.
if. VPA TERIAL and Method.—The following volume-

-’* measurements were made for Mr. Clarence King, on
a typical sample of diabase which he furnished.

The method of testing the volume-behaviour by allowing
the rock to expand in a vertical tube provided with an index
was suggested to Mr. King by Lord Kelvin. I therefore pre-
ferred it to a method of my ownf, in which the behaviour in
question is to be determined by high-temperature air-volumetry,
with the rock enclosed in a glazed platinum bulb-and-stem
arrangement. In place of the index or float I employed an
electric micrometer, believing a probe of this kind to be more
trustworthy (§ 13). Imay state here, that the fact that the con-
traction of the magma in passing from liquid to solid can
actually be measured by the simple burette method was to mea
great surprise. After many trials I found, however, that by
allowing the furnace to cool so slowly that the platinum vessel
remained rigid relatively to the charge, the contraction of
the latter could be followed even into the solid state. As
a consequence of slow cooling, moreover, the magma was
probably undercooled, and | thus obtained the whole volume-
difference liquid-solid at a given temperature. The data are

* Cf. note in American Journal, xli. p. 498 (1891).

+ Communicated by the Author.

t Cf. Phil. Mag. July 1892, where this method is tentatively employed
to measure the expansion of white-hot porcelain.

174 Mr. Carl Barus on the Fuszon

sufficient to compute the corresponding contraction at other
temperatures.

2. Literature—The question has elicited voluminous dis-
cussion ; but literary comments are superfluous here, since
‘Prof. F. Niess*, of Hohenheim, not long ago made a careful
survey of all that has been done on the subject. The reader
desiring specific information is referred to this interesting
pamphlet. ‘Hs ist ein durch Contraste buntes Bild,” says
Prof. Niess (loc. cit. p. 36), “welches in der vorstehenden
Citatenlese dem lLeser zu entrollen war, und aus dem
Wirrwarr entgegengesetzter Ansichten heben sich nur zwei
Korper: Wismuth und Hisen, heraus, iiber welche man wohl
mit absoluter Sicherheit die Acten als geschlossen bezeichnen
kann, und zwar in dem Sinne, dass fiir sie die Ausdehnung
im Momente der Verfestigung als zweifellos bewiesen gelten
kann. Die iibrigen Metalle stehen noch im Streit, und fiir sie
gilt dasselbe was wir fiir die kiinstlichen Silicate zu fordern
Hatten’. 52). 2 ” Now iron, in virtue of the occurrence of
recalescence (Gore, Barrett), is scarcely a fair substance to
operate upon; and it heightens the confusion to find that
Prof. Niess, after weighing all the evidence in hand, is
obliged to conclude that rocks expand on solidifying.

The present experiments show beyond question, I think,
that at least for diabase this is not true. I find that this
rock not only contracts between 3°5 and 4 per cent. on solidi-
fying, but that such solidification is sharply broken and only
apparently continuous with temperature, and that the fusion-
behaviour throughout is quite normal in character. Hence,
with certain precautions which I shall adduce in the course
of this paper ($ 21), the volume thermodynamic relations
which I derived by acting on organic bodies may be applied
to rock magmas.

3. Lifect of Fusion. Density—The rock after fusion is
changed to a compact black obsidian, and quite loses its
characteristic structure. It was therefore important to examine
the volume-relations of this change, preliminarily. This is
done in Table I., where the dersities obtained with lumps of
the rock (mass M) at the temperature ¢ are given, A being
the density before, A’ after fusion.

* “ Ueber das Verhalten der Silicate ete.,” Programm zur 70, Jahresfeier
d. k, Wirtemb. landw. Academie, Stuttgart, E. Koch, 1889. Cf. Niess u.
Winkelmann, Wied. Ann, xiii. p. 43 (1881); xviii. p. 364 (1883).

Constants of Igneous Rock. 175

TasLEe 1.—Density of Diabase before and after Fusion.

Before Fusion. After Fusion.

_ Sample M. | t. | ac Sample M. Z, ie ieee
No | | No. a

—- | |

ie ec y
I. | 228950, 25 | 30161 || *Z |699330] 21 |2-701é] -104

|

Tf. | 45:3654| 21 | 30181 ‘II. |33-'7659 | 19 |2:7447] -090
Ill. | 547208) 21 | 30136 || +IIT. |29:9777 | 19 | 2°7045} -1038

IV. | 69-4940! 21 | 3-0935

The rock was fused both in clay and in platinum crucibles.
In the latter case the density of the known mass of metal had
been previcusly determined, and the glass was not removed
from the crucible. In the other case the clay was broken
away from the solid lump within, and its density then measured
directly. A few small bubbles were visible on the fresh
fracture of the glass, due, I presume, to the ejection of dis-
solved gases on solidification. At some other time I will
make vacuum-measurements of the density of powders both
of the rock and the glass, but I do not believe the data of
Table I. will be seriously changed by such a test.

From Table I. it appears that the mean density of the
original rock is 3°0178; that of the glass after fusion is only
2-717, indicating a volume increment of 10 per cent. as the
effect of fusion. This remarkable behaviour is not isolated.
Niess (J. c. p. 47), quoting from Zirkel’s Lehrbuch, adduces
even more remarkable volume-increments of the same naturet;
viz., in garnet 22 per cent., in vesuvianite 14 per cent., in
orthoclase 12 per cent., in augite 13 per cent., &.: but I
doubt whether the great importance of these facts has been
sufficiently emphasized. Suffice it to indicate here that it
makes an enormous difference into what product the magma
is to be conceived as being solidified ; and that throughout
this paper the molten rock solidifies into a homogeneous
obsidian. I am only determining, therefore, those volume-

* Fused in a clay crucible. Glass detached when cold.

+ Fused in a platinum crucible. Glass not detached.

t Cf. Thoulet, Ztschr. f. Kryst. u. Mineralogie, v. p. 407 (1881); Bull,
Soc. Min, de France, iii. p. 34 (1880).

176 Mr. Carl Barus on the Fusion

changes which lie at the margin, as it were, of the more
profound and chemically significant volume-changes (poly-
meric passage from homogeneity to organized rock-structure),
even though the latter may be conceived as producible by
pressure alone, under conditions of nearly constant (high)
temperature. I may add, in passing, that the magnitude of
the chemical changes of volume makes it advisable to carry
the work on the effect of pressure on the chemical equilibrium
of solids and of liquids, and on the solution behaviour solid-
liquid, into greater detail than I have thus far attempted*.

APPARATUS.

4, Temperature Measurement.—In work of the present kind
an apparatus for the accurate measurement of high tempera-
tures is the fundamental consideration. I may, however,
dismiss this subject here, since I discussed it in the intro-
ductory papert. The temperature-measurements of this
paper were made with a thermocouple of platinum and pla-
tinum with 20 per cent. of iridium, which had been frequently
compared with my re-entrant porcelain air-thermometer
throughout an interval of 1100° C., and tested for freedom
from anomalies beyond this interval. Inasmuch as the
electric method consists in expressing thermoelectromotive
force by aid of a zero method, in terms of a given Latimer-
Clark standard cell, the temperature-apparatus is of the same
order of constancy as to time as the standard cell.

To find in how far my earlier data were trustworthy after
the lapse of upwards four years, I made fresh check measure-
ments of the boiling-points of mercury and of zine. The
latter only need be instanced here. My original mean datum
of the boiling-point of zinc, expressed as electromotive force
for the couples under consideration, was (1887) e.=11,074
microvolts, the cold junction being at 20° C. The new expe-
riments (1891) gave me data as follows :—

Thermocouple No. 35, és) = 11,168 (microvolts),

e No. 36, 5 hdl 2
5 No. 39, joe Tai =
is No. 40, 72) aa a

Means eis. 12d aliag =

* American Journal, xxxvii. p. 339 (1889); ibid. xxxvyiii. p. 408
(1889) ; ibid. xl. p. 219 (1890); ibid. xli. p. 110 (1891) ; ibid. xlii. p. 46
et seg. (1891). Also Phil. Mag. [5] xxxi. p. 9 (1891),

tT See this Magazine, July 1892, p. 1.

Constants of Igneous Rock. 177

agreeing very closely with subsequent specially careful
measurements, v1z.:—

Thermocouple No. 86, é) = 11,131 (microvolts),
Nor 30, ,, tlts4 i

The difference of values, new and old, is 60 microvolts, only
about 4 per cent. as regards electromotive force, and corre-
sponding to about 4° at 1000°. In view of the excessive use
and abuse to which the couples had been put in the lapse of
time this result is gratifying.

Endeavouring to ascertain where this discrepancy was to
be sought, I also made new comparisons between the Clark
cell and a normal Daniell of my own (Bull. 54, U.S. Geolog.
Survey, p. 100), in which the cells are separate, and only
joined during the time of use. Supposing the electromotive
force of the former to have been e=1°435 throughout, the
following succession of values obtained for the standard
Daniell :—

March SSO 20e Cr eee 38,
mugust ~ 18871,.238° C., 1:139,
September 1891, 27° C., 1:147.

If, therefore, instead of regarding the Clark cell as constant
I had attributed* this virtue to the standard Daniell, the
small thermoelectric discrepancy equivalent to 4° at 1000°
would be altogether wiped out. Now I made the Clark cells
in question as far back as 1888, when less was known about
details of construction than is now available. I conclude,
therefore, that the discrepancy is very probably in the standard
cells, and that the thermocouples have remained absolutely
constant, a result which is borne out by my boiling-points of
cadmium. ,

Apart from this, the new standardization with boiling zine
fixes the scale relatively to the accepted value for this datum.

5. General disposition of Apparatus.—This is given in
Plate V. on a scale of 1: 4, where figs. 1 and 3 are sectional
elevations showing the parts chiefly with reference to their
vertical height, and fig. 2 is a sectional plan, in which the
parts are given with reference to the horizontal.

The molten rock, Z Z, contained in a long cylindrical pla-
tinum tube, largely surrounded by a tube of fire-clay, FF’, is
fixed vertically in a tall cylindrical furnace, DD, LL. The
heat is furnished by six burners, B, B,..., fed by gas and an

* Our laboratory affords insuflicient facilities for the direct measure
ment of electromotive force.

178 Mr. Car] Barus on the Fusion

air-blast, laden, if need be, with oxygen. These burners are
placed at equal intervals along the vertical, three on one side
and three on the other (see fig. 2), and set like a force-couple,
so as to surround the platinum tube with a whirlwind of flame.
Suitable holes are cut in the walls of the furnace for the sym-
metrical insertion of the insulated thermocouples, T, and also
at S for fixing the sight-tubes, A, near the top and the bottom
of the furnace. Parts of the envelope of the platinum tube
are cut away, so that the upper and lower ends of the (red
hot) platinum tube can be seen in the telescope of an external
(screened) cathetometer. Thus the expansion of the platinum
tube is measured directly. A vertical micrometer, Kkd
(figs. 3 and 4), insulated so as to admit of electrical indica-
tions of contact, furnishes a means of tracing the apparent
expansion of the rock Z Z, within the fusion-tube.

In principle, the excessively slow cooling of the furnace is
to be so conducted that the magma may always remain much
less viscous than the practically rigid platinum envelope
(§§ 1, 18).

The furnace stands on a massive iron base perforated by
eight holes, into which vertical iron uprights are screwed,
symmetrically surrounding the furnace and at a distance of
4 or 5 centim. from its circumference. Only one of these
is indicated at QQ (fig. 8), the rest with other subsidiary
parts being omitted to avoid confusing the figure. ‘T'wo of
these uprights h hold the vertical micrometer, two hold the
burners in place, and two subserve as buffers for the clay
arms, H, H,... by which the fusion-tube is adjusted verti-
cally. The sight-tubes are suitably clamped to the seventh
and the insulators of the thermocouples to the eighth. All
these uprights are hollow, and a swift current of water con-
tinually circulates through them, issuing still cold to the
touch. The same current also flows through the bent screen,
X X, of the vertical micrometer, and through the vertical flat
screen of the cathetometer.

6. Lhe Furnace-—The burners, B, are each fed with the

same amount of gas and air by properly branching the large
supply-tubes. A graduated stopcock is at hand for regulating
the supply of gas to a micety. Hence the furnace is fed with
a mixture of gas and air, and temperatures between 400° and
1500° are obtained by ‘simply making the influx poorer or
richer in combustible gas. Oxygen ‘has not thus far been
necessary”.

- * Burners suitable for the above purpose are shown in Bee little shi
on high temperatures (Leipzig, Barth, 1892).

Constants of Igneous Rock. Ig

The products of combustion are carried off by the two
oblique tubes, E, H, in the lid LL (fig. 4). Nete that the
water-screen bends around the vertical micrometer in such a
way that flames issuing from E do no injury, and a perforated
free plate, mm, closes the vertical hole in the lid L L.

Two large size Fletcher-bellows, set like a duplex-pump
and actuated by a gas-engine, furnished the air-blast.

In order to insure greater constancy of temperature, and
at the same time increase the high temperature efficiency of
the furnace, it is essential to jacket both the latter and the lid
heavily (1-2 centim.) with asbestos.

7. Fusion-tube-—The platinum tube holding the molten
rock ZZ is 25 centim. long and about 1°5 centim. in dia-
meter, drawn as accurately cylindrical as possible and provided
with a flat bottom. To protect this tube from gases, to keep
it from bulging in consequence of the fluid-rock pressure
within, and to insure greater constancy and slower changes
of temperature, the platinum tube is surrounded by the fire-
clay tube F F (figs. 1 and 6) fitting loosely. Care must be
taken to allow for shrinkage of the clay, which in a fresh
tube, after some hours’ exposure to 1500°, exceeds 3 per cent.
or more, and is permanent. After this the tube expands nor-
mally. It rarely warps, and may therefore be fixed by fire-
clay arms, H (figs. 1, 2, and 7), suitably clamped on the
outside of the furnace. Near the bottom a perforated ring,
CC (figs. 1 and 5), embraces both the tube FF and a pro-
jection, G, in the furnace.

8. Thermocouples.—In addition to figs. 1 and 2, figs. 6 and

8 give a full account of the adjustment. The tube FF is
laterally perforated with three pairs of fine holes, t, corre-
sponding to the two canals of the insulator*, TT. The wires
of the thermocouple are then threaded through ¢ and the
insulator canals, in such a way that the respective junctions
lie in small cavities at ¢, immediately in contact with the out-
side of the platinum tube. Holes are left in FF and the
furnace for this operation.
_ The cold junctions of the thermocouples terminate in three
pairs of mercury-troughs, insulated by hard rubber, and sub-
merged in a bath of petroleum. With these troughs the
terminals of the zero method are successively connected, and
the temperatures of the top, the middle, and the bottom of the
fusion-tube measured by § 4.

* The method of making these is given in Bull. No. 54, U.S. Geolog.
Survey, p. 95.

180 Mr. Carl Barus on the Fusion

9. Seght-tubes.—Grunow’s excellent cathetometer is placed
on a pier, so that the prism of the instrument is only about
50 centim. oft from the fusion-tube. A tall, hollow screen,
30 centim. broad, 70 centim. long, and 1 centim. thick, fed
with cold water, and movable on a slide, is interposed
between furnace and cathetometer. Slots, cut through the
screen and closed by plate glass, correspond to the two posi-
tions of the telescope ; and the lines of sight pass through
S, 8, near the top and the bottom of the furnace (see figs. 1
and 2). Thus the ends of the fusion-tube, one of which pro-
jects above the clay tube F F, and the other is seen through
the perforation O in © C (figs. 1 and 5), appear as sharp
lines in the telescope, against the red-hot background of
clay.

It is necessary, however, to prevent the escape of flame and
gas at S, and hence these holes are provided with porcelain
tubes A (only one shown in the figure) about 15 centim. long,
the outer end of which is ground off square and closed with
a piece of plate glass b, by aid of a clamping device aa.

10. Vertical Micrometer. — Figures 3 and 4 give a full
account of this instrument (also made by W. Grunow), both
of which are sectional elevations at right angles to each other.
The millimetre-screw plays easily through the massive block
of brass, P P, and the fixed lock-nut gg. P P is bolted down
to the rigid bridge of brass, NN, by means of screws, RR,
and the counterplate U U. The ends of NN are provided
with sleeves, p p, and a clamp-screw, M, whereby the whole
micrometer may be moved up or down or fixed in any posi-
tion along the uprights, QQ. To secure insulation of the
screw K £, R, Rare surrounded by jackets n, n of hard rubber,
and plates, 7,7, q of this material are suitably interposed be-
tween PP, NN, U U, and other parts.

Sufficiently wide slots are cut in the bridge, N N (see
figures), whereby the plate may be shifted in any direction,
and then clamped in position.

In view of the heat which rises from the furnace, an N-
shaped screen, X X, through which water rapidly circulates
(entering and leaving at diagonally opposite points, V and Y,
at the top), nearly envelopes the micrometer. The micro-
meter-screw passes through a narrow tube in the bottom of
XX; hence the screen must also be adjustable, and a way is
shown in the figure. Thus the micrometer and its water-
screen slide as a single piece, along the upright QQ. Q and
Y are joined by a sufficient length of rubber hose, a connexion
merely indicated in the figure.

Constants of Igneous Rock. 181

Finally K & is prolonged by a straight cylindrical tube of
platinum dd, which may be fixed to the steel rod & by the
clamp ¢ in any position along the vertical. The tube fits the
rod & singly, and a special steel rod is provided by which the
tube may be straightened, should it become warped.

The lower end of d is clearly visible in the telescope of the
cathetometer, through the sight-tube A. On being screwed
down, d enters the fusion-tube axially, supposing both tubes
(d and Z Z) to have been properly fixed in position. In how
far such adjustment has been made, can be seen by tempo-
rarily removing one of the efflux tubes, H (fig. 4), when the
parts concerned are visible to the eye.

11. Telephonic Registration—Since it is necessary to find
the depth of the meniscus of the molten rock ZZ below the
plane of the top of the fusion-tube, the moment of contact of
ZZ and d is registered electrically. Above, say, 500° C., rock
is a good conductor. Hence, if a current be passed into the
screw K k, through the clamp-screw / (fig. 3), it will issue at
the bottom at the clamp-screw c (fig. 1), provided ¢ be electric-
ally connected (platinum wires) with the bottom of the fusion-
tube, Z Z

A telephone actuated by Kohlrausch’s small inductor is
more conyenient for the present purpose than a galvanometer.
Contact is then indicated by a loud roar, and the observer’s
attention is not further distracted. Ifthe glass Z Z be sticky,
the drawing out of a thread corresponds to a more or less
gradual cessation of the noise, so that the character of the
fusion can be pretty well indicated in this way. Care shouid
be taken to insure a small sparking-distance.

If the expansion of the rock be known, and the tube dd
be sunk deeply into the mass, it is clear that the present
method admits of a measurement of the relation of the electric
resistance of the glass and temperature. JI mention this,
believing that not only will a suitable method of temperature
measurement be thus available, but that the volume diagrams,
constructed below, may also be derived solely from measure-
ments of electrolytic resistance *.

Mertuop oF MEASUREMENT.

12. Consecutive Adjustments.—Thus far I have only studied
rock-contraction. For this purpose, the graduated faucet,

* Cf. Am, Journ. Sci. xlii. pp. 134-35 (1891), where I have already
speculated on the character of electrolytic resistance referred to tem-
perature.

182 Mr. Carl Barus on the Fuszon

§§ 5, 6, is turned on in full, and the furnace fired as far as
1400° or 1500°, when the measurements may be commenced.
The length of the fusion-tube is first accurately measured by
cathetometer observations at the bottom and the top. The
telescope is then left adjusted for the top, and the vertical
micrometer (centrally fixed) screwed down until the image of
its lowest point is in contact with the cross hairs. After this
the micrometer is further screwed down, until the telephone
indicates contact between the platinum micrometer-tube and
the meniscus of molten rock. The difference of readings
gives the depth of the latter below the top plane of the fusion-
tube. I usually repeated these measurements three times.

Hereupon. the temperature measurements were made by
connecting the terminals of the zero method with the lower,
the middle, and the upper thermocouple.

Finally, the cathetometer and micrometer measurements
were again repeated in full. Uniform heating presupposed,
it was permissible to regard the two sets of length measure-
ments as coincident with the intermediate temperature mea-
surement.

This done, 1 frequently waited 15 minutes or more, to
make another complete measurement, under better conditions
of constant temperature.

The graduated stopcock was then partially closed by a
proper fractional amount, and after waiting a sufficiently long
time, the same series of measuring operations was gone over
again. Thus I continued until the glass became sticky and
solidification imminent, when longer waiting and more finely
graded changes of temperature were essential. Fortunately
the observer can infer the state of fusion very well, by noting
the time necessary for the glass threads drawn out by the
micrometer to break, § 11. Finally, the enamel on the end
of the micrometer-tube becomes solid and ceases to change
its form, simultaneously with which the marked contraction
of the molten mass in the fusion-tube begins.

Having waited long enough for the lowest position of the
meniscus, temperature may be varied in larger steps again.

When the furnace is dark, measurement is no longer pos-
sible. I then allowed the whole arrangement to cool over
night, and next morning determined both the depth of the
solid meniscus and the length of the cold tube. The former
was computed from bulk measurements (with water) as well
as measured micrometrically. These are the normal or
fiducial data to which all the other volumes were referred.

Constants of Igneous Rock. 183

13. Computation.—Let the linear expansion of the platinum
fusion-tube be given by /=h(1+/(é)), where / and J) are the
lengths at ¢ degrees and at zero respectively. Let » and Ay
be the depths of the meniscus below the plane of the top of
the fusion-tube, and v and wv the volumes of the enclosed
molten magma at ¢ and zero respectively. Then, if (1+/(¢) )’
is nearly enough 1+ 3/(é); if the expansion constants of the
fusion-tube and of the micrometer-tube be the same, and if
in consideration of the small motion of the latter and the
high temperature in the furnace, the air temperature outside
of it be nearly enough zero, since

0/0) = (g—A)(1 +/(t))?/(lo— Ao);
(ve— v9) /Vp=3F (4) + Ap—A)(1L + 8/(4) (lo — Av)» «1D

Here 3 /(¢) is directly given at each observation, or may be
computed by some smoothing process from the data as a
whole.

The equation, therefore, gives the actual expansion of the
rock, in terms of unit of volume of solid rock at zero Centi-
gerade. If this be multiplied by the initial specific volume,
the absolute expansion is obtained. An inspection of (1)
shows that in the factor Ay»—A, the micrometer value of the
length 2X is to be inserted in both cases, supposing the contour
of the meniscus to remain similar to itself; whereas in /)—)A,
the value of \y determined from bulk measurements of the space
at the top of the cold tube is suitable, since the tube is
flat-bottomed.

I may add in passing that if 6H be the rise of a flat-bottomed
cylindrical float of platinum, submerged to a depth A in a
column of magma of height A, then nearly

eee GROEN Nn vusule Cory (2)

Since, therefore, the float shortens the efficient length of the
fusion-tube and there is difficulty in determining A in this
case, the above micrometric method is preferable quite aside
from flotation errors due to viscosity and capillarity, to the
easy welding of white hot platinum surfaces, to the tendency
of gas bubbles to accumulate on the surface of the float, to
the cessation of true flotation during the change from liquid
to solid, &e.

14, Lrrors—The change of temperature from top to
bottom of the fusion-tube is measured. The change of tem-
perature from circumference to axis of the fusion-tube is nel

184 Mr. Carl Barus on the Fusion

in proportion as the furnace cools slowly. The latter con-
dition is met at least so long as glass is liquid, and data for
the former are fully given below. ‘To avoid strains of dilata-
tion it would be desirable to make the glass solidify from the
bottom upward. This, however, my furnace as yet fails to do.
Indeed, I have frequently noted lateral holes shaped like an
inverted funnel and terminating in the otherwise smooth
surface of the meniscus. This may indicate the occurrence
of gas bubbles under the free surface or be a strain effect,
§ 3. The tendency of these nearly unavoidable difficulties is
to make the solidification contraction too small; and I have
therefore not been disturbed by them.

Only at very high temperatures (above 1500°) did I obtain
apparent evidence of the viscosity of platinum relatively to
the pressure of the column of 25 centim. of molten rock,
whereas the combined system of platinum and clay tube with-
stood this pressure. There is also a slight deepening of the
meniscus from day to day, and a similar decrease of the
length of the platinum fusion-tube ; but, thus far, I have
encountered no serious error due to the high temperature
viscosity of the vessel, § 18.

The assumption that the meniscus remains similar to itself
in form at all temperatures cannot be quite true. At white
heats, however, the glass wets platinum so thoroughly that
convex forms of meniscus need never be apprehended. It is
futile, however, to endeavour to make allowance for meniscus ;
but data for the difference between the (cold) bulk and micro-
metric measurements are given below. Although too much
reliance must not be placed on the behaviour of the solid
state, yet the values are redeemed from the character of mere
estimates by the close coincidence of the expansion of pla-
tinum and its solid glass core. Strains imposed on both the
metal and the glass do not probably exceed the limits of
elasticity of either, §§ 17,18. When cooling is conducted
slowly enough, the experiments show that the platinum tube
is not dragged along seriously by the solidifying magma; and
the data thus retain a degree of trustworthiness greater than
was anticipated, even in the solid state. At the same time
dilatational strain is reduced to a minimum, and constancy of
temperature throughout efficient parts of the furnace is
promoted.

One error much in my way thus far has been the allowance
to be made for the expansion of the platinum probe dd (fig. 3).
It is not merely the amount by which the probe is lowered

that is subject to expansion, but a considerable length of the

Constants of Igneous LItock. 185

metallic screw K kdd passes from a lower to an indeterminable
higher temperature. I hope, however, in the future to obtain
an estimate for this discrepancy, by measuring a given amount
of thrust through the sight-tube with the cathetometer, and
comparing this value with the corresponding value to be read
off on the vertical micrometer. Hollow screws and water
circulation would be exceedingly difficult to attach here.

RESULTS.

15. Arrangement of the Tables.—In the following tables /
and vp denote the length and radius of the (cold) fusion-tube,
and A, the bulk value (water measurement) of the mean
depth of the meniscus, these measurements being made on the
day after the fusion experiments. ‘The temperatures at the
bottom, the middle, and the top of the fusion-tube are given
under 0, @2, 03, respectively. For each value of mean tempera-
ture @, two data for the apparent expansion of the rock, for
the volume-expansion of the fusion-tube, and for the actual
volume-expansion, (v%—v)/vp= Ov/v,, of the rock are given,
and they were obtained before and after the intermediate
temperature measurement, respectively. Reference is thus
made to unit of volume of solid rock at zero Centigrade,
throughout. The data enclosed in parentheses show that for
them, the value applied for the expansion of the fusion-tube is
obtained as a mean result of all the measurements made,
otherwise the value directly observed was directly applied.
The chief constants are summarized at the end of each
table.

16. Contraction of Diabase. Series 1. and I1.-——The results
of these series, being of inferior accuracy and serving chiefly
to substantiate the remarks of § 14, may be omitted here.
They showed a liquid volume-expansion of 50/10° per degree,
a solid expansion of 20/10° per degree, and a solidification
contraction of about 3 per cent. only, owing to the occurrence
of dilatational strain.

17. Contraction of Diabase. Series I1., Tables.—This work
was done on October 20, 1891, and the data are given in
Table II. Precautions for slow cooling were fully taken, and
the solidification point is therefore sharply apparent. ‘The
results will be discussed in connexion with the next series.

Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893. O

186

Mr. Carl Barus on the Fusion

TABLE II.—Contraction of Diabase.

{y= 25°466 centim.,

03:
0,. | Mean
G2. 0.
a: oC:
1360 | 1886
1596
1403
1286 | 1300
1504
1311
1163 | 1166
1167
1168
1097 | 1093
1093
1089
1102 | 1095
1095
1088
929 | 896
897
863
461 | 468
453
510

20

| Rock, mean actual expansion, solid, 0°-1000°

Apparent | Volume-

volume- | expansion

expansion
of Rock.

Sele
452
4D4

437
438

406
409

376
300

14
13

bo

33

39

of the
tube.

8l

Ov/ Up »

x 104.

810
812
(808)
(810)
77
ee
(771)
(772)
703

706
(706)
(709)
646
603
(657)
(614)

288
286
(296)
(295)
211
(213)

0

Mean.

6v/Up.

0811
(-0809)

‘0079

0000

99

39

Series III.

Time.

Minutes.
| Liquid.

0

23

86

hit

185

Ap=1'424 centim., 7>=°75 centim.

Remarks.

oT eT. Cd

Liquid.

Sticky.

Very sticky.

To be drawn

out in threads.
Eventually

solidifying.

Solid.

Solid.

Solid.

Next day.| Cold.

liquid, 1100°-1500°
a contraction on solidification (1094°)
Rock, mean apparent expansion, solid, 0° 1000° . :
{ a liquid, 1100°-1500° -0000205

Tube, mean v olume-expansion below 1000°
above 1100°

99

99 29

29

-0000250
“0000470
°0390

"(000007

0000240
0000265

18. Contraction of Diabase. Series TV. Tables and Chart.—

The data of the last series of experiments (made on October

21, 1891)

are given in Table ILI.

results correspond to each step of temperature.

‘wo complete sets of

Constants of Igneous Rock.

187

TasBLe II1.—Contraction of Diabase. Series IV.
() =25°447 centim., Ay’ =1:220 centim., ry=75 centim.

se Ap parent Volume-
; ean.| volume- | expansion . Mean. ,
o> 8. | expansion Of the 8u/% ovjv ue.
3° of Rock. tube.
2G: oC: Sail: x 104. x 104. Minutes.
1374 | 1388 403 397 760 -0760 5
1394 404 (356) 761 (0760)
1395 | (759)
(760) |
1415 | 1421 407 302 768 ‘0770 20
1431 409 (304) Tel (0771)
1417 (771)
(773)
#318 | 1319 | . 394 341 734 (0731) 50
1324 | i giicleyy (339) 727 (0730)
1315 (733)
| (726)
| 1304 | 1305 383 350 733 0736 65
1308 390 (335) 740 (0721)
1304 (718)
(725)
1204 | 1190 307 316 673 "0672 90
1189 399 (305) 671 (0661)
1176 (662
; (660)
yg | 163 355 299 655 0652 105
1158 349 (299) 649 (0652)
1153 (655)
(649)
esse LV 339 286 625 “0628 128
1109 344 (286) 630 (0628)
1090 (625)
(630)
1117 | 1092 200 275 475 "0475 151
1088 155 (280) 430 (0480)
1072 91 366
1109 | 1092 333) 282 315 0287 175
1081 5 (280) 287 (0285)
1086
946 914 13 213 226 0223 198
903 6 220
893
900 855 3 199 202 0202 210
827 3 202
837
20 0) 0 0) ‘0000 |Next day.

a 5 a liquid, 1100°—1500°
- conbenchion on solidification, at 1092°

Rock, mean apparent expansion, 0%1000°. . .
6 ie . 1100°-1500°

j Tube, mean volume-expansion below 1000° . .
above LL0Q°...

O2

xy mean actual expansion, solid, 0°—1000° .

( 9 39 39 °?

Remarks.

Liquid.

‘Liquid.

Liquid.

Liquid.

Sticky.

Very sticky.
To be drawn
out in threads. |

Top en-

crusted,

Solidifying. |
Solidifying,
Solid.

Solid.

Cold.

“QOV0250
‘0000468
°0340
“QQOOQ005
“O0V0218
“Q000235
"O000260

188 Mr. Carl Barus on the Fusion

‘These data are given in the chart (fig. 10), temperatures in
degrees C., as abscissee, volume- changes as ordinates. A
ae of the same character may also be constructed from
Table IL., but this is superfluous. In figure 10 the actual
expansion of the rock is shown by the heavy line debef, and
the numbers attached to the points of observation indicate
the times at which they were made. ‘lhe apparent expansion
of the rock is shown by the light line /kgh, where the ordi-
nates of the solid contour are nearly zero. Finally the ex-
pansion of the fusion-tube is represented by the dotted line
deat. The amount of break at a, which is even smaller in
Series ILI, indicates the amount of drag or a shortening of
the length of the platinum tube by the solidifying rock
within, and furnishes an estimate for the trustworthiness of
the solid results. It is interesting to note that in both
Series Il].and IV.the first length measurements of the tube
are smaller than the second at the same temperature, showing
ay the tube has to some extent recuperated from the strain,

r that the amount of end thrust has diminished. It is
Se auladle possible to note the sag as expressed by the cold
lengths (25°49 centim. in Series II., 25:47 centim. in Series
get ., and 25°45 centim. in Series IV.) of the plaiinum fusion-
tube. Finally, the depth of the liquid meniscus at the outset
of Series III: and IV. ., and at about the same temperature,
was X=*5() centim. and A="62 centim., showing enlargement
of the bulk of the tube. These changes, which are in part
allowed for, show that viscosity introduces no serious dis-
crepancy. Regarding the differences of A, and A, the
remarks made in § 14 apply.

An inspection of the curve dbef as a whole indicates
the occurrence of sharply marked solidification at 1093°.
This is sufficient evidence to prove that rock-fusion (diabase)
is thoroughly normal in type. A method is thus given in
which the solidifying-point is determined free from non-
intrinsic tests.

Finally, the contraction on solidification, 3°9 per cent. in
Series ILI., and 3:4 per cent. in Series IV., is established,
for diabase at least, beyond question. It is to be noted, more-
over, that the smaller value (LV.) corresponds to a larger
drag during solidification on the platinum tube (cf. Tables I.
and IIl.). Hence the value 39 per cent. is the more
probable. In general, temperatures (@,, 62, 63) are nearly
alike so long as the glass is liquid. This ceases to be the case
after solidification ; and since the top of the fusion-tube is
apt to be colder than the bottom, some of the solid contraction
expresses itself in dilatational strain, § 14.

Constants of Igneous Rock. : 189

19. Flotation.—Naturally I made a few tests on the flota-
tion of solid rock on the molten magma. Cf. § 3. To my
surprise such flotation usually occurs, notwithstanding the
fact that the original cold rock may be 8 per cent. + 10 per
cent. more dense than the molten magma. The cause, how-
ever, is crudely mechanical, since the rock, in virtue of its
weight and temperature, hollows out a cavity and chills its
surface simultaneously, forming a little boat in which it He
on the very viscous liquid below. ‘This is indicated in fig. 9
where a is the body of rock, AA the molten magma, and bb
the solidified skin. I also attempted to make Niess and
Winkelmann’s “ Fundamentalversuch” (Niess, J. c. p. 16),
by submerging the rock; but here, both on account of the
intense white ‘elare of the furnace and the tendency to chill
at the surface, I did not reach a definite point of view.

INFERENCES.

20. Hysteresis-—In the above experiments I have only
studied the solidifying magma. It does not appear, there-
fore, whether solidification and fusion take place at identical
temperatures, or whether they will comprehend a volume-lag.

In other work, in which the rock of the fusion-tube was
alternately fused ‘and solidified, the loci are oy clic in marked
degree, covering considerably more than 50°. It so difficult,
however, to discriminate between true hysteresis and the
accompanying discrepancy due to insufficiently rapid heat
conduction as compared with the insufficiently slow change
of temperature, that experiments made with a tube which is
not at quite the same temperature throughout its length are
not unassailable. Having failed to perfect the experiments,
I omit the data altogether.

21. Melting-point “and Pressure.—Since the fusion of rocks
like diabase is thoroughly normal, it follows that melting-
point must increase with pressure. It is well to examine
tentatively into the nature of this relation, and for this pur-
pose I have constructed certain unpublished results of mie
for thymol, in the same scale as used for the rock, in fig.

The curve mn'olp! shows the contraction of thymol at Fe
melting-point (somewhat below 50°), where the substance
is quid along o’p’ and solid along m'n'. The curve mnop
similarly applies at O°C. It is seen, therefore, that here
solidification contraction and thermal expansion (solid or
liquid) decrease together. This is also true on passing from
thymol to the rock. Could liquid thymol be cooled down as
far as —25°, it would then show the same solidification con-

traetion as fie silicate.

190 Dr. J. R. Rydberg on a certain Asymmetry

Analogously the latter must show decidedly smaller com-
pressibility than the organic body, and hence it follows that
whereas the lower critical pressure (solid-liquid) of naphtha-
lene, for instance, lies in the region of some 10,000 atmospheres
in my experiments, the corresponding (critical) pressure of
the rock magma will be indefinitely higher.

From this, however, it is by no means to be inferred that
the relation of melting-point to pressure (d@/dp) will be
different in the silicate and in the carbon compound. In the
latter case data for normal fusion are available for wax,
paraffin, spermaceti, and naphthalene. These lie within a
margin of ‘020 to ‘036. Taken into consideration with the
difficulty of obtaining these data, the preliminary character
of the experiments, the lack of crystalline definiteness in many
of the compounds, and the fact that even for the same sub-
stance* the coefficient may vary as much as ‘027 to -035, the
said margin may reasonably be regarded as narrow. It
appears to me probable, therefore, since fusion in the organic
bodies and the silicate is alike in type, that the same factor
d@/dp will correspond to both cases.

Direct evidence in favour of this view will be adduced in
my next paper.

XXIII. On a certain Asymmetry in Prof. Rowland’s Concave
Gratings. By Dr. J. R. RypBere, Docent of Physics at
the University of Lund, Sweden f.

I. i order more especially to obtain a series of observations

fitted for a continuation of the studies on the spectra
of the elements, of which the commencement has been pub-
lished in my “ Recherches sur la constitution des spectres
linéaires des éléments chimiques ”’ (K. Svenska Vetensk. Akad.
Handl. Bd. xxiii. No. 11), a spectroscope with one of Prof.
Rowland’s concave gratings (10,000 lines to the inch) was
procured for the Physical Institution of the University of
Lund. It was mounted in a most excellent manner by the
Mechanician of the Physiological Institution, Hilding Sand-
strém, according to the instructions of Prof. Rowland (see
Ames, Johns Hopkins University Circulars, viii. No. 73,
May 1889; Phil. Mag. [5] xxvii. p. 369), but with full
freedom in the details of construction. The adjustments
also were executed according to the same instructions, but

* See my work for Naphthalene in American Journal, xlii. p. 144,
el seg., 1891.
+ Communicated by the Author.

rn Prof. Rowland’s Concave Gratings. 191

with greater precision in the special determinations with the
intention to obtain by the exactness of the adjustment the
same scale through the whole spectrum.

However, when all adjustments were completed, no distinct
image could be obtained in any part of the spectrum. In
the visible spectrum of the first order the image was not very
much out of focus, but the deviation increased gradually, so
that it became necessary to displace the eyepiece several
centimetres to obtain well-defined images of the spectra of
higher orders. All details being executed with the same
accuracy, there was nothing that could indicate the cause of
the discrepancy, so that nothing remained but to make all
the adjustments over again, determining at the same time
the extreme limits of the errors. [or this purpose I have
made use of new methods of adjustment, and I have ascer-
tained by these researches :—

1. That the courses which the apex of the grating and the
cross hairs of the eyepiece follow in their movement on the
rails do not deviate in any point from straight lines by more
than 0°2 millim.

2. That the angle formed by the average directions of
the rails did not differ from a right angle by more than
15” (corresponding to an arc of 0°5 millim. at one of the ends
of one of the rails), the difference probably not amounting to
more than a third of this value.

3. That the middle of the slit could not be more than 0:2
millim. from the crossing-point of the lines that are described
by the apex of the grating and the cross hairs of the eye-

1ece.

A, That the apex of the grating and the cross hairs of the
eyepiece were not more than Q'l millim. distant from the
axes of the carriages.

5. That the distance peraean the centre of curvature of
the grating and the axis of the carriage on which the eye-
piece was placed, did not amount to 0°5 millim. during the
whole movement.

6. That the lines of the grating and the direction of the
slit were parallel and at right angles with the plane of the

. That the grating was entirely free from all constraint
a of spherical form, the j images in the centre of curvature
being of excellent definition.

8. That the optical state of the slit was perfectly normal.

With these results it was only in the grating itself that
the cause of the displacement of the spectra could be looked
for, either in some imperfection of the theory or in some

192 Dr.. J. R. Rydberg on a certain Asymmetry

fault in the execution of the work, at least with regard to
the special grating in question. Hitherto, I had not deemed
it possible to make any of these assumptions, as it seemed that
Prof. Rowland himself and other spectroscopists who have
used the concave gratings ought to have recognized such an
anomaly, if it existed.

During all the adjustments the grating was left in the
same position in its holder, so that I had made use only of
the spectra on one side of the grating. Now it was removed
from its holder and, after being reversed, it was adjusted in
the same manner as before, with the intention of learning
whether the focal curve that passes through the centre of
curvature is symmetrical with respect to the principal axis of
the concave mirror. ‘Then it was found that the distance
between the grating and the eyepiece ought to be increased
in order to get distinct images, while before it was necessary
to diminish it. From this it was evident that the inaccuracy
in the position of the images was due to the grating.

II. First of all the question was to determine the true
form of the focal curve that passes through the centre of
curvature of the grating. According to Prof. Rowland’s
theory this ought to be a circle, which should have as a
diameter the straight line that unites the centre of curvature
with the apex of the grating. Ifthe form of the curve differed
perceptibly from a circle, it would not be possible with these
gratings to obtain spectra of a uniform scale.

Fig. 1.

ay

SS

0, 0)

_ The form of the focal curve can be determined with the
greatest facility, if the apparatus is altered in such a manner

in Prof. Rowland’s Concave Gratings. 193

that the slit is made movable along the rail that carries the
grating.

Let G,G, (fig. 1) be the grating, C its apex, O its centre
of curvature, CLOM the theoretical focal circle, ClL,O,; OM,
the true focal curve that passes through O,L the slit in
its original place at the point of the right angle which
is formed by the rails LO and LO. Then, on displacing
the slit along LC or its elongation to a certain point Ly,
it will always be possible to obtain distinct images of the
spectra, supposing in all cases that such can be given by the
erating. This point L, belongs to the curve in question,
whose polar coordinates will be determined by measuring the
radius of curvature CO (p), the displacement LL, (d), and
the angle LCO (w). For then, supposing d to be positive,
when the slit is moved away from the mirror, the radius
vector L,C=r=pcos w+d and the vectorial angle =p.

Denoting the wave-length by A, the number of order of
the spectrum by n, the distance between two adjacent lines of
the grating by w, we should have, if the theory were exact,

Si = Ee 2 is nv=— . LO,
p ©) p

To decide whether the same formula can be applied in the
present case, it will be sufficient to displace the slit along the
rail LC and to observe if any change is produced in the
spectrum, viz., if the same value of mw always corresponds to
the same value of 2» independently of the value of r. In
reality small irregular variations were found, which did not
seem to exceed one of Angstrém’s units, and which were
doubtless due to imperfections in the rails and the adjust-
ment, According to the theory of concave gratings a dif-
ference of one Angstrom’ s unit in the spectrum corresponds to
a lateral displacement of the slit varying in the spectra of
different orders between 0°25 and 1 millim. Consequently
the formula is exact within the limits of error of our
experiments. It follows that the angle ¢ of the segment CL,O
is determined by the equation

Boo Nae
LON p.nr

In this formula d and nd being the only variables, we see

Cone

that it is sufficient that their quotient © be constant, in

order that the angle e may be so too.
III. The measurements were executed in such a way that
the spectroscope was directed on some known line of the

194 Dr. J. R. Rydberg on a certain Asymmetry

spectrum and the movable carriage that bears the slit dis-
placed along the rail LC, until a distinct image was obtained
in OQ. The position of an index, attached to the carriage,
was read on a millimetre-seale fixed to the rail LC. Hach
of the numbers given in the following table under a, and a,
is the mean of 10 of these readings, the carriage being alter-
nately brought near to and removed from the grating. The
column a, corresponds to the spectra on one side of the
grating, the cclumn a, to those on the other; a greater
value denotes a greater distance from the grating. It was
found that the slit could be displaced through the space of
about one millimetre without it being possible to distinguish
any variation in the definition of the image. The probable
errors of the means amount in general to 0°2 millim., they
never exceed 0°4 milliim. Using as a source of light some-
times the sun, sometimes the yoltaic arc, I directed the
spectroscope in the spectra of the first four orders to the
weak lines between D,; and D, (A=5893) and to the double
lines 6; and 6, of the solar spectrum or the strong doublets
of the neighbouring band of carbon (A about 5165).

| : Calcu- |
iat Wave: | Observed. | lated. |
ow lengih- fae al ies. 3(44+4,) od
—. | 4. | ae
I. ,.../1%5165| 1838] 1538 | - 1438 | —100| +100] 94
I. D...|1x5893| 183-4] 1556] 1445 | —104!/ 4118] 108 |
IL. 8,...}2 X5165, 1232 | 1617 | 1425 | —206/ 4179] 139 |
IL. D...| 2 x5893| 121-8 | 1652 |- 1435 | —220| 4214) Sip |
IIL. 8,...|8x5165) 1158 | 1716 | 1437 | —280) +278] 283 |
IIL. D...|3x5893| 1120 | 1757] 1438 | —318 | +319] 323 |
IV. 2,....4X5165| 1060 | 1816] 1438 | —378| +378] 377 |
IV. D...|4x5893| 1014 | 1876} 1445 | —424|) +438) 430 |

Mean 143°8

The first column contains the number of order of the spec-
trum and the line to which the spectroscope was directed ;
the second the approximate wave-length. In the fifth
column are the means of the values of a; and aj, which cor-
respond to the same line in the spectra on the two opposite
sides of the grating. These means approach, as we see, to
a constant value 143°8, which corresponds evidently to the
normal position of the slit at the vertex of the right angle
formed by the rails. On determining by direct measure-
ments this position, I have found 144°8+0°1. But the
difference of one millimetre between the two numbers is

zn Prof. Rowland’s Coneave Gratings. 195

perfectly explained through the uncertainty in the two
adjustments of the centre of curvature of the mirror on the
axis of the carriage of the eyepiece, first in the direction of
the girder that unites the two carriages, and secondly, in
the lateral direction. Of this I have convinced myself by
another series of determinations. by displacing intentionally
the centre of curvature. A fault of 0°5 millim. in the deter-
mination of the radius of curvature is sufficient to explain the
before-mentioned difference.

Thus the point 143°8 is to be considered as the vertex of the
right angle of the rails, through which passes in the present

oO
ease the theoretic focal circle of the grating, or rather a

y)

eurve which differs from it very slightly. Using this
number (a) I have calculated the differences d,=a,;—dy and
dy=d,—d,), which are found in the table under the heading
“observed.” A glance at these numbers shows that they
are at least very nearly proportional to the corresponding
values of nd, which implies that the angle ¢ of the segment of
the true focal curve is constant. To examine this more
closely, we will insert in the preceding equation of ¢

p cot ¢

= Ww
i) 5)

and we will calculate by the method of least squares the exact
value of w trom the 16 equations of the form

i,

which we obtain from the preceding table on using all the
values d, and dg.
In this way we find the value

ee wo 18261 +80.

The numerically equal values of d, and d,, which are
obtained on making use of this value of x, are given under
d in the last column of the table. The differences between
these numbers and the observed values being confined within
the limits of errors of observation, it must be considered as
proved that the angle € in the segment of the focal curve ts a
constant.

A segment of which the angle is a constant belonging
necessarily to a circle, we can express the result of our re-
searches as follows :—

The focal curve which passes through the centre of curvature
of the mirror ts a circle, which, however, has not the radius of
curvature in the apex of the grating as a deameter.

196 Dr. J. R. Rydberg on a certain Asymmetry

Always supposing, as in the preceding, that this curve also
passes through C, we see on fig. 1 where OO, is a diameter
of the true focal circle, that the angle between CO and CO,

is =b=5-«,

even hee tan 6= cot c= 18261".

The determination of the radius of curvature has given
p=6484+41 millim. According to the statement engraved
on the grating, a=0:0001 inch =0:00254 millim. From
this we obtain 6=24’ 47” and the are OO,=p tan 6=18261 @
=46°4 millim. The difference between the diameters CO
and CO, amounts to 0°17 millim.

IV. Though there could be no doubt as to the obliquity of
the grating, it was possible that we had to do with some
accidental anomaly peculiar to our special grating. or that
reason it was of great interest for me to find an opportunity to
examine another grating of the same kind, and this has been
made possible through the kindness of Dr. A. H. Andersson
at Kristianstad, who has been good enough to place at my
disposal a concave Rowland grating of exactly the same kind
as the preceding.

The measurements, which have been executed in the same
order as before, follow here :—

> >| : Calcu-
Spectral | WWave- | | Observed. lated.
Seon een: ay. Ce 3 (a+ 4,) 3 ‘|—
| 107m2r. | aoa 4. d
I. 6,...) 1 X5165| 180°3 | 155°6 143-0 —123 | +13°0 | 116
I. D...| 15893 | 129°2 | 158:5 143°9 —134 |} +159 13:2
TO, ses | 25¢ 5165 | 118735). 16456 141°5 —243 | +220 23°2
e512 <o8ds | Slo a a lesa 14271 —27°1 | +261 2674
TAD, 2.. (OocoloD |" L086) 174 143-0 —340 | +548 348
III. D.:.|3xX5893| 1042 | 181-1 142°7 —384 | +38°5 39°7
IV. b,...,45165| 95°5 | 189°6 142°5 -47-1 | +47-0 46°4
TV. D...)45893|. 89-7 | 1953 142°5 —529 | +52°7 52°9

Mean 142°6 |

The probable errors of the values of a are a little greater
than in the preceding case, and amount in maximum to 0°5
millim. Moreover the adjustments of the grating are not of
quite the same exactitude, owing to the limited time I had at
my disposal for making these determinations. Hence, there
is nothing astonishing in the fact that the mean, 142°6, of
the values of a differs a little more from the normal value,

in Prof. Rowland’s Concave Gratings. 19%
144°8, = is _ case with he other grating. ke eu

of the fe lanes to be determined. A
On calculating as before the queues me obtain

- as = 22440 +120.

The radius of curvature of this grating was found to be 40°3
millim. greater than that of the other, viz., 6474 millim., the
uncertainty amounting to about 2 millim. With this value
of p and the nominal value of o, we find 6=30/ 16” and
OO,=57:0 millim.

To judge from the inscriptions on the gratings the obli-
quity ought to have the same direction in both cases.

V. The focal curve that passes through the centre of cur-
vature of the grating being a circle, as shown above, it will
always be possible to adjust the spectroscope in such a
manner as to obtain in all positions distinct images of the
spectra without altering the distance between the grating and
the eyepiece. It follows from the preceding that this 1s
effected by causing the girder to act the part of the diameter
O,C of the true focal circle instead of that of a radius of
curvature of the grating. Hence, in the first grating the
girder ought to be lengthened by 0°17 millim., then turned
round the ] point C through an angle 6= 24'47". ‘The easiest
way of doing this is to displace the cross hairs of the eyepiece
in O with the micrometer through a distance equal to the
corresponding arc 46°4 millim. (to left or to right according
to the side of the grating which we wish to make use of),
and afterwards turning the grating until the cross hairs and
their image coincide again. Then in all positions of the
girder the slit ought to remain on the true focal circle. The
exactitude of the theory and the measurements is confirmed
by the fact, that after the execution of these adjustments the
image became perfectly defined through the whole spectrum.

It would also be possible to obtain distinct images in all
positions by another method, viz., by altering the angle of the

rails by a quantity 6. In that case the centre of curvature

ought not to be displaced, but it is necessary to turn the
micrometer and the photographic box through an angle 64,
so that they may be always tangents of the focal circle.

However, the supposition which we have made, that the
true focal circle passes through the apex C of the erating,
does not possess any very high degree of probability, ‘because
in that case the curve would intersect the surface of the

198 Dr. J. R. Rydberg on a certuin Asymmetry

grating. It seems more likely that it touches it, but at
another point, which, as can be seen by construction and
calculation, would be situated at a distance of 46°4 millim.
from the apex C. In reality, the conclusions that could be
drawn from the measurements would remain almost the same,
if we had replaced in fig 1 the circle CL,0,OM, by a circle
passing through O but not through C or O, and touching
the grating at C,. This circle would have a radius equal to p,
that is to say 0°17 millim. less than that of the former. As

ae
to the variation AS of the angle 6, we find sin Aé= Ss 6
2 COS wb

a quantity varying with w, but which falls within the limits of
errors of observation in all parts of the spectra, that we can
use. The are CC, differs from the are OO, (46:4 millim.)
only by some tenth of a millimetre. Under this new sup-
position an exact adjustment according to Prof. Rowland’s
theory is obtained by displacing the grating 46°4 miilim.
along its own surface, until the point of contact of the focal
circle fails in with the axis of the carriage, where the apex of
the grating was situated before. The considerable ob‘iquity
that the position of the grating would show in that ease is
the only difficulty with this arrangement. Hence I have
preferred the first method of adjustment, after having con-
vinced myself that the difference is of no importance from a
practical point of view.

VI. On the other hand, the last manner of considering the
matter seems to possess a considerable advantage, because it
will allow us to account in a simple way for the relations
between the true focal circle and the grating. In reality,
the accordance with Prof. Rowland’s theory is perfect and
the obliquity is only due to the point of symmetry of the
grating not coinciding with the apex of the concave mirror.

Let AC,CBO (fig. 2) be a section through the centre of
curvature, perpendicular to the surface ACB and to the
lines of the grating. Let AB be the chord of the section,
which is perpendicular to the radius CO that passes through
the apex of the spherical cap. The lines of the grating
keing drawn perpendicular to the axis of the dividing-
machine (and perpendicular according to our supposition to
the plane of the paper) it will always be possible to draw in the
plane of the paper a straight line EF’ parallel to the axis in
question. Ona tangent plane TT, to the spherical surface,
parallel to EF and perpendicular to the plane of the paper,
the dividing-machine would draw equidistant lines. On both
sides of the point of contact C, of this plane the distances of
the corresponding lines are also equal, C, is the point of
symmetry and the point of contact of the focal circle. Then

3

in Prof. Rowland’s Concave Gratings. neg

it is immediately seen by the figure, that the angle which is
formed by the straight lines AB and EF becomes equal to

the angle 6 between the radii CO and C\O. AB being =
150 millim. the values of the differences Ihene een Ali and BF
in the two gratings are found to be 1:08 and 1°32 millim.
respectively.

In this way the asymmetry of the gratings is explained in
a manner as simple as it is complete. However, the found
differences being much greater than would be supposed in a
work of such perfection as are the gratings of Prof. Row-
land, we cannot exclude another hypothesis, the same that
M. Cornu* has made use of in order to explain the focal
properties of plane gratings, viz., a systematic variation in
the distances of the lines. Such a variation would arise from
an irregularity in the screw of the dividing-machine, and in
the plane gratings this explanation seems to be the only one
possible. But in the concave gratings the same fault might
also arise from another cause. The two sides of the gratings
giving spectra of different brightness, we may conclude that
the furrows which the point of the diamond makes in the
reflecting surface are not symmetrical in section. Then it is
easy to see, that the distances of the lines are subject toa
continual variation from one side of the grating to the other.
But without knowing all details of w ork in the ruling of
gratings, 1t would be useless to enter more closely into ‘this
hypothesis, and impossible to decide whether it is superior
to the preceding.

SOs laxxy py 645:

[ 200 ]

XXIV. Separation and Striation of Rarefied Gases under the
Influence of the Electric Discharge. By H. 0. C. Baty*.

OME time ago, on examining with a spectroscope a
vacuum-tube which happened to contain a small quantity
of hydrogen, during the passage of the electric spark I noticed
that the hydrogen lines, while strongly visible in the negative
glow, could not be seen in the body of the tube. The hydrogen
appeared to be, in fact, withdrawn from the tube and collected
about the negative pole. Finding the same result in a tube
which I fitted up for the purpose, it appeared to me to point
to a separation of the gases in the tube ; and I determined to
make a series of experiments with a view to investigating the
matter and the behaviour generally of different gases under
similar conditions.

The tubes 1 employed were about 9 inches long and 2 inch
internal bore. The electrodes were of aluminium wire, and,
except in certain cases to which I shall refer, about 13 inch
in length. Two of these tubes were connected to the pump
at the same time, one direct and the other through tubes for
the absorption of mercury vapour ; so that in all the expe-
riments results were obtained in the presence and in the
absence of mercury vapour. Gas-generators, fitted with
purifying and drying apparatus, were connected so as to
allow of varying quantities of the particular gases under ex-
amination being admitted io the tubes as might be required.
The pump, I may mention, was a modified form of the
Geissler mercury-pump, to which I was able to attach an
automatic apparatus for working it—a very great saving of
labour. Measurements of the vacua were obtained by means
of an ordinary barometer-gauge, and varied from 15 millim.
to # millim.

I first worked with varying quantities of carbon dioxide
and hydrogen. On using certain mixtures of these gases
exhausted to about ? millim., when the current was first passed
a white glow appeared throughout the tube, no strie being
visible, giving a mixed spectrum of the two gases. After a
few seconds the negative glow changed to a pink colour, and
well-defined strize, whiter than the preceding glow, began to
appear. On watching this change with the spectroscope,
the hydrogen lines in the tube were seen to become fainter
and gradually to disappear, leaving only the spectrum of
carbon dioxide, while those in the negative glow became

* Communicated by the Physical Society: read Feb. 10, 1893.

Separation and Striation of Rarefied Gases. 201

extremely brilliant. The current was then stopped, and the
tube allowed to rest for about an hour, when, the current
being passed again, the same phenomenon precisely occurred.
Judging that if this were caused by actual separation of the
two gases, it ought to be possible to frac-
tionate out the hydrogen into another
tube, I endeavoured for a long time un-
successfully to do so; but at length suc-
ceeded by using a double tube of the shape
shown in the figure. The longer of the tubes
consisted of two chambers joined by capillary
tubing, the smaller tube being connected
to one of these by a narrow neck capable
of being sealed off. Both tubes were
furnished with electrodes. One of those
in the large tube was sufficiently long to
project through the capillary into the second
chamber, and being connected at its base to
the sealed platinum by a weak spiral wire
could be dropped sufficiently far to touch
the opposite electrode. This rod was made
of copper, as being heavier than aluminium.
It fitted the capillary fairly well, and
was furnished with small stops of cotton-
wool in order to close the capillary, and thus prevent as
much as possible the diffusion of the gases.’ The tube,
after being filled with the gases carbon dioxide and _ hy-
drogen, was exhausted and sealed from the pump. The
copper rod was caused to touch the opposite electrode, and
the current was passed so as to make the whole of the long
tube the negative pole and the electrode at the lower end of
the smaller tube the positive. The current was continued for
a considerable time, when the connecting-neck between the
tubes was sealed off and the copper rod shaken back to the
stop. On comparing the spectra of the two tubes, it was
found that the small tube (containing the positive pole)
showed only a trace of hydrogen, while the other showed it
brilliantly.

This, | think, may be considered a proof of an actual
though not complete separation of the two gases.

I then tried hydrogen mixed with many other gases
amongst them nitrogen, carbon monoxide, sulphur dioxide,
iodine, and mercury vapour; and in every case, without
exception, I found that the hydrogen was collected about the
negative pole in exactly the same manner as I have par-
ticularized.

Phil. Mag. 8. 5. Vol. 85. No. 214. March 1893. Ing

202 Mr. EH. C. C. Baly on the Separation and

I proceeded to examine mixtures of other gases. With
carbon monoxide and carbon dioxide, the carbon monoxide is
separated out and appears in the negative glow. With
carbon dioxide and nitrogen the carbon dioxide is separated
out, while the nitrogen remains in the tube, the separation
being remarkably distinct. In this case it is the heavier gas
which is separated out; and the same is found with carbon
dioxide and sulphur dioxide, the sulphur dioxide appearing in
the negative glow.

It would thus appear that the separation of two gases does
not depend on their relative molecular weights. On ex-
amining a tube of air, however, the components of which are
of fairly equal molecular weight, a separation was found to be
very difficult, and only occurred after carrying the exhaustion
toa much higher point than was usually necessary. The
nitrogen remained in the tube, and the negative glow gave a
spectrum presumably oxygen; I say presumably, for I am
unable to see what else it can be. 1 was unable to produce
the same spectrum in a tube with oxygen, but I was prevented
from proceeding further. The spectra of oxygen Professor
Schiister has shown to be very varied under different con-
ditions. Is it not possible that the two spectra in an oxygen
tube, the banded one in the negative glow, and the bright-
line one in the rest of the tube, may be due to separation of
two gases ?

From these experiments it is evident that when the elec-
tric current is passed through a rarefied mixture of two gases,
a process similar to electrolysis is set up, one of the gases
being separated out and collected about the negative pole, the
other gas remaining in the tube; the proof being that the gas
separated out may be fractionated into another tube by the
method I have above described. In pursuing these experi-
ments [I was struck by the apparent close connexion between
separation and striation ; that is to say, I found strongly
marked strize when there was good separation, and feeble striz
when the separation was difficult; [also found that the first
appearances of these phenomena were coincident, the torma-
tion of striz being always the sign of the commencement of
separation. ‘There were no exceptions to this, the action in
all the tubes I made being the same.

It was evident to me that, if the connexion were real and
the separation of the gases could in some way be prevented,
by avoiding the negative glow, strie would not be formed.
I accordingly made a tube the negative pole of which did not
protrude from the little glass collar in which it was placed,
the positive electrode being made as usual. The tube was

Striation of Rarefied Gases by the Electric Discharge. 203

filled with a mixture of hydrogen and carbon dioxide and
exhausted. Ata pressure of 24 millim. the current was
passed ; instead of a negative glow appeared a little bunch of
light about } inch below the negative point. If this bunch of
light impinged on the side of the tube, the glass became strongly
phosphorescent. At 4 millim. there was no bunch of light or
negative glow; there was no sign of any strice, the tube
giving a spectrum of hydrogen and carbon dioxide, and no
evidence of separation. I then reversed the current ; imme-
diately strize formed, separation began and became well-
marked.

I tried various mixtures of gases and always obtained the
same result, viz., that when the negative glow was avoided by
the use of the minute electrode point, neither striz nor sepa-
ration occurred, but in reversal of the current strongly
marked strize and good separation.

My next step was to experiment with a pure vapour,
which, if my contention be correct, should not striate. It is
known that a tube of pure mercury vapour does not stratify.
I prepared a tube for the purpose, one end of which was con-
nected with the pump and the other with a bulb containing
mercury. After exhaustion, I strongly heated the tube and
boiled the mercury, which thus distilled through the tube.
On passing the current, as I expected, no striz appeared,
but simply a beautiful phosphorescence throughout the tube,
giving aspectrum of pure mercury only. On ceasing to boil
the mercury and allowing the tube to cool, a small quantity of
other gas was necessarily drawn in from the pump. Immedi-
ately striee began to appear, beginning at the end of the tube
connected with the pump; the negative glow changed at the
same time and gave a spectrum containing other lines in
addition to those of mercury, thus strongly confirming my
previous conclusion.

Thinking that possibly the absence of strie might arise,
not from the purity of the mercury vapour, but from its
molecules being monatomic, I repeated the experiment with
pure vapours of iodine, sulphur, arsenic, and mercuric iodide,
which are not monatomic. ‘The result was in each case pre-
cisely the same—the tube while heated showing no striz, but
on cooling both strize and separation.

Wishing if possible to obtain a pure gas which did not
stratify at ordinary temperatures, | made many attempts to
prepare a tube of pure hydrogen. The nearest approach to
success was with hydrogen prepared from pure caustic potash
and aluminium. ‘The gas was then absorbed by red-hot
palladium, which was re-heated in the vacuum. On passing

P 2

204 Dr. Gladstone on some Recent Determinations

the current, the tube showed an even phosphorescent light
throughout, with a very faint line of the most delicate striz,
very difficult to distinguish. The strize did not become any
plainer on carrying the exhaustion to a considerably higher
point. I think it may be safely assumed that a tube of per-
fectly pure hydrogen would not striate at all.

From the foregoing results I think the following conclusions
may be drawn :—

First, that when an electric current is passed through a
rarefied mixture of two gases, one is separated from the other
and appears in the negative glow.

Second, that striz are caused by the separation of the two
gases, and do not occur in a single pure gas or vapour.

XXV. Notes on some Recent Determinations of Molecular
Refraction and Dispersion. By J. H. Guavstone, D.Se.,
died aS)

MONG the various indices of refraction which have

been published by different observers of late years, there

are some which have led me to further studies bearing on

the general relation of this branch of Physics to Chemical

theory. ‘The following notes relate to the new metallic car-

bonyls, the metals indiumand gallium, sulphur, and to liquefied
oxygen, nitrous oxide, and ethylene.

I, Merauuic CARBONYLS.

Messrs. Ludwig Mond and Nasini t determined the mole-
cular refraction of nickel tetracarbonyl for the red ray of
hydrogen (H,) as 57:7, and the specific dispersion between
the lines y and a of hydrogen as 0:03475, which will give a
molecular dispersion between those limits of 5:93. This
indicates a very great refraction and an enormous dispersion.

Through the kindness of Mr. Mond I have been able to
determine the refraction of two specimens of iron penta-
carbonyl for several lines of the spectrum, with the following
result. The second and third lines in the Table relate to the
same specimen, the latter representing measurements taken
in a very acute-angled prism, and under the most favourable
circumstances for seeing the more refractive rays; nevertheless
the spectrum was cut off so suddenly about the bundle of
rays at G that I cannot be sure of the exact measurement,
but think it differs little from the line y of hydrogen.

* Communicated by the Physical Society: read Feb. 10, 1893.
t+ Lincet, Rendiconti, vii. 411.

a:

of Molecular Refraction and Dispersion. 205

Speci- | Temp. Sp.Gr.} ps
| bys

men; | 0, Pe reen ec ca lectern eal ant sat le | eae

....| 23 1:460 | 1-5026, 1-5076) 1-5096} 1-5180) 1°5289,

II. ...| 15-5 | 1-4705/ 1-5063) 1-5117] 1:5146) 1-5224) 1-5329

TI. ...| 13:4 | 1-474 |1:5071) ... . | 152380; ... | 1:5446) 15650

From these observations we obtain the following molecular

refraction, ent feet

d
| =
Bie hae Re hom Rel Re: BS
aga 6747 | 68:14 | 68-41 | 69:54 | 71-00
Tae 67-48 | 6820 | 6859 | 69-63 | 71-08
Was. Gras | So | AS) cee) eae

It is evident that in the iron compound also the refraction
and dispersion are very great. ‘The molecular refraction
for the line a of hydrogen may be assumed at 68°5, and the
molecular dispersion between the lines y and a of hydrogen
at 6°6. If we reckon for the lines A and H, we may assume
H would be about 78:0, which would give a molecular dis-
persion between these limits of about 10°5.

In discussing their observations, Messrs. Mond and Nasini,
assuming that CO has a molecular refraction of 8°4, reckoned
the atomic refraction of nickel at 24°1, instead of 9°9, which
I had assigned to this element in solutions of its salts, and
which subsequently has been fairly corroborated by Nasini’s
own experiments. This difference they attributed to a dif-
ference of valency in the metal. By parity of reasoning the
atomic refraction of iron for the line C would be 26:5, or
25°5 for the line A, instead of 11°6 previously determined for
bivalent iron from solutions of its salts.

But this involves the assumption that CO in these carbonyls
has the same value as we should expect to find in an organic
substance. It also assumes that the nickel has 8 valencies,
while the iron has 10, in the above-named compounds, and

that iron has presumably 9 in diferrohepta-carbony]!; and that

206 Dr. Gladstone on some Recent Determinations

potassium in its compounds with CO has still other valencies.
There is also another difficulty; for if we determine the atomic
dispersion of nickel and iron on the same principle, it will
be found to be 4°8 and 52 respectively for the interval
between the lines y and a*; these numbers are about one fifth
of the atomic refraction of the two metals given above, viz.,
24-1 and 26:5. But the ratio between the atomic dispersion
(y—a) and the refraction of the most dispersive elements
hitherto calculated, sulphur and phosphorus, is only about
one tenth.

It seems more probable that the metals really retain their
ordinary valency, and that the excessive refraction and dis-
persion is to be sought rather in the peculiar arrangement of
the CO. In such compounds we may imagine the CO
playing a part similar to that of the CH, in ordinary organic
compounds, which may be increased or diminished in number
without altering the general type of the substance. In fact
T accept on optical grounds as well as chemical, the ring-
formulze indicated in Mond’s lecture at the Royal Institution.

- va
~ C=O: cs

Va
otf c=0

ery oc ono
C

In that case the molecular refraction due to each CO would
be, from the nickel compound about 11:9, and from the iron
compound about 11:3. |

Although the atomic dispersion of nickel or of iron has not
yet been definitely measured, it cannot greatly exceed 0°5 for
y—a. Itis evident therefore from the figures for the disper-
sion, viz., Ni(CO),=5°9, Fe(CO);=6°6, that the molecular
dispersion of each CO must be about the same in these two
compounds, viz. 1°3, or thereabouts.

Il. Iypium Anp GALLIUM.

In 1885 I calculated the atomic refraction of indium and
gallium from determinations of the refraction of certain
alums made by M. Charies Soret. Very shortly afterwards

* “Proc. R. 8. xl. p. 401.

of Molecular Refraction and Dispersion. 207

he published another paper giving fresh and additional values
for alums containing these metals *.

For indium the available data are derived from rubidium
and cesium indium alums, and for gallium from no fewer
than five compounds, viz., potassium, rubidium, cesium,
thallium, and ammonium gallium alums. Calculated from
these data, I find as mean values for the atomic refraction of
these two metals the following :—

‘ . : | Specific
Metal. Atomic Weight. | Ronee R.
[iG 1 ear 113°4 0-121 13:7
Gallium.............4. 69-9 | 0166 11°6

These no doubt are nearer the truth then the higher figures
previously given, though they must still be looked upon as
only approximate. In regard to the atomic dispersion of
these metals, the new observations quite confirm the previous
remark that the order is “iron far the highest, chromium,
indium, gallium, and aluminium lowest.”

III. SuLpuur.

In the following Table is given the atomic refraction of
sulphur, either uncombined, or in very simple combination :—

Gondition. Mee ence) een pe ory) fy El
NSIOIIG! Sas SOe eee ee aeee a arene 15:7 16:0
find ess 15908) ee 16°47
Grane Ouse eekly sakes Gey ah ees
In solution ...... 15:5 15:7 16:0 16:7 17:3
HramsCSs.......--| 15:8 16-05 163 17:05 Weer 18-4

ees Oo 158° | 160

POLES el we uma Oates. 15-9 16:1

PEL EUS stesieeth, sessata LG SOAS pcs |

Sulphur in the solid condition is deduced from the observa-
tions of Descloiseaux and other physicists; but as the crystals
of sulphur give three different indices of refraction for the
same ray, the arithmetical mean of these three indices has
been simply taken as the basis of calculation.

Sulphur in a liquid condition is from the observations of

* Archives Se. Ph. § N. Geneve, xiv. p. 96.

208 Dr. Gladstone on some Recent Determinations

myself and the late Pelham Dale. It agrees, as far as D is
concerned, with a determination by Becquerel. R,=16°86.

Saline in the gaseous condition was determined be Le Roux
in 1861. The specific refraction was calculated out by me
shortly afterwards, and recently by Nasini and Costa*. I
give their number for the atomic refraction in the Table.

The sulphur in solution is from five determinations of this
element dissolved in carbon bisulphide which I made some
years ago with another object, and which have never been
published. The solutions contained from about 22 to 27
per cent. of sulphur. Two determinations of somewhat weaker
solutions were lately published by Nasini and Costa, and were
practically identical with mine. The refraction of 17°3 for
the line y is deduced from their figures alone.

The four last lines give the values of sulphur reckoned
from its simplest compounds.

In the case of bisulphide of carbon the figures in the Table
are derived from my own most recent observations, which
agree closely with those of other observers. The deduction
made for the atom of carbon is 5:0 for the line A, 5°26 for the
line H, and proportional numbers for the intermediate lines.

In the case of bichloride of sulphur the calculations have
been made from the observations of Costa ; and in that of
chloride of sulphur from those of Haagen, Becquerel, and
Costa, which fairly agree. The refraction due to an atom of
chlorine is assumed to be 9:95 for the line C, and 10°05 for
the line D. Costa, in treating of these substances, has adopted
a slightly smaller value for chlorine.

In the case of the bromine compound the sulphur is cal-
culated from Becquerel’s observations, taking the value for
bromine at 15°35.

The figures for sulphur derived from these various sources
are very similar. I doubt, however, whether the sulphur
dissolved in bisulphide of carbon and the sulphur which forms
part of that compound do exert exactly the same influence
upon the rays of light. If we were to reckon the value of
carbon in bisulphide of carbon by deducting the value found
for sulphur in solution, we should get for A, "36°6—31-0=5" 6,
a higher figure than we ever find for carbon in a saturated
compound. The difference would be still greater if reckoned
by Lorenz’s formula.

The accordance of the dispersion as exhibited throughout
the Table is worthy of notice.

From the elaborate paper of Nasini and Costa, already
referred to, it would appear that in some organic compounds,

* Universita Inst. Ch. Roma, 1891.

of Molecular Refraction and Dispersion. 209

such as the xanthates, sulphur has at least the value of 16-0 ;
but in the large majority of cases it has a distinctly lower
value. In its oxygen compounds it is known to be far less
refractive and dispersive.

IV. Liqurrizp OxyeEn, Nitrous OxipE, AND ETHYLENE.

In the recent paper of Professors Liveing and Dewar (Phil.
Mag., Aug. 1892) they give determinations of the specific
refraction of liquefied oxygen, nitrous oxide, and ethylene.
It is, of course, possible to compare these interesting results
with what theory would have led us to expect. The authors
have themselves done so in the case of liquid oxygen at its
boiling-point of —182° C. They remark that the refraction-
equivalent, 3°182, which they found, differs but little from
that deduced from gaseous oxygen at the ordinary tempera-
ture, viz. 8°0316, and “corresponds closely with the refrac-
tion-equivalent deduced by Landoit from the refractive indices
of a number of organic compounds,” which was 3:0. It
actually comes between the two values, 2°8 and 3°4, which
were assigned by Briihl to oxygen in its different states of
combination with carbon, and to which an intermediate value
has since been added.

Liveing and Dewar were able to determine the refraction
of liquefied nitrous oxide for six different wave-lengths, the
extremes being the red ray of lithium and G. These gave

pw—l
for 7

0°2595 and 0°2691 respectively, and for the mole-

cular refraction of the red ray 11:418,and of G 11°840. The
molecular dispersion between G and the lithium-line is there-
fore 0°422, which would indicate about 0°63 between H and
A. Now it is difficult to say what the rational composition
of nitrous oxide is, and therefore what its theoretical refraction
and dispersion should be. Nitrogen in ammonia and its con-
geners is reckoned at 5°1, in nitriles at 4°15; oxygen double-
bonded is reckoned at 3:4, with two separate bonds at 2°8.
We therefore, according to our theoretical views, might reckon
nitrous oxide at 13°6, 13°0,11°6, or 11:0. The probability is
therefore clearly in favour of the lower figure for nitrogen.
As the dispersion-equivalent of nitrogen in ammonia is as
high as 0°38, this would also seem to exclude the idea of the
nitrogen in nitrous oxide being in the same condition as in
ammonia. This will probably be considered the most likely
alternative also on chemical grounds.

On calculating Messrs. Liveing and Dewar’s numbers for
liquid ethylene, we obtain the molecular refraction of 17:2 for

210 High Resistances with the D’ Arsonval Galvanometer.

the line D. But Professor Dewar has kindly furnished me
with a more recent determination of what he believes to be a
purer specimen. The refractive index, at the boiling-point,
for the line C is 1:3445, and for the line F is 1°3528, the
specific gravity being 0°55. These figures give 17:53 as the
molecular refraction for the line C, and 17:92 for the line F.
These will indicate about 17°41 for the line A. The theo-
retical value for ethylene, for the line A, is 17-4.

Co . = 1090

hee tir =,
Double-linking . = 2-2
LT

The coincidence between experiment and theory is very
striking.

XXVI. High Resistances used in connexion with the D’ Ar-
sonval Galvanometer. By FrepERIcK J. Situ, Millard
Lecturer in Mechanics, Trinity College, Oxford *®.

HE great utility of the D’Arsonval galvanometer for
determining current by the fall of potential method
must have been felt by all who have used it for this purpose.
When the instrument is thus applied, a large resistance is
required in the galvanometer circuit. This is usually made
of wire, and costs much. In 1890 I read a short paper before
the Ashmolean Society of Oxford on the subject of resistances
made of non-metallic substances and mercury jet-contacts.

Since then resistances of this kind have been constantly in
use in the Millard Laboratory, and they have proved them-
selves to be both reliable and constant. They are made thus:
Dry plaster of Paris and electrotype plumbago are intimately
mixed together in suitable proportionsf, the composition is then
rammed tightly into a glass tube furnished with a platinum
terminal; when nearly full another terminal is introduced
and fixed in the substance by compression; the end of the
tube is then closed over the wire in the blowpipe flame, and
the resistance is finished.

In one resistance thus made the glass tube is 10 centim.
long and O-4 centim. in internal diameter, and has a resist-
ance of about one megohm. Very finely powdered glass
mixed with plumbago makes a good composition for high

- * Communicated by the Author.
+ Equal quantities of each in a tube 0'4 centim. diameter and 115

centim. long gave a resistance of 65,000 ohms.

The Laws of Molecular Force. 211

resistances, but it is not so easily manipulated as the plaster
and plumibago. Out of a large number of different substances
tried, I find these two the most reliable. A megohm made
by the method I have described costs only a few shillings.

Since October 1888 a D’Arsonval galvanometer has been in
constant use here, in combination with a photographic appa-
ratus, whereby a cylinder carrying bromide paper is constantly
exposed to the reflected light from the galvanometer which
shines through a long narrow slit placed in front of the re-
volving cylinder; by this means a constant record is kept of
the current in a certain circuit. When the resistance of the
galvanometer circuit is very high, the dead-beat action of the
instrument is somewhat affected. I find that if a few turns of
fine covered copper wire are wound on the outside of the
rectangular coil of the instrument so as to form a closed circuit,
it gives the same reading as before for a given potential
difference, and is perfectly dead-beat in its action, so that
with the addition of tois damping-coil any amount of re-
sistance may be used in the circuit of the galvanometer.

Trinity College, Oxford,

Feb. 10, 1893.

XXVIL. The Laws of Molecular Force.
By WILLIAM SUTHERLAND, M.A., B.Se.*

i my last paper on this subject (Phil. Mag. April 1889)
it was shown that if the law of force between two similar
molecules is 3Am?/r*, the parameter A could be calculated
for a large number of bodies from Robert Schiff’s measure-
ments of their surface-tensions, and a law was announced
connecting the values of A with chemical composition ; but
as this law was affected with exceptions in the case of the
organic bromides and iodides and the amines, and as the
argument from surface-tension requires the introduction of a
considerable number of assumptions, I felt that it was very
desirable to secure some other means of finding A. It soon
appeared that the only satisfactory plan would be to return
again to the search for the true characteristic equation of
fluids on the model of Clausins’s virial equation, as I had
found that not one of those hitherto advanced was capable of
general application. Fortunately the experimental material
now available is so abundant and so well placed that I was
completely successful in the quest, in the more tedious parts
of which I had the advantage of assistance from my brother,

* Communicated by the Physical Society: read Oct. 28, 1892.

212 Mr. William Sutherland on the

Mr. John Sutherland. Amagat’s exhaustive study of the
compression and expansion of gases, along with Ramsay and
Young’s work on ethyl oxide, were the groundwork of the
research.

As the true characteristic equations for fluids are the key
to many chambers of molecular physics, I have been able to
enter many of these, and especially to discover the true law
of the parameter A without exception. ‘To give an idea of
the scope of these investigations free from detail, I furnish the
following table of contents :—

1. Establishment of characteristic equation for compounds
above the region of the critical volume, with proof that there
is discontinuity in the liquefaction of compounds.

2. The same for the gaseous elements, with proof of con-
tinuity during liquefaction in their case.

3. Brief discussion of exceptional compounds such as the
alcohols and ethylene.

4, Establishment of characteristic equation below the region
of the critical volume, its main feature being the occurrence
in it of the same internal virial constant as in the equation
for the region above the critical volume.

5. A short digression on the general interpretation of
Clausius’s equation of the virial.

6. Consideration of Van der Waals’s generalization that if
each substance has its temperature, pressure, and volume
expressed in terms of the critical values as units, one and the
same law applies to all bodies ; proof that this is true for
elements and compounds separately, above the critical region,
and approximately true below.

7. Five methods of finding the internal virial constant :
first, from the expansion and compression of the substance as
gas or vapour ; second, from its expansion and compression
as liquid ; third, from its latent heat ; fourth, from its critical
temperature and pressure; fifth, from its surface-tension :
all the methods being afterwards proved to give accordant
results for a large number of compounds.

8. The fifth or capillary method treated in greater detail,
with digressions on the Brownian movement and molecular
distances.

9, Establishment on theoretical grounds of Hotvés’s rela-
tion between surface-tension and molecular domain (volume).

10. Tabulation for a large number of bodies of the product
of the square of the molecular mass by the virial constant
determined by several methods, and verification thereby of
the general principles preceding.

11. Establishment of the law connecting the virial constant

Laws of Molecular Force. 213

of a substance with its chemical composition. Definition of
the Dynic Equivalent of a substance and determination of its
value for several radicals.

12. Close parallelism between Dynic Equivalents and
Molecular Refractions. .

13. Return to the discontinuity during liquefaction of com-
pounds, and proof that it is due to the pairing of molecules.

14. Brief discussion of the constitution of the alcohols as
liquids.

15. Methods of finding the virial constant for inorganic
compounds, including a theory of the capillarity and com-
pressibity of solutions.

16. Tabulation of the product of the square of the molecular
mass by the virial constant for inorganic compounds, and
determination of the Dynic Equivalents of the metals in the
combined state. Ayain a close parallelism between dynic equi-
valents and molecular refractions or refraction-equivalents.

17. Meaning of this parallelism ; general speculations as to
the volumes of the atoms and their relation to ionic speeds.

18. Attempt to determine the velocity of light through the
substance of the water-molecule.

19. Suggested relation between the change in the volume
of an atom on combination and the change in its chemical
energy.

1. Establishment of the characteristic Equation for Com-
pounds above the region of the Critical Volume, with proof
that there is discontinuity in the liquefaction of compounds.—
Amagat established (Ann. de Chim. et de Phys. sér. 5, t. xxii.)
that for gases Qp/OT is a function of volume only down to
volumes near the critical, but that at lower volumes it begins
to vary with temperature. Ramsay and Young (Phil. Mag.
May 1887), while verifying the independence of Qp/dT on
temperature above the critical volume for such bodies as ethyl
oxide and the alcohols, sought to show that this independence
continues right into the liquid state ; but, as a matter of fact,
their temperature-range in the experiments below the critical
volume is not great enough to decide the question one way or
another. We shall see that in the case of compounds Amagat’s
conclusion is the correct one, while in the case of the elements
Ramsay and Young’s contention appears to hold. The con-
viction that Op/dT becomes slightly variable with temperature
below the critical volume was one reason that determined me
to represent the behaviour of fluids by two equations merging
into one another ; the one applying down to near the critical
volume, the other below that.

214 Mr. William Sutherland on the

Clausius’s equation of the virial is to be our guide in
studying Op/oT,
Spv—> 5 mV? —t. +> he

where V is velocity and R is force between two molecules at
distance 7 apart.

According to the law of the inverse fourth power, the
double sum of the internal virial reduces to an expression
varying inversely as the volume and independent of the tem-
perature, as I have shown before (Phil. Mag. July 1887).

If we integrate Amagat’s relation 0p/dOT=/(v), we get

p=SOT +o);
and as in the perfect gaseous state pv= RT, where v being the
volume of unit mass and T reckoned as temperature C.+ 273°,

R varies inversely as the molecular weight of the substance,
we will-write our equation in the form

pv= RTvf(v) + vd(v),

where we see that rf(v) stands for the internal virial-term.
If, then, according to the law of the inverse fourth power, the
internal virial varies inversely as v, then v’f(v) ought to be
constant. Now Ramsay and Young have carefully tabulated
the values of R/(v) and ¢(v) for different values of v in the
case of ethyl oxide ; so it is easy to tabulate Rv/(v) and v’(v),
as we proceed to do in the following Table, where v is the
volume of a gramme of ethyl oxide in cubic centimetres, and
the metre of mercury is the unit of pressure. These units
will be used throughout when we are dealing with experi-
mental results involving pressures ; but when necessary, for
theoretical convenience, we will convert to absolute units.

Tasie [.—Hthyl Oxide.

v. Rof(v). | voce). || Rof(v). | v?¢(v). |
| Perfect gas. "842 | 33 1°758 2413
100 ‘912 5710 |) 3 1:865 | 2366
50 ‘973 5190 2°79 2013 | 23871
20 16029 4554 2-5 2°30 2487
15 1-201 4302 2-4 2°42 yay ks)
10 1327 3908 2°3 2°56 2550 |
8 1-409 3661 2:2 2°73 2589
6 1-525 3308 2-1 2°95 2646
5 1595 3047 || ~=2:0 3°19 2691
4 1654 2656 || 1:9 3°54 2771
37 1682 | 2534

Laws of Molecular Force. 215

The critical volume of ethyl oxide is between 5 and 4; so
that if Qp/OT does become variable with temperature below
the critical volume, the values of Rv/(v) and v’¢(v), calcu-
lated for volumes below 5, on Ramsay and Young’s assump-
tion that even below the critical volume 6p/OT is independent
of temperature, will be affected with an error of more or less
importance ; they may therefore be regarded as a first approxi-
mation only and are added for comparison.

The first point to notice in these numbers is that Ruf(v)
increases steadily from its limiting value *842 in the perfect
gas state to double that amount near the critical volume, while
at the same time v’¢(v) diminishes from its limiting value in
the gaseous state to the half of it near the critical volume.
This result would seem at once to contradict the law of the
inverse fourth power ; but we shall see in the sequei that, in
compression down to the critical region, there is a process of
pairing going on among the molecules and producing this de-
parture from the requirements of the law of the inverse fourth
power, uncomplicated by such a process.

It is to be noted that the limiting value of v’¢(v) is diffi-
cult to determine experimentally, because o(v), the quantity
measured, tends to the limit zero. But while below volume 4,
Rzj(v) increases with increasing rapidity, v’d(v) remains
almost stationary, it dips a little and then increases; but
remembering that its values count only as first approxima-
tions, we may assume that v’f(v) attains near the critical
volume a value which remains constant in the liquid state,
and is about half of the limiting value for the gaseous state.
Thus there is discontinuity in the passage from the region
above the critical volume to that below (or, more briefly but
less accurately, during liquefaction). We must note carefully
that in the range of volume from 4 to 1°9, which is a large
liquid range, v°¢(v) remains constant, as it should avcording
to the law of the inverse fourth power, now that the process
of pairing is completed.

To represent Rvf(v) I found the form R{142k/(v+k)? to
be efficient ; it gives the limit 2R to the function when v=:;
and as ‘842 is the known value of R, each of the above
tabulated values of Ref(v) yields a value of £, the mean value
4:066 having been adopted by me. ‘The other function,
v’(v), proved no less amenable to simple representation, the
form found to fit it being lv/(v-+&), which attains the value
lj2 when v=k ; and as the value of & is known, we can calcu-
late from each tabulated value of v’d(v) a value of J, and
ayain adopt the mean value 5514. Hence down to near the

216 Mr. William Sutherland on the

critical volume we have the behaviour of ethyl oxide repre-
sented by the simple form of equation

2k l
pe Roi ony with k=4°066 an ;
involving only the two constants & and J peculiar to ethyl
oxide.

We will now compare a few values of the pressures, in
metres of mercury, given by this equation with those found
by Ramsay and Young.

TaBsnn Ld.
| Wolwine *22 2557522 100. 50 20 10 6
175° G. {| Pressure, experiment. | 3:500 6°620 13-88
fo" ’* 1) Pressure, calculated. | 3:5388 | 6634 | 13°78
|
195° C { _ Pressure, experiment. | 3°710 7020 1506 | 23:00} 27-00
_ Pressure, calculated. 3719 | 7021 14:90 | 22:99| 27-44
280° C Pressure; experiment. |. ic.c25-0" |. 0 easan 19°80 | 34:59] 49°62
Pressure: calculated: “|* ceces-uu |) scot 19°69 | 34:28} 49-00

The agreement is as close as can be looked for; because
although Ramsay and Young measure volumes to within
‘01 centim., and pressures to within 2 centim. of mercury, the
quantities measured cannot be considered known with that
degree of accuracy; for the discrepancies between their mea-
surements and those of Perot (Ann. de Chim. et de Phys.
ser. 6, t. xill.), who made special determinations in a large
globe of the saturation-volume of ethyl oxide at different
temperatures, are greater than those in Table Il. Accord-
ingly it would be useless to seek a better empirical represen-
tation of Ramsay and Young’s results than the above ; and
as we are chiefly interested in establishing our simple form of
characteristic equation, we had better proceed at once to the
consideration of Amagat’s experiments on carbonic dioxide,
practically identical with Andrews’s, but more extensive.
Amagat’s unit of volume is 334, of that occupied by the gas
at 0° and 1 atmosphere ; taking the weight of a litre of the
gas at 0° and 1 atmosphere as 1:°9777 gramme, we can
convert Amagat’s data to the gramme and centim. as units.
The following Table is arranged in the same way as
Table [. :—

Laws of Molecular Force. 217
TasLeE I1].—Carbonic Dioxide.

v. Rof(v). | v?6(v). | v. Rof(v). | v?o(v).
| Perfect gas. | 1-421 | 264 | 256 | 1661
7 3A 1:92 2159 || 2:35 2-64 | 1566
(7-00) (211) | (2500) | 2:05 | 277 | 1482 |
5:14 ise 207 ||, ot 2:86 | 1440 |
(5:00) (237) | (2400) || 1-76 3:02 | 1430
3°67 2°31 1858

(The bracketed numbers are introduced from Andrews.)

A glance at this Table shows the same facts to be in it as
m Table I. The critical volume of CO, is somewhere about 2;
and we notice that near this volume Rv/(v) tends to double
the value 1°421 in the gaseous state, while at the same point
v’h(v) approaches a constant value about the half of what
must from inspection be estimated as the upper limit of it.
Both functions are accurately represented by the same forms
as in the case of ethyl oxide with 4=1:762 and /=2773.
With these values the following pressures were calculated for
comparison with experiment :—

TABLE LV.—Carbonic Dioxide.

Wolumenssi2.. 11°74.) 88. | 5:87. | 3:67. | 2°64. | 2:20.

100° C Pressure, experiment. | 39 49-8 | 69 | 968 | 124 | 143
§ Pressure, calculated. | 39°4 | 50-4 | 70 99 £29) 137

roo Cc Pressure, experiment. | 34:5 | 43°7 | 588 | 79:5 | 95 | 105
2 ; Pressure, calculated. | 34°38 | 44:0 | 594) 80:0 | 94 | 100
35° C Pressure, experiment. | 29°7 | 36°5 | 46°4 | 55:8 61 63°6
0 “|| Pressure, calculated. | 295 | 365 | 47:0 | 57: Sey

The agreement is quite satisfactory except at the lowest
volume, which is near the critical ; and I have shown (Phil.
Mag. August 1887) that near the critical point in capillary
tubes the relation of pressure to volume becomes fickle, the
measurements of Andrews and Amagat differing from one
another as much as experiment and calculation in Table IV.
To illustrate this at higher volumes I introduced into Table III.
a couple of Andrews’s values of Rvf(v) and v’f(v), from values
of Rf(v) and ¢(v) calculated by Ramsay and Young (Phil.
Mag. 1887), after conversion of Andrews’s air-manometer
indications to true metres of mercury. It will be seen that

Phil. Mag. 8. 5. Vol. 35. No. 214. March 18938. Q

218 Mr. William Sutherland on the

Andrews makes 0p/OT a little larger than Amagat ; and this
being so, it is not worth while to seek for closer agreement
than that in Table LV., at least at present.

We have, however, a sensitive means of determining whether
the form and the values of the constants adopted truly repre-
sent the behaviour of CQ, closely enough at high volumes,—
namely, Thomson and Joule’s and Regnault’s experiments on
the cooling of CO, when it escapes through a porous plug
from under pressure (Phil. Trans. 1854-1862; dém. de? Acad.
xxxvil.). Natanson (Wied. Ann. xxxi.) has repeated the Joule
and Thomson experiments on CO, under the more favourable
conditions afforded by the commercial sale of the fluid in
large quantity and great purity, so that he has been able to
measure not only the cooling effect for a given pressure excess,
but also its variation with pressure. Taking all these experi-
ments together, we have a delicate test for the equation at
high volumes.

The most convenient expression for the cooling effect for
our present purpose is

K donde

ape aeee:

where 6 is the cooling effect, K,, is the specific heat at constant
pressure, and @ is temperature on the absolute thermo-
dynamic scale. In previcus papers I took from Joule and
Thomson’s original investigation @=T+°7°, not then aware
that Sir W. Thomson, in his article “ Heat” (Hncye. Brit.),
had by a fuller discussion of all the experimental data proved
6=T, and so removed the difficulty that the term *7 opposed
to the harmony of the thermodynamic and molecular kinetic
conceptions of temperature.

With our characteristic equation the cooling effect is, after
the appropriate reductions, given by

dé

aaa

= 2(I/RT—h) +p{4(/RT—k)(/RT—2h)
—2k(l/ RT — 2h) —lk/RT RT.

Within Joule and Thomson’s range of pressure this can be
reduced to

Kea, =2(1/RT—f) ;

and dé can be made to stand for the integral cooling effect if
dp stands for the integral excess of 2°54 metres of mercury,
to which they reduced their results, The term in p will be

Laws of Molecular Force. 219

taken account of when we come to Natanson’s results. From
Regnault’s data we have, in dynamical measure

K,=424(:187 + 000272).
TABLE V.

(Cooling effect of CO, escaping through a porous plug under
a pressure excess of 2°04 metres of mercury.)

Wemperature ©....) 7°42.) 8°o 11991. )35°°6.| 54°, | 91°°5.| 93°°5 | 97° 5

Th. and Joule ...| 4:4 42 3°9 3:4 | 2:9
Caleculated......... 4-4 4°4 4°] 3°7 | 3:4 2-7 Path 2°6

Temperature OC. |—25°| 3°. | 100°.

Repnault ......... 6:3 4-1 26
Caleulated......... 55 4:5 2°6

The agreement is as good as possible if both sets of experi-

‘ments are taken into consideration. But Natanson’s result

affords a more delicate test; he found that at 20° up to 25
atmospheres the cooling effect for a pressure excess of one
atmosphere could be represented by

dé

Fp Fe 18 +°0126 p ;
while the theoretical equation above gives

a) :

which is practically identical with Natanson’s. On account
of the closeness of this agreement we obtain as an indirect
conclusion, that the experimental work on CQ, taken as a
whole makes the absolute thermodynamic zero —273°, the
same result as Sir W. Thomson has obtained for air and H
in the article “ Heat” (dincye. Brit.), while for CQ,, using
only Regnault’s coefficient of expansion and Joule and his
own cooling effects, he found —273°°9. Now that CQ, is
seen to be in harmony with the other two more perfect gases,
the number 273 may be accepted definitely as the absolute
temperature of melting ice.

The equation therefore applies accurately at high volumes,
a fact which we can prove by another test, seeing that Amagat
carried out a special research (Compt. Rend. xciii.) to determine
the ratios of pv top'v! at different temperatures and up to values
of p! about 8 atmospheres, v being double v’.

Q 2

220 Mr. William Sutherland on the

TaBLe VI.
(Values of pv/p'v' at high volumes for CO,.)

(p=5'T metres of mercury : v=20')

Temperature C. ...... DO: KOO: 200°. 300°.
AMA AL bo doedes ee eee 1:0145 1-0087 1-0040 1:0020
Calculated: -a.-es: es. 1:0156 10092 1-0026 10000

As the experiments are not free from liability to an error of
1 in 1000, the agreement is again close enough to prove the
applicability of the equation at high volumes. |

In the sequel it will be shown that this equation applies to
the great majority of compounds, but meanwhile the only
other experimental determinations similar to those already
discussed for ethyl oxide and carbonic dioxide are Amagat’s
for tH), O>, No, CH, and C,H; Roth’s for SO, and NH; (Wied.
Ann. xi.) ; Janssen’s for N,O (Wied. Bedi. Fes and Ramsay
and Young’s on methyl and ethyl alcohol (Phil. Mag. Aug.
1887). Our form of characteristic equation applies to
SO., NH;, and NO successfully, but not to H,, O., No, and
CH,, which require a still simpler type, the alcohols on the
other hand requiring a less simple type. These are the
values of & and / for SO,, NH3, and N,O :—

SO,. NHL. N,0.
kk yes £208 4°8 2°3
[oe AO 22040 3420

with which the following pressures have been calculated for
comparison with the experimental data, the latter being taken
direct from air or nitrogen amen rats without comceae for
departure from Boyle’s Taw.

TABLE VII.

SO, at 99°-6. NH, at 99°-6. | N,O at 25°1. |
|
i

v. pexp. | p calc, Veta PIeXD. a wprcallies U. pexp. | p cale.

41-9 9 80 4) 172 76 76 7:0 39:1 | 37-2
17-6 i rel| 17-0 85°7 14:8 14-7 5°36 426 | 42-4
| 136 21:2 20°8 65:4 13:8 18°9 3°78 43°9 | 46-7
9:9 26:0 26°2 40-0 28:6 29:1

At 183°, At 183°. At 43°°8,

182 ) 21-7 | 22-0 | 160 103. | 10-2 5:83 ) 49:4 ) 47-9
| L6 | 198 19-6 4-62 | 556 | 544

| 409 | 421 || 347 | 614 | 610
275 | 982 | 935 | 162 | 826 54 || 282 | 641 | 643

Laws of Molecular Force. 221

This comparison has been made only to show that the form
is applicable to other bodies as well as to ethyl oxide and car-
bonie dioxide ; full confirmation of the form will come later
on, in the study of many of its applications.

2. Establishment of the Characteristic Equation for the
Gaseous Hlements, with proof of continuity during liquefaction.
—tThe simplest plan in the case of the gaseous elements will
be to take nitrogen as typical and tabulate for it Ref (v) and
v’d(v) from Amagat’s experiments up to 320 metres of
mercury.

Taste VILII.—Nitrogen.

\ | {
v. Ruf(v). | v?o(v). Vv Rof(v). v2). |
Perfect gas 2-233 me ASD 3°20 1188 |
9:22 263 | | 3°69 3°40 1007 |
| 6-91 aT eT, 3°46 3°44 982
5°76 peat? fie LooOu hk one 3°80 1250
4-61 i ee a SUSRe sh |

The values of v*$(v) are unsteady, because the departures from
Boyle’s law are so small that ¢(v) cannot be determined with
accuracy ; but it is clear enough that v*d(v) does not tend to
diminish within the range of volume available, not a wide
enough one, however, to convince us that there is a radical
difference between the course of this function in elements and
compounds. But if we adopt from this Table as it stands the
only pessibie conclusion that v’7d(v) is constant, we shall be
able to justify it by its consequences. In contrast to the
constancy of v?p(v) is the tendency of Rvf (v) at low volumes
to double its perfect gas-value.

In the case of H, and O, the two functions run a similar
course to that for No, but it is a more unexpected fact that

they also do the same for the soup bn methane, CHy, as is
shown in Table LX.

TabBLe [X.—Methane.

v. Rof(v). v7o(v). || v. Ro/(v). v°o(v).
Perfect gas. 3908 peta 5:24 6900
32:3 4°16 | 10:09 5:43 6400
28:2 4°30 5600 || 8:07 5°95 6500
24-2 4-39 6200. 0|| 7:27 6-47 7000
20-2 4-73 6900 6-46 6°80 6800
161 4°73 3200 || 6:05 673 6200

It is evident that we have here to do with v*f(v) asa constant,

229 Mr. William Sutherland on the

that is with an internal virial varying inversely as the volume
down to near the critical volume, and Rv/{v) tending some-
where near that point to about double its value in the perfect
gas state. The course of Rvf(v) in these four gases is repre-
sented by the simple form

nied (8)

which attains the value 2R when v=k. Hence the charac-
teristic equation down to v=; is

2

Peer 2
2 /
a form which I had already adopted for air (Phil. Mag. Aug.
1887). The following are the values for & and 1 :—
H. N.. O.. CH,. AGh geoe
Heong > 20) 2°64 1°78 Dol 2°47[2°11]
Die A100" Ao So 6460 1110[ 910]
The values given in brackets for air are those previously
found by me from Amagat’s data (Compt. Rend. xcix.), but as
these data are not carried to such high pressures as those for
N, and O,, I have calculated values for air by adding to four
fifths of the values for N, one fifth of the values for Oy».
This equation is almost identical with that of Van der
Waals, but it is a little simpler. It gives the following pres-
sures for comparison with Amagat’s experimental results :—

l
”

TABLE X.
Hydrogen. Nitrogen. Oxygen.
Atl7-7° C. PD IUCN = Oh At 14-727G:

v pexp.| peale.| ». pexp. | p cale. v. p exp. | p cale.

166-9 575 56-9 || 13-83 46 45°7 5°73 88°9 89°7

100-1 99 99 6-91 92 91 3°58 | 141 142
60-1 | 176 176— || «461 145 142 2:58 | 201 203
46°7 | 238 241 | 3869 194 188 2°43 | 216 219

| 323 223 226
At 100° C. At 100 C. At 100° C.

1669 14-2 73°3 || 13°83 60 60°5 |} 5°73 123 124

100-1 -).129 123.) 1) OOL 125 124 3°58 204 204
60:1 | 230 229 4°61 200 199 2°58-| 300 301

AG fan ies lal 31 Lat | eS) 270 266 2°43 322 327
| 3-23 320 323

Laws of Molecular Force. 225

The experimental numbers for oxygen are taken from Amagat’s
data-in the Comptes Rendus, xci.

The most delicate test we can apply to our form at high
volumes is, in the case of air, to compare the calculated with
the experimental Thomson and Joule cooling effect. When
I did this with the previous equation for air (e— 2b and
{=910), 1 assumed the difference :7° to exist between the
melting-point of ice on the thermodynamic and gas ther-
mometers ; but, as already pointed out, Sir W. Thomson
having proved this difference not to exist, there must have
been a compensation of errors in the application of the
previous equation. Thomson’s expression for the cooling
effect, applied to our equation for air, becomes

K,d8/dp = 21/RT—k/2,
which gives the following calculated values :—

Cooling effects of air escaping through a porous plug into
the atmosphere under a pressure excess of 2°04 metres

of mercury. |
Pemiperature C............. (alls ae 3976. 92°'8.
Experiment . . . °88 "86 Ue “oil:
Calenlation= {9 2. 2°84 80 ‘ali “5D

The agreement is the closest to be looked for and proves the
accuracy of our equation for air at high volumes.

At low volumes we can test the form for all the elementar y
gases and CH, by applying it to the calculation of the critical
volume, pressure, and temperature in each case. To do this
at the present stage we must assume that our form can be
trusted to hold not only to the critical volume but also a little
past into the liquid region, a legitimate assumption for the
elements, where we have seen the internal virial varying
inversely as the volume, and so giving a guarantee of con-
tinuity, but not legitimate for the compounds where dis-
continuity occurs. Then, applying James Thomson’s idea
of the passage from the gaseous to the liquid state, as pre-
cisionized by Maxwell and Clausius, we have the critical point
determined by the conditions Qp/Ov=0, 0?p/dv?=0

Along with the characteristic equation tees lead to the fol-
‘ih ring values:—critical volume ve= = 38k/2; critical temperature

= = 161/27Rk; critical pressure p.= Al/27 12 ,---to compare with
os experimental values found by Olszewski for O, and Ny
(Compt. Rend. ¢.), by Wroblewski fer air, and by Dewar
for CH, (Phil. Mag. 1884, xviii.).

224 Mr. William Sutherland on the

TaBLe XI.
|
| H,,. N.. Ox CH,. | Air.
| Critical { EXPO: kl ay eee 34 2°5
Wielumme.: {(\cal. sis] -wceeae 3°96 267
Critical EXperere | Geis. —146 | —119 | —995 —140
Temperature. {cale......) —229 —155 | —127 | —99 —149
Critical Sie dee 27 38 37 30
Pressure. Gales Les 25 40 | 32 | 27

The agreement is all that can be looked for in view of the
difficulties of measuring these low critical temperatures and
their associated pressures. With regard to hydrogen all we
know is that Olszewski (Compt. Itend. ci.) has submitted it to
a temperature estimated by him as —220° without a sign of
liquefaction. If our equation is to be trusted, it would indi-
cate that he would need to go some 10 degrees lower before
the only unliquefied gas is conquered. Wroblewski has pub-
lished data on the compressibility of 11, up to pressures of 70
atmospheres at temperatures of —103° and —182° (Journ.
Chem. Soc. 1889), and with these our equation is in accord,
but there is hardly need of tabulated proof.

3. Brief discussion of exceptional Compounds such as the
Alcohols and Ethylene.—To complete our survey of the ex-
perimental materia! on bodies above the critical region we
have to consider Ramsay and Young’s observations on methyl
and ethyl alcohol, and Amagat’s on ethylene. Ramsay and
Young point out that at low volumes the values of Op/OT for
the alcohols are not so reliable as for ethyl oxide, being deter-
mined froma smaller temperature range ; hence our values of
Ref (v) and v*f(vr) are not so reliable as before, but they
suffice to show the exceptional nature of these bodies.

Taste X1I.—Methyl Alcohol.

| v. Ref(v). | v?d(v). OF | Rof(v). | 0d(2).

—————— ee | eo. a’ ee

| Perfect gas. | 1-950 25 3°50 24800
340 2-14 20 3:70 23060
40 2-32 45500 18 3-79 22000
20 2-40 48000 | 16 3:97 21700
i 2-46 46109 | 14 4-18 20900
135 2-56 43700 | 12 4-38 19900
100 2-70 41000 | 11 4-46 19600
70 3-04 42100 | 10 4-53 179v0
50 3:10 33500 | 9 4°58 16700 |
40 3:20 30200 | 8 4-5 15000
30 S37 26800 | 7 4:39 12900

Laws of Moleculur Force. . 225
Table XII. (continued) —Hthyl Alcohol.

| v. Rof(v). | v?¢(v). v. Ref(v). | v?o(v).
| Perfect gas. 1:35 8 343 11300
ee LOS 2 | 165 | 18000 6 334 8600
53-4 1°83 | 15000 4 3°37 6200
30 2°16 15000 3 ddl 5000
2671 \* isk 16000 | 2-4 3°93 4600
18-2 | 2:83 | 17000 2 4:87 4700
12 | 332 15000 18 5°83 4900
| 10 | 341 | 13500 16 7-06 4900
9 _ 3843 12500 1-4 881 4700

The numbers for methyl alcohol do not extend as far as the
critical volume, while those for ethyl alcohol go considerably
beyond it, lying as it does between 3 and 4; but we notice
in both cases that Rv/(v) increases from the limiting gaseous
value, but attains a practically constant value before the
critical yolume is reached. In ethyl alcohol we may say that
the value 3:4 is retained from volume 10 to volume 3, and
moreover this 3°4 is not now double the initial 1°35, but about
2°5 times it. In methyl alcohol the value 4°5 may be said to
be retained constant from volume 11 to 7, the lowest on the
table ; so that it is probable that, as in the case of ethyl alcohol,
this value will be retained down to the critical volume: here
again, also, the 45 is more than double the initial 1-95, but is
only 2°3, not 2°5, times it.

Note that, in ethyl] alcohol, as soon as the critical volume is
passed Rv/(v) begins again to increase rapidly, just as
happened in the case of ethyl oxide. But for our present
purpose more interest attaches to the course of v*p(v). In
methyl alcohol at high volumes it seems to approach a limit
which we may assign as 45,000, and then at volume 16,
where Rvf(v) has risen to double its initial value, v*d(v) has
fallen to almost half of 46,000, but as Rv/(v) continues to rise
v?(v) continues to fall, and still continues to do so even when
Rof(v) has become constant. In methyl alcohol we cannot
follow the changes right down to the critical volume, but in
ethyl alcohol we see that v*f(v) attains at the critical volume
a value which is carried constant into the liquid state, this
constant value being about one quarter of the apparent limiting
value 20,000 at large volumes. The constancy of v°f(v) below
the critical volume is in striking contrast to the rapid variation
of Rvf(v).

I have not sought to represent by formulas the course of
the two functions for the alcohols, as I have doubts about

226 Mr. William Sutherland on the

0p/OT being independent of temperature in the case of the
aleohols ; if it is variable then the values of our functions are
affected with error. In any case we have seen that above the
critical region the alcohols behave differently from our two
typical compounds, ethyl oxide and carbonic dioxide ; in
section 14 it will be seen that in the liquid region, on the other
hand, the alcohols approach the regular compounds in many
respects, but are still exceptional in others. There remains
now only ethylene to consider as to its gaseous behaviour.

Taste XIII].—Hthylene.

v. Ruf(v). | v?9(v). | v, Ruf(v). | v?o(v).
Perfect gas. | 2°22 4-61 4°15 4500
20°75 Ze 5800 415 4:45 4500
16°14 2°78 5320 3 69 4°81 4400
11°53 3°07 5500 322 571 4700
9-23 3°24 5300 | ATT 6-41 4400
6°92 3:58 5100 | 2°65 6°63 4200
576 3°83 4900 | 2°54 787 5000

According to Cailletet and Mathias (Compt. Rend. cii.),
the critical volume of ethylene is about 4°5 ; so that again in
the above table we see Rv/(v) near the critical volume attaining
double its initial value and increasing rapidly thereafter. Once
more, too, we see v’d(v) attaining near the critical volume a
value which it retains constant below; but ethylene is excep-
tional in that this value is not half the limit at high volumes.
The facts in the above table may be summarized in the state-
ments that Rvf(v) may be represented by the form R(1+4/v),
and v’d(v) by the form vl/(v+a); so that the characteristic
equation for ethylene is

k l
oes A a Fe
with k=4°15, a=1°64, and 1=6270.
The form for ethylene is intermediate in simplicity between
that for the simple gases and that for compounds, except that

it has an extra constant. It is also worth noting that the
forms

5 | (5) k/v, and 2k/(v+h)
are special cases of a general form

nk/{v+(n—1)k},

with n=34, 1, and 2.

Laws of Molecular Force. 227

A. Establishment of Characteristic Equation below the
region of the Critical Volume.—Now that we have practically
exhausted the available data of the gaseous state, we see that
by themselves they do not give much scope for generalization ;
but if we can secure an equation applicable from the critical
volume down to the volumes of liquids in the ordinary state,
then, with two equations covering almost the whole range of
fluidity, we shall have a much larger experimental area laid
under contribution for information on the characters of mole-
cules.

Already we have secured one important fact towards the
acquisition of such an equation, namely that below the critical
volume the internal virial term varies inversely as the volume ;
and in the case of ethyl oxide we know its actual amount /2v
with /=5514. We have therefore only to add to 1/2» Ramsay
and Young’s values of pv at different temperatures for different
volumes below the critical, and we obtain the values of the
kinetic-energy term in the desired equation ; we can then
proceed to study how this quantity depends on temperature
and volume, and express the resulting conclusions in a
formula.

As to the form we have this clue, that it must join on con-
tinuously with the previous one where that ceases to be appli-
cable. Now the first fact to notice is that our form for
compounds above the critical region cannot, like that for the
elements, give a critical point by itself at all; for given p
and JT it is not a cubic but a quadratic in v, and hence cannot
give us the three equal roots which are adopted as charac-
teristic of the critical point when we apply the conditions

Op/dv =0, d2p/9v? = 0.

This emphasizes the discontinuity in compounds as contrasted
with elements. However, we know as an experimental fact
that at the critical point 0p/dQv=0, which with the charac-
teristic equation gives us only two relations between the
critical temperature, pressure, and volume. As a third relation
that would perfectly define these three quantities I was led to
believe that the critical volume is proportional to k, and found
cat critical volume v,=7k/6

is the relation which, with the two others, gives successfully
the numerics of the critical state in agreement with ex-
periment. As this will be proved subsequently (Section 10)
for a large number of substances, I will not delay at present to
give examples, except for those compounds for which we have

already found k and J,

228 Mr. William Sutherland on the
Taste XIY.
Critical temperature, T,=120//409 R& ; critical pressure,
p =86 1/409 FP’.

(C,H,),0. | CO,. | “SO, Seas eee:

Critical experon...| Wot 32 155 130 35

Temperature. | cale....... 199 52 | e125 96 36

Critical expetye| 20d. 800 60 87 57
Pressure.

cale....... 293 | 786 56 84 57

The want of accuracy in the agreement in parts of this
table is to be ascribed partly to inaccuracy in the ordinary
determinations of the critical point, as I have already pointed
out that capillary action must sometimes largely affect the
numerics of the critical state when these are determined in
capillary tubes (Phil. Mag. August 1887). Regnault, in
his account of his experiments on the saturation-pressures of
CO,, expressly declares that be had liquid CO, at 42°, which
is 10° above the apparent critical temperature in capillary
tubes ; and Cailletet and Colardeau (Compt. Rend. cviii.)
have shown that although the meniscus between gas and
liquid CO, disappears to the eye about 31° or 32°, yet cha-
racteristic differences between liquid and gas can be proved
to exist several degrees higher than this. Hence an error of
at least 10° is possible in ordinary determinations of critical
temperatures. On the other hand, an error of 5 per cent. in
the value of an absolute temperature of about 40U° as given
by our equation would amount to 20°. Table XIV. is to be
taken in the light of these facts.

We have now ascertained a second property that our
equation for volumes below the critical is to possess : it must
begin to apply when v=7k/6, as the other form cannot apply
below this volume at the critical temperature. At this volume
the kinetic-energy term in our form above the critical region
becomes

BC +12/13),- or 25RT/13-
so that 25R/13 is the lower limit of the term which in the new
equation is to take the same place as Rvf(v) hitherto. Hence
for this term the form

25R(1+F(v))/18

naturally suggests itself, and as F(v) is to vanish when
v=7k/6, we get (7k/6—v) /(v) as a suggestion for its form ;
and it only 1emains from the data obtained, as I have said, by

Laws of Molecular Force. 229

adding //2v to Ramsay and Young’s values of pu for voluines
of ethyl oxide below &, to determine the form of the function
W(v). This was found, after a rather tedious search, to come
out in the simple form

VT(v—£)/B ;

so that finally we have the following as the equation for ethyl
oxide below the volume kf:

with the following values for oe Liane :

fe 2 n/t eo. boob B= lh,
R, k, and / as before.

I propose to call this the infracritical equation. It is to be
noticed that we have introduced only two additional constants ;
so that, as regards number of constants, we could hardly
look for a simpler form.

Above the volume 7k/6 the appropriate form was proved

to be
2k
ae ees

which I propose to call the supracritical equation.
Between & and 7k/6 we have the circacritical form

a/R ye les was
‘y—B otk

This, then, gives the complete representation of ethyl oxide

in the fluid state if we establish the sufficiency of the infra-

critical form, as we now proceed to do. In the next table are

compared the pressures found by Ramsay and Young and
those given by the equation.

py= RIT (14+

Taste XV.—Liquid Hthyl Oxide.

aVolurnel. sce Reece 3-7. 2-75, | 2:25. 2. 16g

- Eee! exper. .| 28 Boo 43 |
ae c.f Tea tet ae 26 45 |
- IPTESSUPey ex peters ee wanccnes || ace 19 43
oC: { sy: | as CHLOR Re Uc ate.6 | km seians 14 48

A IPMESSUPO,EXDGL hs tmaee Bik Rcvess fo) Rescues |! Seseue 19°5
ae SO able ie aade | SA aeost | Gige doe. 4 [hs Ree 20

230 Mr. William Sutherland on the

For the proper appreciation of this table it must be borne
in mind that as soon as we enter the liquid region the pv term
of the characteristic equation becomes the small difference of
two terms, a small percentage error in either of which becomes
a large one in pv. The fact that the above table brings out
is that from 150° to 195° the relation between volume and
temperature given by the equation is so accurate as to make
only the small errors in pressure in the above table. But to
show this more directly, we will now compare the volumes of
the liquid under a pressure of 9 metres of mercury between
O° and 100°, as determined by Grimaldi (Wied. Bezbl. x.) and
as given by the equation. The specific gravity of ethyl oxide
at 0° and under one atmosphere is taken as °7366.

Taste XVI. (p=19°5 metre.)

Temperature ......... 0°. 50°. 100°. 150°.
Volume, experiment......... 1355 1-469 1-630 19
ee eplewlated ss.g.42-:| 1 obe 1-467 1 6383 1-9

This, taken in conjunction with Table XV., shows that the
equation represents with a high degree of accuracy the ex-
pansion of liquid ethyl oxide right up to the critical volume.
It is now to be tested as to its power to give compressibilities
correctly. The next Table contains the calculated compressi-
bilities of liquid ethyl oxide, and also the experimental as
given by Amagat (Ann. de Chim. et de Phys. 5 sér. t. xi.),
Avenarius (Wied. Seidl. 11.), and Grimaldi (Wied. Berdl. x.).
Amagat’s values bad to be interpolated for comparison with
the others.

TaBLE XVII.

Compressibilities with metre of mercury as pressure-unit.

Temperature ......... oe 40°. 60°. 100°.
Menaedios feos. oh: 000200 | 000309 | -v00380 | -000730
AGRE Te ene 000178 | -000817 | -000403 | -000654
Grin as 00207 | -000316 | -00e407 | -000682
at, eee 000183 | -0003G0 | -000392 | -000710

Laws of Molecular Force. Dek

The agreement here is again satisfactory, and we have now
seen that our form, with only two constants in addition to
those characteristic of the gaseous state, can give both the
expansion and compression of the liquid at low pressures ;
but Amagat has measured these also at high pressures up to
2000 and 3000 atmos. (Compt. Rend. cil. and ev.), and the
following Table compares first his values of the mean co-
efficient of expansion between 0° and 50° at pressures from
76 up to 2280 metres with those given by the equation, and,
second, his values of the mean compressibility at 17°4 and at
pressures up to 1500 metres with those given by the equation.
If v, and v, are the volumes at p, and po, then the mean com-
pressibility is taken as (vj—v)/v,\(p2—p1). The apparent
compressibilities given by Amagat are converted to true values
by adding 000002, which he has since given as the com-
pressibility of glass.

TABLE XVIII.

Mean Coefficient of Expansion at high pressures.

pinmetres... ‘76. 380. 760. 1140. 1520. 1900. 2280.
PATNAGAG oe ieee 0s 00170 +-00112 -00091 ‘00077 -00070 -00063 -00056

Hquation™:.:...... 700170 ‘00101 ‘00076 00066 -00056 -00050 -00047

Mean Compressibilities at high pressures.

pin metres ... 76 to 114 to 866 to 654 to 933 to 1218 to 1500

| | | | | |
Amagat ........0. ‘000208 -000143 -000112 -000086 -000070 -000062

Equation ......... 000197 -000128 -000085 -000060 -000046 -000037

As regards expansion the equation goes fairly near to the
truth ; except at the lowest pressures, it gives coefficients
somewhat smaller than the experimental, but it parallels
closely the main phenomenon of the rapid diminution of the
coefficient with rising pressure. But in the compressibilities
there is an increasing divergence between experiment and
equation with increasing pressure, although again the equation
is true to the main fact of the rapid diminution of compres-
sibility with increasing pressure. We may conclude from the
last table that our equation holds within the limits of experi-
mental accuracy up to 760 metres ; beyond that it begins to
fail. A simple empirical modification would adapt the form
to the whole of Amagat’s range, but as it stands it will be
found good enough for our applications.

We will now consider briefly how this form applies to car-
bonic dioxide below the critical volume ; and the comparison

232 Mr. William Sutherland on the

is interesting, as it relates to temperatures both above and
below the critical. The values of the constants are B=54,

TABLE XIX.
Carbonic Dioxide below critical volume.

V olumie nce. ye ees 1526; 23) | 1220s: 1-105: 1-027.
Ei ° Pressure, ne 150 274 cy
i 0.4 Wie lei 24 qipns266
or Pressure, exp....... 69 126 187 320
35° 0. { eh ag ae 120 184 320
180 G, { Pressure, exp...) cece | teens 99 200

5 -of CC A RR (am ere o7 208 |

|

The agreement is within the limit of experimental error at
the high pressures. Cailletet and Mathias have determined
(Compt. Rend. cii.) the density of liquid CO, at various tem-
peratures under the pressure of saturation. Here is a com-
parison with a couple of their results :—

Temperature. . . —34°. | G2:
Volume—Cailletet and Mathias . °946 1:087
ait SellQUAtiON Seka ae tli: sn eee 1:086

As far as compound gases are concerned, the applicability
of the form for volumes below the critical has now been de-
monstrated in two typical cases. The elementary gases have
now to be considered as to their behaviour below the critical
volume. The data are again those furnished by Amagat
(Compt. Rend. evii. and Phil. Mag. Dec. 1888) on the com-
pressibility of these gases between 760 and 2280 metres of
mercury. Our study of these bodies above the critical volume
has given us the knowledge that the internal virial term below
k must be J/v, and the kinetic-energy term at the critical
volume is 38RT/2, and with these guides the complete form
required is soon found from the experimental numbers. It is

3k—~v y
po = §RT(140% —

C—

with the following values for the additional constants B
and b :—

k. B. b.
Enya rocen. tlh 2. ok? 43 "480
Nitrogen. =s = 2°64. “81 "420
Oxyoen OL eS “604 "4415

Methane .. . [5°51] EP59] > ee

~ Laws of Molecular Force. 233

The approximate equality of the values of the constant b is
worth noting. I have also reproduced here the values of k at
the side of those for @, in order to point out that @ is nearly
k/3 in each case. Amagat has not published data for methane
at volumes below the critical region, but the numbers given
in brackets for methane were obtained indirectly as explained
below. These relations of 8 and 0 give our equation such a
degree of simplicity as largely to establish the soundness of its
form. The next Table shows the degree of accuracy with which
it represents the experimental facts.

TABLE X X.—Oxygen at high pressures.

MHOUUTIIG: “J cekceste esses 1277. | 1:097. | 1-008. 949, ‘905.
| 150 ¢, { Prossure, exp....... 760 | 1140 | 1520 | 1900 | 2280
: eee 79 | lia | sipia | 1363") 2096

The agreement is quite as good for hydrogen and nitrogen.
By means of this equation we can calculate the volumes of
-a gramme of liquid nitrogen and oxygen at their boiling-
points under a pressure of *76 metre, for comparison with
Wroblewski and Olszewski’s determinations of the same
(Compt. Rend. cii.; Wied. Bebl. x.; and ‘ Nature,’ April
1887).

Oxygen. Nitrogen.
ates Wroblewski. . °85 1:20
eae Olszewski . . °89 at — 108
Meuation:... (7; 20 1:26

The equation is seen to give the volumes of these two bodies
at these low temperatures within the present limits of experi-
mental accuracy, and accordingly it covers a range of 2000-
metres pressure and almost the whole experimental range of
temperature. In the case of methane, if we take Olszewski’s
value 2°41 for its volume at —164°, and assume 0 is the mean
of 6 for H,, Nz, and Oy, then we can calculate the value of 6
which is tabulated above.

To ethylene above the critical region we had to assign a
special form intermediate between that for ordinary compounds
and that for elements ; so that we had better do likewise for
its infracritical equation, which I have cast in the form

Ty Ay l k
Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893. R

934. Mr. William Sutherland on the

with B=56:5, 8=1°53. For the elements we had v,=dk/2,
for ordinary compounds v,=7k/6 ; so that to make ethylene
intermediate v, is taken as 5k/4, all these being of the general
form (1+2n)/2n, with n=1, 2, 3.

With the values of the constants B and 6 given above as
derived from Amagat’s results at high pressures, we can
determine the density of liquid ethylene; at —21° under
saturation-pressure the density is ‘414, identical with the
experimental value of Cailletet and Mathias (Compt. Rend.
cli.).

It will be as well at this stage to extract clear from among
the argumentative detail the most important results so far
obtained.

First, in the elements the internal virial varies inversely as
the volume over the whole experimental range.

Second, in compounds there is mathematical discontinuity
in the value of the internal virial at volume & ; from volume k&
downwards the internal virial varies inversely as the volume :
from the volume & upwards it tends towards variation inversely
as the volume as the limiting law, the limiting constant being
double that which holds below the volume & ; between the two
limiting cases the internal virial of compounds varies inversely
as (v+h).

Third, a fact of the highest importance in connexion with
the kinetic-energy or temperature term in the equation arrests
our attention, namely, that the coefficient of T in it, or the
apparent rate of variation of the translatory kinetic energy
with temperature at constant volume, attains near the critical
volume double its value in the gaseous state, and below the
critical region increases rapidly with diminishing volume (see
column Rvf(v) in Table I.), becoming at ordinary liquid
volumes as much as ten times as large (see coefficient of 'T in
infracritical equation). Now the specific heat of liquids at
constant volume, which is the rate of variation of the total
energy with temperature, is rarely much more than twice that
for their vapours. Hence we must seriously consider the
interpretation to be put on the different terms of our equations.

5. A short digression on the general interpretation of Clausius’s
Equation of the Virial.—Returning to Clausius’s theorem of
the virial,

2 pe = %gmV?—F.3 >> Ry,

we see that strictly the kinetic-energy term includes not only
the energy of the motion of the molecules as wholes, but also
that of the motion of their parts, and at the same time the

~ Labs of Molecular Force. 235

internal virial includes the actions between the parts of the
molecules as well as those between the molecules. Calling
these actions the chemic force, we can write the theorem
thus:

3 pv = the total kinetic energy—chemic virial—virial of
molecular forces.

Now in the usual treatment of the equation it is assumed
that the chemic virial is equal to that part of the total kinetic
energy which is due to the motion of the parts of the mole-
cules relatively to their centres of mass, and neutralizes it in
our equation, reducing it to

3 pv = translatory kinetic energy of molecules as wholes
—virial of molecular forces.

But if we retain the full equation, and assume that the virial
term we have been finding for various bodies is the true virial
of the molecular forces, and includes none of the chemice virial,
then the term usually regarded as the translatory kinetic
energy of the molecules as wholes is really the total kinetic
energy minus the chemic virial.

Let E be the total kinetic energy of unit mass, V the virial
of the chemic forces, and P their potential energy ; then, above
the critical volume,

and

+h

which in the limiting gaseous state becomes 3R/2.
Also

0

or

the specific heat at constant volume.
Below the critical volume,

9 eee VT ki—v
E V=§R'T(1+ 4 =e)

S(E-V)=gR (1+ =)

API) IK

0 AY == Supy 9 Aa il ki —-y

and, again,
| 0 (H— —P)'=K..
R 2

or

236 Mr. William Sutherland on the

Now we can calculate K, from the experimental values of
K, by the relation

Let us then make a comparison in the case of ethyl oxide,
using E. Wiedemann’s value “3725 for K, for the vapour at
0°, and Regnault’s value ‘529 for the liquid at 0°; then, con-
verting to ergs per degree C., we get

Vapour at 0°. Liquid at 0°.

fe) ree : 16 Fe 6
sq) = - I-65 5ca0 15°3 x 10°,
Sauce S. (E—P) = 144 x10® 17-9 108,

Thus we see that while in the liquid 6(H—V)/OT is nearly
equal to O(E—P)/OT, there is a great difference in the
vapour :

0(V—P)/d9T=12'7 for the vapour and only 2°6 for the liquid.
Or, while K, is nearly the same in the two states, 6(H—V)/oT
has in the liquid state increased to nine times its value in the
vaporous. We have here, therefore, an interesting opening
into the regions of chemic force ; but meanwhile we must
restrict ourselves to the question of molecular force at present
in hand, calling attention, however, to the fact that our energy
term in its two forms for elements and its two forms for com-
pounds is well worthy of the closest study. It summarizes a
lot of information about the internal dynamics of molecules—
perhaps about the relations of matter and ether; but these
would need to be extracted by a special research on the term
and its relation to our experimental knowledge of specific heat.
It is worth mentioning here that Clausius’s equation of the
virial, as usually applied to molecular physics, takes no account
of the mutual action of matter and ether—an action which we
know must exist, from the radiation of heat by gases as well as
by liquids and solids. According to ordinary views of the
eether this may be neglected, on account of the smallness of
the mass and of the specific heat of the ether; but it is well
to remember that we are neglecting it.

6. Consideration of Van der Waals’s generalization.—We
are now in a position to consider how far Van der Waals’s
generalization holds, namely :—If the volume, pressure, and
temperature are measured for each substance in terms of the
critical values as units, then one and the same aw holds for
all substances.

Laws of Molecular Force. Dad

In the first place, we see from what has gone before that
the same law cannot apply to both elements and compounds,
nor can the alcohols and water follow the same law as regular
compounds. “s

In the case of the elements and methane we have the critical
volume, pressure, and temperature given in terms of R, J, and
k by three relations (see end of Section 2),

4 f 16 J
v= 8k/2, Pe= 97 re T= 57 Rk

Whence, in the supracritical equation replacing R, J, and & by
their values in terms of v,, p,, T,, we get

po 18 ee 1 nee

3

which shows that when the critical values are made the units
in the measurements of the variables, one and the same law
holds for the elements above the critical volume.

Below the critical volume we have

We have seen that 6 is nearly the same for these bodies and
that 8/v, is approximately constant, so that below the critical
volume the elements and methane all follow approximately
the same law.

In the case of compounds, we have (see Section 4, at the
beginning)
| 36 1 120 1
M= THC, P= 409 ~°= 409 BP
with which, eliminating R,’, and / from the supracritical
equation, we get

—+1

foe wal) Ab 2 409 1
pe rob s/o ai ePbsot st
( U )

6 v

Prose le

ee

Hence, above the critical volume the compounds follow the
same law among themselves.

In the same way, below the critical volume we get for
compounds :—

238 Mr. William Sutherland on the

7 es
po 20 2 Ti Vt
se age es Bu BR

One and the same law holds for compounds below the
eritical volume only if B varies as the square root of the
critical temperature, and if 8 is proportional to the critical
volume : in the elements we have found the latter condition
to hold approximately, and so we are prepared to find it do so
for compounds. The following Table compares B with /T,
and 8 with k, which is 6v,/7 for the five compounds for which
we haveas yet found &. The values of B and 8 for NH; and
N.O were obtained from Andréeff’s data for the expansion of
these bodies as liquids (Ann. Chem. Pharm. ex.) and for SO,
from Jouk’s (Wied. Bezbl. vi.).

TABLE X XI.
| |
he. | B. k/p. | B. | B/N Te.
(CAPO 4066 | 111 | 37 | \@sqgiaess
OO, 20 ce 176 | -69.| 40 | 54 7p
SOe NS cat, ai 208 | ‘55 38. | 36
INET Schen Ms 4-8 1:22 | 39 70 36
NEOR Sate Lage 2:3 66 | 35 55 31

In these bodies we find a fair approximation to propor-
tionality between @ and & on the one hand, and between
B and /T, on the other; to the same degree of approxi-
mation Van der Waals’s generalization can be applied to
compounds below the critical volume (excluding of course
such exceptional bodies as the-alcohols and water).

The accurate statement of the generalization ought then to
be as follows :—When the variables are expressed in terms of
their critical values as units, then down to the critical point
compound bodies with certain exceptions have all one and the
same characteristic equation, but below the critical point they
have closely similar but not identical equations, -

It is a remarkable tact that Van der Waals should have
been led to his valuable generalization by means of a form of
equation which completely fails to apply to the substances
which are the subject of the generalization. Asa point in the
history of this branch of molecular physics, it calls for mention

that Waterston, in the Phil. Mag. vol. xxxv. (1868), had prac-

Laws of Molecular Force. 239

tically discovered the generalization, and expressed it in its
most striking aspects by means of several diagrams for a
number of bodies ; but the verbal expression of his results was
so unsystematic, and withal so crabbed, that his work has been
overlooked. 3 |

There is one typical application of the generalization which’
is of special importance—to the relation between pressure and
temperature of saturation. If with the aid of our equations
we trace the complete isothermals for temperatures below the
critical, we shall get curves with the James Thomson double-
bend as shown in Ramsay and Young’s isothermals for ether
(Phil. Mag. May 1887).

According to Maxwell’s thermodynamical deduction, the
pressure of saturation at a given temperature is that cor-
responding to the line of constant pressure which cuts off
equal areas in the two bends, a result which Ramsay and
Young verified by actual measurement on their curves.

Let v3 and v, be the volumes of saturated vapour and liquid
at pressure P and temperature T; then Maxwell’s principle
gives us that the pressure of saturation is defined by the three
equations :—

P(m—a)= | pate

2k l
Py, = RI(1+— 5 Tose

VT Lk—v ae,

= 25 gees f LB) | ee

Pu, = #RT(1+-4, — aa

v3 is given in terms of P and T by a quadratic, and can

therefore be eliminated from the integral when evaluated ;

v, is given by a cubic, but as Pv, can for practical purposes

be put 0, a very close approximation to v, can be obtained also

from a quadratic. The resulting relation between P and T,

which is the law of saturation, involves the constants R, &, J,
B, and £.

The actual evaluation of the integral would of course
proceed in three stages, corresponding to the supra-, circa-,
and infracritical equations. The law of the integral in the
first stage from v3 to 7k/6, with critical values of the variables
as units, would be the same for all compounds ; and we have
seen that the integral in the other two stages will follow
approximately the same lawin all cases. Hence if saturation
pressures and temperatures are expressed in terms of the
critical values, the law of their relation will be approximately
the same for all regular compounds.

If this were an absolutely accurate relation, the best means

240. Mr. William Sutherland on the

of testing it would be to take Regnault’s formula, with one
exponential term, |

loot — atba*,

and by a simple recalculation from his values for a, b, and «,
to cast it in the form
T/Te

log p/p, = et+dy"”,
proving that the constants e, d, and y are approximately the
same for all compounds. But the objection to this plan soon
becomes obvious on trial, as the formula owes its empirical
convenience to tLe power of adjustment amongst the con-
stants ; and the same difficulty would be experienced with
any purely empirical equation.

Accordingly, to test this matter, I have thought it best to
compare the pressures of a number of bodies at temperatures
which are constant fractions of their critical temperatures,
such as ‘6T,,°7'T,, and so on. The ratio of the pressure of

any substance to the corresponding pressure of ethyl oxide
ought to be approximately the same for that substance at all
values of the fraction. Great uncertainty attends the mea-
surement of critical pressures: an error of 20° in the critical
temperature is not a large fraction of its value measured from
absolute zero, but it makes a large difference in a saturation-
pressure, and the critical pressure is the limiting saturation-
pressure. In the subjoined Table the critical-pressure ratios
are given for what they are worth in the column T.,.

TABLE XXII.
Ratios of Saturation-Pressures at constant fractions of the

critical temperature to the Saturation-Pressures of Ethy]
Oxide at the same fractions of its critical temperature.

|

Fractions of Te.

Te.

6. 65. otk ‘75. "3. OD: HilaasO:
ACEEONE J24ec0-- 0° 506 ‘OF | "90) | 0272 04s tenes 1-4
Methy] oxide...... 404 | 1°7 15 14 14
SOs aeree are: ADS AN 7 i ale ar hes, 17 Li, sen jigileeee
ENDED go eee esotes cok 404 | 26 | 26 | 25 | 2:5. >| "2: sila ee
LS Sheer ets aes 373 —- | oO | 32141928 Bee sop 2°6
CON: poet. dhe 5 305 se be v3. at LSet) eae
NSO eet bucesseace 308 = fe: 5a sae 2°44) 1B ee eat
OS casedaunaeoh sedans: Ow ole 2. || Dd. alee = epee f°
(0) OVS caacmaaace DOO Oe RIES LM, cS! 1 aleD sep 16
CHOIR Breve 5387 | 16 5s) | el 1-4 1-3 16
C15 E01 |: aan ADA a lelenal Gago p | vile 815 Mea ax 2:1
(ORE (3 ©) ranean a 456 | 1-4 1-4 lies} [2 Slab 1-5
Ca OB Tas. cczscase DOO a apd Oa iateS eae lG APalcs 1-4
BenzeneO, Hi, ...). 7060 4) Adele 12 | a2 Lat 1-4

Laws of Molecular Force. 241

This table makes it clear enough that, in applying Van der
Waals’s generalization below the critical volume, we have to
do with a first approximation only. The curves for all these
diverse bodies excepting CS., while not identical, would form
a compact bundle about a mean curve from which each body
would have its own characteristic departure ; and this is just
what our study of B and 8 in Table XXI. should lead us to
expect.

7. Five Methods of finding the Virial Constant.—The first
method is that which we have already exhausted, namely, by
means of extended enough observations of the compression
and expansion of bodies in the gaseous state.

Second method : to obtain the virial constant / from one
measure of the compressibility and of the expansibility at the
same temperature of the body as a liquid.

Writing our infracritical equation thus,

RT JT eae) _ l
at) (1+ B 'v—B/ Qv?’
op __ BR 38R VT Bed bP Ry 3p

Aw. 2 B.t7=6 2 2eE oe OT

But at ordinary low pressures the term p/T is a negligible part
of this expression, and we can write

Oia 6 pide

OT 4° wT QW
Now

Op _ ov /dv_ _m dT _%
or Oo Open 4 loo oO

where a and w are the coefficients of expansion and the com-
pressibility at T as usually defined.

81 _ R_wa,
Ae Do aie
4. a
1= 5 (wo+$R) of = 5 (wo +39R Jo.

In addition to giving usa value of J, this last equation gives
a test as to whether the equation applies to a body or not, as
the expression on the right-hand side is to be constant at all
temperatures if ~ is measured at low pressures. But on

|

| O,H,, (Grimaldi)...! 8520 |

————q“— —— ——— Se ——___

242 Mr. William Sutherland on the

account of the experimental difficulties hitherto met with in
the measurement of w, the equation gives no very delicate
test, although it might with the improvements in accuracy
made within the last few years. In addition to ethyl oxide,
the two substances for which we have measurements of both a
and p over the widest range of temperature are ethyl chloride,
studied as to expansion by Drion and as to compression by
Amagat, who has corrected Drion’s coefficients of expansion
for change of pressure, and pentane, studied by Amagat and
Grimaldi. The following are the values of / calculated from
the data at different temperatures for these two substances,
with the megadyne taken as unit of force.

Temperature C..../ 0°. | 11°. | 139, 60°; / Bee:

|

| ee ed

| 7450 | 7230 | 8000 | 8300 | 9250

| Cli GAmagat)...)0 2. | ce | 9200). | 2. | or

|
VORTEC Rees naee eee allel aoeabeys |

|

5450-4 "Es | 5270

|

This comparison has been made to show how, from mea-
surements of liquid compressibility at present available, we
can get only a fair idea of the value of /, but not an accurate
measurement of it.

Amagat has determined the compressibility of several other
liquids at different temperatures (Ann. de Chim. et de Physique,
sér. 5, t.xi.) ; so have Pagliani and Palazzo (Wied. Bezbl. ix.)
and de Heen (Wied. ezdl. ix.), but their discussion would
bring out nothing more than the above comparison has. De
Heen’s results would appear to make / diminish with rising
temperature in every case; but he measured his com-
pressibilities in comparison with that of water at the same
temperature, and to calculate their values used Pagliani and
Vincentini’s values for water (Wied. Beibl. viii.), which make
the compressibility of water much more variable with tem-
perature than Grassi’s. If we used Grassi’s values in
de Heen’s experiments, / would remain. nearly constant.
We will accordingly use the compressibility-method of cal-
culating / subsequently, only to illustrate the general agree-
ment of. values derived from purely mechanical experiments
with those found by the more accurate methods to which we
now proceed. The values found by this second method are
tabulated later on in Table XXIV.

Third method of finding the virial constant 1: from the
latent heat. If we differentiate with respect to T our equation

Laws of Molecular Force. 243

for = eration -pressures (see Section 6),

P(v—v%)) = " pdv,

vy V7}

we get

dP avs a) dv oy dv,
av (3 =) +P( (7 aT )=(°Ss ah do ot P (in dT

CA ae ae 30p
aT (v3 v1) =|" spo:

Now from thermodynamics we have the relation
JXN=(v3,—v,) TdP/aT,
where X is the latent heat,
oe ee
a. oe JA= : Tsp

which of course could have been written down immediately,
for if we write it in the form

Ir =|" {Gi oH )dv+ PoP,

we remind ourselves that the latent heat of evaporation of a

liquid is the heat supplied to neutralize a Thomson and
Joule cooling effect.

We must evaluate the integral in three stages,

Op 1 OP ap
Jf. TSpee= | tan o+ {08 T= pao | Toh ike

using in each integral the ae that holds between its
limits.

In the first,

vutk otk
Op _ Ry, 24
or A 7)
Op - l
Cpe Baar,

B ‘v—p

0st AG i er5 )-

944 Mr. William Sutherland on the

In the third,

T kv l
po=RT(1+¥, =)

19h = RT
a Pt Op 2)7 QW
Hence

n= | "(p+ oy Jao | ° {3 ( (p+ a) + Se
+) (CG sa)- 5 he

03 1(*# % Idy 1(” Idv
=| “piv + |, par | loth) * ie +h)
3 Céldv 3|

2 Vv

4 | Oe v
164 l 2v5 l 2K!
= P(v3—%) 2) pdv + 7,08 ae) 3 9; °S wad
+(- 2 i) oe
v 4. v7} k 2 aa
We must now evaluate the only integral that has been left
unevaluated,

te (LED ge ¥ dv (ld
fi pav= | =, (lt 9) es le

1 1

(aa it
=RTlog= + DT, se Flog”)
il

]

8 2 ee
Qk! byt :)

— 7°74, Ree

These last expressions are the only ones that introduce B and
B into the value of JA, and it is desirable to remove these
two constants. At low pressures we can neglect the pu term
in the infracritical equation, and we get

RT VT ad. oe By} v%31—-8

=e Co ot ae
removing B by means of this we get

pubig
TN=P(vy—vy) + Glog, S +5(5- i)

1G wen) =2 (PBB : =)

Laws of Molecular Force. 245

We can now remove # and greatly simplify this equation, if
_ we apply it to latent heats near the ordinary boiling-point
Ty. The last term taken in its entirety has a small numerical
value compared to the rest, so that in it we can make approxi-
mations without any sacrifice of accuracy worth considering :
we have seen that 6 is approximately proportional to k (see
Table X XI.) and v,, the volume of the liquid at the boiling-
point, may be assumed to be approximately proportional to /
the volume at the critical temperature, and k'=7k/6: hence
the coefficient of (//2v,—R’T) in the last term is approxi-
mately the same for all bodies and we can evaluate it for
ethyl oxide; call it C. Again, in P(v3—v) neglect v, and
assume the gaseous law Pv,;=RI,. And further, & is small
compared to v3, so that 2v3/(v3+) is nearly 2, and its value
for ethyl oxide can be applied to all bodies. B! =25R/13.
Hence multiplying by M the ai weight we can write

M/ Pie E 2Vs
= 5(~ 1) tle = + 5 =} JU+MR (7 5 0—1)t.
MRis the same for all bodies, and T, is the absolute boiling-
point. This equation still involves & as well as /; when & is
not known we must eliminate it by means of our previous
assumption, namely, that k is proportional to v,, which we
know to be approximately true; in so far as it is inexact it
will introduce inexactness into our calculation of 1. Accord-
ingly in symbols k/vy=7, where 7 is the same for all bodies,
and can be found for ethyl oxide. Making the numerical
reductions we get
Ml/v,=66°5 MA—101T,

as the equation which gives J in terms of the megadyne as
unit of force, when A is the latent heat of a gramme in
calories and v, its volume in cubic centimetres at the absolute
boiling-point T,. ‘This equation will be abundantly verified
afterwards in Table XXIV.; but meanwhile, if to test it we
apply it to calculate the latent heat of ethyl oxide, we find
X= 83'4, whereas several experimenters have agreed in an
Betimate of about 90; but, on the other hand, Ramsay and
Young (Phil. Trans. 1887) have made a special study of the
terms in the thermodynamic relation JA= (v3—v,) TdP/d dhe
and have so calculated values of % almost up to the critic: al
temperatures, their value at the boiling-point is 84°4, and
there is the same amount of discrepancy between their values
at higher temperatures and Regnault’s experimental deter-
minations. Yet Perot, who has made an elaborate study
(Ann. de Ch. et de Ph. sér. 6, t. xiii.) both of X experimentally

946 Mr. William Sutherland on the

and of the quantities involved in its calculation by the ther-
modynamic relation, has found the most perfect harmony
between the results of the two methods. Now at 30°C.
Perot gives as the saturation-volume of the vapour 400°4, and
the saturation-pressure °635 metre, while Ramsay and
Young’s values are 374 and ‘648 metre; but if ethyl oxide
were a perfect gas, under Perot’s pressure of *635 metre it
would have a volume of 400°8, almost identical with his value:
yet we cannot imagine that ethyl oxide under this pressure
and at this temperature is so nearly a perfect gas as this would
imply, unless there is some remarkable discontinuity in its
behaviour at high volumes. Accordingly, in ‘spite of the
thoroughness of the researches of both Perot and Ramsay and
Young, we are on the horns of a triple dilemma, from which
only some experimental repetition can deliver us, and de-
monstrate where the cause of these discrepancies lies. Wiillner
and Grotrian (Wied. Ann. xi.) have put on record the results
of experiments which indicate the cause; they find the pressure -
of condensation measurably different from the ordinarily
measured saturation-pressure,—a fact explaining the difficulty
of measuring v3; accurately, and showing also that the values
of dP/dT are not so reliable as usually supposed.

Our last equation is verified by, and shows us the cause of,
an interesting relation that has been independently discovered
and expressed in different forms, between the molecular latent
heat and the boiling-point, by Pictet (Ann. de Ch. et de Ph.
sér. 5, t. ix. 1876), ‘Trouton (Phil. Mag. xviii. 1884), and
Ramsay and Young (Phil. Mag. xx. 1885), namely, that the
molecular latent heats of fluids are nearly proportional to
their absolute boiling-points. Now we have seen that
T,=1201/409Rk (Section 4), and I have noticed that a large
number of substances have their ordinary absolute boiling-
points nearly equal to 2T,/3, and & is nearly proportional to
v%, say is equal to 2°8v,, as it is for ethyl oxide. Hence we
have

3 ere WAU)
2 409 R282,’

oe M/= 14°3 M RyT, = 1190»,T,,

when the megadyne is the unit of force; hence from our
equation for M/ in terms of X we have

— 1190T,=66°5 MA—101 T, ;
©. 1291T,=66°5MA or MA=19-4T,,

~ Laws of Molecular Force. 247

or the molecular latent heat is proportional to the absolute
boiling-point.

(It is to be noted that M/=1190,T, gives a rough means
of obtaining / from the boiling-points and the volumes at the
boiling-points of liquids, which might be convenient when
better data are wanting.)

Robert Schiff (Ann. der Chem. cexxxiv.) has made the
most accurate determinations to test this relation between
molecular latent heat and boiling-point. For 29 compounds
of the form C_H,,0,, from ethyl formiate up to isoamyl vale-
rate, he finds MA=20°8T, in the mean, the greatest departures
being 20°4 for propyl isobutyrate, and 21:1 for propyl for-
miate ; for 8 hydrocarbons of the benzene series he finds a
mean coefficient 20 with 19°8 for cymene and 20:6 for benzene
as the greatest departures. To these 37 examples we will
add the following from Trouton’s paper, doubling his numbers,
as he used density instead of M.

Taste XXITT.—Values of MA/T,.

| O,H,Cl. CCl, | CS,. |

|
CHCl,. AsCl,. | SnCl,. | SO,,.
21 29 | 21 a1 20 | 23 Pin |
| |
| | | |
(C,H,),0. (C;H,,).0. (CH,).CO. C,H. | (C,H,),C,0,,.
22 24 23 22 | 23

The mean value of the coefficient is higher than that deduced
theoretically above (19:4), because in round fraction we wrote
T,=2T,/3, but the general truth of the relation is well enough
brought out.

Fourth method of finding the virial constant /: from the
critical temperature and pressure. Now we have (Section 4),

T,=1201/409Rk, p,=361/409 k?,
*. T,/p,=10K/38R and 1=409R?T?/400 p,,

this is for compounds; for elements/=27R?T?/64p,.. Where
both the critical pressure and temperature are known, this
gives / theoretically with accuracy, but practically the diffi-
culties in measuring the critical pressure introduce inaccuracy.
In the relation T’,/p,=10%/3R, as R varies inversely as the
molecular weight, we see that the molecular domains (Mole-
cular volumes) of bodies at the critical temperature are

948 Mr. William Sutherland on the

proportional to the quotient of critical temperature by critical
pressure, a relation which Dewar has proved experimentally
(Phil. Mag. xviii. 1884) for 21 volatile bodies, for which he
has determined and collected the data. ‘These with other
data since published enable us to determine values of / for
certain bodies for which the other methods are not available.

As there are many more critical temperatures determined
up to the present than critical pressures, and as we have seen
that an error in the critical temperature is of less relative
importance than an error in the critical pressure, we can
make ourselves independent of critical pressures with ad-
vantage, by employing the approximation that has already
been useful to us, that k is proportional to the volume of the
liquid at the boiling-point or k=2°83v,. Then

M/=409MRT /120= 800T 2;

approximately, with the megadyne as unit of force. This is
a more accurate form of the relation M/=1190T,v, given

above, in which we assumed the approximation T,=2T,/3.

8. Fifth or Capillary Method of finding the Internal Virial
Constant, with digressions on the Brownian movement in
liquids and on molecular distances.—So far we have been
proceeding on a purely inductive path, with two deductive
guides in Clausius’s equation of the virial and in the law of
the inverse fourth power, which requires that the internal
virial should vary inversely as the volume. JBut now, in
passing on to our fifth and most useful method of finding /
from surface-tension, we must employ a deductive relation
between / and surface-tension, furnished by the law of the
inverse fourth power. In a previous paper (Phil. Mag. July
1887) it was shown that if the law of force between two
molecules of mass m, at distance 7 apart is 3Am?/r*, then the
internal virial for the molecules in unit mass is 57Ap log J./a,
p being density, and L a finite length of the order of magni-
tude of the linear dimensions of the vessels used in physical
measurements, a being the mean distance apart of the mole-
cules. ‘The ratio L/a remains the same for a given mass
whatever volume it occupies, but I also assumed that J/a is
so large a number that log L/a would hardly be affected by
such large variations as might occur in the value of L when
the behaviour of a kilogramme of a substance was compared
with that of a milligramme. ‘T'o remove the haziness of this
assumption, I will now make a more accurate evaluation of
the internal virial. } 7 :
~ By definition it is $.4.223Am?/7*, and we will evaluate it

Laws of Molecular Force. 249

for a spherical mass. To cast it into the form of an integral,
take any molecule m amongst the number n in a spherical
vessel of radius R; gather it to its centre as a true particle
and spread the remaining n—1 in a uniform continuous mass
separated from m by a small spherical vacuum of radius a, so
chosen that the virial of m and the continuous mass is the
same as that of m and the n—1 molecules.

Suppose m at the point O, and the centre of the vessel at -
C, and let OC=c. Take OC as axis of x and any two rec-
tangular axes through O as axes of y and z. Let polar
coordinates r@q be related to these in the usual manner.
Then the equation to the surface of the sphere is

(a—c)*? +y?+22=R? or r?—2er sin 0 cos 6 +c? —R?=0.
Let 7, and r, be the two roots of this equation in 7 so that
= R*?—c?. Then m?/r* can be replaced by

mpr® sin 0 dé do dr/r*,
and
m?/r> by {\\mp sin 6 d@ dd dr/r.
If we integrate with respect to 7 on oneside of the plane yz from
ato 7, and on the other from a to 7, and add the two results,
then we have to take @ and ¢ each between 0 and 7, thus:

Lm2/r° =| ‘ome sin Od 0 db [| dr/r Dy dj],
0/0 a a

The two integrals in brackets give

log 7 7,/a?=log (R?—c?)/a?.
Hence

2m?/r> = 2armp log (R®+ ¢?)/a?.

Lo perform the second summation we can first add the values
of the last expression for all the molecules at distance ¢ from
the centre of the vessel, and write the result in the form

2apAmpc*dc log (R? —c?)/a?,
and we then have

R-a
4. 42233Am7/ = cnt e’'de log (R? —c*)/a?.
0

Kyaluating the integral, this becomes

a

1 ; 2 R?, %*R+a
BAnip? | 5 (R—a)*log a LS (R—a)?— 3 R°(R—a) + =z log },
in which, neglecting unity in comparison with the large
number R/a, we get
A7**R?{4 log 2R/a—16/3}.
Phil. Mag. 8. 5. Vol. 35. No. 214. March 1898. S

250 Mr. William Sutherland on the
But if W is the total mass in the vessel, then

W =47r'p/3,
and we get
Warmp{3 log 2R/a—4}.

When W =1 the first term of this becomes identical with the
value of the internal virial previously given, with 2R written
instead of L. Replacing R by its value in terms of W and p,
we get for the internal virial of mass W,

WaAmp(log 6W/mpa*—4).

As pa® is constant, we see that for a given mass the internal
virial for molecular force varying inversely as the fourth
power is rigorously proportional to the density, but it is not
purely proportional to the mass. Although the number
6W/mpa’ is a large one, and has a logarithm varying slowly
with W, yet large enough variations in W can affect it
appreciably, as we see if provisionally we accept Sir W.
Thomson’s estimate of 2 x 10~-* centim. as the lowest possible
value fora. Suppose 7p=38, then 6W/7pa’ is 10°°W/4, and
if W is 4000, 4, or :004 grm., then the values of log 6W/zpa’
are as 30, 27, and 24, and we have a larger mass variation of
the internal virial than is likely to have escaped detection in
its effects, such as a difference in the density, expansion, com-
pressibility, latent heat, and saturation-pressures of a liquid as
measured on a milligramme, from their values as measured on
a kilogramme. The raising of this difficulty suggests to us
in passing that there exists a department of microphysics in
which little has as yet been done by the experimenter, and
that great interest would attach to a research determining
when a mass variation of the properties usually spoken of as
physical constants actually sets in. ;

But meanwhile we must scrutinize more closely the meaning
of our last result. According to the views of Laplace (and
of the early elasticians), if a plane be drawn dividing a mass
of solid or liquid into two parts, then, in consequence of mole-
cular force, the one part exercises a resultant attraction on
the other, and this has to be statically equilibrated by a
pressure (called the molecular or internal pressure) acting
across the plane, a conception which is necessary in any purely
statical theory of elasticity. Adopting for the moment this
mode of viewing things, we see that our result amounts to
this, that the internal pressure is measurably greater at the
centre of a kilogramme than of a milligramme. |

But if we try to carry out the kinetic theory in its integrity,

Laws of Molecular Force. 251

we must reject the idea of a statical pressure, and replace it
by its kinetic equivalent of a to and fro transfer of momentum ;
this may take place as a quite indiscriminate traffic of indi-
vidual molecules across the plane, or as such a traffic modified
by the existence of streams of molecules in opposite directions.
If streams, or motions of molecules in swarms, actually exist
in fluids, then our interpretation of the equation of the virial
would have to take account of their existence. The kinetic
energy of the motion of a swarm as a whole would not count
as heat but as mechanical energy, and for the amount of it
we should have approximately the kinetic energy of the swarm
motion equal to the virial of the forces between the swarms.
Therefore we require to divide the energy into two parts,
that of molecular motion inside the swarm constituting heat
and that of the swarm ; in the same way the internal virial is
divided into two parts, one within each swarm, the other be-
tween the swarms. But the swarms could on the average be
regarded as equivalent to spheres of radius L, where L must
be supposed nearly independent of mass and liable to the same
variations with temperature and pressure as the linear dimen-
sions of any quantity of the liquid, so that L is proportional
to a, and our expression (theoretical) W Azp(3 log 2L/a—4)
for the internal virial becomes purely proportional to the
mass and purely proportional to the density, as 3W//4v our
experimental internal virial for a mass W of a compound
liquid is.

This hypothesis would affect somewhat the rigorousness of
certain thermodynamical relations as usually interpreted, such
as JA=(v3—v,) [dp/dT, since it provides a supply of internal
mechanical energy not taken account of ; but if this supply
is only slightly variable with pressure and temperature it
would make little difference in most parts of thermodynamics.

With the addition of this hypothesis of molecular swarms,
which will be used only in calculating molecular distances,
and will not affect at all the rest of our work, the law of the
inverse fourth power is brought into strict harmony with the
behaviour of compound liquids and of elements both as liquids
and gases. We must therefore inquire what experimental
evidence there is for the existence in liquids of a motion of
swarms of molecules, possessing the remarkable property of
not being degraded to heat as ordinary visible motions are.
In the motion long familiar to microscopists as the Brownian
movement we have such evidence. Gouy has _ recently
(Compt. Rend. cix. p. 103) recalled the attention of physicists
to this remarkable ceaseless motion of granules in liquids.
He states that it occurs with all sorts of granules, and with an

S 2

252 Mr. William Sutherland on the

intensity less as the liquid is more viscous and as the granules
are larger. It occurs when every precaution is taken to en-
sure constant temperature, and to ensure the absence of all
external causes of motion. Granules of the same size but as
different in character as solid granules, liquid globules, and
gaseous bubbles, show but little difference in their motions—a
fact which proves that the cause is to be looked for not in the
granules themselves but in the liquid, the granules being
merely an index of motions existing in the liquid. The most
pronounced character of the motion is its rapid increase with
diminishing size of granules, so that all that is seen under the
microscope is the limit of movements of unknown magnitude.
Gouy considers the Brownian movements to be a remote
result of the motion of the molecules themselves, but according
to what we know of molecular dimensions I fancy that the
Brownian movement must be considered rather as a sign of
the motion of swarms of molecules. If swarms of molecules
are weaving in and out amongst one another, so that the
average transfer of momentum at a point is the same in all
directions, then the vibratory agitation of granules amongst
the swarms is just what we should expect. The striking fact
about the Brownian movement is that it is ceaseless; it is
never degraded into heat. This alone forces us to conceive a
form of motion existing in liquids on a larger scale than
molecular motion but possessing its character of permanence ;
in other words, the motion of swarms of molecules.

The existence of swarms would not affect our views of the
rise of liquids in capillary tubes as a purely statical question;
so that, for the connexion between molecular force and
surface-tension, we can use the calculation given in another
paper (Phil. Mag. April 1889) (rather badly affected with
misprints), where I have shown that the surface-tension of
liquids that wet glass, measured in tubes so narrow that the
meniscus-surface is a hemisphere, is given by the equation

amp’ Ae/(2+V 2);
where p is the average density of the capillary surface-film
(to be written also 1/v), and ¢ is the distance which we must
suppose to be left between a continuous meniscus and the base
of a continuous column raised by its attraction, if the action
between the continuous distributions is to be the same as in
the natural case of discontinuous molecular constitution of
meniscus and column. The distance e is not identical with
the length a which occurs in our theoretical value of the
internal virial of unit mass,
31
Amp (3 log 2L/a—4) = 9 Oe

Laws of Molecular Force. | 253

but it is closely proportional to it. If we can find the relation
between e and a, then from capillary determinations we can
obtain relative values of the virial constant / which, as we
have already found some absolute values of /, can be converted
to absolute values ; at the same time, too, we shall be able to
find a value of a the mean distance apart of the molecules.

To find the relations between e and a we can proceed thus.
If we have a single infinite straight row of molecules at a
distance a apart, the force exerted by one half of it on the
other is

N=0 _N=O 3An?
Swi =r, (p+n)ia®

which can easily be evaluated as approximately 3°6Am?/a’.
Two infinite continuous lines in the same line, of density m/a
with distance e between their contiguous ends, would exert a

force
DM (ni a aay
CTD (Cae)

on one another; this is equal to Am?/2a’e. If, then, the
continuous distribution is to be equal to the molecular, we
nave

Ca Oe ame 10) ul

Again, if along two infinite axes one at right angles to the
other and terminating in an origin O at its middle point
molecules are arranged along each at distance a apart starting
from O, then the force exerted by the unlimited row on the
other is :

P=O qN=O 3Amn p=o 3Am
Pyar Paar Gry nich 1 pia”
which can be evaluated at about 5Am?/a‘.

Replace the rows by two continuous line-distributions of
density m/a, the one terminating at a distance e from O: it is
required to find e so that the force may be the same as this.

The force is
al { ees = Am?/a?e*.
a é 0 (x? +y?)3

Hence in this case
Gps | 6 0/ao er.

From these two simple cases we get an idea of the relation
between e and a. The case of a meuiscus attracting the
column which it raises in a capillary tube is more analogous
to the second than to the first, and it is easy to see that in the

254. Mr. William Sutherland on the

case of the meniscus we can say that ¢ is not less than a/2°2.
It will suffice to write e=a/2°2.

Now according to the definition of a in our theoretical
expression for the internal virial, it is the radius of the sphe-
rical vacuum artificially used to represent the domain of a
molecule ; but as it occurs in the expression log 2L/a, where
2L/a is a very large number and the value of LL is indefinite,
we see that there is no inaccuracy in making it identical with
athe mean distance apart of the molecules. However, for
the sake of formal completeness, we can easily find the rela-
tion between the two quantities which we have denoted by
the one symbol a. Let us now denote by # the mean dis-
tance apart of the molecules, that is the edge of the cube in
a cubical distribution of the molecules; then, from the defi-
nition of a, z and a are connected by the relation

R
LAm?/7? = { Am Anidr/a*r,
the summation being extended to all the molecules in a sphere
of radius R. By actual summation up to R=5z we find
approximately a="9x.

With our previous estimate of e as a/2'2, which we must
now write 7/2°2 on account of our change of symbol for mean
distance apart, we have the two equations,

l= Am(4 log 2L/‘9x—16/8),
a=mp’Ax/2°2(2 + / 2),

We can replace p by p, the difference between them being
necessarily very slight. Then for ethyl oxide we have the
following data: « at the boiling-point according to Schiff is
1:57 grammes weight per metre, or 1:57/10° kilog. per em. ;
lis 7500 kilog. em.*, and v,=1:44cm.? Eliminating A from
the two equations, we have a relation between w and L,
namely

2=T-5u 5 (9-2 logy 2L/-94—16/8).

L being hypothetical is not known to us, but we can give ita
series of possible values, and calculate by trial from the last
equation the corresponding series of values for x, with the
following results :-—

L. Le
1/10° cm. 4°6/107 cm.
1/10* 7) rig | 7) P)
1/10° ,, 7) Ge

Laws of Molecular Force. 255

As it is subsequently to be shown that in liquid ethyl oxide
and in all regular compound liquids the molecules are paired,
and that each pair acts on the others as if it were a single
molecule, we may estimate it as likely that the mean distance
apart of the pairs in ethyl oxide is between 1 and 10 micro-
millimetres (1/10® mm.). This result, though 100 times as
large as Sir William Thomson’s limits for the distance apart
of molecules in liquids, namely 2 x 10-9 em. and 7 x 10-9 em.,
is yet in better agreement with the estimate of molecular dis-
tances arrived at by Riicker (Journ. Chem. Soc. 1888) as the
most probable result obtainable from the most important
attempts yet made to measure the range of molecular forces.
The most suggestive of these is Reinold and Riicker’s dis-
covery, that the equilibrium of a soap-solution film becomes
unstable when its thickness is reduced to between 96 and 45
micromillimetres, but again becomes stable when the thickness
is still further reduced to 12 micromillimetres. At the latter
thickness the film shows black in reflected light. If the
intermolecular distances are nearly the same in soap-solutions
as in liquid ethyl oxide, then the black film must be regarded
as consisting of a single layer of molecules or groups of mole-
cules (in the case of water the molecules will subsequently be
shown to go in double pairs). This is an intelligible result,
and gives the simplest explanation of Reinold and Riicker’s
beautiful discovery of a stable thickness supervening on the
unstable, for we recognize a single layer of molecules as a
stable configuration. Of course it is to be understood that
what we mean by the thickness of a single layer of molecules
is the one nth part of the thickness of n layers; and if the
black film is really only a single layer, it is in this sense that
Reinold and Riicker’s estimate of 12 micromms. is to be taken,
for they did not measure an actual distance from the front to
the back of a black film, but only estimated from accurate and
accordant measurements, made in entirely different manners,
that the number of layers in the black film is to the number
in a thickness of 1 centim. as 12 micromms. is to 1 centim.

If the black film consists really of only a single layer of
molecules, it is surely a hopeful sign for molecular physics
that measurements should have been possible on it, though
only visible through its invisibility.

If, encouraged by this experimental support, we say that in
round numbers the mean distance between the pairs of mole
cules in liquid ethyl oxide is 10 micromms., then one gramme
contains 2v, x 10° molecules, or the mass of a single molecule

1s
1/2°88 x 108 orm. =3°5/10%,

256 Mr. William Sutherland on the
and so the mass of an atom of H is
3°5/74 x 10° =5/10" grm. nearly.

It would lead us too far from our present purpose to discuss
other estimates of molecular distance, especially as Reinold
and Riicker’s measurement of the black film is the most defi-
nite and striking yet made of these minute distances ; but the
question of the range of molecular force is of special import-
ance to us.

Quincke (Pogg. Ann. exxxvii.) determined what thickness
of silver it is necessary to deposit on glass so that the capil-
lary effect on water may be the same as that of solid silver;
that is, at what distance the difference between the molecular
attractions of glass and silver for water becomes too small to
be measured. He found the thickness to be about 50 micromms.

Now, according to the law of the inverse fourth power, the
attraction of a cylinder of radius c, length h, and density p on
a particle of mass m on the axis at a distance z from the
nearest end is easily calculated as

1 i 1 1

2g eth Ve+2 Vet (ethy
If the cylinder consists of a length h, of silver with a length
h of glass, the silver being near the particle, then, the suffixes
1 and 2 applying to silver and glass, the attraction of the
composite cylinder is

1 1
2A,mp; Pe 2m (Aipx — Aspe) (= +h, Ve Ge rise a
“Tees

e? + 2?

il 1
— 2A ,mpo7 (== ES
etht+th, e+ (e+h, +h,)?
Making the circumstances correspond to Quincke’s experi-
ment, we have z nearly equal to the mean molecular distance
in water, about 10 micromms.; h, is small compared to hy and ¢,
and, according to Quincke, is 50 micromms. when the composite
cylinder exerts the same force on m as if it were all silver ;
accordingly the last expression reduces to the two terms

2A mp, /2—2m7 (Ayp,—Agp2)/(2 + hy),

which permit us to compare the molecular force range /, with
the molecular distance z. That the second of these terms
should become negligible when h, is 50 micromms. is a result
quite in accordance with the value 10 micromms. for z.

Let us briefly compare the magnitudes of molecular and
gravitational force. The most convenient plan will be to
compare the two forces in the case of two single ethyl-oxide

Laws of Molecular Force. 257

molecules at a distance of one centim. apart; that is, to
calculate Am? and Gm?, where m is the actual mass of the
molecule, and G the constant in the expression Gm?/r? for
gravitation.

In the expression

a=mp*Ax/2°2(2+ V2),

using the value 10 micromms. for # and the values previously
given for the other quantities, we can find A, and then using
the value 3°5/10" for the mass of a molecule of ethyl oxide we
find Am?=9/10* in terms of the dyne. To calculate G we
have 981 as the acceleration of gravitation ; the mass of the
earth is 6 x 10° erm. and its radius is 6°37 x107%cm., so that
Gm? = 2°1/10* in terms of the dyne. Hence at a distance of

(1 centim. the gravitation of two ethyl-oxide molecules is
about double their molecular attraction, or, allowing for un-

|

/ | certainties in our calculation, we may say that at about

1 centim. apart two molecules exert the same gravitational as
molecular force on one another.
- We now return to the main business of this section, which
is the Fifth Method of finding the virial constant J. This
consists In using the equation already used for calculating
molecular distances in the form

[=7-5r%x(4 log 2,/:92—16/3)/s.

Now , the molecular distance for different liquids, varies as
mé v3, and the expression in brackets may be assumed to be the
same for all bodies ; hence /=cavt/m*, where c is a constant
whose value can be obtained on substituting in the case of
ethyl oxide the known. values of /, 2, v, and m, or, more
safely, by taking a mean value from several substances.

But we must remember that we are using v the volume in
the body of the liquid, instead of v that in the surface-film; a
replacement which is not justified by experiment, seeing that
for a given liquid «v* measured at different temperatures is
not constant, the reason being that v varies much more rapidly
with temperature than v. But, in our ignorance of the rela-
tion between surface and body-density, all that we seek for
from the above equation for /, is true values for / from mea-
sured values for « Accordingly the question arises, Can we
choose temperatures at which to measure @ for different sub-
stances, so as to get true relative values of / irrespective of
our ignorance of v?

As we have seen (Section 6) that at equal fractions of their
critical temperatures, and under equal fractions of their critical
pressures, one liquid is approximately a model of another on

258 Mr. William Sutherland on the

a different scale, we conclude that if we use the value of the
surface-tension measured at a constant fraction of the eritical
temperature, and under a constant fraction of the eritical
pressure, we ought to get correct relative values of 7; as
surface-tension is not appreciably affected by pressure, we
can dispense with the condition as to pressure and use mea-
surements of a made under a pressure of one atmosphere at a
constant fraction of the critical temperature. I have chosen
the fraction as two-thirds, because it gives a temperature near
to the boiling-point of most liquids.

Schiff’s abundant measurements (Ann. der Chem. ccxxiil.,
and, further, Wied. Gezb/. ix.) include not only the height to
which different liquids rise in a capillary tube at their boiling-
points, but also its temperature-coefficient, which is such as
to show that the height in every case vanishes near the critical
point.

Let H be the height to which a liquid rises in a tube of
radius 1 millim.; then if H really vanished at the critical
temperature and varied linearly with temperature, we should
at 2T,/3 have H=T,b/3, where b is the temperature-coefficient.
But to use this would be to depend too much on the accuracy
of b,

If H, is the value at T;, the boiling-point, then T,=T, + H,/d,
and

H=H,+ (T,—2T./3)b=H,/3+ 1.6/3,
which depends partly on H;, measured by Schiff, and partly
on 6. Now «=Hp/2=H/20 ;
“. Lor cav3/ms=cHv3/2m:,
l= c( H,/3 -- T,b/3)v3/2ms.

If H is measured according to the usual practice as the
height in millimetres for a tube of radius 1 millim., that is, if
a is measured in grammes weight per metre, then if / is
desired in terms of the megadyne, gramme, and centimetre as
units, ¢/2=5930, a mean value. Apart from all hypothesis
about molecular force, our last relation between the virial
constant and the constants of capillarity will be amply con-
firmed by the extensive comparisons soon to be presented in
Tables XXIV. and XXV. Meanwhile a few consequences of
the relation may be glanced at.

9. Establishment on Theoretical grounds of Eétvés’s relation
between surface-tension, volume, and temperature——dAccord-
ing to the modified equation of the fourth method of finding
1, M’=800T.v,; and according to that of the fifth method,
l=cavi/ms. The first of these equations would be more
accurate if we replaced v, by v, which in the second means
the volume at 2T,/3 ; so. M/=800T,v, and m the actual mass

‘Laws of Molecular Force. 259

of the molecule is proportional to M its molecular weight ;
so that from the second we have M/ proportional to «(Mv)z,
and hence e(Mr)% measured at 2T,/3 is for all bodies pro-

portional to T,. Now in our notation the relation discovered
by Hotvés (Wied. Ann. xxvii.) is

d{a(Mv)3} /dT='227,
or a(Mv)?=:227(T—T/),

where T,! is a temperature very close to the critical ; and this
is only a more general statement of the relation we have just
deduced.

As Hoétvos has verified his relation experimentally for a
large number of bodies, his result is a verification also of our
general principles. The form of his relation also induces us
to examine a little more closely an important consequence of
the form of our infracritical equation, which, when multiplied
by M with the pv term removed at low pressures, becomes

Mi _ VT Eee T
25." Bo v— =) :

Now R’M is constant, and Ml/v is proportional to a(Mv)s, if

a and v are measured at 2T,/3, or any other constant fraction

of the critical temperature, and under these circumstances

a( Mv) has been shown to be proportional to T,; hence if T
is al, a being a constant fraction, we get T, proportional to

VT k—v
(14 sae . —=;) aT.
; VT ki —v
so that 1+ B ip=6
critical temperature, is approximately the same for all bodies,
a result which our study of Van der Waals’s generalization
showed us to be approximately true. This shows that Hoétvis’s
relation is rigorous only to the same extent as the constancy
of this last expression is rigorous; as a matter of fact, exclu-
ding the alcohols and water, Hoétvés finds the constant whose
mean value is taken as *227 to depart from this mean value
by not more than 5 per cent. in any individual case. ‘This
brief discussion of Hétvés’s relation has therefore furnished
us with additional proof of the general accuracy of the ap-
proximations we have been forced to make in parts of our
work.

One of the main difficulties in the way of pushing on with
the many interesting inquiries opened up by these relations
lies in the fact that we do not know the relation between the
densities in the body and in the surface-layer of a liquid.

RM (1+

, measured at a constant fraction of the

260 Mr. William Sutherland on the

We have to replace our relation
E ein
a varies as Ap*m*
by the less accurate one,
e 5 1
a varies as Ap*m*.

Multiplying by (Mv)? or (M/p)*, we get the «(Mv)* of
Hotvés proportional at all temperatures to AMp; and as
d{a(Mv)*} dT is constant, and has been shown by Hétvés to be
constant almost right up to the critical temperature, and to be the
same for all bodies, we ought, if our assumptions were rigorous,
to have AMdp/dT constant almost up to the critical tempe-
rature and the same for all bodies (whence another approximate
method of finding A or 1). Now dp/dT has been shown by
Mendeléeff to be constant for many substances within ordinary
temperature-ranges ; but the constancy does not hold up to
the critical temperature, and the ultimate meaning of the
apparent contradiction between Hétvés’s result and this is
that, while for most purposes we may safely enough assume
p proportional to p, we cannot so accurately proceed to the

consequence dp*/aT proportional to dp /dT ; in fact, a change
of temperature being accompanied by a change of stress in
the surface-layer, the change of p with temperature is more
complex than that of p. But within the range of temperature
for which dp/dT is approximately constant, we have the
important result that

w/e ae = T

d wrpr
op MR (1+ eae
is constant and, is approximately the same for all bodies.

As I now consider the term differentiated to be not two
thirds of the translatory kinetic energy of the gramme-
molecule, but two thirds of the sum of the total kinetic energy
and the chemic virial, I must replace the verbal statement of
the last result as given in my paper (Phil. Mag. April 1889,
p. 812) by the following :—The temperature-rate of variation
of the sum of the total kinetic energy and the chemie virial
of a molecule, measured at low constant pressure, is the same
for all bodies (approximately).

10. Tabulation of Values of the Virial Constant, determined
by four of the five methods described, and multiplied by the
square of the molecular weight.—In the first place, I will
give a comparison of the values of M*/ for those bodies to
which existing data allow the application of three or four of
the previously described methods. The multiplication by M?
is for future convenience. The values obtained by the second

Laws of Molecular Force. 261

(liquid compression and expansion), third (latent heat), fourth
(critical temperature), and fifth (capillarity) methods are
entered in the columns marked 2, 3,4,and 5. (The modified
fourth method was used, namely, M/= 800 T,v,.)

The units are the megamegadyne (10” dynes), grm.,
and cm.

TABLE XXIV.

re

Substance. . 3. 4. 5.

Sa Ne esti 26°5 257 27-2 26:9 |
1? Ly Ss Sanne Bee Rene pep oe COs erro rone oof 41°7 43°4 |
COI Spec eOne ois Seen Baecel ap RARE 46:3 462 -| 456
2G) aaerecrreprepeccen 33:0 382 36'1 36°8
eNO fr civicaasis aac ae 22°3 28°3 26°5 |
EP scioec des see rceline |i odes o2l 31°5 29:0 |

BE os crecich cic'sansns xc age AS OR aia sree 45°3 Alpell |
OE ses aecia owes sistsaieice yg Orr = steno 58:5 593
ipl BAIR See eae 40:0 43:1 42°7 43°8
O15 LA eee 59-0 558 56°2 56:4
(OLS FO een ner eee 360 31°3 ital
Methyl butyrate ...... 65:0 60:4 556 56-1
Ethyl butyrate ......... 84:0 74:6 69:5 TAE3

The satisfactory agreement of these values, calculated for
such diverse bodies from such diverse data, must be taken as
the verification of the main principles so far unfolded—the
chief of which as rezards molecular force is that for most
compound bodies the internal virial term of the characteristic
equation is //2v below the volume &, and //(v+) above that
volume.

We see, too, now how important for molecular dynamies is
the detailed study of each of the constants k, B, and @ in the
characteristic equations ; but for the present we must refrain
from entering on such a study, and must consider the com-
parison in the last table as closing for the present the general
discussion of the characteristic equation.

Our immediate object is now to ascertain the law connecting
the value of M*/ for a body with its chemical composition.
On the hypothesis of the inverse fourth power (with the sub-
sidiary one of molecular swarms),

ml = mm A(4 log 2L/a—16/3) ;
so that, the bracketed expression being the same for all
bodies, m7/ is proportional to m?A, and the law of m/ or M?/
will be the law of mA in the expression 3Am’/r* for the force
between two molecules. In the Phil. Mag. for April 1889 |
announced a law for the parameter A, calculated from Schitt’s
capillary data, which applied fairly well to a large number ot
organic compounds, but was affected with exceptions subversive
of its generality. Applying now the more accurate method ot

262 Mr. William Sutherland on the

calculation described as the fifth to all Schiff’s data, we obtain
ample material for generalization, which can be supplemented
by values calculated by the other methods.

In the following Table the units are again the megamega-
dyne, grm.,andem. For brevity the radicals methyl, ethyl,
and propyl, &., will be denoted by the first two letters of
their names, while the acid radicals-—-formic, propionic, &¢.—
will be denoted by Fot, Prt, and so on, so that PrPrt stands
for propyl propionate. The numbers entered under the
heading $ will be explained when we are discussing the law
of NPE

TaBLeE XXV.—Values of M7/.

First Method.
| MI. S. Ml. S.
1 By Oa seer cae | 40:2 4:5 Te nicte nee Semone 22 “O04
COs os. ee aig: aligtc07 || Nuc.) ce eae 1:23 205
SO Scatter cece | 15-0 2°05 OFA ci. create eee 1:16 "195
ING en recbasce ts [ee eRe 1:25 Os Pipes <= 2-2 00
AN Oo etece caunat ceee | 88 1:3 O, 71 j.bcsecteeee 6:5 1:0
Third Method. |
wz. | 8. | Mee hibit
i) Oy Faerie Sad ee 61:3 6-1 IsoBwihet 28 G2 (ei
ASO erick 4 does 49-0 52 HtDut:?.. gees 769 715
ES OIL Sener aes Mee 23°5 2:95 || -PrPrts yee 773 72
SiC ieacce- secant 473 5:05 Tso AmmHOt ..--2 ee 78:7 73
OL SLy aaa nee me Ec: 27-4 33 PrisoBut \). ie 89:1 8:0
Eee dies oe A007 «|, .4-5. | HtVaten. ee 895 | 80
ATCA) el OOo 79 Tso Burt. oe 92:5 8:15
PAA Oe cess 61:8 6°15 IsoAmAct ......... 93-1 8:15
Nit eae eae 48-7 5b, || Prue ee 92°5 815
CHa ate oe ee 35°0 4:0 TsoBuisoBut ...... 105 8-9
Led a are alae 90°4 8-0 PrVats eee hoe 106 89
idee. teats te 109-0 | 91 || IsoBuBut ......... 109 9-1
CH Benes. es. 49°4 5:2 IsoAmPrt ee 110 oly
BU SO SO) dertcipae oid 109-0 all IsoAmisoBut...... 125 9°95
OM eae aaee 44-] 4-8 TSOREViat soso 126 10
aD) a0 er pee 35°6 41 IsoAmBut ......... 129 10°15
IMGACL iikats csc 36:0 4-1 TIsoAmVat ......... 147 11
BI ALCE Snore sono 47-6 Dall Ge onc coke eae 43:1 4:7
MeRrE 22k cae 47-5 Sil CF er ee 55'8 57
Lig Reece Pees 50°2 5p @, Nt eee 69°5 6°65
MeButiso ......... 60-4 6-04 C3H,, (meta)...... 714 68
isoBulloties es. 63°7 6:3 CH Pr. 2.2 85°9 775
18 oR IRe PR a ee 62°4 6:2 C,H,.(mesitylene)| 86:1 775
BEAGLE creep ns 62°8 6:2 C,H,, (pseudo- 87-1 7-8
MeBute .....c0 4. «0. 61°8 6°15 cumene)......
EtisoBut ......... 74:6 70 C,H, (eymene) .| 101 86
MGV 2S scot <2 74:1 70
|

Laws of Molecular Force. 263

Table XXV. (continued).
Fourth Method.

| Mz S. M2, S

| BU icc ank 58 Dipl Pe@ligmtecue too 346. |. 40
BI os cinws l@oee elo > NER oe uk... 100 | 1-4
bi. eee 96°) 14°” | IN Merc. c..1..00- 176 |..23
Oe ac. 2: AO, | NIEIMEM ele 23:5. | 30
Cn oe Aa teed Se | Nie, sai. Pe 36. Aa
Ci) BGO 49" NA Bb ewe 2 | 27
Se FO oS ||| NH Bia es 41-4 | 4:55
0. 2 Tees || Nite wee. 655..| 6-4
Et TOs Se YN Pref 33-4. |. 3-9
C0 ae poe eee “| NE Deka: 676 | 65
Suc. 2 er 26:6 | 8:25

Fourth Method modified (not using critical pressures).

|
M. S. ee es:
(ome), |... 380 | £3 || EKO,H,O ......... 48-6 ae B15
CHECHICL.) «02. 377 4:3 EON et date menret oe" ele
Oh a LO) ae ener: 340 4:0 Mie © lire uate 16°8 2°2
CH,(OCH.). EC ot. a cece 26°4 32
(ethylal; Me } Sea 9 Pe@leine tre 326 | 38
GEMOTOOT). par (eg. | NEs cence noes 76) 11
Geval) os. i : NESMet eos 1b6:> | 21
TL, haa 418 -| 46 || NHMpe, .......:.... 935 3:0
COD IEU pdcocaen cena 51:2 5:4. INIMent er ame hoke 310- | 37
C12 cao SOON aia eer NIE! Sheet h 4-4 3:05
OIE pace eaoe eee 81:1 TA INAH Grr dae ee 43°5 4°75
EG a DO ue ea2sGs. Neen ee 66-4 | 65
JULES 3 CG ae 29:9 36 TBI) Bie e nese cuceaticn 31:0 o7
HEPrO _....-c.-s 524. | 5450 WNP oh 686 | 66
Fifth Method.
\
M*/ 8. MZ S
SE, cain os i000 ohee= 321 38 tet Cis Geena ates. 72:3 6°85
IMIG AGE 61 j..0.t000 35°6 4-1 el SOMS UG) cased cae. TAS 6°8
12 Ye) Cae Rear 44-2 48 Moe Viatt ywencte se sos. 69°7 6°7
135. eee See 45°4 49 TsoAmAct ......... 87-3 cs
MMSE Rt occ je. esusd 44-8 4°85 TsoBuP rt) avis. 87:7 785
HO BWH Ob. «01... /05 56°9 5:8 Pr Bina eeenceeec cas 89°35 C95
PERN brs ciicieiicieicniselts 579 5:85 PrisoB nilieusk cess 87:7 T'85
EIDE SB esas oiciavesoueierd 58:5 5:9 HEN GIRO aiiidie cick ack | 86:5 78
DECIR UE... .necentiet 58'2 59 lisjoysWanl Seven secenee | 105 8°85
MeisoBut ......... d6°1 575 || IsoBuBut ......... + 106 8:9
IsoAmFot.........| 716 | 68 || IsoBuisoBut ...... 103 875 |
TsoBuAct. ........< 70°6 675 || PrisoVat ......... | 103 SiS. |
OE sie coscewsn ones 73:°3 6:9
|

264 Mr. William Sutherland on the

Table XXV. (contenued).

M/. 8.
COREL SE ress chess ane®e eee: Normal hexane) 2.c:2sc.cessee- 59°3 6:0
COB 2 1 sere anatene metres on Diisobutyl..cs..-tek eee eee 90-6 8:0
Oh * josseneenecce ete Disoamyl! 7c. sseeceeee eee 1256 10:0
OE a (Pe tay 5, 4 ey Amylene "2. c.c2. cess oaneeeee 45:0 4:9
CER s Ui eean eae Caprylene: sis..cc.neesacseeeeee 91°8 81
OFA s RE in sas ara Ler penelich.ce.-saceomaeceneee 107-4 9:0
OTN aioe eee caste Diallya esc yecccnsceseseeee ceteris 54:8 5'6
(OF IER catann cy cen en Benzene! Shc cto..e-tee eee eee 43°8 4°75
CLTA SY. osttare tn toneee Volwene se ©: knee keane eee 56°4 5°75
Og nee oc aa ae ae Orthoxylene: ix. estas. secre 69-7 6°65
AUST. ce caterers enemas Maetaxyleme nase o:.ce sean le “Omg 6°65
COREL Fac hyena ane eee iParaxylene\.sec.snecateesssecee 70°3 6°7
OF leh Aupnsneehee roe mtanee Hithy benzene een. c.tors--2 cee 70°6 6-7
Ce acanaiearn: «cescaree Normal propylbenzene ...... 86°9 78
LE [ele sean ree on rae a Hthyltoluene paiess.e-ss ee eee 86°1 tip
ORE sirsces, Socatac sanenue es IMesitylene:. cescse-panostecwcmse 85:3 7°65
CHANEL eet es etn OyiMMeno ecstacy eae | 103-0 8-75
G25 Omen e ts peel Chilorotoginissc sca acer eee 36°9 4-2
Oli sac teat Mec acurt ce Carbon tetrachloride ......... 45°6 4:9
(CECI) kek eens cece: Ethylene chloride ............ 44-4 4:8
CHE CHO gare scctass ccs Ethidene chloride ....... ate 38:1 4:3
PC gs eae oe Sans iPropyluchloride -.trscceeeee 37°9 4:3
J ESoyl Bi G1 Irs pe oe te a Isobutyl chloride ............ | 270 5:4
PSO AGW Hck anaes Isoamyl chloride ............ 66:4 6°45
CC). sak eens os C blorobenzener . 2.2. .cereeeee 57-7 5°85
(Dele Ie O/ Meaaen eee ae Chlorotoluene).>...sstes. nce 76:0 ee
Cole Cl. acate asa cncpeee iBenzylechiloride = eee pee 82:2 75
0751 c Fal 0 | BAS nha os ee Propylene chloride............ 56°8 58
or ©) Hip Sire mina ae See ATS NC DWN RAN 2a ane anette. 65°6 6-4
Orie TA Oi ae acc nedeesiar Prichlorethame |< -.se8<.caeace 58-2 59
OE CO: 8 hecencces Hpichlorbydtin’ <....2:.-.---0 49-8 5°25
COPCOR: poke eens Chilorals 253 anos seca 509 5°35
CER CICO, Ht....<.<ccs-2 Ethyl chloracetate ............ 63°2 6°25
CHE COs Ut:.......9.bc 60. Ethyl dichloracetate ......... 79°6 7:35
SC COMNE = la. 8 ce Ethyl trichloracetate ......... 93°5 8:2
OF Lab O) 6) terre aa ames Benzoic chloride............ .. 79°6 7°35
Cal SIA 0] Se eae eee Benzilidene chloride ......... 89-4 8:0
LOVE Relate nt ees Bhi bromid ecasen.-a-eeeeeree *28°9 35
BOBS eee ae oa vciebe Propyl bromide. =. . sseness 41-4 4-6
TSOBRB Re. Meta cscuses® Isopropyl bromide...... ..... 41-2 4:6
OSG Isis Bee etree sais): Allty bromides. .2. oor 39°9 4°45
GSOIDUIBE 7 cli ose nc. tei<: Isobutyl bromide ............ 533 5d
TSOAMAB Ec ce stenwel sc TIsoamyl bromide ............ 66°2 6°45
(O/E1S Pal St aan Bromobenzene........0.<. 06.028 66°8 65
CERT cine a otape sites Orthobromotoluene ......... 81°5 7:45
CIE oad hes om shave: Ethylene bromide ............ 51:2 5°35
OEE ac biteen cs atte Propylene bromide ......... 615 6-1
INT ie Se sees ae Methyliodide o.2ce.: dec 25°6 315
Re A ncse sv se atskss Hi Ghiyde Odie Sigs. s08sc ea 38'1 4:3
Sd een ie hese bp nave Propylitodide focse.c53. 0045 50°9 53
TSOP ees ates decisis Isopropyl iodide............... 49°8 5:25
CED. eee cee Beas Ally todd eveeie sets dows sence 50:2 53
TSOUSIL eenac Beteuessies Isobutyltodide: 222 6.4....0.685 62°4 62
NISQATIN coeecseccnet actus Tsoamyl iodide ............... 80:0 735

Laws of Molecular Force,
Table XXV. (continued).

——— —— ——_ ———————

Cas 3! ee hodobenzene so sucha sass
EE IEE cae cc ss -cecss se. Bropyeamime i. cecesic ae ossige
BY PCR ES sci neccess-- ea. Ally Wamminte i eact- ee -ce coarse
NR SOE ares. 4.6... Tsohutyl amines... .2c5:..p..0:
INE ISO AMA... ). 3.5 03 soamyl amine oes. ...c..¢s00-%
RIE erase gate 5. ec ea a00- Diethyl amine 2255,...-..--..-4:
SUD EES OE eee eee Drethyl amine: ....,,,0-04s:
NCE TS Os hoe eee J MOMIUT OVE cq OR ORE SAP eee abc
Cah) eee J PALE CGUN TK Rete A SORE RE cree BASE
Neen ciau'w ones: PAPETIGUWC. ces wceseaer cere
EOIN SERS... ok ec oe. Chinoline oi. eer
MTeN Oye etcehtieasveces: Nitromethane .............06...
CIN OE on aes se Chiorapicena tigi 24.5. siento ee
PO ec sicine ach me sie + TENE ny Wann tet gs cinieinonis gsc ions
dso Am NO} S40... Tsoamyl nitrate ...............
CONG iba istes 5. sies. Hsobutylmitriley, sccceee- cute
CRON icacenetestensds Crichonanllii al Gee aenacneanosobonee
Blais Ch ose aReeeeee naan HSENZOMILT IOs ee dacker sme ate
OU Sitio Re AEE Eee Carbon disulphide ............
SIN Gey. bn, aoisdetel Allyl sulphocarbimid .........
(CNS C7 5 Reis ee Methyl sulphocyanate ......
GISTS OS & a as aaa Ethy! sulphocyanate .........
LOGS) obs cadena Biihy ll suilplides esd... .c-cne:
eae aoc oe so s~| PEL LL) BBEN de SRT os le ons
Goss), aiea nce teinecinienade
JEG GA & 2 ©) ESS eee Ethoxypkosph. chloride .....
JE OT oo obhoo tonto’ ACCCBER ia IRC Secon eee erraa
(Ole) WO) Bases aaa /NEGIIOSIS)) <SoahActodadebo ahansouoon
Cpls 5 Ops e ena eee Ranaldehyder sens ccnsa cea:
CHECTH(OCEH:,),” <..--. Dimethbylacetal ...............
CHPCH(OC,H.)3....... Wiethylacetalygs...n4s 904:
BOM Re siciciviie sire.ee Hithy lt oxiceraten ence aaaeeey
(OH ©O).O” ..... 2.05 .<: Acetic anhydride ............
PE COSC. | oo. cusee Ally acetate. cesar. uses
MeisoAMO! 2. ....5..%% Methylisoamy]l oxide .........
BT Ooi dace tio eive'seleainine's Hithwloxalatele. sou: a-sae s:
War CO OTH s0).ci52.65 Methyl benzoate...............
et COSC LH .. ou. .tee. Bich lsbenzoa lew rsasnsds--ce.
CH,(CO),CH,OEt .,.| Acetacetic ether ...............
= OO re ATISOW HOE Rie sake nese
Cale CLO) 5 Rae epee henet holies. pace ccehetes tof
OEE OCT 3 oo. ete caees Methyl! paracresolate.........
(OCH. )... .. esses Dimethyl resorcin ............
pe -OHCOH ........, Hine folt cast sunetsan-adosacn sa
ROPEIE OUFT 555... heb ieultey Waleraldehyderns: ...c2).s0t- =
Pere COH i... ...0-0es Cunning lec sos heesc hace
PEI Oe a eco ves ceeags Oaiy Ole ass cmos sase sector steer
(col) .CCOCH, ...... TMA BO MIVON 5 Mote sheeitecis cee

or

TORHTTE DHE AAMoONe
or OVS On

Pee Ooo
Or Or Or

POON MN DTI PRTO WOOD NNT NATO D Co Gm C2 EXOD
or

Cd Gd OD RH 09 09 Go HT

The following are the chief sources of the data from which the above
table has been constructed :—Latent Heats from Berthelot (Chimie
Mécanique) and R. Schiff (Ann. der Chem. cexxxiy.). Critical Tem-
peratures from Sajontschewski (Wied. Letbl. i1i.), Pawlewski (Ber. deut.
chem. Ges, xv., xvi.), Nadejdine (Wied. Bevd/. vii.), and Dewar (Phil.
Mag. xviii.). Surface-tensions from R. Schiff (Ann. der Chem. ecxxiii. ;

Wied. Bezbi. ix.).

Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893.

i

266 Mr. William Sutherland on the

To make clear the two simple laws that rule these tabulated
values, it will be advisable to confine our attention at first
only to those values obtained by the fifth method, using those
by other methods only to fill gaps. It will also be well to
consider first a single chemical family, such as the paraffins,
for which we have the following values :— me,

CHyye CH, ° 0,1. . (Ct) oo
2°2 14:7 593 90°6 125°6- +> .

These show that there is not a constant difference in the value
of M7 corresponding to the difference in the number of CH,
groups contained. We can amplify this list of paraffins by
using the material furnished by Bartoli and Stracciati (Ann. de
Chim. et de Phys. sér. 6, t. vit.), who have determined the more
important physical constants for all the paraffins from C;H),
up to Cy,H3,. Their values of the capillary constants were
found at about 11 degrees in every case. To obtain those at
two thirds of the critical temperature, we have to use the
values of the critical temperatures calculated by them from
Thorpe and Riicker’s convenient empirical relation (Journ.
Chem. Soc. xlv.), .
p/(2T,—T) = constant,

p being density at T.
The following are the values of M*/ thus obtained :-—

C;5H,.. C.Hy.. C,H, ¢. C,H, 6° CAs. C,H». C,H...
AT*2 08 1 71 79°6 912 110 127
C,,H,,. C,H... C,H. C,,H,5. C, 5H. Ont,
147 iva LOB? Praieels 230 . wae

Considering the assumptions involved in the.calculation of
these values and the difficulty of obtaining the paraffins pure,
the agreement for C,Hy,, CgH,,, and C,H. with Schiff’s
numbers is excellent; but the higher we go in the series the
larger is the temperature-interval for which we have to
extrapolate, and the more uncertain do the values become.
However, they are useful as giving a general idea of the
course of M?/ in an extended series.

On plotting these numbers as ordinates with abscissee
representing the number of CH, groups in the molecule,
a curve was constructed which proved to be the parabola

M2] = 68 +-6682,

where 8 is the number of CH, groups. It is only necessary
then to determine on this curve the abscissa corresponding to

Laws of Molecular Force. 267

the value of M?/ for any substance to obtain the number of
CH, groups to which its molecule is equivalent as regards
molecular force.

11. Definition of the Dynic Equivalent of a substance, and
determination of its value for several Radicals—lIn the manner
just described were obtained the numbers entered in Table
XXYV. under the heading 8, which I propose to call the
Dynic Hquivalents of the substances. The dynic equivalent
of a molecule is the number of CH, groups in the molecule of
the normal paraffin that exerts the same molecular force as it.

The table shows that the atom of an element contributes
the same amount towards the dynic equivalent of all molecules
in which it occurs (except in the case of the simpler typical
compounds) : thus, for example, consider the iodides from
methyl to amyl iodide, and notice that each CH, group has
the same value unity as in the paraffins, and that the iodine
atom is equivalent to about 2°3CH, in every case. The same
law holds throughout the table ; so that each elementary atom
or radical has its own dynic equivalent, which can be easily
determined.

In the first place, it appears that the extra H, in the
paratiins C,H,,,, can be neglected in a first approximation,
because C;H,) has practically the same dynic equivalent as
C;Hy., and CgH,, the same as CgHjs. It may be that the
double binding in the unsaturated compounds compensates
for the H, of the saturated, but I think that the simpler idea
for the present is that the two terminal H atoms in a paraffin
chain have a dynic equivalent so small that we may neglect
it, or more generally the middle H in a CH; group is negligibie
in a first approximation. If there is really such a ditterence
between the middle H and the two others in CH;, we ought
to find the dynic equivalents for the iso-compounds smaller
than for the normal; and the table shows that the isobutyrates
have equivalents smaller by °1 than the butyrates, while the iso-
butyl salts of the fatty acids have dynic equivalents nearly all
less than 1 greater than the propyl salts. But this is rather a
matter for the chemist to work out in detail; it suffices to
indicate the idea here, and to point out that it is in harmony
with the lowering of boiling-points among isomers with in-
creasing number of CH, groups. Accordingly, as a matter of
detail, in the estimation of the dynic equivalents of the elements,
it was assumed that the equivalent of C,H, ,,, C,H,,,,, and
C,H,, is in each case n when normal and n—‘lp when the
molecule departs from normality by p CH; groups. (In
constructing my curve for dynic equivalents, for the sake of

T 92

—

268 Mr. William Sutherland on the

simplicity at first, I ignored the fact that two of the paraffins in
Schiff’s data are iso-compounds.)

From the tabulated values for the alkyl salts of the fatty
acids, we get the following mean values for the dynic equi-
valent of CO”O!:—in the formiates 1°85, acetates 1°92, pro-
pionates 1°91, butyrates 1:92, isobutyrates 1°91, and iso-
valerates 1°83, the mean for all being 1°9.

From the oxides (ethers) and other compounds containing
single-bound O, we find for its mean value °6, although in the
ethers containing the benzene nucleus it comes out *8, while in
the benzoates CO’’O' is about 2°5 ; so that the junction of the
benzene nucleus with other groups seems to be accompanied
with an increase in its value : witness also the bromide, iodide,
and amine of O,H;, equal to the bromide, iodide, and amine of
CH, although O,H, is less than C;Hj. by *25. This slight
variation of the value of C,H, is the only anomaly amongst the
numbers of Table X XV. excepting the simple typical com-
pounds. The values ‘6 for O'and 1:9 for C’O! are in harmony
with the results for all the other compounds containing oxygen.

From the values for the benzene series of hydrocarbons we
can get a value for H, in CH, and also some light on the
important question of the structure of the benzene nucleus.
Thomsen has been led by his thermochemical investigations to
the conclusion that in benzene each carbon atom is bound
to three other carbon atoms by a single bond to each (the
“bond” phraseology is used merely for brevity, and not as
expressing definite statical or dynamical facts). If we accept
this conclusion, then the dynic equivalent of C,H,, minus that
for C,H, is equal to the dynic equivalent of 3H, ; similarly,
from the other members of the benzene series we get the values
for 3H,, the mean result being 1:29 or °43 for Hy.

The accepted structure for C,H,, diallyl is (CH,CHCH,),,
or four whole CH, groups and two CH, groups with H removed
from each ; and as the dynic equivalent of C,H,) is 5:6, we find
that of H, to be -4. Again, recent investigations on the ter-
penes (Wallach, Ann. der Chem. cexxy., ccxxvii., cexxx.; Briihl,
ecxxxv.) show that the two ordinary forms can have their for-
mule written CH;C;H,;(CH,).(CH).0, ; that is to say, they
have 6 hydrogen atoms cut out of CH, groups, and as the dynic
equivalent of CjoH,, is 9 we have that of 3H, as 1:0 or that
of H, °33. Since the value °43 is derived from 10 accordant
members of the benzene series, we will take it as the value of
the dynic equivalent of H, in CH,.

By similar but simpler reasoning the dynic. equivalents of
Cl, Br, I, and other radicals are easily found, and the
following is a list of mean values :—

Laws of Molecular Force.

Taste XXVI.—Dynic Equivalents.

269

CH,. 1a C. C"O'. O'. NETS. CN.
1-0 215 ‘OT 1-9 6 1-23 1:35

NO; CNS. s’, Cl. Br. I.
2:2 2°85 16 13 1-6 2°3

To illustrate the applicability of these values, I furnish a
comparison of the values calculated by means of them for
twenty substances with the values tabulated in Table XXV.

TABLE XXVIII.

Comparison of calculated and tabulated Dynic Equivalents.

Cale.
OREN? ess botetedas 4°8
(Ch dee a ee 88
(C518 1. C) eee area ean 4°3
Cab 6 aa eee 6:3
CREB ry fee sce.cs bce 36
O15 1531 3) a ae eee 6-6
OA8)S Ree 4:3
a kcces..: US
JNUE GTO & Banepa 4:23
INH SEN Sei 6°23

Cale. Tab.
Jager 5:35 53
a ee, 56 56
4°85 48
SEWARD 2°6 26
eee 66 6:5
i et 78 (Nl
Be We 52 54
Ee 5:3 51
Sanaa ee 4:9 4-9
SETAE 79 79

If we now look at the dynic equivalents of the uncombined
elements given in the first part of Table XXV., we may notice
that they are remarkably small compared to the values in the
combined state ; thus, that of H, is ‘04, of N, -205, of O,
"195, and that of CH, is small too, 35, instead of 1 as it
should be, seeing that CH, is the first of the paraffin series.

Other typical compounds have small values :

CO, has 1s 05,

while CO”O! in more elaborate compounds has a value 1° 9,

C,H, has 1, while C,H, has 2; and so on.

been noticed in connexion with the molecular refraction of

The

same fact iis

some of the typical compounds and some of their immediate
derivatives, and it will yet prove a most important one in

chemical dy namics.

But meanwhile it is of greater importance

270 Mr. William Sutherland on ae

for present purposes to notice that the dynic equivalents given
for various radicals in Table XXVI. are closely proportional
to their molecular refractions.

12. Close parallelism between Dynic Equivalents and Mole-
cular Refractions.—As is well known, there are two methods
according to which the molecular refraction is estimated, the
first by means of Gladstone’s expression, (n —1)M/p, where n
is index of refraction; the other by means of -Lorenz’s,
(n? —1) M/(n? + 2) p.

In a brief paper (Phil. Mag. Feb. 1889) I showed that the
experimental evidence taken as a whole is in favour of the
Gladstone expression, for which also a very simple theoretical
proof can be given ; and, further, it was shown that it is best
to measure (n—1)M/p if possible in the gaseous state. But
as comparatively few measurements have been made on
bodies in the vapour state I suggested that, as the Lorenz
expression had been empirically proved to give more nearly
the same value in the liquid and vapour states of a body, its
value as determined in the liquid state and multiplied by 3/2
could be taken as giving the value of (xn —1)M/p in the vapour
state. The result of the theoretical argument was that, if
M/p is taken to measure the molecular domain wu, and if U is ©
the volume occupied by the molecule in the same units, and N
is the index of refraction for the matter of the molecule, then

(n—1)u = (N—1)U.

Landolt, Briihl, and others have determined the values of the
atomic refraction for several elements (Ann. der Chem. cexiii.
p- 235), and by means of these and Masini’s data for sulphur
(Wied. Sezbl. vi.) and Gladstone’s latest determinations
(Journ. Chem. Soc. 1884), I have obtained the values of the
refraction-equivalents of the preceding radicals in terms of
that for CH, as unity. Mascart has given (Compt. Rend.
Ixxxvi.) values of the refraction of a number of substances in
the vapour state, from which, for the sake of comparison, I
have calculated the refraction-equivalents for as many radicals
as possible.

The following Table contains in the second column the
dynic equivalent, in the third the refraction-equivalent caleu-
lated according to the Lorenz expression, in the fourth the
refraction-equivalent calculated according to the Gladstone
expression from Mascart’s data for vapours, and in the fifth
that calculated by Gladstone from liquid data. The value for
CH, in every case is 1.

E Laws of Molecular Force. — 271
| Taste XXVIII.

Comparison of Dynic and Refraction Equivalents.

1 2 3. 4 5
GH te 10 1-0 1-0 1-0
LT eile ‘215 | 28 19 17
eee a Aled ‘BT 54 62 66
BOLO: ot icae 1-9 1-4 15 15
(ae 6 35 4 37
1: 3 gelesen ae i 8 el need cl ied fase 1-01
oo eee P35) oh 1-18) oles 1-2
i eee 2-2 OT audd don 1-9
BW Nes ne DOG ete bees: 3-0
<a 1-6 lgtietail wal aaa 19
Gi ho nin ithe 1:3 1:3 15 13
eee 1-6 2-0 17 2-0
Lie 23 31 27 3-2

_ This table brings out the remarkable fact that the paral-
lelism between the dynic and refraction-equivalents is so
close as almost to amount to proportionality. I shall not
discuss the meaning of this relation until I have shown how
to obtain the dynic equivalents for the elements usually
occurring in Inorganic compounds, and established the same
relation for them also.

Meanwhile it will be useful to compare the dynic and
refraction equivalents of the uncombined elements and of
those simpler typical compounds to which we have said the
summative law does not apply as regards dynic equivalents and
does not accurately apply as regards refraction-equivalents.

TABLE XXIX.

Ratio of Dynic to Refraction Equivalents, each measured
in terms of that for CH, as unity.

OF | New Cl. |.CH,).\C, He! B.S. | GH,.| CHCl,/|.C8,.

‘09 °21 °22 38 “32, *45 “79 wi “94 “(2

© N,. | HCl. | CH,ClL.| N,. | CO}. | S0,. |-N,O. | PCI,. | COl,. |(CH,),0.

Oe >. Mr. William Sutherland on the

We see that the ratio is small for the uncombined ele-
ments and CH, and C,Hy,, a result of the important fact that
while the refraction-equivalent of a non-metallic element is
almost the same in the uncombined state as in the combined,
the dynic equivalent is much smaller in the uncombined state
of an element. The meaning of this fact will be discussed
later on ; connected with it is the fact that the ratio for most
of the typical compounds in the last table is notably less than
unity. A molecule has to reach a certain degree of com-
plexity before the summative law holds as regards its dynic
equivalent ; the same may be said about its heat of formation.
Further comment on the connexion between dynic equivalent
and heat of formation must be deferred for a little.

We can now give a formal enunciation of the law of the
virial constant :—If the molecule of an organic compound is
of a degree of complexity higher than that of the ordinary
typical compounds, then the virial constant for one gramme
of the compound is given in terms of the megamegadyne,
gramme, and centimetre as units by the relation

Ml = 68 +6682,

where M is the usual molecular weight of the compound, and
S is the sum of the dynic equivalents of the atoms in its
molecule (measured in terms of that for CH, as unity).

According to the law of force 3 Am?/r*, Am? is propor-
tional to M?/ and therefore follows the same law.

13. Return to the Discontinuity during Liquefaction of
Compounds and proof that it 1s due to the patring of Molecules.
—The interpretation of the form of the internal virial expres-
sion above the volume & is of the highest importance in the
theory of molecular force, and can now be attempted in the
light of the law for M7/. If the molecules of a substance do
pair to produce an actual chemical polymer of it, then its
molecular mass changes from M to 2M, while S the dynic
equivalent changes to 2S, and consequently

l or (68+°66 8?) /M?
changes to a value given by
’ = (68/2+°668?)/M?.

When § is small we see that the pairing of molecules to pro-
duce a polymer causes the virial constant (for one gramme)
to diminish to nearly the half of its value for free molecules ;
when 8 is larger this statement becomes less exact. In the

Laws of Molecular Force. — 273

ease of CO,, for example, if from Table XXV. we take 8
as 1°05, then

l="00367 and’ U’=-00206,
but in the case of ethyl oxide, with S=4'5,
[="00738> and, —/7==:00491.

In both cases we see that the pairing of the molecules to
form a new chemical compound or polymer is attended
with a reduction of the virial constant towards one half,
but not exactly to one half of the original value. Now the
data given in Tables I. and ILI. and the form of virial term
taken to represent them, //(v+), along with the fact that
below volume & the form is //2v, mean that in the limiting
gaseous state the virial term is practically d/v, just as below k
it is //2v ; hence we must regard the pairing of the molecules
to be such as to cause the virial constant to become one half
of its higher limit—in other words, the pairing must be
different from polymerization. We are therefore led to
differentiate the chemical and physical pairing of molecules
by the statement that while chemical pairing alters the virial
constant in the ratio

(68+°66 8?)/(128+2°648?) or (14+°118)/(2+°448),
physical pairing alters it in the ratio
68/128. or 1/2,

The term °66 S? would thus appear to have a certain chemical
significance.

And now as to the form //(v+) connecting the two ex-
treme cases. We can explain it in the following manner :—
It will be shown when we come to treat of solutions that if a
salt having a parameter of molecular force 3A (proportional
to its virial constant /) is dissolved ina solvent with parameter
3 W so that there are n molecules of salt to one of solvent,
then the solution behaves as if it consisted of molecules
having a parameter 3 X given by the singular relation

X= (W-4+nA“)/(L +7).

Now, in a gas being compressed towards the volume f, let us
assume that there are a number of pairs of molecules propor-
tional to & and a number of single molecules proportional to
w—k, and that the same relation applies to the mixture of
paired and single molecules as to the solvent and salt in a
solution, then, replacing W by J and A by //2 and n by

274 Mr. William Sutherland on the

k/(v—k), we get for the reciprocal of the virial constant of
the mixture

ia( beets (relat ee

X=lv/(v+h),

and therefore the virial term is //(v +h).

This would be no demonstration of the pairing of molecules
in compounds, if we did not already have it proved in the
case of the elements that the virial term varies inversely as
the volume at all volumes. Remembering this we can accept
our form //(v+k) as indicating the existence of a mixture of
paired and single molecules, the number of pairs at volume v
being to the number of single molecules as k to v—k.

The form of the energy term,

2k
RT (i+),

must also be partly determined by this existence of pairs, but
it would be foreign to our immediate subject to attempt to
investigate it.

14. Brief Discussion of the Constitution of the Alcohols as
Ligquids.—To learn a little more on the subject of pairing, it
will be of some profit to consider briefly here the alcohols and
water, which so far have been left aside, after having been
proved in Table XII. to follow in the supracritical region a
different law from the usual one. But also in the liquid state
the alcohols and water, while conforming to the general liquid
laws in many respects, are still exceptional in others. Thus
Hotvos (Wied. Ann. xxvii.) has shown that the alcohols will
conform to his generalization if at the lower range of tempe-
rature, from 20° C. to 170° C., the molecules be considered
complex (double relatively to ordinary liquids) and water
also conforms if from 100° upwards its molecules be con-
sidered double ; the molecular lowering of the freezing-point
of water produced by the solution of bodies in it as measured
by Raoult and compared with the molecular lowering for
other liquids proves that relatively to these the molecule of ~
water is double. Taking all the facts into consideration, it
seems to me that the alcohols and water may be assumed, in
the liquid state, to have the pairs of molecules again paired,
the second pairing, however, not being of so intimate a nature

Laws of Molecular Force. . 205

as the first, consisting of a mere approximation of the first
pairs without any change in the values of A or of J.

According to this assumption we should expect the beha-
viour of the liquid alcohols to be represented by a form similar
to our infracritical equation, and we will assume

_ Rr VT 3) fs
jg R'T(1+ Rie aw Goal Dy

where R" is about 2R.
It was on the infracritical equation that: our second method
of finding M?/ was founded, giving the relation

which can be applied to Amagat’s data (Ann. de Chim. et de
Phys. sér. 5, t. xi.), and Pagliani and Palazzo’s (Wied. Beil.
ix.) for the alcohols.

Again, our assumption enables us to apply the fifth or
eapillarity method of finding M2 to the alcohols, if only we
remember that the molecular domain becomes twice as large
and its radius 2° as large as it would be with only one pair-
ing; hence the equation for the fifth method becomes for
the alcohols

l= cav'/(2m)3.

Schiff’s data are available.

As the latent heat and critical temperature are largely
dependent on the supracritical equation, we ought not to
expect the formule for M?/ furnished by the third or latent-
heat method and by the fourth or critical-temperature method
to apply to the alcohols. But as the relation

Mx = 19-4T,,
or, empirically,

MA = odes

which was deduced in the dideuudl of the third method,
does apply approximately to the alcohols, the constant being

6, we may as well, for purposes of comparison, see what the
formule of the third and fourth methods give in the case of
the alcohols.

276 Mr. William Sutherland on the
TABLE XX X.—M2/ for the Alcohols.

Method ...... Second. Third. Fourth. Fifth.
Methyl .0..-<0.0-: 8 22 (11) 17 AS) 9:4
13; sh eager aneeeeoc 14 38 (19) PAL) 176
Propyl “..s<acecos TE Ns eal Ghee 34 (26) 27°8
Isopropyl ........: eee ete ee 33 (25) 27°6
Tsobubyleseacceee Set ey |! ay hoes 46 (38) 378
lisoamiyl in. -eeeene 47 82 (41) 57 (49) 48:1
Cétyl eee eel kan. 326 (163)

Weiter eee so oe.5e8 11 (5°5) 9 6

The second and fifth methods give results in substantial
agreement with one another; the third gives numbers which,
when halved as in the brackets, come into agreement with
the others; while if 8 be subtracted from the numbers furnished
by the fourth method as in the brackets, the resulting num-
bers are in very close agreement with those given by the
fifth method. That the two discrepant columns should be
capable of harmonization with the two others by the simple
operations of halving and of subtracting a constant is signi-
ficant of some really simple principle on which the abnor-
mality of the alcohols in the supracritical region depends.

But too much importance must not be attached to the
general agreement among the numbers, as they are all founded
on tentative assumptions ; they simply prove that our idea of
a second loose pairing of molecular pairs in the liquid alcohols
is not discordant with facts.

The following are the dynic equivalents corresponding to
the values of M*/ found by the fifth method compared with
those calculated from the dynic equivalents of the elements
and placed in the third row.

AlconOls ereawes a. Methyl. Ethyl. Propyl. Butyl(iso). Amyl(iso).
Dynicequiv.found 1°35 2°35 3:4 4-3 D1
"9 Puecalcul.-. jl: 2°8 3°8 A°7 a7

For water the dynic equivalent found is ‘91, while 1-03 is
the calculated value. The values found for the alcohols are
about *5 smaller than those calculated. If from the capilla-
rity data we had calculated the values of M?/ and the dynic
equivalent as if the alcohols were not exceptional in any way,
we should have got:—

Alcohols ......++. Methyl. Ethyl. Propyl. Butyl. = Amyl.
Mey Ae eaten ea LIES 22°2 30 A7°6 60:6
Dynic equivalent 1°65 2°8 3°9 Sal Gal

Laws of Molecular Force. Fa

These values of the dynic equivalents agree well with the
calculated ones above, but then the values of M7/ being all

increased in the ratio of 2® to 1 are no longer in agreement
with the values got by the second method.

Accordingly we see that the alcohols will require an
exhaustive study for themselves, if the interesting features of
their molecular structure are to be thoroughly made out. I
have merely sketched lines on which their abnormality may
be hopefully investigated. Those bodies, such as nitric per-
oxide, studied by the brothers Natanson, and acetic acid,
studied by Ramsay and Young, which have been proved to
have double molecules split up both by the action of heat and
reduction of pressure have not been touched on in this paper;
they also would require a special investigation in which our
characteristic equations would lend an assistance much
required.

15. Methods of finding the Virial Constant for Inorganic
Compounds, including a theory of the Capillarity and Com-
pressibility of Solutions——So far I have secured only two
methods of finding the virial constants and dynic equivalents
of inorganic compounds from existing data, and only one of
these is practically useful, namely the first, in which the
surface-tensions of solutions are the source of the values ;
tie second is based on the compressibility of solutions. Using
our expression for surface-tension in terms of molecular force,

a = mp?Ae/(2+ /2),
in the form a = Ap? m/e,

where ¢ is a constant, I was led to imagine that it could be
adapted to the case of a solution by means of the following
suppositions :—First, that in a solution containing » mole-
cules of dissolved substance of molecular mass p to one of
solvent of molecular mass w, the solution may be assumed to
be a substance of molecular mass

m= (w+np)/(1+n) ;

second, that if 3W is the parameter of molecular force for the
solvent and 3A for the dissolved substance, then the parameter
3X for the solution is connected with W and A by the relation

X11 = (W1+nA—)/(147n).

This seems highly arbitrary, but will be completely verified
by the results to which it leads. I conld make no progress

Ce as ET ee Ee

278 Mr. William Sutherland on the

in the handling of solutions until, in the course of some work
on the elasticity of alloys, I discovered a relation similar to
the above to hold, and this proved to be the immediate clue to
the treatment of solutions.

Let , be the surface-tension of water, then we have the

following equations giving A :—

§(/w+np\3/ 1

A = X14: (X7—W>)jn.

These equations ought to give the same values of A~! what-
ever the strength of the solution may be; and herein lies a
first test of the truth of the principles involved.

The following values of cA for NaCl are calculated from
Volkmann’s data (Wied. Ann. xvii.) for its solution in water
at 20°; w is taken as 18, although we consider the water
molecule to be complex, but this does not affect the purely
relative comparison being made :—

ait ahs "105 084 "052 (35 ‘017
cA! . ° 1°34 1°38 1°47 1°46 4:42

Considering that the solutions range from saturation down
to considerable dilution, the approach to constancy is satis-
factory; but it will be noticed that, on the whole, there is a
tendency for the value of cA—! to increase with diminishing
concentration, and this same phenomenon is to be seen in
the case of almost all Volkmann’s solutions, most pronoun-

cedly in that of CaCl, :—

eT Se eee ‘O91 "068 ‘O41 ‘O21 ‘O11
GRE) fe PeN 2A 2 op ZG 2°95 Ae &

This case shows us that there is a certain amount of incom-
pleteness in our theory of the capillarity of solutions, as indeed
we ought to be surprised if there were not, when we try to
apply our arbitrary definition of the molecular mass of a solu-
tion to one which contains 56 parts by weight of CaCl, to 100
of H,O as the solution for which n=*091 does, and also when
we assume that the concentration in the surface-layer is the same
as in the body-fluid at all strengths up to saturation. If our
object were an exhaustive representation of the connexion
between the surface-tension of a solution and its concentration,
it would be easy to introduce a slight empirical alteration into
the above equations to make them exhaustive. For instance,

ae

Laws of Moleculur Force. 279

we might imagine that the effective value of W in a solution
experiences a small change proportional to the concentration ;
but the equations as they stand will prove to be sufficient for
our purpose if, in comparing solutions of different substances,
we calculate cA! for the same value of 2 throughout.

In all. subsequent calculations n=18/1000. The experi-
mental data for surface-tensions of solutions are abundant, the
chief that I know of and have used being those of Valson
(Compt. Rend. \xx., lxxiv.), Volkmann (Wied. Ann. xvii.),
Réntgen and Schneider (Wied. Ann. xxix.), and Traube
(Journ. fiir Chem. cxxxix.).

The following Table contains the values of cA! for a certain
namber of compounds, the surface-tension being measured in
‘rammes weight per linear metre and the half molecules of the
salts of the bibasic acids being regarded as molecules.

TABLE XX XI.—Values of cA.

ior Br pcCk NO. POH: sO, 400,

ib. S Gaetan 4°15 | 2°46 "83 | 161 83 | 161

Sich, oe SO0e p22 tr) 670), |, ode | 2. | 145
oe 4°74 | 3:06 | 1:45 | 2:30 | 1:37 | 2:30 | 1-95
ik ae 4:99 | 3:31 | 1-78 | 2:55 | 1-71 | 2-72 | 2-21

The study of this table brings out the fact that the differences
of the numbers in any two rows or in any two columns are
constant: thus the differences for the iodide and chloride of
the four bases are in order 3°32, 3°29, 3°29, and 3:21, while
the differences of cA—! for the Na and Li salts of the mono-
basic acids are in order *59, °60,°62,°69, and °54. Accordingly
each atom contributes a certain definite part to the value of
cA for the molecule in which it occurs, and that part is
independent of the other atoms in the molecule. I shall call
this part the parameter-reciprocal modulus of the atom ; we
have not at present sufficient data to get its absolute value in
any case, but if we make Li our standard positive radical, and
Cl the standard negative, we can calculate the average values
of the difference between the parameter-reciprocal modulus of
a radical and its standard,—thus in the case of iodine this
difference is 3°28, and in the case of Na ‘61, and so on.

Before tabulating these mean values I will give the values
calculated for the salts of some other metals with the values
for the same salts of Li subtracted.

280 Mr. William Sutherland on the
TABLE XXXII.

I Br Cl NO,. | 480,
ob een ne Re 39 35 53
MGe ai... 632: 44 73 67 DD s
ar Gi ce ¥ 1-67. | Smt
Ba tae Vee 249 | 2:52
I7n j= liad. 1-35 2 1:33
10d ab bes 224 | 242 | 215 2:29
Min = lui c...s 1:17 93 | 12

To these we may add the following values, cbtained from
the sulphates 3Fe—Li 1:27, 3Ni—Li 1:19, $Co—li 1:15,
4Cu—Li 1:49, JAI—Li *6, Fe, —Li *5, and 4Cr,,— Li 1:0;
and the two following from the nitrates Ag—lLi 3°91, and
4Pb—Li 4°51.

The following Table contains the values of the parameter-
reciprocal moduluses of the different metals minus that for
Li and of the negative radicals minus that for Cl.

Tapia XXL.

Mean Values of Parameter-reciprocal Modulus for the Metals
with that for Li subtracted.

|
Na. K. NH. | 3Mg.| $Ca. | 4Sr. | 4Ba.

6L | 90 |—15] 42 | 6 Rhy a ae
{

1:33 | 2:3 12

]
Pree
. | $Ni. | 4Co.
us |

Ag. | 4Pb. | 2Al.
ee ere 2 Ail

|
|
1:27 | 1:2 Hy 1:5

39 | 45 | 6

The same for negative radicals with that for Cl subtracted :—
ie Br. NO,. On. / 380/59 apes
3°28 1°56 “81 ‘04 “86 “46

It may be worth mentioning that these differences show a
pretty close parallelism to the corresponding differences of
the atomic refraction given by Gladstone (Phil. Trans. 1870)
but not close enough to be worth dwelling on.

In the case of the organic bodies studied there was nothing
analogous to this singular property possessed by these inorganic¢
compounds of having the reciprocal of the parameter A of
molecular force separable into a constant and definite parts

~ Laws of Molecular Force. — 281

contributed by each constituent of the molecule. Thus we

have characteristic of inorganic bodies in solution another of
those properties called by Valson modular, who discovered
that the density, capillary elevation, and refraction of normal
solutions (gramme-equivalent dissolved in a litre of water)
could all be obtained from the values for a standard solution
such as that of LiCl by the addition of certain numbers or
moduluses representing invariable differences for the metals
and Li and for the negative radicals and Cl. Other properties
of solutions have since been proved to be modular, as for
instance their heats of formation from their elements and
their electric conductivities. I think the modular nature of
some of these properties of solutions is the outcome of this
modular property in the parameter reciprocal of molecular
force along with the additive property in mass. To prove
this in the case of density would require a special investiga-
tion, but if we assume the property for density we can easily
deduce Valson’s result that the property applies to capillary
elevation. Let h be the height to which a normal solution of
any salt RQ rises in a tube of radius 1 millim., then
hy poke HDR
h=2a/p=2Xpi( ats Je.

Let r and g be the density moduluses of the radicals R, and
Q, being small fractions, then p=d+r+q where d is a con-
stant nearly 1 ; also

X1=(Wt+nA)/1+n),
so that

l+n (wknp\?

n= 2( way naa )atr+ gyi ro |.
Remembering that in the case of a normal solution n is small,
being 18/1000, we can develop the last expression in powers
of n as far as the first ; and it is evident that as p the mole-
cular mass possesses the additive property and A~! possesses
the modular property, then 4 must also possess the modular
property, which is Valson’s result.

16. Second method of finding the virial constant for inorganic
bodies or solid bodies in general from the properties of their
solutcons.—In this method the compressibility of solutions is
used. Ifa solution could be treated as an ordinary liquid we
might attempt to apply the equation of our second method for
liquids, namely,

PyeG: AOi a
a= 3(%% + gg rel 3

but as the solutions to be dealt with are all aqueous, and as a
Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893. U

982 | Mr. William Sutherland on the

for water at ordinary temperatures is quite abnormal, it would
be useless to attempt to apply this equation to them; but
from the “ dimensions” of the physical quantities involved in
it we may make it yield a correct form of empirical equation
for solutions. If we neglect the small term 25R/26, and also
the difference between v and v, at ordinary temperatures, the
equation above suggests the simple form / varies as 1/up?, that is
X-! varies as wp”, say KX~1=yp*, where K is a constant,
and for water KW-!=y,, the compressibility of water, and
as before we have X-t=(W-!+nA7})/(l+n). But on
account of the rapid alteration of the compressibility of water
with pressure, and its anomalous variation with temperature,
we must be prepared to admit that the part of the com-
pressibility of a solution due to the water in it is altered from
its value in pure water, and is more altered the more the
water is compressed in the process of dissolving the salt. Let
this compression be measured roughly by the total amount of
shrinkage that ensues when 1 molecule of salt is dissolved in
1000 grms. of water, call the shrinkage A, and let us amend
the equation given above to KX~!=ypp?+/(A): Let suffixes
aand 6 attached to symbols refer them to two different bodies,
then

, KX —KXs*=1,p2— Papi +F(A,) —7(4,);

ut
KX7!—KX1=Kn(A7!—A;,1)/A +n),

oe Kn(Apt— As*)/(L +2) = ape— Hops thAa) — F(A»).
Hence selecting pairs of bodies for which A,=A, approxi-
mately, we ought to get “,p7— @,p; proportional to cA7*—cA;*,
the values of the last expression being obtainable from
Table XX XI.

To facilitate the comparison I furnish the following broad
statements about A founded on the study of data as to the
molecular volumes of salts, both solid and in solution, given
by Favre and Valson (Comp. Rend. Ixxvii.) Long (Wied.
Ann. 1ix.),and Nicol (Phil. Mag. xvi. and xviii.). The modular
property applies approximately to shrinkage on solution ; the
shrinkage of a gramme molecule of LiCl is 2, and the shrinkage

for : gramme molecule is increased when for Li is substi-
tute

K. Na. NH; _ 30a, 38r, $Ba.
by-o' ‘i —d 10 {h 127s
and when for Cl is substituted
Br. i NO,. - 180, 2oe"

by 0 0 0 8 14,

Laws of Molecular Force. 283

After giving the values of up? in the next table we can pro-
ceed with the comparison.

TaBLE XX XIV.—Values of 10"pp?.

cna) aa i We ENO gl SO ACOs

Ms. | Soc ciae- 432 484 541 457 433

Witte he oe ..| 441 496 550 468 444 498
LC 454 507 557 480 450 437
ELS 443 493 544 466 449,

Or ian 464

Soe ae 497

so 521

Lhe experimental data used are those of Rontgen and
Schneider (Wied. Ann. xxix.), and those of M. Schumann
(Wied. Ann. xxxi.) for CaCl, SrCl,, and BaCl,, in the case
of which I calculated the compressibility for the half-gramme
molecule according to his result that w—p,,=cp where p is
percentage of salt, using a value of ¢ got from the more con-
centrated solutions.

An inspection of this table shows that 10’yp? possesses the
modular property; it gives for instance the following dif-
ferences for Na and Li, 9, 12,9, 11,11, with a mean value 10,
and so on for the other metals; the mean values for the metals
minus that for Li are :—

Na. K. NH,,. Ca, iS8r. Ba.
10 20 8 32 65 89 ;
and for the negative radicals minus that for Cl :—
Br. L NO, 380, 300,.
52 105 25 0 —15.

We can now select pairs of bodies for which A, =A, and test
if {1,07 —[,0; is proportional to cA '—cA>1.

The following are pairs of elements ands acterized by nearly
equal shrinkage on solution with the values of the differences
of 10’up? and of cA~ and also their ratio.

TABLE XXXV.

HKqual shrinkage pair...| K,Na. | Sr, $Ca.| 3 Ba, $Ca. | Br, Cl.| I, Cl.

—_—_~—- -

Mean diff. of 107up?...| 10 33 57 52 105
Mean diff. of cA~?...] 29 1:05 1:85 | 1:56 | 3:28
Ratio of differences ...} 34 3l 31 33 32

984 Mr. William Sutherland on the

The agreement here is excellent, as will be seen more clearly
if we compare bodies not having equal shrinkage, as K and
Li, for which we get the 10"up? difference 20, the cA~* diffe-
rence ‘90 with a ratio 22, or K and NH,, for which the two
differences are 12 and 1:05 with a ratio 11.

The agreement above is a verification of the theory of the
compressibility of solutions, here barely outlined, and the
equation

10°(4,p2—Myp;) =32 (cAZ!—cA;")

when A,=A, nearly constitutes a second method of getting
values of cA~1; but we will not use it, as it adds no bodies to
our list. It suffices to have partly verified the principles on
which the first method is founded by their application to quite
another physical phenomenon, and especially the principle
involved in the remarkable equation

X—1=(W-!+nA)/(1+72).
With the values in Table XXXITI. and that for LiCl, namely,

83, we can obtain the value of cA—! for any salt whose con-
stituents are to be found in the table, or we can if we like use
the actual values in Tables XXX. and XX XI1.; we can then cal-
culate M?/cA—, which is proportional to M*/, or M77=CM*/cA—,
where C is a constant. To connect the values of M?/ thus
found with those previously given absolutely in Table XXV.,
we must find the value of C/c, which we can proceed to do in
the following manner :—

We have seen (Section 14) that we had better regard the
molecule of water as doubled relatively to that of ordinary
liquids, and as we have shown that the molecules are paired
in ordinary liquids the molecules are doubly paired in water ;
but it was suggested that the second pairing of the pairs was not
attended with any alteration in the parameter of molecular
force, and that the only effect of the second pairing was to make

the radius of the molecular domain of water 2? as large as if
water were an ordinary liquid. And, again, in the case of
solutions the surface-tensions have been measured at about
15°C , whereas for comparison with our previous work they
ought to have been measured at 2T,/3, which for water is about
150°C. At this temperature the value of the surface-tension
of water reduces, according to Hitvés, to about °6 of its value
at 15°C. Hence the equation, which treating water as an
ordinary liquid and at 15° we wrote a, = Wwi/c, ought for
double pairing and at 150° to become ‘6a,—=W23w#/c, and
similar statements hold for the equation for «; so that values

Laws of Molecular Force. — 285

of W, X,and A, as deduced from measurements at 15°, ought
to be reduced by the factor ‘6/23, or 1/2, to give the desired
values. Now in the case of homogeneous liquids in the
equation l=cav*/m? giving 1 in terms of the megadyne we
found a value 5930 for c/2, with the megamegadyne as unit
of force c/2=00593; and we can use this same value in the
case of solutions after we have halved our values of A, or
doubled those of cA—! so far given ; hence using the values
of cA so far given we get M*/=:00593M?/cA—1.

Fortunately, a test of this argument is made possible by
means of Traube’s data for the surface-tension of solutions of
certain organic acids and sugars, for which the values of
‘00593M?/cA— are given in the following Table, as well as
values of S found by the relation M?/=6S (the term ‘668?
being omitted), and also values of S calculated from the
dynic equivalents in Table XX VI.

TaBLeE XXXVI.

Oxalic Acid.) Citric Acid. Glycerine. | Mannite.
(COOH),. |C,H,OH(COOH),.) C,H,(OH),.) C,H,(OH),.

We ae es hove on gelo ds 19-4 43°5 33°5 63-0

Sa MPYIG. oa cees ss Be "2 56 10°5

S from dynic equiv. 4:2 9°7 5:0 10°0
Tartaric Acid. Dextrose. | Saccharose.

C,H,(OH),(COOH),. | C.H,.05. | Ci.H»,0)).

-| JU U) nee 6c eget On ee eee 389 721 112°5
IME OP eae retshi sa.ceeses ss 65 12:0 188

S from dynic equivalents 74 9-6 18:1

The agreement between the two sets of numbers is not all
that could be desired, but it is good enough to show that the
only part of M?/ effective in a solution is the linear term in
M*%=6S+°66S?; and we have already seen that when the
molecules of ordinary liquids pair during liquefaction the term
‘66S? is inoperative in the process, so that there is a certain
resemblance in the relations of two paired molecules and those
of solvent to those of substance dissolved.

Returning to the inorganic compounds we can now tabulate
the absolute values of M2l, calculated according to the rela-
tion M7/=:00593M?/cA—. The manner of calculation is best
illustrated by an example, say for KBr; first °83 is taken as
the value for LiCl, and to it are added -90 and 1°56, taken
from Table XX XITI., as the differences for K and Li and for

286 Mr. William Sutherland on the

Br and Ol; the square of the molecular weight of KBr is
divided by this sum and multiplied by -00593 to give the
tabulated value of M2/ in terms of the megamegadyne. From
the value of M2/ thus found the dynic equivalent S is caleu-
lated by the relation M2/=6S, which has been seen to be
appropriate to values of M?/ obtained from solutions.

TABLE XXX V1I1I.—Values of M?/ and 8.

Cl. Br. i NO,. 180n S)e 260.
M7. S. | Mz. S. | M% S.|M¥%. S. | MW S. (Mz S
Li...) 125 29 | 167 3-1) 257 43 171-28 qOGeees
Na. ...| 13:7 23 | 208 35 | 28:0 4-7 1.188 3 1)) deems
K ...| 185 $1 | 283° 4:7 | 82:4 5-4 | 235 39 | 1725 aaa
NH, | 23:0 3:8'| 27-0 4:5) 81:0 52 | 25:0 427) 170m@e
iMg | 104 1-7 | 17-7 80] 251 42 | 156 26) toa
4Ca...| 120 2:0 | 19-4 3:2 | 267 451173 29
ASr ...| 142 2-4 | 21:8 3:6 | 293 49] 195 32
3Ba...| 18:8 3:1 | 264 44 | 339 56 | 240 40
Ae Oa Dold gece ote eee? et tn jock: ieee 21 |
40d... 15°7 26 | 23:2 3:9°| 305 51 | 21:0 35 | 162527
4 11° 9G in | 168 eee Sie

AgNO,. |3Pb(NO,),.| 3CuSO,. 4FeSO,. | 3NiSO,.
IM 30°6 26°3 lS 11°4 12°3 oa
Risentisece Bri 4:4 ied) 1-9 20
3CoSO,. sAl,(SO,);. | ¢Fe,(SO,)3. | 4Cr.(SO,),.
IMEI bcccsnaen 12°7 89 12°6 9°6
iad Bs aakuree 21 1-5 21 16

The additive principle holds amongst both sets of numbers
except in the case of NH,; see for instance the following list
of the differences of S for the iodides and chlorides :—2°2, 2:4,
2°3, 2°D, 2°, 2°8, 2°59, 2°5. Now we have already seen that
the modular principle applies to cA— (the modular principle
applies when a quantity is given by the addition of moduluses
to a constant, the additive principle is a special case of the
modular in which the constant is zero) ; the additive principle
apples to M the molecular weight: hence it would appear

Laws of Molecular Force. 287

to be a mathematical impossibility that the modular or additive
principle should apply also to M?/cA—!, rigorously ; or, more
accurately, if the modular principle applies rigorously to one
of the quantities cA~! and M?/cA—! it cannot apply rigorously
to the other: but practically we find such relations amongst
the numbers that both are approximately obedient to the
modular principle. The case of NH, casts some light on the
question, for with it cA—! shows the same differences in the
values of the chloride, bromide, iodide, and nitrate as with
the other positive radicals, while M?/cA—! does not do so:
this case would make it appear that the modular principle
applies rigorously to cA}, but not so rigorously to M?/cA—}.

But leaving out of the count this case of NH,, significant as
it is, we can find mean values for the differences of the dynic
equivalents of all the metals and Li, and of all the negative
radicals and Cl; if we can obtain the absolute value of the
dynic equivalent of Li and of Cl, we shall have those for all
the metals and radicals. Now from the organic compounds
we have already got a value 1°3 for the dynic equivalent of
Cl, and hence from the value for LiCl we could obtain that
for Li. The value tabulated for LiCl is 2:1, but we can
obtain a mean value fairer to all the other bodies by sub-
tracting, for example, from the value for KI the mean difference
for K and Li, and for I and Cl; in this way we arrive at a
mean value 1:9 for LiCl, from which, taking the value 1°3 for
Cl, weshould get °6 for Li. But the refraction-equivalents of
the halogens are supposed by Gladstone to be a little larger
in inorganic than organic compounds ; so that in the light of
our previous knowledge of a close parallelism between dynic
equivalents and refraction-equivalents it might be safer to
assume that the dynic equivalents of Li and Cl in LiCl are in
the ratio of their refraction-equivalents in that compound,
namely, 3°8 and 10:7. According to this assumption the values
for Li and Cl come out ‘5 and 1:4, which we will adopt as
true and use in the calculation of the dynic equivalents of the
elements given in the following Table. These are measured
of course as before in terms of that for CH, as unity, and,
again, for comparison there are written along with the dynic
equivalents the refraction-equivalents in terms of that for CH,
as unity, calculated from Gladstone’s values (Phil. Trans.
1870).

288 Mr. William Sutherland on the

TABLE X XXVIII.

Li. | Na. | K. | $Mg.| 3Ca. | 2S

Pete ee | | |
|

Dynic equivalent ...... te 3D ‘Sh AGG ‘3 | 758 ‘9 | 4)
Refraction-equivalent.. °5 63| 1:06] -46-| -68 | ‘90 | 1:04 ‘674
|

= i i
Ag. | 4Pb. | 3Cu.| $Mn. | 3Fe.

|

Dynic equivalent ...... 2°70 | 20 6 "5 6 xf 8 >| 8
76) 8 | +80 1) 5690 aga eayaeetoos

Refraction-equivalent .. 2:06 1-63

4Cr.| Cl | Br. | ZL | NO, | 480,|400,.|4Cr0,.

Dynic equivalent ...... 3 | 141 27 | 88 | 23 | 135
Refraction-equivalent.| °7 14 | 90°71 3:6" | 9-6 eee

| | i

Again we see a remarkable parallelism between the dynic
and refraction-equivalents of the elements and radicals. Of
course there are refinements which will yet have to be made
in the calculation of the dynic equivalents, but it is not likely
that they will make the parallelism seriously closer.

17. Meaning of the Parallelism between Dynic and Refraction
Equivalents, and general speculations as to the volumes of the
atoms and their relation to ionic speeds—We are now called
upon to consider the meaning of this parallelism which has
been demonstrated both for organic and inorganic compounds,
and we shall be helped thereto by the very simple theory which
I have given of the Gladstone refraction-equivalent (Phil. Mag.
Feb. 1889), showing that to a first approximation

(n—1l)u = T(N—1)U,

where n is the index of refraction and w the molecular domain
of a substance, N the index of the matter of an atom, and U
its volume in the molecule. Hence the refraction-equivalent
of an element is the product of the refractivity (Sir W. Thom-
son’s name for index minus unity) of the substance of its atom
and the volume of the atom (the volume of the atom being
measured in terms of the unit in which the molecular domain,
usually called molecular volume, is measured); so that the re-

Laws of Molecular Force. 289

fraction-equivalent is a function of the two variables only,
namely, the volume of the atom and the velocity of light
through it. Now we have seen that the expression M/, as a
whole, in one aspect appears to be not dependent directly on
the molecular mass M, seeing that M?/ can be represented in
terms of certain quantities which we have called dynic equi-
valents. Hence, as / is proportional to A in our expression
3Am?/r* for molecular force, we see that in one aspect mole-
cular force seems to be not directly dependent on the mass of
the attracting molecules; and yet, on the other hand, in con-
sidering solutions we found that the quantity A asserted its
individuality as separate from the whole expression Am?, so
that in another aspect there does appear to be a mass action
in the attraction of two molecules. However, regarding
M?/ or Am? as a whole, the simplest hypothesis we can make
about the mutual action of molecules is that it depends most
on the size of the molecules. This would make Am? a simple
function of U; so that the dynic and refraction equivalents
would have this in common, that they are both simple functions
of U. Suppose, now, that the velocity of light through all
matter in the chemically combined state is approximately the
same, or that N is approximately the same for all atoms as
constituents of compound molecules, then the refraction-equi-
valents given by Gladstone are directly proportional to the
volumes of the atoms in the combined state, and then the
parallelism between dynic and refraction equivalents would
mean that 8 is nearly proportional to the volume. It is very
interesting, therefore, to inquire briefly whether there is any
evidence to prove that Gladstone’s refraction-equivalents are
proportional to the volumes of the atoms; and I think that
in Kohlrausch’s velocities of the ions in electrolysis we have
such evidence. If different solutions, such as those of KCl,
NaCl, or 4BaCl, ere electrolysed under identical cireum-
stances, then we know, according to Faraday’s law, that
each atom of K and of Na, and each half-atom of Ba, may be
considered to receive the same charge, so that they acquire
their ionic speeds under the action of the same accelerating
force. Accordingly, the ionic speed characteristic of an atom is
reached when the “ frictional” resistance to its motion is equal
to this accelerating force ; hence the “ frictional ”’ resistance is
the same for all atoms, or rather for all electrochemical equi-
valents. Now the “ frictional ” resistance will be a function
of the velocity of the atom and of its domain (atomic volume)
and of its actual volume as well as of the domain and actual
volume of the molecule of the solvent; but if water is the
solvent in all cases, the only quantities which vary from body

290 Mr. William Sutherland on the

to body are the velocity and the domain and volume of the
ions, so that we can say

“ frictional” resistance = $(V, u, U),
v V = F(u, U).

Now the simplest connexion that one can imagine between
the velocity and the domain and volume of the ion is that
the velocity will be greatest when the free domain or the
difference between the domain and the volume is greatest,
or, to be more general, when the difference between the
domain and some multiple of the volume is greatest; but
if N is the same for all combined atoms, then U is proportional
to the refraction-equivalent g. Hence the form of F is such
that it contains w—ag, where a is a constant. On studying
the experimental data I found that a might be considered
unity, and that V is a linear function of w—q. There is a
little difficulty in determining with accuracy the domain of an
ionic atom in a solution. Nicol, in his work (Phil. Mag. xvi.,
xviii.) on the molecular domains of inorganic compounds in
solution, has confined his attention almost entirely to differ-
ences of domains, making the assumption suitable to his purpose
that the inolecular domain of water is unaltered in solutions,
whereas we should expect that the greater part of the shrinkage
occurring on solution of an inorganic crystal happens in the
water, which is far more compressible than the crystal.

Accordingly I take the molecular domains of salts in the
solid state, as given by Long in his paper on diffusion of
solutions (Wied. Ann. ix.), as nearer to the true domain when
they are in solution than Nicol’s values ; but to allow to a
certain extent for the change of state on solution, I have assumed
that in each case the water experiences four fifths of the total
shrinkage and the dissolved salt one fifth. This is an arbitrary
adjustment, and is of no material importance to the comparison
to be made except as showing that the point has not been over-
looked. In the following Table are given under wu the mole-
cular domains, under g the molecular refractions (Gladstone’s),
in the next column their differences, under & the specific mole-
cular conductivities determined in highly dilute solution by
Kohlrausch and shown by him to be equal to the sum of the
velocities of the ions in each case. These are taken from his
paper (Wied. Ann. xxvi.), with a few additions from an
earlier one (Wied. Ann. vi.). Under & (calculated) are given
values of the conductivity calculated from the equation

k = 684+2°2 (w—g),

7

Laws of Molecular Force. 291

expressing the linear relation between conductivity or sum of
ionic velocities and u—gq.

TABLE XX XIX.

U. q. uUu—q. k. X (cale.).
AU een tees» 3 =i 53°5 39°3 18 107 108
ERE fi. esses 44 25 19 107 110
Lh a oee eee 36 18°8 iby 105 105
Shoe 41 32 9 87 88
1 (C151? deen poeR ee 32 21°7 10 87 90
ite OW ee roe 24 155 8:5 87 87
BG ine 55.2 5000 20°5 145 6 78 81
£MgCl, .....005. 20 14 6 80 81
2 02) 0: Lear 22 16 6 81 81
He 0] Ree 24 17-5 6:5 83 82
PCL, wowosina' 24 186 D4 86 80
22/710 Ul ule paeeeee 23 15°8 7 17 83

The agreement is here such as to prove a true connexion
between conductivity and u—q, the more striking as no relation
can be seen between conductivity and wu or q taken separately.
The only bodies I have omitted from Kohlrausch’s latter list
are the nitrates of some of the above metals and of silver, the
hydrogen compounds of the halogens, and the ammonium
compounds. These do not give results in harmony with
those in the last table, and, indeed, we should hardly expect a
compound radical like NO; to experience frictional resistance
in the same manner as a single atom like Cl, and as to the
hydrogen compounds they form a class by themselves with
respect to many physical properties. It will be as well to
show the amount of departure in these cases in the following

Table :-—

U. q. u—4. k. K (eale.).
ASS ists’ pss 56 26 30 327 134
Teg) ere anaes 50 16 34 327 142
RG 2? earee snes 42 11 dl 324 136
KEN 53 72. as 47 22 25 98 123
NINO N 8 oat se 36 19 17 82 LOD
INIEMINO Do Buccs 475 25°5 22 98 L116
iis L(G) ie areas 35°95 22-2 13 104 97

Kohlrausch has pointed out that there is some difticulty in
determining the true connexion between ionic velocities and
conductivities in the case of the bibasic acids SO, and COs, so
that we must leave them out of the count for the present.

292 Mr. William Sutherland on the

18. An Attempt to Determine the Velocity of Light through
the substance of the water-molecule.-—In spite of the excep-
tions, the relation demonstrated in Table XX XIX. is suffi-
ciently striking. To explain it, let us replace g by its value
(N—1)U ; then, in interpreting the expression u—(N—1)U
as occurring in our expression for the conductivity of a solu-
tion, there are two methods of procedure: first, we can assume
that w—U, the free or unoccupied part of the domain, is the
most likely to occur, in which case N=2; second, that w—cU
occurs in the expression for conductivity, and that ¢ happens
to have the same value as N —1, on which supposition it would
be desirable to determine N. .At present I know of only one
way of attempting to find N or v/V, the ratio of the velocity
of light through free ether to its velocity through the matter
of an atom, namely by means of Fizeau’s experiment, repeated
by Michelson and Morley, on the fraction of its motion com-
municated by flowing water to light passing through it.
Exactly in the manner of my paper (Phil. Mag. Feb. 1889,
p- 148) we can estimate the effect of the motion of matter on
the light passing through it. Let s be the distance travelled
by light in water flowing through the ether at rest with
a velocity 6 in the same direction as the light, v the mean
velocity of light through the flowing water, v' the mean
velocity through still water, v its velocity through free ether,
V through a molecule of water, J the mean distance through
a molecule, and a its mean sectional area ; then the total loss
of time experienced by a wave of unit area of front or a tube
of parallel rays, or, briefly, a ray of unit section in passing
through the matter-strewn path s instead of a clear path in free
zether, will be equal to its loss in a molecule multiplied by the
number of molecules passed through in the path. This
number, when the matter is at rest, is proportional to s, to a,
and to p/M, or it varies as sap/M ; but when the matter is in
motion it is reduced in the ratio 1—6/v": 1. The loss of time
in each molecule is found thus: J/V is the time taken to pass
through a molecule, and in this time the molecule moves
a distauce 1/6/V and the unit wave-front moves a distance
(1 + 6/V), which in free ether would take a time /(1+6/V)/v ;
so that the loss of time in a molecule is 1/V—/(1+8/V)/2.
Hence, the total loss of time in the path s may be written

)
ksalp (1 Lea 1 3)
abe) ge

But the loss of time is also s/v!—s/v; equating the two ex-

Laws of Molecular Force. 293

pressions and putting M/p=u and al=U, v/v"=n", o/ V=N
we get |

u(n!’—1) =U(N-1 _ “x )(1— en

as k& is equal to 1, seeing that if 6=0 and U=w, then N must
be equalto x. This equation is the companion to that for
still matter, namely,
u(n—1)=U(N—1).

But to allow for deformation of the wave-front in passing
through molecules it was shown (Phil. Mag. Feb. 1889,
p- 150) that this first approximation might be altered to the
form

u(n—1)=U(N—1) +09,
where ¢ is a constant, and this form was verified, so that we
may write

u(n!!—1) =U(N-1- °N) de ° nt + cp

5S & N Of,

neglecting the term in 6? ;
; ws N
as u(nl!—n) = —" U(N—1)(x oa +n")
een UCN!) nee ON

pee ed N"
i os Ou(n—)) in ay) +n}.
Now
Mice Ted =U; vd xO
MUR ah Galareaiue approximately,

where z is the fraction of the water’s velocity imparted to the
velocity v’ to change it to v’. Fizeau (Ann. de Ch. et de Phys.
sér. 3, t. lvii.) found a value °5 for 2, while Michelson and Morley
(Amer. Journ. Se. ser. 3, vol. cxxxi.), ina more extended and
accurate series of experiments, found a value e="43+:02,
which we will adopt. U(N—1)is equal to w(n—1) measured
in the vapour of water, for which Lorenz (Wied. Ann. xi.)
gives the value 5°6; the value for water at 20° C., according
to his data is 6, and n is 1:333, which may also be taken as the
value for n” where it occurs ; all these values being substituted
in the equation
ING) edt odie 4») 6 (i= ht)
Noten, Und), -

) i!

294 Mr. William Sutherland on the

give the value N=9. Hence the velocity of light through
the water molecule appears to be one ninth of that through
free ether. But before we could ascribe any degree of
accuracy to this estimate we should need to be surer of the
value of 2, whose measurement is attended with great experi-
mental difficulties. It is much to be desired that we had
similar measurements for other bodies than water, both liquid
and solid, to permit of other estimates of N, so as to see if it
is the same for all compound bodies, and also to decide be-
tween the theory here sketched and Fresnel’s hypothesis,
that matter carries its own excess of ether with it, so that
a= (n?—1)/n?, which in the case of water is ‘437, in excellent
agreement with Michelson and Morley’s experimental number ;
but one such agreement is not sufficient to establish an
hypothesis founded on such artificial grounds. However, if
N=9 then N—1=8, and we have the electrical specific mole-
cular conductivity k=68+2°2 (u—8U). Itis only a coinci-
dence that this agrees so exactly in form with Clausius’s
calculation that the number of encounters experienced per
second by a molecule of volume U moving amongst a number
of others of volume U is greater than that experienced by an
ideal particle moving under the same circumstances in the
ratio w:u—8U. Further experiment must elucidate the
subject-matter of these speculations.

19. Suggested relation between the change in the volume of an
atom on combination and the change in its chemical energy.
—Returning to the idea that the dynic equivalent furnishes
a measure of the volume of its atom, we can get a suggestive
glimpse into the relation between the volume of an atom and
its chemical energy. Kundt has recently (Phil. Mag. July
1888) shown that the velocities of light through the metals
(uncombined) are as their electrical conductivities, being in
the case of silver, gold, and copper greater than through free
ether, and as in this case both n—1 and N—1 are negative,
we see that (n—1)u or (N—1)U for the metals changes
greatly when the metals pass from the combined to the free
state. Now this is in strong contrast to the behaviour of the
non-metallic elements, which have been shown in the case of
O, N, C, 8, P, Cl, Br, and I to possess nearly the same values
of (n—1)u in the combined and free states, and the same may
perhaps be said of H. Again, in contrast to this approximate
inalterability of (n—1)w for these non-metals we have the
fact, already pointed out, that the dynic equivalents of H, O,
and N are much smaller in the free than the combined state.
If, then, the dynic equivalents give a measure of the volumes

Laws of Molecular Foree. 295

of the atoms in both states, we must consider the volumes of
free H, O, and N to be smaller than when they are combined,
the change of volume corresponding to the change of energy
on combination. [f this is true, then the elasticity and density
of the non-metallic atoms (or the equivalents of these proper-
ties in the electromagnetic or any other theory of light) are
so related that although the density changes (N—1)U re-
mains constant, whereas in the metallic atoms the relation
between density and elasticity must be quite different, because,
as we have seen, (N —1) U actually changes sign in some cases.

It would be possible to determine approximate values for
the dynic equivalents of the uncombined metals from Quincke’s
data for the surface-tension of melted metals, and also to get
some light on the constitution of salts from his measurements
of the surface-tension of melted salts, but these would be
most appropriately discussed in connexion with a general
study of the elastic properties of solids. I have, however,
satisfied myself that the dynic equivalents of the uncombined
metals are different from their values in the combined state.

To show the existence of an intimate relation between dynic
equivalents and chemical energy we can enumerate the follow-
ing propositions :—That in the great majority of inorganic
compounds the evolution of heat accompanying the passage
of an atom from the uncombined to the combined state is
almost independent of the nature of the atoms it combines
with, similarly the change of dynic equivalent of an atom on
combination is almost independent of the nature of the atom
it combines with ; that in organic compounds with the excep-
tion of the simpler typical forms the same proposition as this
applies both as regards heat and dynic equivalent.

These general remarks are intended to indicate the most
hopeful direction for the continuation of these researches to
open up new fields ; and yet in old fields there is abundance
of scope for the application ef the law of molecular force
towards the acquisition of a knowledge of the structure of
molecules, in the elasticity of solids, in the viscosity of gases
and of liquids, in the kinetics of solutions, and many kindred
subjects.

Melbourne, February 1890.

i996]

XXVIII. The Fusion-Constants of Igneous Rock. — Part III.
The Thermal Capacity of Igneous Rock, considered in its
Bearing on the Relation of Melting-point to Pressure. By

CaRL BarRus*.
[Plate VI.]

1. FNTRODUCTORY.—tThe present experiments are in

series with the volume-measurements of my last paper,
and the same typical diabase was operated upon. Since it is
my chief purpose to study the fusion behaviour of silicates,
more particularly the relation of melting-point to pressure,
the observations are restricted to a temperature-intervyal
(700° to 1400°) of a few hundred degrees on both sides of
the region of fusiont (§ 11).

2. Literature—LHxperiments similar to the present, but
made with basalt, were published quite recentlyt by Profs.
Roberts-Austen and Riicker§. The irregularities obtained
by these gentlemen with different methods of treatment
(heating in an oxidizing or a reducing atmosphere, repeated
heating, sudden cooling), the anomalously large specific heat
between 750° and 880°, where basalt is certainly solid, and the
absence of true evidences of latent heat||, contrast strangely
with the uniformly normal behaviour occurring throughout
my own results. Basalt is chemically and lithologically so
near akin to diabase (particularly after melting) that I anti-
cipated a close physical similarity in the two cases. Unfor-
tunately the account given of the basalt work is meagre.
Detailed comparisons are therefore impossible.

The elaborate measurements of Hhrhardt (1885) and of
Pionchon (1886-7) are less closely related to the present work.

APPARATUS.
3. The Rock to be tested About 30 grammes of diabase

were fused in the small platinum crucible together with which
they were to be dropped into the calorimeter. Two such
charged crucibles were in hand, to be used alternately. ‘The
molten magma, after sudden cooling, shows a smooth, appa-
rently unfissured surface, glossy and greenish black. After

* Communicated by the Author.

T The geological account of the present work is begun by Mr. Clarence
King, in the January number of the American Journal.

{ This was written some time ago. See American Journal, December
1891 and January 1892, A forthcoming Bulletin, No. 96, U.S. Geological
Survey, contains the work in full,

§ Roberts-Austen and Ricker: this Magazine, xxxii. p. 855(1891).

| Supposing basalt to solidify (§ 18) below 1200°,

The Fusion Constants of Igneous Rock. 297

drying and weighing, the mass is often found to have gained
5 per cent. in weight. I was at first inclined to believe that
this was attributable to water chemically absorbed by the
viscous magma; but the water is only mechanically retained,
for it passes off after 24 hours of exposure to the atmosphere,
or by drying at 200° C. for, say, 30 minutes. Hence I
weighed my crucibles at the beginning of each measurement,
having previously dried them at 200°. The solid glass, sud-
denly cooled from red heat, soon shows a rough and tissured
surface, and its colour changes from black to brown, possibly
from the oxidation of proto- to sesquisalt of iron, possibly from
mere changes in the optical character of the surface (§ 2).

Throughout the course of the work the charge of the
crucibles was neither changed nor replenished.

4. Thermal Capacty of Platinum.—Data sufficient for the
computation of the heat given out by the crucibles were
published in 1877 by Violle*, whose datum for the high
temperature (t) specific heat of platinum is ‘0317 + °000012¢.
Hence the increase of thermal capacity from zero Centigrade
to the same temperature is ¢(°0317 + -000006¢), which is the
allowance to be made per gramme of platinum crucible.

5. Lurnace.—Inasmuch as heat is rapidly radiated from the
white-hot slag, iit is necessary to transfer the crucible from
the furnace into the calorimeter swiftly. I discarded trap-
door, false bottom, and other arrangements for this purpose,
because the mechanism clogs the furnace, interferes with con-
stant temperature, and is too liable to get out of order. The
plan adopted is shown in figs. 1 and 2 (Plate VI.), in sectional
elevation and plan. ‘The body of the furnace consists of two
similar but independent bottomed half-cylinders, A A and
BB, of fire-clay properly jacketed, which come apart along
the vertical plane cece. The lid, LL, however, is a
single piece, and fixed in position by an adjustable arm (not
shown). Hach of the halves of the furnace is protected by a
thick coating of asbestos, CC, DD, and by a rigid case of
iron, HH, FF. Set ser ews, 9999, pass through the edges
of this in sucha way as to hold the fire-clay and asbestos in
place. The horizontal base or plate of the casing H F is bent
partially around the two iron slides, GG, along which the
two halves of the furnace may therefore be ‘moved at pleasure
while the lid is stationary ; as is also the blast-burner, H,
clamped on the outside (not shown), and entering the furnace
by a hole left for that purpose.

* Violle’s calorimetric work will be found in C. &. Ixxxv. p. 5483 (1877),
Ixxxvii. p. 981 (1878), Ixxxix. p. 702 (1879); Phil. Mag. [4] p. 818 (1877)

Phil. Mag. 8. 5. Vol. 35. No. 214. March 1893. X

298 - Mr. Carl Barus on the Fusion

The charged crucible is shown at K (figs. 1, 2, and 3), and
is held in position by two crutch-shaped radial arms, N,N, of
fire-clay, the cylindrical shafts of which fit the iron tubes
P, P, snugly, and are actuated by two screws, R, R. More-
over P, P are covered with asbestos (not shown), and thus
subserve the purpose of handles, by grasping which the two
halves of the furnace may be rapidly jerked apart. It is by
this means that the crucible is suddenly dropped out of the
furnace into the calorimeter immediately below (not shown).
Care must be taken to have the arms N, N free from slag. ~

6. Temperature.—As in the former work, the temperature
of the furnace is regulated by forcing the same quantity of
air swiftly through it at all times, but lading this air with
more or less illuminating-gas, supplied by a graduated stop-
cock. The amount of gas necessary in any case is determined
by trial, and observations are never to be taken except after 19
or 20 minutes’ waiting, when the distribution of temperature
is found to be nearly stationary. Nevertheless the tempera-
ture of the crucible is never quite constant from point to
‘point. I therefore measured this datum at three levels—near
the bottom, the middle, and the top of the charge, after the
stationary thermal distribution had set in (see Tables, § 10).
For this purpose the fire-clay insulator*, ¢¢, of the thermo-
couple, ab, passing through a hole in the lid, is adjustable
along the vertical. Before dropping the crucibie the thermo-
couple is withdrawn from the charge and suspended above it.
The cold junction is submerged in petroleum and measure-
ments made by the zero method. . -

When the charge is solid, a small platinum tube previously
sunk axially into the mass (see fig. 3) enables the observer to
make the three measurements for temperature as before. In
my later work I also encased the insulator of the thermocouple
in a platinum tube closed below (see fig. 1) when making
these measurements for the molten charge. Slag being a
good conductor at high temperatures, hydroelectric distor-
tions of the thermoelectric data may not otherwise be absent.

I state, in conclusion, that when constancy of temperature
is approached the hole in the lid is closed with asbestos, and
the products of combustion escape by the narrow seam in the
side of the furnace, through which, moreover, crucible and
appurtenances are partially visible.

* These are cylindrical stems, 0°5 centim. thick, 25 centim. long, with
two parallel canals running from end to end, through which the platinum
ee are threaded. Cf. Bulletin U.S. Geolog. Survey, No. 54, p- 95

Constants of Igneous Rock. — 299

7. Calorimeter.—A hollow cylindrical box, provided witha
hollow hinged lid, through both of which a current of cold
water at constant temperature continually circulated, sur-
rounded the calorimeter on all sides. Thus the temperature
of the environment was sharply given, and the correction for
cooling could be found and applied with accuracy. :

The calorimeter was a vessel of thin tinned sheet iron,
28 centim. long, 8 centim. in diameter, having a water-value
of 19 gramme-calories, and holding a charge of about 1200
grammes of water. The inside of the vessel was provided with
a fixed helical strip running nearly from top to bottom, and
was supported on a hard rubber stem. This could be actuated
on the outside of the outer case from below, and served as
a vertical axle around which the calorimeter could be rotated.
In this way the water within the vessel was churned, and
three small hard rubber rowels near the top gave steadiness
to the rotation. I pass the description of this apparatus
rapidly here, but shall recur to it in connexion with other.
calorimetric work.

The box or outer vessel of the calorimeter, with its pro-
jecting stem, was movable on a small tramway, the. tracks of
which lay at right angles to the slides G, G (figs. 1 and 2).
Thus at the proper time the lid of the box was opened and the
calorimeter rolled directly under the furnace. After receiving
the crucible the calorimeter was again rolled away and the box
closed, whereupon the temperature-measurements were made
by a sensitive thermometer inserted through a hole in the lid.

Were I to continue work like the present I should make the
crucible bullet-shaped, and provided with a permanent central
tube much like fig. 8. The splashing of water by the drop-
ping crucible (an annoyance which is sometimes serious)
would then be to a great extent obviated.

RESULTS.

8. Method of Work.—While waiting for stationary furnace
temperature I made the initial measurements for the cooling
of the calorimeter in time series. Knowing, therefore, the
time at which the body was dropped I also knew the tempe-
rature of the water into which it was dropped, accurately:
Similarly the three measurements for the temperature of the
charge had just before this been made in time series.

The experiments showed that ten minutes after submer-
gence the crucible and charge might safely be considered
cold, for the maximum temperature of the calorimeter was

X 2

300 Mr. Carl Barus on the Fusion

reached after 5 minutes. Hence the time from 10 to 15
minutes was available for making the final measurements for
cooling ; knowing the extremes, I found the intermediate
rates in accordance with the law of cooling. Thus, while the
calorimeter was being constantly stirred, its temperature was
measured at the end of each minute. Hence I knew the mean
excess of its temperature above its environment during the
course of every minute, and was able to add the corresponding
allowance for elation and evaporation at once. How im-
portant this correction is the Tables (§ 10) fully show. The
only drawback against sharp values is the lag error of the
thermometer ; but this is eliminated in a long series.

I have bated that both the calorimeter aa the eaeible.
were weighed before and after each measurement. The latter
data were taken.

9. Arrangement of the Tables——The two crucibles (§ 3)
and tubes (fig. 3) are designated I. and II. In all cases m
is the mass of the charge, M the calorimetric value of the
calorimeter (corrected for temperature), 7 the temperature of
the environment. © is the temperature at the top, the
middle, and the bottom of the charge at the time of submer-
gence. The mean value is also given. The temperature of
the calorimeter at the time specified is given under @, and a
parallel column shows the correction of @ for radiation.
Finally, the computed thermal capacity of the platinum cru-
cible and appurtenances (correction fh), and the thermal
capacity * h of the charge computed up to each of the con-
secutive times, are found in the last columns. A few obvious
remarks follow. Note that h reaches its true (constant) value
in proportion as the body is cold.

To avoid prolixity I have only given full examples of the
data here defined at the head of each table. The remainder
is abbreviated.

10. Tables——In the data of the first series (Table I.) only
one value of ® is in hand for the liquid state. Moreover the
construction of the furnace was somewhat faulty, not being
flat-bottomed. Hence these results are of inferior accuracy
as compared with Series II. (Table I1.), which are the best
obtained.

* The constant / is really the increase of thermal capacity above zero
degrees Centigrade.

Constants of Igneous Rock.

301

Tasie I.—Thermal Capacity of Diabase. First Series.

Platinum crucible, I., 11:169 g.; Platinum tube, L[., -985 g.
Platinum crucible, II., 11°271 g.; Platinum tube, IL., -654 g.

. | |
: | Mean 6. 'Correc- | Correc-
ae meeetme., | OQ... | ME) 6. tion tion h.
; | | ho, Ue | re h.
i———-| | ee |: ape? ee ee on eee ance Sees nee |
| °C. | Minutes.; °C. | 2. °C. | g.-cal. | g.-cal. |
eS ‘Dai esta NBO See ORAS Bape Ge daey: eases Immersion |
. ee 12022. | 22:30) +02) | 179 | 967 | Taquid. |
2 ih oa 33:36 g.| 25:20) -06 355 |
3 | | 25°50) -11 367
| 5 | 25°58| -20 372 | |
| 8 | 2540| -33 370 an |
11 25:25| 46 370 |
14 | 25:12] +60 370
iy Cee ee TBOGeHN5- OO ly eae || Sela Immersion |
ernie) 2.2... 1145 g. | 36-04} 1:10 | 166 | 364 | Liquid.
MMSE reir | ses... 33°75 g.
Bagh ge |. 1378° | 99-16] ...... Ce REA ee Tare ceou
| pie | 1202 g. | 30-97] 1:11 | 20°77 | 385] Liquid.
Peas 29°32 g.
| I} ia 1397 PCIe oe eee ae ee ae eeeiereion
| La EAE tls Bios 1196 g. | 2440; 69 18-0 373 Liquid.
OEE eg ere 32°22 g.
a Se. eee eee yee) Dice ey mean es. iitverten
fee | Ales, 1196 ¢g. | 29-98} 1:10 | 17-1 358 | Liquid.
Bosse 29°16 ¢.
| sel ee O | 1199 | 1166° PAs NPAs tail a eee |) See Immersion
14 1163 | 1195 ¢. | 22-98) -81 | 167 311 | Solid.
1138 | 82:22 ¢.
ete O- | L 100) | LOT8S | | NOTIG | Si ee Immersion
14 1074 | 1196 g. | 27:25] -74 | 164 | 263] Solid.
1060 | 29:16 ¢.
—- ce |S oe ———$————— —_—_—— =——_——___| __.___ Se
ete | tt 0 LOR | PLOOWC 4 SOh = ees ee emia ah Immersion
iu 998 | 1196 ¢. | 21°31] -47 | 139 | 242/ Solid,
| 983 | 32-23 ¢.
II. | 11 0 1035 | 1025° OG) SOONER De erate eet hee Immersion
14 1025 | 1195¢. | 25:55) -73 | 15:5 | 253] Solid.
1015 | 29:16 ¢. |
oe | ee ee | ee ee | ee
ef. 0 889 880° TGAHOUM Ah eeu a lvere meee Nt g eet ae Immersion
| 11 880 | 1198 g. | 21:59} 41 | 120 | 204] Solid |
872 | 32:24 pg.
Se eee eee Cea Eee
iC a ) B27 | WSO9Cm 0-07 ues] one Lt eee Immersion |
14 | 827 | 1192g. | 2439) 65 | 121 191 | Solid.
hee) | 833 | 29°16 g.| | |
{ | ; i |

302

Mr. Carl Barus on the Fusion

TasLe [1.—Thermal Capacity of Diabase. Second Series.

— =

10

10 |

PALER

10

997
995
987

1260
1251
1243

| 1354
1333

948
949

| 1364

| 1854 —

| 1339

877
873
870

| 1176
1164
1158

1215
1191
| 1186

782
780
780

| 1204
| -1195°
| 1183

Mean 0.

1319

| 954

1

993°

26:27 g.

i

M.

Mm.

1251°
1189 g.
26°39 g.

1192 ¢.
32°22 g.

1251°
1190 g.

26°07 g. |

1334°
1190 ¢. |

948°
1186 g.
32°22 g.

1352? >, |
1194 g. |
26°05 g. |

873°

| 1191 g. |

32°20 g. |
11GG2 |
LISis. |
25°97 g.

197°
1192 ¢.
25°95 g.

781°
1189 g.
3219 g.

1194°
1195 g.
25°90 g.

(mecca

1

| Correc-| Correc-. |
Time. 0. tion tion | Coe =
6. hee |
Minutes. °C. | °C. | g.-cal. | g-cal. : yh
fe) 18°94). o.0) =e Immersion
1 24-60; -04 206 | 236 Liquid.
2 26:°05| -10 305
3 26:52) -16 329 |
9) 26:61| -30 339
8. | 2645] -50 341
11 | 2625) -69 au) Gyo
14 26:08; -88 341
OF AAT. cence ee =. Immersion
igi 20°61) -22 13:38 | 2383) Solid.
0 1934) \.c2%.) | 22 eee TS See:
4, 2649) _. 80 20°38 | 842°5| Liquid.
0 13°78) <2... | 2.28 Immersion
14 | 21°79| °84. | 224 | Sirah Ss nguid:
0 | 20-24) ...... eee Immersion |
14 | 2581, -94 | 18:0 | 2266) Solid.
hues ae! Lose FV ee Sess
0 AAS) eee [gees tae | Immersion
14 24:82| °87 | 23:1 (| 3660) aiid:
0.) 14°83 sce ee eee Immersion
14 .| 20:13|- 46. | 2:9 9202 Salad:
Os] 17-40, vezi | eae ee: | Immersion |
14 | 24-21) 77 | 19:2 | 3095) Liquid.
0 | (4488) <2) hee Immersion
ea | 2113; 62 199 | 3185; Liquid.
0 19°36 Petes. Immersion
yaa Be 23:61) -94 104 | 179-7 Solid.
pot tl et : nod
0. 114:54|" cect | eee Immersion
145 | 21:22) -66 19:99 | 3179 Liguid.
|
|

Constants of Igneous Rock. — 303
Table LI. (contznued).

| Cone Mean 9. | Corree-| Correc-
N pins é. M. Time. Q. tion LOMey yas
fae |
Mm. | 0
ser OC, | Minutes.| °C. °C. | g-cal. | g.-cal.
era ibis | Li71° Y) TO S8i ee eee a AOE aot Immersion
BETO |) 1192 ¢- 14 27°30 2 VAD | 16°7 | 301°6 Solid.
1166 | 32:20 g. |
E |) 11 | 1106 | 1096°-| 0 - | 16-28! ...... | Behe Immersion
1094 | 1195¢: 14 | 23°24 “OL Lar 268°2 Solid.
1088 | 32-21 g. | |
mene 95) 4ge 0, TSF) | ea... Immersion
1244] 1191v.| 14 | 2655; -89 | 21-1 | 3888] Liquid.
1238 | 25°49 g.
MINIS | 1216201 0 81 13°67) ee ee Seasee Immersion
1216 | 1188¢.| 14 - | 21-60| “69 |-17-7 | 3303| Liquid.
/ 1202 | 29-43 ¢.
ee ae = pe a, es aah CEES
He ebie 1924)" 1215° 0 oS a 0 Wa C3, nega Peon See Ls Immersion
1216 | 1185 ¢. 14 26°27 ‘95 20°4 326°6 Liquid.
1205 | 25°57 g.

For brevity the later observations were averaged per
3 minutes, and under / the mean value for the last 11 minutes
is usually given.

In Series I. the increase of temperature from top to bottom of
the crucible is as large as 60° at 1200°, usually much smaller,
however, and falling off pretty regularly to 6° at 829°. In
Series II. the corresponding mean difference is about 25° at
1300°, 14° at 1000°, 10° at 800°. ‘The errors thus involved
cannot be greater than 2 per cent. in the extreme case ; but
since the distribution of temperature 1s measured, it is probably
negligible except at very high temperatures. I am inclined
to infer that the greater constancy of the solid distribution
as compared with the liquid is due to greater thermal con-
ductivity in the former case (solid), convection being neces-
sarily absent in both.

Considering the observational work as a whole, the data
are satisfactory, seeing that an error of 0°1°C. in the calori-
metric temperatures, initial or final, must distort the results
at least 1 per cent. But the real source of error is probably
accidental, and is encountered when the hot body falls through
the surface of the cold water.

INFERENCES.
11. Digest and Charts—In Tables III. and IV. I have

summarized the chief results on a seale of temperature. The

304

Mr. Carl Barus on the Fusion

results of the latter (Series II.) are graphically shown in the
chart (fig. 4), in which thermal capacity in gramme-calories
is constructed as a function of temperature *.
are drawn through the points, showing the mean specific
heats for the intervals of observations, solid and liquid. The
letter a marks the region of fusion.

TasiE III.—Thermal Capacity of Diabase.

Mean specific heat, solid, 800° to i100°
liquid, 1200° to 1400° .

Latent heat of fusion, at 1200°, 24 g.-cal.; at 1100°, 16 g.-cal.

99

Solid.
‘romp Teena | 2
| 829 | 191. |} 1025
| 80 | 204 || 1078
1001 | 242 | H1166
| |

Digest, of. § 15.

| Thermal

‘| capacity.

253
263
all

Straight lines

“304.
350.

Series I.

Liquid.

Thermal

‘| capacity.

358

Taste [V.—Thermal Capacity of Diabase.
Digest, ef. § 15.

Mean specific heat, solid, 800° to 1100° f
liquid, 1100° to 1400° .

Latent hea of fusion, at 1200°, 24 g.-cal.; at 1100°, 16 ¢.-cal.

29

Solid.
Temp. ee Temp.
oO te)
781 180 1096
873 202 (i171
948 227
993 238

|
|

Thermal

capacity.

Thermal

‘| capacity.

———

370
385

|
|
|

Series II.

290.
360.

| 1352

Liquid.
| |

Temp,| capacity. | T%P+ capacity

evinaeiel. - é
1166 | 310 || 1248] 339
1194 | 318 || 1251 | 340
1197] 319 || 1251] 342
1215 | 327 || 1334] 377
1218 | 330 367

* The corresponding chart for Table III. is almost identical with this.
+ Incipient fusion (?) at the base of the crucible.

Constants of Igneous Rock. 305
In both the tables, III. and IV., the solid points lie on lines

which, if reasonably curved, would be nicely tangent to an
initial specific heat of about 0°2 at °C. The grouping, in
other words, is so regular as to exclude the probability of
anomalous features, either in the observed or the unobserved
parts of the loci. The solid point near a (fig. 4, a similar point
occurs in Table III.) alone lies markedly above the curve ; but
inasmuch as in my volume work | found solidification to set in
at 1100°, it is altogether probable that the occurrence at 1170°
is incipient fusion (¢ 13).

The regularity of the liquid loci (Tables III. and IV.) is
slightly less favourable; but the discrepancies which occur
are above 1300°, and obviously accidental (§ 10, end).

12. Specific Heat.—As regards the mean specific heats be-
tween 800° and 1100° in Tables III. and IV., it will be seen
that the intermediate datum would satisfy both groups of
points about as well as the individual data given. A tracing
made of the first group practically covers the other. The
same remarks may be made for the liquid state. I have not
attempted any elaborate reductions, since the equations of
the necessarily curved loci would have to be arbitrarily
chosen, and since values for specific heat are of no immediate
bearing on the present inquiry.

13. Hysteresis.—Recurring to the suggestion of the pre-
ceding paragraph, it appears that the fusion behaviour of rocks
must be accompanied by hysteresis* of the same nature as
that which I observed with naphthalene and other substances:
for, whereas in my volume work with diabase I was able to
cool the rock down to 1095° without solidifying it, evidences
of fusion (at a, figs. 4 and 5) do not occur in the present
work until 1170° is reached. The magnitude of the lag is
thus of the order of (say) 50°, and its pressure-equivalent
may be estimated as 500 atmospheres.

14. Latent Heat.—In virtue of the fact that the (upper) end
of the solid locus (Tables II]. and IV.) may be carried so
near the beginning of the liquid locus, the datum for latent
heat is determinable with some accuracy, in spite of its sur-
prisingly small (relative) value. Difficulties, however, present
themselves in the determination of the true melting-point, a
datum which can only be sharply defined when the tempera-
ture of the crucible is quite constant throughout. I have,
therefore, considered it preferable to state the conditions at
1200° and at 1100°, the former being nearer fusion and the
latter very near solidification. The latent heats for these

* Am, Journal, xlil. p. 140 (1891); of ibid., xxxvili. p. 408 (1889).

306 The Fusion Constants of Igneous Rock.

temperatures are 24 and 16 respectively. The coincidence of
results in both of the independent constructions (Tables ILL.
IV.) is in a measure accidental. :
15. The Relation of Melting-point to Pressure.—The first and
second laws of thermodynamics leid to the equivalent of
James Thomson’s fusion equation, which in the notation of
Clausius* is dT/dp=T(o—7)/Hr’ ; where T is the absolute
melting-point, c—7 the difference of specific volumes solid
and liquid at T, 7’ the latent heat of fusion, and EK Joule’s.
equivalent. *

Combining the present Series I. of thermal measurements
with the former Series III. of volume measurements, I ob-
tain at 1200°, since T= 1470°, co—r="0394/2°72 (where 2°72,
is the density of the solid magma at zero), and 7’=24. |

dT
== == (ile
ak

and-at 1100°, since T=1370°, c—rT='0385/2°72, and 7 =16,

—,
—— 7 oe
(a 1100

Similarly, combining the present (heat) Series IJ. with the
former (volume) Series IV., at 1200°, since o—T='0352/2°72,
and 7’ = 24,

dT

—— =°()19 ;
dp pe

and at 1100°, since o —7T=°0341/2°72, and te 16,

([) ~-026
dp 1100

Hence the probable silicate valuet of dT/dp falls within the
margin (‘020 to ‘036) of corresponding data for organic sub-
stances (wax, spermaceti, paraffin, naphthalene, thymol). I
may, therefore, justifiably infer that the relation of melting-
point to pressure in case of the normal type of fusion is
nearly constant irrespective of the substance operated on, and
in spite of the enormous differences of thermal expansibility
and (probably) of compressibility. And in the measure in
which this is nearly true on passing from the carbon com-
pounds to the thoroughly different silicon compounds, is it

* Warmetheorre, i. p. 172 (1876). 2
+ For reasons to be stated elsewhere, 6m =a+'025p (where On is the

melting-point in °C. at the pressure p atmospheres) will be assumed in
making geological application of the above data.

Notices respecting New Books. 307

more probably true for the same substance changed only as
to temperature and pressure. In other words, the relation
of melting-point to pressure is presumably linear. « In my
work on the continuity of solid and liquid * these relations
are corroborated for naphthalene within an interval of 2000
atmospheres.

XXIX. Notices respecting New Bowes.

Treatise on Thermodynamics. By Purer ALEXANDmR, M.A.
London: Longmans, Green, and Co. 1892.

rom the preface it appears that this book is ambitious: it

claims to have elevated the science of Thermodynamics into
an organic unity from being a mere collection of detached propo-
sitions, to exhibit the thermodynamic relations as the outcome of
physical, as opposed to mathematical, considerations, to have
cleared away the fog that has enw rapped the subject of irreversi-
bility, and, by an enlarged definition of entropy, to have opened
up a mode of dealing with this subject, and, finally, to have
dissipated the haziness that has overlain the subjects of Motivity
and Dissipation of Energy.

The idea is to be deprecated, however, that, as hitherto treated,
the science of Thermodynamics has consisted of any more detached
propositions than the two, representing the two laws, which are
the necessary basis of this as of every other treatise on the sub-
ject, viz. that of the conservation of energy and that of the perfec-
tion of a reversible engine or its equivalent, together with their
consequences ; and indeed a set of relations, which are the expres-
sions in different forms of the same fact and which are all deducible
from each other by simple transformations, does not constitute
different but identical propositions. What the author has really
done is to express the two laws, 7. e. practically the values of the
dynamical equivalent and of Carnot’s function, in a manner even
more general than that worked out (though not otherwise employed)
by Clausius, viz. in terms of two general variables with any scale
of temperature whatever, and then from these expressions to deduce
particular thermodynamic relations by the substitution of particular
variables : and it is these relations, which are necessarily identical,
that constitute the “ detached propositions” above mentioned.

Eyen if this method does not really tend to promote the organic
unity of the science, it has without doubt its advantages and, by
reason of its generality, should find place in some form or other
in every formal text-book : it is certainly convenient if only as a
simple mode of demonstrating certain identities and even of bringing
to light identities, unimportant enough it may be, that might
otherwise escape recognition. At the same time it is unlikely that
general resort will be made to it for obtaining the really important

* Am. Journ, xlii p, 144 (1891).

303 Notices respecting New Books.

forms of the thermodynamic relations, each of which is patent on a
glance at the corresponding infinitesimal cycle.

In his investigation of these general expressions, the author
prefers not to avail himself directly of the fact that infinitesimal
changes of entropy and intrinsic energy are perfect differentials,
and so, according to Lord Kelvin’s simple plan, to apply the corre-
sponding criteria forthwith, this method savouring of mathematics
only: he follows Clausius’ original lead instead, without, however,
Clausius’ elaboration, and, taking an infinitesimal cycle composed
of two pairs of thermal lines of any different types, he sums up the
heat absorbed all round the cycle and also the changes of entropy,
and equates the former sum to the area of the cycle and the latter
to zero, this lengthier process being chosen as being of a more
distinctly physical character than the other. In the second of
these calculations the criterion of a perfect differential 1s of course
necessarily arrived at, since the process of determining the eri-
terion is essentially that of the method pursued ; attention might
therefcre with advantage have been called to the mathematical
character of this resulting equation, more especially as after
reading Chap. XV., wherein is given Lord Kelvin’s method, a
student will not be likely to have recourse to the other. Advan-
tageous, too, would be the omission in this calculation of the signs
of integration, which are finally discarded as quite unnecessary
and are not even introduced into the other calculation on p. 42.

With respect to irreversibility, itis pointed out that there may
be processes which, though not actually reversible, are, so far as the
working substance is concerned, in one direction equivalent to pro-
cesses that are reversible, in which case the changes of entropy
that occur in the working substance itself during such processes
(termed conditionally irreversible, in contradistinction to zintrinsi-
cally irreversible processes which have no such equivalents) depend
only on its initial and final states. But we are not really helped
by these considerations—which are not new—since it is the actual
sources &c. and the actual variations of entropy with which we
are really concerned.

The proposed enlargement of the definition of entropy which is
to help with the treatment of irreversibility greatly needs defence.
It is ushered in with an objection to the definition of the entropy
of a body or system as the sum of the entropies of its parts,
‘‘ which seems to me as unwarrantable as to define the temperature
of a body or system as the sum of the temperatures of its parts,” so
that to speak of entropy per unit mass “‘seems to me as un-
warrantable as to speak of temperature per unit mass”; though no
reason whatever is given or even hinted for likening entropy to
temperature rather than to such another physical property as
energy or volume. Such a definition of entropy is then desired
as will make the entropy of any system whatever invariable when
no heat passes into or out of it; and the author considers that he
has obtained such a definition—which satisfies also his previous
objection—in the formula X.rmg/S.7m, where m is the mass

Notices respecting New Books. 309

of a portion of the system of which the entropy and absolute
temperature are ¢ and r.

Assuming, however, the formula for a single mass, consider a
system of two masses m,, m, of the same substance with entropies
¢,, ¢, and at absolute temperatures 7,,7, respectively; and let
these masses be respectively expanded and compressed adiabati-
cally to the temperature - and then respectively compressed and
expanded isothermally to the pressure p: the system is now in
equilibrium, and, if vis taken such that no energy is lost or gained
by the system and that the heat lost by the one mass is equal
to that gained by the other, it is in that state of equilibrium
which the system would finally attain in isolation. If, then, ¢ is
the final entropy of the system, the heats lost and gained are
m,t (¢,—¢) and m,7 (¢—@,), whence ¢=(m,¢,+m,9,) /(m,+m,),
which does not satisfy the proposed formula except for r,=r, or
ce ao, being thus considered a debatable subject, it is surpri-
sing to see it postulated in the Introduction as an evident property
of a substance and to find it treated as such without debate or
explanation till the last chapter. In Maxwell’s opinion, “ itis to be
feared that we shall have to be taught thermodynamics for several
generations before we can expect beginners to receive as axiomatic
the theory of entropy.”

The account given of thermodynamic mnctivity and dissipation of
energy is good and clear, and it is properly remarked that Clausius’
theorem of the tendency of the entropy of the universe to a maxi-
mum is only a restatement in terms of entropy of Lord Kelvin’s
dissipation theorem published thirteen years earlier.

Though the book, therefore, does not seem quite to fulfil the pro-
mise of the Preface, it will doubtless prove a useful mathematical
introduction to the subject, which it does not pretend to treat
experimentally, the few experiments that are referred to being
mentioned only briefly and without detail.

Its arrangement seems capable of improvement. Thus, it is not
broken up into articles and its equations zre numbered consecu-
tively from first to last, so that references are tedious: the theorem
of the dependence on pressure of the temperature of the maximum
density of water is placed where it seems to be dependent on
thermodynamical considerations, while that of the equality of the
ratios of the principal specific heats and of the principal elasti-
cities is actually proved by such considerations, of which it is
absolutely independent—as is obvious, since it was known to
Laplace: and two general equations of very great importance,
(216) and (217), are deduced only incidentally to prove that the
principal specifie heats of superheated vapours are approximately
functions of temperature only.

There is some looseness of expression: thus the word perfect
is used as equivalent to efficient, which leads to the solecisms
more perfect and equally perfect ; the dyne, centimetre, and erg are
called French units: the dynamical equivalent of heat is said to be

B10 Notices respecting New Books.

-* 772 on the Fahrenheit scale”; Mayer is credited with an experi-
ment which was repeated by J oule, whose object in experimenting
-is-rather made to appear as the justification of Mayer's hypothesis.
Technical terms, too, are used without definition: thus the idea of
efficiency 1s introduced on p- 26 without any explanation though
-its quantitative measurement is concerned, and, indeed, when an
-tmplicit definition is finally given on p. 35 in connexion witha
Carnot cycle, it is in terms which are neither general nor such as
Carnot could have accepted. it may also-be pointed out that
in Chaps. XVI. and XVII. there is no Wee symbol for
absolute temperature, though everywhere else the letter 7 is used ;
that in Chapter XV. the muiceeieal specitic ation of entropy Abas
from that adopted elsewhere; and that in (151) only a particular
integral is given of the partial differential equation (150), the
general solution of which is K=7* f(;*—3Ar,"p) corresponding to
the characteristic v/7= U(p)+Ard\de 7—*f(7°--3Ar,"p).

The notation is not all that can be desired; that of partial
difterential coefficients is specially abused, after Clausius’ example,
_In being applied to denote thermal capacities, and in Chap. XI.
‘the differential coefficients of p and A with respect to ¢ are con-
tinually enclosed in brackets armed with some such subscript as 4,
which is entirely incorrect, as these are not partial differential
coefficients at all except with respect to the state of saturation ;
elsewhere, too, occurs repeatedly the meaningless form (dr/dt)g,
wherein 7 is an acknowledged function of ¢ only.

These are, however, blemishes which do not impair the value of
the book, but might be considered in view of a second edition.
_Among its good points must specially be mentioned the stress that
is laid on the proper definition of absolute temperature, though
on p. 168 the author himself uses the definition to which he objects ;
and there is an in‘eresting modification of Rankine’s characteristic
for gases suggested w hich deserves discussion. It is further well
remarked that even on the caloric theory Clapeyron’s version of
-Carnot’s operations (which is that adopted in the book) would be
improved by the adoption of Clausius’ modification,—which, by the
way, is ascribed to J. Thomson, though contained in that memoir
of Clausius which first set the subject on its new basis. It may
_be here remarked that Carnot’s own version of his cycle requires
no modification whatever, even from the new point of view.

Die physikalische Behandlung und die Messung hoher Temperaturen.
By Dr. Cart Barus. Leipzig: Barth, 1892.

THE subject of pyrometry, although forming an important
application of physics to manufactures, has not received from
physicists the attention which it deserves. One reason for this is
undoubtedly the difficulty of maintaining a constant high tempera-
‘ture, and another is to be found in the fact that the subject neces-
-sitates a detailed study of the alterations produced in the properties
-of matter by excessive heating. In order to measure any tempera-

Notices respecting New Pooks. 311

ture absolutely, we must assume that some property of a substance
remains constant at that temperature and at other known tempe-
ratures. If this is not the case, the same temperature will have
different values according tc the method by which it is measured,
and its true value will most probably be that found by a majority
of the methods. The author in his present volume has criticized
the different methods of determining temperatures, and has given
the results of experiments by himself and other workers in the
same field, from which it appears that only three properties remain
constant over wide ranges of temperature. These are the expan-
sion of gases, the change of their viscosity with temperature, and
the thermoelectric properties of certain wnetals, All these methods
yield consistent results for the value of a given high temperature. .

The second part of the volume is a discussion of the applicability
of these three methods, and Dr. Barus pronounces in favour of the
thermoelectric method. He then goes on to discuss the various
forms of apparatus which might be used in applying this method ;
from which it appears that a junction of platinum with an alloy of
platinum and iridium or rhodium gives the best results.

The book is the outcome of several years of difficult experi-
menting, and it is to be hoped that it will encourage a closer study
ot the properties of bodies, and especially of metals, at high tem-
peratures. James L. Howarp.

Hilfsbuch fur die Ausfuhrung elektrischer Messungen. By Dr. AD.
HEYDWEILLER. Leipzig: Barth, 1892.

Txis volume is not intended to serve as a text-book, but merely as
an epitome of the various processes of electrical measurement. It
gives in a collected form the different methods available for any
particular kind of measurement, together with a short description
of each; the formule necessary in order to calculate the results
being likewise quoted, but not proved. In the majority of cases,
however, the original papers and treatises are referred to for more
complete information on this latter pomt. Under each experiment
the author mentions the sources of error to which it is liable, and
the devices for avoiding or eliminating them are stated, when such
exist. This portion of the work has been carefully written, and
will be found useful when the choice of a suitable method of
measurement has to be made. At the end of the volume the
various electrical constants have been tabulated, and four-figure
logarithm and trigonometrical tables are also to be found there.
Although the title of the book refers to electricity only descriptions
of magnetic observations have also been given; but, as the author
tells us im his preface, these are treated more briefly, and only
those which are necessary in electrical measurements have been
described. JamEsS L. Howarp.

XXX. Proceedings of Learned Societies.

GEOLOGICAL SOCIETY.
(Continued from p. 150. }

December 21st, 1892.—Prof. J. W. Judd, F.R.S., Vice-President,
in the Chair.

Sheet following communications were read :—
1. “On a Sauropodous Dinosaurian Vertebra from the Wealden
of Hastings.” By R. Lydekker, Esq., B.A., F.G.S.

2. “On some additional Remains of Cestraciont and other Fishes
in the Green Gritty Marls, immediately overlying the Red Marls of
the Upper Keuper in Warwickshire.” By the Rey. P. B. Brodie,
MAS, EeG:S:

3. “ Calamostachys Binneyana, Schimp.” By Thomas Hick, Esq.,
B.A., B.Sc.

4. “Notes on some Pennsylvanian Calamites.” By W. S.
Gresley, Esq., F.G.S.

5. “Scandinavian Boulders at Cromer.” By Herr Victor Madsen,
of the Danish Geological Survey.

During a visit to Cromer in 1891 the author devoted much
attention to a search for Scandinavian boulders, and obtained three
specimens; one (a violet felspar-porphyry) was from the shore, and
the other two were from the collection of Mr. Savin. ‘The first was
considered to come from S.E. Norway, and indeed Mr. K. O. Bjorlykke,
to whom it was submitted, refers it to the environs of Christiania.

The author considered that the two specimens presented to him
by Mr. Savin, who had taken them out of Boulder Clay between
Cromer and Overstrand, were from Dalecarlia; and these were
submitted to Mr. E. Svedmark, who compared one of them (a brown
felspar-hornblende-porphyry) with the Gronklitt porphyry in the
parish of Orsa, and declared that the other (a blackish felsite-
porphyry) might also be from Dalecarlia.

January llth, 1893.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.

The following communications were read :—

1. “ Variolite of the Lleyn, and associated Volcanic Rocks.” By
Catherine A. Raisin, B.Sc.

The district in which these rocks occur is the south-western part
of the Lleyn peninsula, marked on the Geological Survey map as
‘ metamorphosed Cambrian.’

_ Some of the holocrystalline rocks are probably later intrusions.
The igneous rocks, which are described in detail in the present paper,
belong to the class of rather basic andesites or not very basic basalts ;
they show two extreme types, which were probably formed by

ee

Intelligence and Miscellaneous Articles. 313

differentiation from an originally homogeneous magma. Corre-
sponding to the two types of rock are two forms of variolite.
These are fully described, and their mode of development is dis-
cussed.

The variolites occur near Aberdaron and at places along the coast.
Their spherulitie structure often is developed towards the exterior
of contraction-spheroids, and in this and in other particulars they
correspond with those of the Fichtelgebirge and of the Durance.
The volcanic rocks include lava-flows and fragmental masses, both
fine ash and coarse agglomerate. They are associated with lime-
stones, quartzose, and other rocks, which are possibly sedimentary,
but which give no trustworthy evidence of the age of the variolites.

2. “ On the Petrography of the Island of Capraja.” By Hamilton
Emmons, Esq.

The rocks of Capraja consist generally of andesitic outflows resting
on andesitic breccias and conglomerates. ‘The southern end seems
to have formed a distinct centre of volcanic activity, whose products
are younger in age and more basic in character than the rocks of the
rest of the island, and may be termed ‘ anamesites.’ The lavas
appear to have flowed from a vent at some distance from the cone
which probably occurred here and gave out highly scoriaceous
fragments. In the other parts of the island andesite is almost
everywhere found, with patches of the underlying breccias here
and there in the valley bottoms. The chief centre of activity prob-
ably lay west of the centre of the island.

Petrographical details of the andesites and anamesites, descrip-
tions of the groundmass and included minerals of each, and chemical
analyses are given. As regards the age of the constituents, the
author arranges them in the following order, commencing with the
oldest :—magnetite, olivine, augite, mica, felspar, nepheline.

XXXI. Intelligence and Miscellaneous Articles.

ON A NEW ELECTRICAL FURNACE. BY M. HENRI MOISSAN.

HIS new furnace is made of two carefully plane pieces of quick-
lime one placed under the other. In the lower one is a longi-
tudinal groove for the two electrodes, and in the middle is a small

cavity more or less deep acting as a crucible; it contains a layer

ot a few centimetres of the substance to be acted upon by the are.
A small carbon crucible may also be placed in it containing the
substance to be calcined. In the reduction of oxides and the
fusion of metals, larger crucibles are used, and through a cylin-
drical aperture in the upper brick small] cartridges of the compressed
oxide and carbon can from time to time be added. The diameter
of the carbons which act as conductors will of course vary with the

strength of the current; after each experiment the end of the
carbon is changed into graphite.

The current most frequently used was one of 30 amperes and

Phil. Mag. 8. &. Vol, 35. No. 214. March 1893. iy,

314 Intelligence and Miscellaneous Artzcles.

55 volts; the temperature did not much exceed 2250°. A current
furnished by a gas-engine of 8 horse-power was 100 amperes and
45 volts produced a temperature of about 2500°. Finally, thanks
to the courtesy of M. Violle, we had at our disposal 50 horse-
power ; the are in these cunditions measured 450 amperes and
70 volts, the temperature was about 3000°.

With high-tension experiments certain precautions must be
taken and the conductors be carefully insulated. Even with
currents of 30 amperes and 50 volts, like those used at the
beginning of the investigation, the face must not be exposed to a
prolonged action of the electrical light, and the eyes must always
be protected by means of very dark glasses. Electrical sun-strokes
were very frequent at the outset of these researches, and the
irritation produced by the are on the eyes may produce very painful
congestion.

The temperatures given are only approximate; they will be
especially determined by M. Violle by methods to be afterwards
described. A certain number of the results obtained are briefly
enumerated.

When the temperature is near 2500°, lime, strontia, and magnesia
crystallize in a few minutes. If the temperature reaches 3000° the
substance of the furnace itself—quick-lime—melts and runs like
water. At this same temperature carbon rapidly reduces calcic
oxide, and the metal is liberated freely ; it unites readily with the
carbon of the electrodes, forming a calcic carbide, liquid at a red
heat, and which can be easily collected. Chromic oxide and magnetic
oxide of iron are melted rapidly at a temperature of 2250°.
Uranium oxide when heated alone is reduced to protoxide, erystal-
lizing in long prisms. Uranium oxide, which cannot be reduced
by carbon at the highest temperature of our furnaces, is reduced
at once at the temperature of 8000°. In ten minutes it is easy to
obtain a regulus of 120 grains of uranium.

The oxides of nickel, cobalt, manganese, and chromium are
reduced by carbon in a few minutes at 2500°. This is a regular
lecture experiment not requiring more than a quarter of an hour.

By this method we have been able to cause boron and silicon to
act on metals, and thus obtain borides and silicides in very
beautiful crystals.

This investigation is being continued.—Comptus Rendus, Dec. 12,
1892,

ON THE DAILY VARIATIONS OF GRAVITY. BY M. MASCART.

I have on former occasions used under the name of a gravity
barometer an instrument by which the variation of gravity between
different stations may be determined. The apparatus has the
drawback of being very fragile, but the same arrangement haa
great advantages in examining whether there are temporary Varia-
tions in one and the same place.

For some years past I have arranged a barometric tube contain-
ing a column of mercury four metres and a half in length, which

Intelligence and Miscellaneous Articles. 315

counterbalances the pressure of a mass of hydrogen contained in a
lateral vessel. The whole apparatus is sunk in the ground with
the exception of a short column of mercury at the top. The level
of the liquid is compared with a lateral division, the image of which is
formed in the axis of the tube, and the points may be fixed to
within the ;4, of a millimetre.

Direct observations at different times of day only showed a
continuous course, the greater part of which was due to inevitable
changes of temperature ; certain results can only be obtained by
photographic registration.

In the proofs submitted the differences of level are multiplied
by 20; they correspond to the variations which are directly ob-
served on a column 90 metres in length.

The curves ordinarily present a very regular and slow course
which is especially due to changes of temperature; but for some
days sudden accidents are seen, the duration of which is from
fifteen minutes to an hour, and which do not seem to be explicable
otherwise than by correlated variations of gravity. These accidents
may attain and even exceed 5), of a millimetre, which corresponds
to so¢yp OF One second per day, supposing that they lasted the
whole day.

In order to have a term of comparison, it is sufficient to observe
that if the difference between high and low water is 10 metres,
the liquid layer would produce a variation of spy of the level
value of gravity, that is one fifth of the preceding,

The existence of these temporary variations of gravity appears
undoubted and deserves attention. I intend to organize at the
Observatory of the Parc Saint Maur an apparatus constructed
with more care, from which all casual trepidation of the ground is
excluded, and the indications of which can be continuously followed.

Observations of this kind will no doubt present a peculiar interest
in voleanic districts if the changes are due to displacements of
masses in the interior.—Comptes Rendus, January 30, 1893.

PRELIMINARY NOTE ON THE COLOURS OF CLOUDY
CONDENSATION. BY C. BARUS.

By allowing saturated steam to pass suddenly from a higher to
a lower temperature (jet) in uniformly temperatured, uniformly
dusty air, the following succession of colours is seen by transmitted
white light, if the difference of temperature in question continually
increases :—F aint green, faint blue, pale violet, pale violet-purple,
pale purple, muddy brown-orange, straw-yellow, greenish yellow ;
green, blue-green, grey-blue, intense blue, indigo, intense dark
violet, black (opaque); intense brown, intense orange, yellow,
white.

Seen by reflected white light, the same mass of steam is always
dull neutral white.

If the colours enumerated be taken in the inverse order, be-
ginning with white, they are absolutely identical with the inter-
ference-colours of thin plates (Newton’s rings) of the first and

316 Intelligence and Miscellaneous Articles.

second order, seen by transmitted white light under normal inci-
dence. ‘Thus it is worth inquiring whether small globules of water,
when white light is normally transmitted, affect it like thin plates.
For a given homogeneous colour, if I be the intensity of the incident
licht and & ( 04 to -05) the reflexion-coefficient, then after a single
transmission the interference maxima and minima are

(1-k)(1+)1 and (1—ky(1—-2 1;

they differ only very slightly. But if there be an indefinite number
of particles all of the same size available, then this process is in-
definitely repeated in such a way that while the coloured light is
not extinguished, the admixed white lght becomes continually
more coloured. Hence, after a sufficiently great number of trans-
missions, the emergent ray will show intense colour. Seen by
reflected light, the case is almost the converse of this. For a single
particle the masses which interfere are (Kl and k(1—<)?1) weaker,
but nearly equal, and the interference is therefore very perfect.
It is not, however, capable of indefinite repetition, for after each
interference the direction is reversed. The light which emerges in
a direction opposite to the incident ray must therefore have passed
through the particles, 7. e. it has been brought to interference both
by reflexion and by transmission, and its colour is thus virtually
extinguished.

The final point to be considered is the occurrence of black between
brown and dark violet of the first order. Here, however, for
relatively very small increase of the thickness of the plate, the
colours run rapidly from brown through red, carmine, dark red-
brown to violet. Hence these interferences are apt to occur to-
gether and an opaque effect is to be anticipated. Particularly is
this presumable, because the opaque field is coincident with the
breakdown of the steady motion * of the jet.

Thus it seems that the colours of cloudy condensation may,
without serious error, be interpreted as a case of Newton’s inter-
ferences by transmitted light. In so far as this is true, one may
pass at once from the colour of the field to the size of the particles
producing it; and the dimensions so obtained agree well with R.
v. Helmholtz’s estimate made in accordance with Kelvin’s equation
for the increase of vaponr-tension at a convex surface. In the
study of the condensation phenomena vapour-liquid, the experi-
mental power of a method, which is adapted for instantancous
observation, and which, for a certain range of dimensions, not only
discriminates between vapour and a collection of indefinitely small
suspended water-globules, but actually defines their size, cannot
be overestimated. An account of my work, together with other
allied observations, will be given in the March number of the
‘American Meteorological Journal.’—Silliman’s Journal, February
1893. |

* IT refer here to Osborne Reynolds’ work (Phil. Trans. iii. p. 935, 1883)
with liquid jets, according to which, after a certain critical velocity is
surpassed, the uniformly steady motion breaks up into eddying motion.
I am also searching for Reynolds’ lag phenomenon (J. ¢. p. 957).

THE
‘LONDON, EDINBURGH, ano DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FIFTH SERIES.]

APREL 1893.

XXXIL, On Plane and Spherical Sound-Waves of Finite
Amplitude. By Cuaries V. Burton, D.Sc.*

Part I.— PLANE WAVES.

1. HE subject of plane waves of finite amplitude has
been considered by Riemann{; and so long as we
confine our attention to the case where velocity and density
are everywhere continuous, his investigation, as is well known,
leaves little to be desired. It will not, therefore, be necessary
here to make further reference to this aspect of the subject ;
but there is one part of Riemann’s work which Lord Rayleigh
has clearly shown to be unsatisfactory, and it is this point
which we have now especially to consider. Lord Rayleigh
says t:— | |
a It has been held that a state of motion is possible
in which the fluid is divided into two parts by a surface of
discontinuity propagating itself with constant velocity, all
the fluid on one side of the surface of discontinuity being in
one uniform condition as to density and velocity, and on the
other side in a second uniform condition in the same respects.
Now, if this motion were possible, a motion of the same kind
in which the surface of discontinuity is at rest would also be
possible, as we may see by supposing a velocity equal and

* Communicated by the Physical Society: read February 24, 1898,

¥ “Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwing-
ungsweite,” Gott. Abhandi. t. viii. (1860); reprinted in Werke, p. 145.

{ Theory of Sound, vol. ii. § 253, p. 41.

Phil. Mag. 8. 5. Vol. 35. No. 215. April 1893. Z

318 Dr. C. Burton on Plane and Spherical

opposite to that with which the surface of discontinuity at
first moves, to be impressed upon the whole mass of fluid. In
order to find the relations which must subsist between the
velocity and density on the one side (w, p,) and the velocity
and density on the other side (wz, p,), we notice in the first
place that by the principle of the conservation of matter
Polg=pity. Again, if we consider the momentum of a slice
bounded by parallel planes and including the surface of dis-
continuity, we see that the momentum leaving the slice in the
unit of time is for each unit of area (p9v.=p1u1)Ue, while the
momentum entering it is p;u,”. The difference of momentum
must be balanced by the pressures acting at the boundaries of
the slice, so that

Pilly (U2— Uy) =p — Po = a(p1— po),

=an/(@), m=an/(%)
U,=a Un =A 5
: We Sosy P2

The motion thus determined is, however, not possible; it
satisfies indeed the conditions of mass and momentum, but it
violates the condition of energy expressed by the equation

whence

Won Lap AS 2 99
3 Ug 7 Uy =a log pi—a log po.

2. The assumed motion here criticised is one in which
density and velocity are constant for all points on the same
side of the surface of discontinuity, while this surface itself is
propagated through the fluid with constant velocity. It is
easily shown, however, that the same objection applies when,
on either side of the surface, velocity and density vary con-
tinuously in the direction of propagation, while the velocity
of propagation of the surface is also allowed to vary. For
let 8 (fig. 1) be a surface of discontinuity which
is being propagated through the fluid, while the Fig. 1.
planes A, B, parallel to S and lying on either |
side of it, are fixed in the fluid. At a given
instant let

distance of S from A = m,
ry) BB, S=n;

density and velocity of fluid just to the left
of Po U4,

density and velocity of fluid just to the right
of S=Ppo, w 5

velocity with which § is travelling = V.

Sound- Waves of Fimte Amplitude. 319

Then, since A and B are fixed in the fluid, they are ap-
proximately moving with the respective velocities uw, ug; m
and n being taken sufficiently small. On the same under-
standing, the mass of fluid between A and B (referred to
unit surface) =mp,+mnp,; and since this mass must remain
constant,

d
ap (mpi + Mpa) =93
2. e. in the limit, when m and n are infinitesimal,

dm dn
Bae aa Pee =0,
or

pi( V —2) =p.(V—w,). ni ir AC a Sabor 5 te

Similarly, if p, and p. are the pressures corresponding to
p; and pe, the principle of momentum gives:—

p\—po= rate of change of momentum between A and B

d
= oF (u3p1m + Upon)
= um pi(V—u)—Uaps(V—ue). » 2 - - + « (2)

If the energy per unit volume corresponding to density p
(in the absence of bodily motion) is called y(p), the principle
of energy would further give

Pi1—Poo= rate of change of energy between A and B

= 3m( spin? + x(01)) + m(4 par +x(02) )}
= feprs’ +x (Pr) (V —1) — faparle’ +x (92) t (Vue). (8)

Since (1), (2), and (3) involve only the instantaneous values
of w, Pi, U2, P2, and V, together with explicit functions of such
values, while the space- and time-variations of all these quan-
tities are absent from the equations, it is evident that the
conditions to be satisfied at the surface S are the same as if
Ur) Pi) U2) P2, V were absolute constants. We conclude then,
that, with our assunvptions, a surface of discontinuity cannot
be propagated through a fluid with any: velocity, uniform of
variable, except under that special law of pressure for which
progressive waves are of accurately permanent type.

3. What, then, becomes of waves of finite amplitude after
discontinuity has set in? We may emphasize this difficulty,
and at the same time obtain a clue to its solution, by con-
sidering the following case (fig. 2):—-A is a piston fitting a

Z 2

320 Dr. C. Burton on Plane and Spherical

cylindrical tube (or, if we Fig. 2.
please, is a portion of an un-
limited rigid plane). All the
air to the right of A is initially
at rest and of uniform density,
and then A is impulsively set in
motion, and kept moving to the right with uniform velocity v.
Consider the speed with which the disturbance generated by
A advances into the still air to the right; it is evident that
in all cases the front of the disturbance must advance faster
than A. ‘Take, then, the case in which

U> a,

where a is the propagation-velocity of infinitesimal disturb-
ances. Two alternatives present themselves :—

(i.) If velocity and density are always either constant or
continuously variable in the direction of propagation, the rate
of propagation at any point will, in accordance with known

principles, be =
d
/ Ere

and therefore at the front of the disturbance, where w=0 and
p = the “undisturbed” density, the velocity of propagation
will be simply =a; that is, less than the velocity with which
A is advancing. Obviously this will not do.

(ii.) If velocity and density are not always either constant
or continuously variable, that is, if one or more surfaces of
discontinuity are being propagated through the air, we are
met by the difficulty explained in the last section.

4, A simple mechanical analogy will help to indicate the
actual motion. A number of equal spheres, of the same
material throughout, are capable of sliding without friction

Fig. 3.
{iHO—0—0—0=0=0-
=1]}@=O=0=—0=—0=O=
— 71 DO©=02 0-0

along a straight bar (fig. 3), and are connected together by a
number of very weak and exactly similar springs (not shown),
so that. when there is equilibrium they are equally spaced

Sound- Waves of Finite Amplitude. 321

along the bar. If one of the spheres were moved backwards
and forwards through a small range, a disturbance would
travel through the whole system, but owing to the weakness
of the connecting springs it would travel very slowly. Sup-
pose, now, that the last sphere on the left hand is connected to
a movable piston by a spring half the length of the others,
but otherwise similar to them; and let this piston be suddenly
moved to the right with a considerable velocity which is kept
constant, and which we may call unity. The weak connecting
spring between the piston and the first sphere produces no
sensible effect until the two are almost in contact, when the
sphere rebounds with velocity 2. This first sphere then
strikes the second, imparting to it the velocity 2, and at the
same time coming to rest. The positions of the spheres after
successive equal intervals of time are represented in fig. 3,
where the number written on any sphere represents its velo-
city just after the impact which it is suffering. No number
is written on those spheres which have not so far been affected
by the motion. From this it will be evident that when the
piston moves to the right with a constant velocity which is
very great compared with the propagation-velocity of infini-
tesimal vibrations of the system, the disturbance advances to
the right with twice the velocity of the piston, provided that
the diameters of the spheres are excluded from the reckoning.

Now suppose that the spheres are too small and too close
together to be individually distinguished; then, at any instant,
the system will appear to be divisible into two parts, in one
of which the velocity is unity, while in the other it is zero;
and in the moving part the spheres will appear to be twice as
thickly condensed as in the still part. That the constant
velocity of the piston is very great compared with the propa-
gation-velocity of small vibrations is of course only a sup-
position introduced for the sake of simplicity. If, on the
other hand, these two velocities are comparable, two adjacent
spheres will always remain finitely separated from one another,
and the velocity of any individual sphere within the disturbed
stretch will never be as small as zero, or as great as twice the
velocity of the piston ; the mean velocity within the disturbed
stretch being equal to that of the piston. When the spheres
are very small and very close together, we shall still have
apparently an abrupt transition frem finite velocity and greater
density to zero velocity and smaller density; and the energy,
which is apparently lost.as the spheres pass from the latter
condition to the former, exists as energy of relative motion
and unequal relative displacement amongst the spheres in the
disturbed stretch. :

5. Let us now compare the case just considered with the

322 Dr. C. Burton on Plane and Spherical

case of § 3 (fig. 2): and first, concerning the nature of the
analogy, it should be noticed that the individual spheres are
not the analogues of the separate gaseous molecules, but that
when both spheres and molecules are very small and very
numerous, the apparently continuous properties of the system
of spheres correspond to similar properties of the gas. The
connecting springs represent the elasticity of the gas, iso-
thermal or adiabatic as the case may be, and the energy of
relative motion and unequal relative displacement amongst
the disturbed spheres suggests that there is a production of
heat over and above that which would be due to the (iso-
thermal or adiabatic) change of density ; that is, a diss¢pative
production of heat. The motion considered in the last section
properly corresponds to the case where there is no conduction
of heat, so that the connecting springs are the representatives
of adiabatic elasticity, and the additional heat generated
remains wholly within the more condensed part of the air.
If we make the somewhat violent assumption that the tempe-
rature of the air remains constant throughout, the additional
heat generated will be conducted away isothermally, and the
equivalent energy will be, for our purposes, entirely lost.
To represent this case by means of our spheres we should
have to regard the connecting springs as representing iso-
thermal elasticity, while the energy of relative motion and
unequal relative displacement among the disturbed spheres,
as fast as it is produced, is to be consumed in doing work
against suitable internal forces.

6. The mechanical system of spheres and springs, having
suggested a solution, has served its purpose, and it now
remains for us more closely to consider the aerial problem in
the light of this suggestion. We may take, first, the case
where the temperature is supposed to be invariable; for
although such a supposition is necessarily far removed from
the truth, it leads to very simple results, which indicate well
enough the general character of the motion. Let the piston
A (fig. 4) be moving to the
right with constant velocity Fig. 4,

v (which may be either less
or greater than a, the velo-
city of feeble sounds in air).
Assume all the air between
A and a parallel plane sur-
face B to have the velocity v
and density p,, while all the air to the right of B is at rest
and has the density pp». Let the plane B move to the right
with velocity V. Then the invariability of mass between A

Sound- Waves of Finite Amplitude. 323

and a plane C fixed in the still air gives

pi(V—v)—pyv=0; . . .. . 4)
while from the principle of momentum,
Pi (V— v) Olam 0's .=, hans Sosy tee (5)

the pressure p being a function of p only, since the tempera-
ture is supposed to be constant throughout. If we assume
for this case the truth of Boyle’s law, so that p=a’p always,

(5) becomes
py(a? — Vv + v7) =pya”, SRR thea (6)

which together with (4) is sufficient to determine V and p;
when v and py are given. Taking all these quantities to
remain constant throughout the motion, we see that at each
instant the following conditions are satisfied :-—

(i) Every necessary condition between A and B, since
density and velocity are there constant with respect
to space and time ;

(1) Every necessary condition to the right of B, since the
air there is at rest and in a constant uniform state ;

(iii) Equality between the velocity of A and that of the
air in contact with it ;

(iv) At B, the conservation of mass and momentum, which
are necessary conditions, and which, together with
our supposition that the temperature is somehow
maintained uniform, are sufficeent to determine what
takes place at B*.

Moreover, if at a time ¢ (reckoned from the instant when
A was impulsively started into motion) we take the distance
of B from A to be (V—v)t, so that initially B coincides with
A, the initial conditions are satisfied.

‘Thus the assumed motion satisfies all the necessary con-
ditions ; it is therefore the actual motion.

7. Let us now examine what occurs when no heat is
allowed to pass by conduction or radiation ; a state of things
much more nearly realized in practice. Suppose the motion
of A and the condition of the undisturbed air to be the same
as in the last section, while the (constant) velocity of B is
now called V’, and the density and pressure of the air between
A and B (called p’, p’ respectively) are also taken to be uni-
form and constant. At each instant, in place of (4) and (5),

we shall now have
AANg= ©) gests hy. se ya nae)
pruCV =v) = pi. ay. ew 6) (8)

* Energy appears to be lost, because dissipatively produced heat is
conducted away isothermally,

324 Dr. ©. Burton on Plane and Spherical

Since we assume that there is no transference of heat by
conduction or radiation, the rate at which the total energy of
the system increases must be equal to the rate at which work
is being done upon it by the piston A. Let @ be the abso-
lute temperature to the right of B, that between A and B
being 0’, and let us further assume for simplicity that

P a const. :

pe
while y, the ratio of the two specific heats, is also supposed
constant. It can then be shown without difficulty that the
total energy per unit mass between A and B exceeds that to
the right of B by
Po O —O% fe es
(y—1)po % 2°

and multiplying this by p,V’, the mass of air which crosses
one unit of the surface B in each unit of time, we obtain the
rate (referred to unit area) at which the system is gaining
energy. Again, the rate at which unit area of the piston does
work on the system

als

Ee ges a ae
Tet a ed eeiae

and equating this to the rate of gain of energy, we obtain

po mes wv PoV'! pe
PO 505 V=PyV 5) + (y—1)0, (0 ,). a ° (9)

We may also write equation (8) in the form
plo(W'—v) = $F (p'6'—pr)s - ~~ (10)
Po%

and (7), (9), and (10) will then serve to determine V’, p',
when ¥, po, 9 are given. Since we have taken all these
quantities to remain constant throughout the motion, we see,
as before, that at each instant all the necessary conditions are
satisfied ; the principles of mass and momentum, together
with our supposition that there is no exchange of heat, being
sufficient to determine what takes place at B. Again, if ata
time t from the commencement of the motion we take the
distance of B from A to be (V’—v)é, so that initially B coin-
cides with A, the initial conditions are satisfied. The assumed
motion thus satisfies all the necessary conditions, and is there-
fore the actual motion.

8. If we compare the results of the last two sections with

Sound- Waves of Finite Amplitude. 325

those given by Riemann*, we shall find complete accordance
so far as §6 is concerned, though with §7 the case is dif-
ferent ; and this may be easily explained. We cannot in
general investigate the motion of a (frictionless) compres-
sible fluid by means of the equations of continuity and
momentum, without further making some supposition as to
the exchange or non-exchange of heat, and so we usually
assume either that the temperature remains constant, or that
there is no exchange of heat: in either case (provided the
motion is continuous), the pressure is a function of the
density only. Ata surface of discontinuity there is not only
the ordinary heating effect due to compression, but also, as
we have seen, a dissipative generation of heat, and so, when
applying the equations of continuity and momentum at such
a surface, we must know what becomes of this additional
heat. Now in all cases Riemann makes the assumption that
the pressure is a function of the density only, and this is
necessarily equivalent to an assumption concerning the trans-
ference of heat. Throughout most of his treatment of waves
of discontinuity Riemann assumes that temperature is
constant and that Boyle’s law holds good; accordingly our
§ 6 is entirely in harmony with his conclusions, in fact (4)
and (5) are only particular forms of equations given by
Riemann. Of course the hypothesis that a portion of gas
can be instantaneously compressed to a finite extent without
any appreciable change of temperature, is not in accord-
ance with experience, but provided we accept the assump-
tion that the temperature remains constant throughout, all that
Riemann says concerning the propagation of waves of discon-
tinuity under Boyle’s law will hold good.

The assumption made in § 7, that there is no appreciable
transference of heat, is probably much nearer the truth; but
this is not in accordance with any assumption made by
Riemann. When pressure is assumed to be a function of
density only, and to vary with it according to the adiabatic
law, 2t 2s wrtually assumed that at the discontinuity just so
much heat remains in the gas as would be due to slow adiabatic
compression, while the further amount of heat which is dissipa-
twely produced 7s completely and instantaneously removed by
conductzon. But though Riemann’s results may thus be
justified by impossible assumptions concerning the diffusion
of heat, we may more reasonably, following Lord Rayleigh,
regard them as involving a destruction of energy. The real
source of error lies in Riemann’s fundamental hypothesis.
At the outset he supposes the expansion and contraction of

* Loc, cit,

326 Dr. C. Burton on Plane and Spherical

the air to be either purely isothermal or purely adiabatic, and
thenceforward he treats the air as a frictionless and mathe-
matically continuous fluid, in which pressure and density are
connected by an invariable law. But in general the existence
of such a fluid is contrary to the conservation of energy ;
for as soon as discontinuity arises, energy will be destroyed.

9. It may not be out of place to conclude this portion of
the subject by a short reference to a paper by Dr. O. Tum-
lirz *. This author starts, as Riemann did, with the assump-
tion that the pressure is a function of the density only, the
law of pressure being further assumed to be the adiabatic
law; and in order to avoid Riemann’s error, he explicitly
uses the principle of energy applicable to continuous motion,
in place of the principle of momentum. But the foregoing
discussion will have made it clear, I think, that the solution
of the difficulty is not to be sought for in this direction. In
addition to the assumptions common to his own work and te
that of Tumlirz, Riemann uses only the principle of mass
and the principle of momentum ; and since by their aid alone
he arrives at a completely determinate motion, it follows
that any other motion consistent with the same arbitrary
assumptions, and with the condition of mass, must violate
the condition of momentum. We have seen, in fact, that
there is dissipation of energy at a surface of discontinuity, so
that the condition of energy applicable to continuous motion
ceases to hold good. We are acquainted, too, with other
instances where loss of continuity involves dissipation of
energy ; for example, there is the case of one hard body
rolling over another.

As the result of his investigation, Dr. Tumlirz concludes
that as soon as a discontinuity is formed it immediately dis-
appears again, this effect being accompanied by a lengthening
of the wave and a more rapid advance of the disturbance.
In this way, therefore, he seeks to explain the increased
velocity of very intense sounds, such as the sounds of
electric sparks investigated by Macht. But it has already been
pointed out [§ 3 (i.) |, that when density and velocity are every-
where continuous functions of the coordinates, the front of a dis-
turbance advancing into still air must travel forward with the
velocity of infinitely feeble sounds. A greater velocity can
only ensue when the motion has become discontinuous.

* “Ueber die Fortpflanzung ebener Luftwellen endlicher Schwing-
ungsweite,” Sitzungsb. der Wien. Akad. xcv. pp. 367-887 (1887).

T Sttzungsb. der Wien. Akad, \xxv., Ixxvii., lxxyiii. Cf. also W.
W. Jacques |On Sounds of Cannon], Amer. Journ. Sci, 3rd ser. xvii.
p. 116 (1879).

Sound- Waves of Finite Amplitude. 327

Part I].—SPpHERICAL WAVES.

10. When plane waves of finite amplitude are propagated
through a frictionless compressible fluid, discontinuity must
always occur sooner or later, and a moment’s consideration
will show that there are at least some cases when the motion
in spherical waves becomes discontinuous ; the question arises
whether in any case it is possible (in the absence of viscosity)
for divergent spherical waves to travel outward indefinitely
without arriving at a discontinuous state. This question was
suggested to me by Mr. Bryan, who at the same time kindly
handed me notes of his manner of attacking the problem.
His method was to write down the exact kinematical equation
for spherical sound-waves, and then to obtain successive
approximations to the integral of this equation. If it appears
that after any number of approximations the integral would
remain convergent for large values of the radius, we may con-
clude that our equation holds good throughout, and hence that
no discontinuity arises. If, on the other hand, the second or
any higher approximation becomes divergent for large values
of the radius, it is probable that the motion becomes some-
where discontinuous. This method I have not followed out;
but by another method which is, I hope, sufficiently con-
elusive, I shall now endeavour to show that discontinuity
must always arise.

The case in which the motion loses its continuity compara-
tively early requires no further consideration here ; we have
only to concern ourselves with the case in which the initial
disturbance has spread out into a spherical shell of very small
disturbance whose mean radius is very great compared with
the difference between its extreme radii. The equations
applicable to the disturbance are then, very approximately,

8
te eee

u or oP ec - for a given part of the wave, . (12)
where p is the mean density, p+ép the actual density at a
point where the velocity is wu, and a 1s the velocity of infinitely
feeble sounds in air of density p; 7 is as usual the distance of
a point from the centre of symmetry. Let us consider two
neighbouring points M and N, on the same radius, each being
fined in a definite part of the wave, the point M being behind
N (.e. nearer to the origin), and the air-velocity at M ex-
ceeding that at N by Au. Then, as the wave advances, each

328 Dr. C. Burton on Plane and Spherical

part of it will be instantaneously moving forward with (very
approximately) the velocity _

dp

-£ +u

dp
determined by the corresponding values of p and w; so that
M will be gaining on N at the rate

’]

Aut! , [2 &xa 2
dp dp du
approximately. We may admit then that the rate at which
M gains on N is
never < BAu,

where B is a constant suitably chosen.

Again, if Aju is the difference between the air-velocities at
M and N at the time ¢=0, and 7g is the corresponding co-
ordinate of M, we may admit that

Ary
19 + at
where A is a constant not very different from unity. Thus
M gains on N ata rate which is

Au,

Aw is never <

a

7 LESS =
never < a Ser Ayu;
and between the times t=0 and t=¢, the distance gained by
M relatively to N will be

at least ABAon|

0

4 pdt
To + at :

io salen ABAu”log °F“, : aR)
0

If B is finite and positive this expression increases indefinitely
with the time, so long as the laws of continuous motion hold
good. If Apr was the distance between M and N at time
t=0, the time required for M to overtake* N will be not
greater than the value of t, given by

ie a
—Ayr=ABAw log foie
Yo

or, when M and N are taken indefinitely close together at
starting, by

Tor Opps Ou
log nt = a { AB( se oe
1.€., we have t =" en Gera. D) — 1) (15)
; ae

* Cf. Lord Rayleigh, ‘Theory of Sound) vol. ii. p. 36.

Sound- Waves of Finite Amplitude. 329

which gives us a finite upper limit to the time required for
discontinuity to set in, provided B is finite. As our assump-
tions only remain approximately true so long as the motion is
continuous, (15) will only give an approximation to the time
when discontinuity first commences, and accordingly the
relation must be taken to refer to that part of the wave for
which its right-hand side is a minimum. If B is negative
(which is not the case for any known substance), the appro-
priate part of the disturbance will be such that Qu/dr is
positive.

To determine approximately the value of B, we may refer
to (13) and the inequality immediately following. If we
assume Boyle’s law of pressure, so that / (dp/dp)=const., we
have evidently

B=1 very nearly.

If we assume that the changes of density take place adia-
batically, so that p ocp’ and y is nearly constant, the approxi-
mate value of B becomes

dap ee fd
ie = oP.
dp V dp : dp

by means of (11) ;
Date

9 e
If, then, viscosity be neglected, we must conclude that under
any practically possible law of pressure the motion in spherical
sound-waves always becomes discontinuous, and a fortiori the
same will be true of cylindrical waves. But inasmuch as
our result for spherical waves depends on the existence of an
infinite logarithm in (14) when ¢, is increased without limit,
we may conclude that for waves diverging in four dimensions
(or, more generally, in any number of dimensions finitely
greater than three) there would be some cases where the
motion remained always continuous.

11. The general question of spherical sound-waves of finite
amplitude is by no means an easy one. In the case of plane
waves we can write down at once from Riemann’s equations
the condition that the disturbance may be propagated wholly

in the positive or wholly in the negative direction. The
respective conditions are* :— .

wat |'a/P dose,
Po dp

where pp is the density of that part of the fluid whose velocity
* Cf. also Lord Rayleigh, ‘Theory of Sound,’ vol. ii. p. 35 (8).

330 Dr. C. Burton on Plane and Spherical

is reckoned as zero. No such simple criterion can be given
for the existence of a purely convergent or purely divergent
spherical disturbance ; a fact which may be readily seen from
the equations for waves of infinitesimal amplitude. If ¢ is
the potential of a purely divergent system of waves, we have

rh=f(at—7), . te)
where / is a function whose form is unrestricted. Let p be
the ordinary density of the air, and p+6p the actual density
at a point where the coordinate is r and velocity u. We
have, then, on differentiating (16) the well-known relations

200 2) ) [Ga _ f(at—r)
haan —_— ype y tea ° ° e (17)
and 5 ;
ogee *90— LAA"), Bees ees

Pp
From (17) and (18),
(a2 —u)e=f(at—n),

whence differentiating with respect to 7, and neglecting small
quantities beyond the first order,

neo —_ 8) 4 2r( a? —u)= —f'(at—?)

by (18) ; therefore

por 7 >; 2 ae (19)
If, then, an infinitesimal spherical disturbance is to be purely
divergent, this equation must be satisfied for every value of
r. But since the left-hand side involves 6p/p as well as u,
du/dr, and 9 (log p)/d”, it is evident that the question whether
or not the equation is satisfied for some particular value of r
does not depend solely on the state of things in the immediate
neighbourhood of this value, but is influenced also by the
value of p corresponding to the undisturbed air. We must
not therefore seek to characterize a purely divergent dis-
turbance by a differential equation expressing that, with
respect to the air at each point, the disturbance is wholly
propagated in the positive direction of r.
12. Not recognizing this, I had attempted to discover such
an equation, and one step of the inquiry is reproduced here,
for the sake of any interest which it may have.

- Sound-Waves of Finite Amplitude. 331

Tt is required to write down the differential equation of an
infinitesimal spherical disturbance, which is superposed on a
purely radial steady motion.

Though a steady motion extending inward to the pole
would involve a violation of the principle of continuity, we
may suppose that throughout a shell of finite thickness the
distribution of density and velocity is such as would be con-
sistent with steady motion ; the motion within such a shell
would then continue steady, provided that its spherical
boundaries were constrained to expand or contract in a
suitable manner. In the absence of constraints the shell of
steady motion would be invaded from without and from
within by disturbances emanating from adjoining parts of the
fluid, but, at points well within the shell, the character of the
steady motion would necessarily be maintained for a finite
time.

Let ¢ be the potential of the steady motion.

Let $+ be the potential of the actual motion so that

and its derivatives are small.

_Let p, p be the pressure and density in the steady motion.

Let p +p, p+6p be the pressure and density in the actual

motion, and assume that the pressure is a function of
the density only. From the ordinary equations for the
motion of compressible fluids we obtain

= 3 (Sf), es (740)
(rie 1 (SP +g oy)
spk . ae ey GO)

when small quantities of the second order are neglected.
Subtracting (20) from (21)

op - oOpow
ee Ae (22)
Now
op _ dp op.
pe dp pie
therefore
0 op _ dp 10.o, ae
Sieieds : Re ee (23)

and the equations of continuity tor the steady motion and the

332 On Plane and Spherical Sound- Waves.

actual motion may be written

Op. _ 0¢ dp
Cae °° See
dp) 6
OP HPP) — — (p+ Bo) V°(h+H)— (SE + SHOR,
whence by subtraction
Oop Opdv dopded

Sp PV PV b= 5 a, = 5 eee

SG ) 3
was (2 (-+- SPS) fs

expanding this and ee in (24) we get
00 ; __0¢0 eyes)
BEM -o(Z) (45h)
dp\— ,__ oP ov
“Dot? (as) Fs ore
dp\\/_ Od _ Hd _ I'GdW 79S
eye Or Or Of Ores Nes

Now differentiate (22) with respect to ¢ and we have, remem-
bering (23),

_ 4 243% _ lap 8p
Or or rode: Ot!

In this equation we have to substitute the value of Qép/dé
from (25), and if we then put y= Wr, and perform the
necessary reductions, we finally obtain as the differential
equation satisfied By br,

OX — (ew) SK + mw Ok 4 USK + v(S¥—%)=
where
a’=the variable 2 (in the steady iota
Be a __ constant
aie or pr?

ie) 2u da __ 2u 2u oa

ra ton2 (2) Ome.
Vx 2au 2 (7) ; ae

On a new and handy Focometer. 333

if the steady motion in question is a state of rest, «=O and
p 1s a constant, so that U=0, V =0, and our equation reduces
to the ordinary form for small spherical disturbances,

If, on the other hand, y=, the motion may, through any
finite distance, be treated as linear. We shall then have wu and
p both constant, as well as a, and as before U=0, V=0. In

that case
Ovo Oh» OY
7 (?— ne =()
YE (a?—wu Jan BE 5
and this, by a change of independent variables, is easily seen

to be the appropriate form for small plane disturbances of a
fluid whose motion is otherwise uniform.

XXXII. On a new and handy Focometer.
By Protessor J. D. Everett, /.R.S.*

| ae focometer is designed to permit the distance of the
_ “object”? from the screen to be varied, while the lens
which is to throw on the screen an image of the “ object” is
automatically kept midway between the two. This position,
as is well known, gives both the sharpest definition and the
simplest calculation.

The instrument is constructed on the principle of the well-
known toy~called lazy-tongs. A number of flat bars (fig. 1),

OOOO

all exactly alike, are jointed together in such a way that half
of them are in one plane and the other half in a superposed |
plane. With the exception of the end bars, each bar in either
plane is jointed to three of the bars in the other plane, one
joint being in the middle and one at each end. The end bars
are jointed at the middle and one end only. All the bars in
the same plane are parallel, and the two sets together form a
single row of rhombuses all equal and similar, a side of a
rhombus being half the length of a bar. The system has only

* Communicated by the Physical Society: read February 24, 1893.
Phil. Mag. 8. 5. Vol. 85. No. 215. April 1893. 2A

334 Professor J. D. Everett on a

one degree of freedom, and its length is a definite multiple of
the longitudinal diagonal of a rhombus.

The joints are arranged in three rows, one down the middle
and one along each edge, and the distance from joint to joint
in any row is equal to this longitudinal diagonal. This
common distance can be varied between very wide limits by
pulling out or pushing in the frame, and we have thus a means
of dividing an arbitrary Jength into any number of equal
parts. I utilize only the middle row for this purpose, and
utilize it only or chiefly for bisecting a variable distance.

The pins on which the middle joints turn are continued
upwards, as shown in fig. 2, to serve as supports for clips
holding the object, the lens, and the screen. The lens is

Fig. 2.

Elevation.

mounted on the centre pin, and the object and screen usually
on the two end pins, as in fig. 2. In order to avoid flexi-
bility, the clips are made short, and the pins, on which they
are held by screws, rise only 14 inch above the frame. The
base of each pin is a substantial disk (see fig. 3) which rests
upon the table ; all the pins, not only in the middle row, but
also in the two outside rows, terminate in such disks, which
serve as the feet of the instrument, and slide upon the table
when the frame is expanded or contracted. ‘The pins are
of brass 4+ inch in diameter, and the bars are of +-inch
mahogany, ? inch wide, and 13 inches in gross length.
There are 18 of them, as shown in fig. 1. There are 9
pins in the middle row ; and when the object and screen
are on the two end pins, the distance between them is
divided by the other pins into 8 equal parts, any two of
which should together make up the focal length. The
unused pins are the most convenient handles for manipulating
the frame.

The screen may converiently be a piece of white card a
little larger than a post-card, and a square of wire-gauze
about half as big may be used as the object ; but a still
better ‘ object’ is a cross of threads stretched across a square
hole in a card. The light which passes through the square
hole is very conspicuous on the screen before the correct
distance is approached, whereas the shadow of the wire

new and handy Focometer. 335 |

gauze is almost invisible. Two thin cards about the size of
post-cards should be taken, a hole a centimetre square should
be cut through both of them, and they should be gummed
together with the cross threads between them, the threads
being in the first instance long enough to project beyond the
eards to facilitate adjustment while the gum is wet. Waxed
carpet-thread, or any very stout thread with smooth edges, is

Fig. 3.

A supporting pin.

the best for giving a conspicuous and at the same time a
sharp image. As the cross will sometimes have to be raised
or lowered, the hole should be much nearer to one end of
the card than to the other, in order to give a greater range
of adjustment in mounting on theclip. One thread should be
vertical and the other horizontal, in order that their simul-
taneous focussing may serve as a check on the correct
orientation of the lens.

The instrument is intended to be used by placing it on a
table of length not less than four times the focal distance
which is to be measured. A lamp is to be placed either on
one end of the table or on a stand opposite the end, at such
aheight that its flame is about level with the tops of the
clips. The clips should be fixed as low as possible on their
supporting pins, unless it is necessary to raise them to suit
the height of the lamp. In default of a lamp at the proper
height, an adjustable mirror may be used instead, and made
to reflect a beam of light from any large gas-flame in the
room so that the beam shall pass along the tops of the clips.

2 A 2

336 Professor J. D. Everett on a

When the lamp or mirror has once been adjusted to throw
its light in the proper direction, it should not be disturbed,
as all necessary adjustments can be better made by moving
the instrument.

The lens and screen may conveniently be mounted first,
and the adjustments made so that the light collected by the
lens falls on the screen as a horizontal beam. The cross is
then to be mounted in such a position that a bright patch
corresponding to the square hole is seen on the screen, sur-
rounded by the shadow of the card. The frame must now be
extended or compressed till the image of the cross appears in
the bright patch ; and the lens, object, and screen should then
be carefully set square by hand before the final adjustment.
If the vertical and horizontal lines of the cross do not focus
simultaneously, it is a sign that the lens needs setting square.

The focussing having been completed, the distance of the
object from the image is to be measured and divided by four.
This will give the focal length ; and the calculation can be
checked by measuring one or more of the four equal parts
into which the distance is divided by alternate pins. Owing
to slight play in some of the joints, or other mechanical
imperfections, the theoretically equal distances may exhibit
sensible differences, especially when the frame is nearly
closed up; but the method of observation is so well con-
ditioned that these inequalities do not practically affect the
correctness of the result.

In fact, if the distances of the lens from the object and
image, instead of being exactly equal, are a+ and a—2,
2
2a
fourth of the whole distance we are simply neglecting 2? in
comparison with a?. Suppose the two distances a+a and
a—x to measure 203 and 194 inches, which is a larger
inequality than is likely to occur, the ratio of 2? to a? is 1 to
1600 ; and this error is negligible, in view of the fact that
the doubt as to when the image is sharpest involves an un-
certainty in the focal length to the extent usually of more
than one per cent. :

When the focal length does not exceed 10 or 12 inches,
the instrument may be supported with the two hands and.
pointed towards a gas-flame, which need not be at the same
level, but may be at any height. A fairly good measure-
ment can thus be made by one person, if there is opportunity
for setting the instrument down on a table or floor when the
lens needs setting square, and when the final measurement
of distance is to be made. The friction at the joints of the

2
the true focal length is rs , and in taking it to be one

new and handy Focometer. Boe

frame is just sufficient to keep them from working while the
instrument is being carefully set down. The chief difficulty
is from flexure.

Instead of receiving the image on a screen, it can be viewed
in mid air. For this purpose I mount the cross on one of
the two end clips, and a piece of wire gauze about the size of
the palm of my hand on the other, setting the wires at a
slope of 45° by way of contrast with the upright cross. The
end which carries the cross should be turned towards the
strongest light; as this renders the cross more visible to an
observer behind the gauze, and also renders the glistening
wires of the gauze more visible when the observer stations
himself behind the cross. The adjustment for focus is made
by lengthening or shortening the frame till parallax is re-
moved. This is a very convenient way of establishing
experimentally the fact of the interchangeableness of object
and image.

The instrument can also be employed to illustrate the
general law of variation of conjugate focal distances, the lens
being for this purpose shifted from the central pin to any one
of the other pins, and the frame being then extended till the
image is correctly focussed. Regarded as an optical bench,
the instrument is remarkably light and handy. Its weight,
including screen, cross, wire-gauze, and lens, is 2 lb. 10 oz. ;
and a lecturer can carry it through the streets of a town
without inconvenience.

The dimensions and number of bars of the instrument as
exhibited are recommended as the most convenient for general
purposes. Ten bars only were constructed for the first trials,
and any number included in the formula 4n+2 might theo-
retically be employed.

In order to prevent looseness at the joints, it would be well
to make the holes in the bars bear against a cone below and
another cone above, with a very slightly tapering wedge for
adjustment, as indicated in fig. 3.

If the instrument were to be set up permanently in one
place, guides might be used for compelling the middle row of
pins to travel without rotation, or the pin on which the lens
is mounted might be a fixture; but as long as portability is
to be preserved, | do not think that any arrangements for
automatically preventing rotation would be practically bene-
ficial. It is only in the large movements which precede the
final adjustment that rotation occurs to any injurious extent.

The instrument has been constructed from my drawings by
Messrs. Yeates of Dublin, and the cost is trifling.

[ 388 ]

XXXIV. A Hydrodynamical Proof of the Equations of Motion
of a Perforated Solid, with Applications to the Motion of a
Fine Rigid Framework im Circulating Liquid. By G. H.
Bryan”.

Introduction.

iE 1 the whole range of hydrodynamics, there is probably

no investigation which presents so many difficulties
as that which deals with the equations of motion of a per-
forated solid in liquid. The object of the present paper is to
show how these equations may be deduced directly from the
pressure-equation of hydrodynamics, without having recourse
to the laborious method of ignoration of coordinates. ‘The
possibility of doing this is mentioned by Prof. Lamb in his
‘Treatise on the Motion of Fluids’ (pp. 119, 120), but he
dismisses the method with the brief remark that in most cases
it would prove exceedingly tedious. I think, however, that
it will be admitted that the following investigation is more
straightforward and simple than that given by Basset in his
‘ Hydrodynamics,’ vol. i. pp. 167-178.

The usual method presents little difficulty when the motion
of the liquid is acyclic, because the whole motion could in
such cases be set up from rest by suitable impulses applied to
the solids alone; anda consideration of Routh’s modified
Lagrangian function shows that in this case the equations of
motion can be obtained by expressing the total kinetic energy
as a quadratic function of the velocity-components of the solid
alone, and applying the generalized equations of motion re-
ferred to moving axes.

If, however, the solid is perforated, and the liquid is cireu-
lating through the perforations, this method presents several
difficulties. If the solid were reduced to rest by the applica-
tion of suitable impulses, the liquid would still continue to
circulate through the perforations, the “ circulation ” in any
circuit remaining unaltered. From this and other circum-
stances we are led to infer that these circulations are not
generalized velocity-components, but rather that the quan-
tities xp are generalized momenta. Now the kinetic energy
of the system is naturally calculated as a function of the
velocity-components of the solid and of these constant circu-
lations (or the corresponding momenta) ; a form unsuited for
obtaining the equations of motion. We ought either to have
the kinetic energy expressed in terms of generalized velocity-
components alone, or to know the “ modified Lagrangian

* Communicated by the Physical Society: read February 24, 1893.

Equations of Motion of a Perforated Solid. 339

function ” obtained by “ignoring” the velocity-components
corresponding to the constant momenta or circulations. Hither
of these expressions involves constants which cannot be deter-
mined from the ordinary expression for the energy alone, and
to determine them in the usual way it is necessary to resort
to arguments based on a consideration of the “impulse” by
which the motion might be set up from rest.

In the following investigation the equations of motion are
deduced from purely hydrodynamical considerations, and from
them the modified function is found. In §§ 12-16 the equa-
tions of motion are interpreted for the case in which the solid
is a light rigid framework and the inertia is entirely due to
the circulation of the liquid, and the results are applied to
interpret the effective forces of the cyclic motion for a per-
forated solid in general.

General Hydrodynamical Equations.

2. Let a perforated solid bounded by the surface 8 be
moving through an infinite mass of liquid (density p) with
translational and rotational velocity-components wu, v,w, Pp, J, 7,
referred to axes fixed in the solid, and let «,, «2, K3...Km be
the circulations in circuits drawn through the various aper-
tures. Then we know that ¢@ the velocity-potential of the
fluid motion may be expressed as a linear function of the
velocities and circulations in the form

p=udut vpyt whut phy t Why t?hrt Zk. + (1)

where evidently ¢,=0¢/du &c., and the coefficients dy...
depend only on the form of the solid.

If dy denotes the element of the normal to S measured
from the solid into the liquid, (/, m, n) its direction-cosines,
then, in the usual way, we have

oe =I1(u—ry +92) +m(v—pzt+re)+n(w—getpy). . (2)

The six coefficients gy... are single-valued functions of
the coordinates, while the coefficients ¢, which determine the
part of the velocity-potential due to the circulations are cyclic
functions making Q¢,/Qv=O0 at the surface of the solid; these
coefficients are supposed known for each form of solid, although
their determination in any given case is generally beyond the
range of mathematical analysis.

3. Let oj, o2,...0, be barriers drawn across the perfora-
tions ; then, in the usual way, the kinetic energy of the liquid

340 -Mr. G. H. Bryan on the Equations of

is found to be J, where

; 3
t= 1p |\p2% a+ 4px ||P do=B.+K. B3)

Here J, is a quadratic function of the velocity-components of
the solid, and is the kinetic energy when the motion is acyclic,
and K is a quadratic function of the circulations.

If the axes were fixed in space, the pressure equation
(supposing no forces to act on the liquid) would be

Pi , of

pot
(where p; = pressure, g, = resultant velocity of liquid).
Owing to the motion of the axes, however, O¢/Q¢ must be
replaced by the rate of change of ¢ at a fixed point, that is by —

+3$9,)’=const.,

dp aan ee op an) O° o¢
a. Uo te) a — sep tet) a ee
whence the pressure equation becomes — |

Pi, Uh ae OG _ pede OF _ = we
me ee) (wv RUS, (5 2

+39°= const. eae 5 | st.)

The Mutual Reactions between the Solid and Liquid.

4, Let X,, Y;, Z;, L,, M,, N, be the component forces and
couples which the solid exerts on the liquid ; then we have
evidently

Seas L, = \\ (ny—mz) p, dS. 21s GD)

_ To reduce these expressions to the required form, we shall
have to resort to repeated applications of Green’s formula.
Since the velocity-potential @ is a multiple-valued function,
it follows that in transforming volume integrals involving }
we shall obtain surface integrals over the barriers 01, dg,... Om
as well as over 8S the surface of the solid. On the other hand,
the pressure p, and the velocity-components 04/02, 0¢/dy,
0¢/02 are single-valued and do not contribute barrier terms
to the surface integrals. Moreover, since the circulations «
are independent of the time,
OF = Ub, +E, FI, + D4, +98, 476,

and 0¢/0¢ is therefore a single-valued function of the velocity-
components of the solid satisfying Laplace’s equation.

Motion of a Perforated Solid in Liquid. B41
We also notice that
Ody feke)
l= a Ye ao ate mare tts (6)

as may be at once seen by differentiating (2) with respect
to w and p respectively.

Substituting for p, in (5) in terms of the velocities, we
have

=e sale ds
p :
+ {lf (u—yr + . + (two similar) F1US

—al|{ (Sey y+ (38) ] pee

The first line of a expression is, from (6), equal to

ee Ou

a eerar rome

by Green’s transformation. os. that @, is inde-

pendent of the time, this integral, taken throughout the liquid,
becomes

=523 2 al|i{ (S*) ey (82) } ans -

pot OL ILS) esa

~ pdtou pot ou —

By Green’s transformation the second line is equal to
={\\3 { (u—yr + 2q) oF + (two similar) \ dx dy dz

= ~ {{\(-22 ¢ at a) dx dy dz
-\\\f (u—yr + 2q) 2 + (two similar) ae dy dz,

which by a second application of Green’s transformation
becomes

Oo

49 Mr. G. H. Bryan on the Hquations of
=\| (mr—ng) dS —Zx\\(mr—ng) do
+ (V{2(u —yr+2q) + m(v—eptar)+n(w—agt+ yp) $ Seas
0p oe
=(\(mr —ngq)odS— Sxc\\(m —ny)do +\| ae ds
by (2).

Lastly, the third line of (7) is, by Green’s transformation,

"(Bb9% , 96 B'S , BH dS
={\\{8 Seo SRORRUN e serps p aedyde

“(£29247
Ov 02 a
Hence, adding the several terms together, we have

The
~ dt Ou

1p {p\\modS = S«p\\mdo} — qip\\nodS _ Sxp\\ndo} 8)
Now by (6),

p\\mddS=p Obe 478
i {| Ov
-e|\| OPIS: , BHIb. , BHO»

a Ode
=Sep| Be Sane AF an aie ~~ \da dy dz

~sl] ie Zaof NG) + REF) Jere

= ao | 2 eee
Therefore

ie = g2_, £2 , aaa we a ”) da}

+9 { S= oe " Cia

6. In like manner we have

— ae-{f (ny —mz) as

+]| | (u~yr+ - a (two similar) (ny—mz)dS

Motion gi 6,08 Solid in Liquid. 343

LO +B“ 08) Jom

“Hboe Yas) (v5! - so) du dy dz
— ||) fy { e-yrte0) 2 + (tro. similar)? 9%

=z} (w—yr+ 2q) o + (two similar) a dx dy dz

On
060 , Of 0 , 060)/(,0b_,0¢
oe By t Bebe) Uae: 0 y Naadyde
eee 02
pdt op

Bs (two sim.) poste ve - $98
—\\\[o(9s 5 eave “(P5o

fol ‘ oe)
Shey yp eee Se Gye 9) — \da dy dz.
(v—zp+2r) e + Cw “g+yp) By c dy

Remembering that in this expression one factor of the
surface integral is zero at every point of S, we have, by
again applying Green’s transformation to the volume integral,

ar
made Op
+w{ p\\m dds —Zxp\\mdo} —vf p\\npdS —Sxp\\ndos
+r{p\\(l (le—nx) dds — —Xxp\\( (lz—na)do}
—qip\\ (ma—ly) ddS — — xp \\ (ma—ly\do$ . . (10)

Now, just as before,

(le—mn)bdS= p || Pega
all = =Sxp || 2 , da

2, (ieee 388, feb Od, 738 08, \ zi a:
alll oe

= Seo (( 0% gq ©
=3ep [|Site 0g’

344 Mr. G. H. Bryan on the Equations of
Therefore,
d OL
1 = dt Op

—w foe + Sep ||(m — oP de \

tne) ge a eo {| (n— =) da |

7 1 oe + xp | (t: —nw— ee da \

+g = == Sap || (may eae} Beene ul

Application to the Equations of Motion.

7. The equations of motion of the solid may now be written
down at once. Let 3! be the kinetic energy of the solid, T
the total kinetic energy =%+ ‘3! ; and suppose that the motion
takes place under the action of a system of external impressed
forces and couples designated by X, Y, Z, L, M,N. Then
the effective forces and couples to which the motion of the
solid itself is due are X—X,..., L—L,..., respectively, and
the six equations of motion of the solid referred to the moving
axes are of the form

dIOS LOS! Hawes! ,
dau "90 ' 230 ~~ 9 ne
AS) SSG Sole Se

tn Se ; q
dt Op Ov w OY or
Hence, on substitution, we see that the required equations
of motion are found by writing T tor J and X, Y, Z, L, M,N
for X,, Y;, Z;, L;, My, N, in equations (9) (11). The resulting

equations may be written :

x= 55, -"(85 +7) +{& +5) yr (14)

t= ae = 0(S +0) 40o(& +6)

=L—1L,. e (13)

where &, 7, &, d, “, v are defined by the equations

Motion of a Perforated Solid in Liquid. 345

g = 2xp|| (I 2 ada, de, ee (16)

N= sep || (x (ny— mz— 928 \do, ewe te ce El)

As Lamb has pointed out (‘ Motion of Fluids,’ p. 140), the
six quantities (&, 4, ¢, A, w, v) are “the components of the
impulse of the cyclic fluid motion which remains when the
_ solid is (by forces applied to it alone) brought to rest” *. They
are linear functions of the circulations and their form depends
on the form of the solid. If there is only one aperture they -
are all proportional to the circulation «.

The Modified Lagrangian Function.

8. We shall now show that the motion of the solid can be
determined in terms of Routh’s modified Lagrangian function,
and shall find the form of this function for the system.
Putting.

H=T+éEu+nvt+Gwt+rAptpqtvr+F (kp), . . (18)
where F'(«p) denotes any function whatever of the quantities

Kp, we see that the equations of motion reduce to the standard
form

@ lel oat lal

ir iu eae (iey
OE ele! OH “Olt. @ils! :

The function H, therefore, plays the same part in deter-
mining the equations of motion of the solid as the kinetic
energy T in the case of an imperforated solid (or any solid
when the motion of the liquid is acyclic). It remains (i.) to
determine what quantities are to be regarded as the generalized
velocities if the quantities xp are regarded as generalized
momenta ; (ii.) to find the form of the function F(«p) in order
that H may represent the modified Lagrangian function.

9. Let y,, be the generalized velocity-component corre-
sponding to the ignored momentum «,p. Then, as Routh has
shown (‘ Rigid Dynamics, vol. 1. § 420), the modified La-
grangian function H is of the form

Ev > in PNR Oe hal F<. ce ts. E28)

* Our & 7, 6, A, w, v are the same as the &, no, fo, A 0) Hoy Yo Of Lamb, or
the’ X,Y), 3, &, Mi, "I of Basset’s § Hydrodynamics.’

346 ‘Mr. G. H. Bryan on the Equations of

and therefore by equating the two expressions for H we must
have

Eutnutfotrptpqtwr+F (x) =—ZKpy. . ~ (22)
Since y,, is the generalized velocity-component corre-
sponding to the momentum kmp, therefore
oH
0. Kp = Xm ° . ° ° e (23)
Now H is a homogeneous quadratic function of the six
velocities (u...,0...) and the momenta xp; therefore

| oH oH oH
2H =2u s- + Sxp sae == 7 —Xkpy. . (24)
Hence, from (21), .
H H H
2139 + Sepy = Sud Sapo AS 5)

The portions of T and H which involve only the momenta xp,
and are independent of the six velocities (u..., p...), must
arise from the terms 2«py in the above expressions (24) (25),
and must therefore be equal and of opposite sign in the ex-
pressions T and H respectively. Hence, since from (8)

T=2'+3,+K,

the portion of H which is independent of the six velocities
(@..., p...) must be —K, so that,

H=2/4+ 31+ (ut nut Gwt+rApt+pyqtvr) —K
=T +(Eutnvtcwt+rAptuqtvr)—2K, . . (26)
and therefore F(ep)=—2K. ..

The function F'(«p) does not enter into the six equations of
motion of the solid, but its form requires to be determined if
we wish to reduce the equations of motion of the whole
system to the canonical or Hamiltonian form.

The Generalized Velocities and Momenta.
10. Comparing (21) with (27), we see that
LKpX=2K—(Eu+ nu+lwt+rApt+puyqt+vr). . (28)
Now equation (3) may be written in the form

Bigg ih) malas +...tp,+...+2«,)d8

+24 2 (ug, + 1 tpbyt...+ 2kde)do. (29)

Motion of a Perforated Solid in Liquid. B47
~ But by § 2, 0¢,/0v=0 all over the surface 8 of the solid.

Hence, equating the terms independent of the six velocities
(w...,p...) on the two sides of (29), we have

79 C= <p|| 2 (Seanjde ey ek Bo G0)
But by (16) (17),
Eutnu+fwtrpt mgt vr

= —ep| 2 (ub. ..+p¢,+...)do

+ Sep\\ {lu +mv+nw+ (ny—mz)p+...tde.
Hence, by (28) and (80),

Spx =SH0| &. Te tees Camino cas XK ) do
— Sp(\{U(u —yr+2q) +m(v—zp +ar) +n(w—aqt yp) }do;

and therefore

‘igs NG —I(u—yr-+2q) — (bwo similar) dom + (31)
Now 0¢/0v is the velocity of the liquid resolved along the

normal to the barrier o,”, and
l(u—yr +2q) +m(v—zp +er)+n(w—xgt+yp)

is the velocity of the barrier o,, resolved normally to itself at
the point w, y, 2, supposing the barrier to be fixed relatively
to the solid. Their difference, therefore, represents the nor-
mal relative velocity of the liquid with respect to the barrier.

Hence Ym represents the total rate of flow of the liquid
across the barrier o,, relative to the solid; in other words, the
generalized velocity corresponding to the ignored momentum
Pkm is the volume of liquid per unit time flowing through the
‘aperture relatively to the solid.

This property is proved in a different way by Basset in his
‘ Hydrodynamics,’ vol. i. page 176.

The Form of the Modified Function.

11. It may be interesting to examine a little more closely
the effect of the circulations on the motion of a solid.

When the motion of the liquid is acyclic, the kinetic
energy isa homogeneous quadratic function of (wv, v, w, Pp, 9,7):
In general it therefore involves 21 constants, but by a suitable

348 Mr. G. H. Bryan on the Equations of

choice of axes it is always possible to reduce this number by
six, and a further reduction may be effected when the body
is symmetrical. When the motion is cyclic the kinetic
energy must be replaced by the modified function which in
addition contains the seven terms
Eutnv+fwtrAp+uq+tvr—K,

of which the last term does not enter into the ge of
motion of the solid. The six coefficients (&,... ..) are
linear functions of the circulations, and they ee con-
stant so long as only conservative forces act on the liquid,
for the circulations themselves then remain constant. Hence
the modified function H may be regarded as a non-homo-
geneous quadratic function of the six velocities involving
28 constants, of which 27 enter into the six equations of
motion of the solid.

Equations of Motion of a light thin framework of rigid wires.

12. To take the simplest possible case, let us suppose the
solid to consist of a network of infinitely thin rigid massless
wires through the meshes of which the liquid is circulating.
If the motion of the liquid were acyclic, the wires would
simply cut through the liquid without setting it in motion :
hence the kinetic energy 3/ + Z, of the acyclic motion
vanishes, and the modified function becomes

H=£u+nv+ fw+rAptugtwr—K, . s (82)
a result otherwise evident from the fact that Z, only involves
surface integrals taken over the infinitely small surface of the
solid, while &, 7, >, », v being integrals taken over the
finite surfaces of barriers are in general finite.

If we choose as our axis of wx the Poinsot’s central axis of
the impulse whose six components are &, 7, £ Ar, @, v, the
modified function will reduce to the form

H=ButAp—Ki eee

If there is only one aperture, &,7,¢, 2, u,v are all pro-
portional to the circulation « and the central axis of the
impulse is fixed in position relative to the solid: if there are
several apertures the position of the axis depends on the
ratios of the circulations through the various apertures, but
throughout the motion it in every case remains fixed rela-
tively to the solid.

The six equations of notion (19) (20) now reduce to

rl); 0, )
Nears, M=wE+rA, " 54.) ee

)

Motion of a Perforated Solid in Liquid. 349

Since these equations do not involve w or p, we see that
no forces will have to act on the solid in order to maintain a
screw motion whose axis coincides with the central axis of the
umpulse.

13. To interpret the equations still further, let us suppose
that w and p are both zero, since they do not enter into the
equations of motion. ‘Then the motion whose components are
(0, v, w, 0, g,7) consists of two screws whose axes are the axes
oi y and z respectively, and, by the theory of screws, these
are equivalent to a single screw whose axis is a certain
straight line intersecting the axis of # and perpendicular to
it. We may take this straight line as our axis of ¢, for
hitherto we have only fixed the position of the axis of «.
We have then

v=0, g=0.

The equations (34) therefore reduce to

4

xXx—(; L=0,
Y=7e, M=we +a} eee too)
Zi=), N=0:

Hence the solid is acted on by a wrench (Y, M) whose axis
is the axis of y. Thus the axis of the impressed wrench is
perpendicular to the central axis of the impulse of the
fluid motion, and to the axis of the screw motion of the body.

Let II be the pitch of the impulse, w the pitch of the
screw motion of the solid, P the pitch of the impressed
wrench, then |

A w M
N=5, ee Pay
and therefore by (35), |
Pesan LL fae Aisa ok: 1a (Gl)

is the relation connecting the three pitches.
In particular, if » = 0 the equations of motion give

Z=0, M=wé#,

showing that a couple M about the axis of y will produce
translational motion with velocity M/E along the axis of z.
14. More generally, let the motion be a screw motion
about an axis whose inclination to the axis of w is @ and
whose shortest distance from that axis is a. Take this
shortest distance as the axis of y, and let the screw motion
consist of a linear velocity V combined with an angular
velocity ©, the pitch V/O being denoted, as besore, by a.
Phil. Mag. 8. 5. Vol. 35. No. 215. April 1893. 2B

350 Mr. G. H. Bryan on the Equations of

It will be readily found that the six components of the
screw motion are
u=Vcosd+QOasiné, p=Ocosé,
v=0, q=9, 3 - (87)
w=VsinOd—Qacosé, r=Qsin 8,
so that the equations (34) now give
A=0, 1;=0,
Y=02siné, M=VEsin@—Oaz cos 0+0A sin | (38)
=: N=0,
The impressed wrench therefore has for its axis the shortest
distance between the axis of the screw motion of the solid
and the axis of the impulse of the cyclic fluid motion. To
find the pitch of the wrench, we have, by division,
= = 5 —a.cot 0+ =
that is,
P= e—acot@+Il. .. 7) yee

15. In the case of a fine massless circular ring A vanishes,
or the impulse of the cyclic motion is purely translational.
For it is clear that the axis of the ring is the axis of this
impulse (the above axis of z), also the fluid motion will
evidently be unaffected by rotating the ring about its axis;
and therefore the modified function is independent of the
angular velocity p.

The equations (34) now become

K—0; L=0,
Se), M=we, | (40)
ZL=—q2, N=—vée.

Hence a constant force Y along the axis of y causes
uniform rotation with angular velocity Y/E about the axis
of z, and a constant couple M about the axis of y causes
uniform translational velocity M/E along the axis of z.

It is to be noticed that the impressed wrench never does
work in the resulting screw motion, in accordance with the
principle of Conservation of Energy.

16. The above results show the effective forces produced by
circulation of the fluid on any perforated solid whatever. In
the general case the modified function contains the quadratic
terms 2+, in addition to the terms of the first degree con-
sidered in the above investigation. If we suppose that the
solid is moving in any given manner, the six equations of
motion (19, 20) determine the components of the impressed
wrench (X, Y,-Z, L, M, N) necessary to maintain the given

Moton of a Perforated Solid in Liquid. 351

motion. This impressed wrench may be divided into two

parts, one being due to the terms 3/+2Z, in the modified
function, the other being due to the terms
Eutnvt+ GwotrAp+pg+yr.

The first portion is the same as if the motion were acyclic,
and represents, therefore, the wrench which would have to be
impressed on the solid in order to maintain the given motion
if there were no circulation. The second part represents the
additional wrench which must be applied on account of the
circulations, and the equations to determine it are of the forms
found above.

We notice, in particular, that if the solid has any screw
motion whose axis coincides with the axis of the impulse of
the cyclic fluid motion, the latter wrench vanishes; so that
the forces required to maintain the motion are unaffected by
the circulations. In other cases the additional wrench is
about an axis perpendicular to the axis of the impulse. This
is true whatever be the form of the solid and the number of
the circulations ; but, as has already been pointed out, the
position of the axis of the impulse relative to the solid is not
in general independent of the circulations unless the solid has
. but a single aperture.

It is probable that these results might be made to furnish
mechanical illustrations of certain physical phenomena ; but
with these we are not concerned in the present paper.

Note on the foregoing Paper.

Concerning the proper measurement of the impulse of the
eyclic motion, a difficulty arises ; for, as Mr. Bryan remarks,
this motion cannot be set up from rest by impulses applied to
the solid alone. Suppose, however, that we close each perfora-
tion by a barrier in the usual way, and let the barriers be acted
on by the impulsive pressures xp, K.p,... respectively. And
instead of these impulsive pressures being due to external
forces, suppose that they are due to some immaterial mechanism
attached to the solid. In general, an impulsive wrench must
act on the solid to keep it at rest, and this wrench ts the
required impulse of the cyclic motion; for the only other
impulses acting on the system are due to the mutual reactions
of the solid and fluid, exerted partly over the surface of the
solid and partly through the barriers and attached mechanism,
and such mutual reactions cannot affect the impulse. The
wrench thus found is of course the same as would be
obtained by supposing the impulses on the barriers to be due
to external impulsive forces, and compounding with these the

2B2

352 Mr. G. H. Bryan on the Equations of

impulse then necessary to hold the solid at rest. This is in
agreement with Prof. Lamb’s investigation, which Mr. Bryan
has quoted.

More generally, if the solid is in motion, and the liquid is
also circulating, we may suppose the instantaneous motion to
have been set up from rest by an immaterial mechanism con-
necting the barriers with the solid at the same time that the
requisite external impulses act on the solid. The resultant of
these last is, as before, the impulse of the whole motion, and
is identical with that found by supposing the barriers actuated
by impulses from without, and compounding with these the
impulse then necessary to give to the solid its instantaneous
motion.

The same point may be further illustrated by supposing the
circulations « to vary continuously during the motion. To
effect this variation we may suppose finite uniform pressures,
P,...P,,, to be exerted over certain ideal surfaces which
occupy the positions of barriers. The rate of variation x of
any circulation is given by P=xp, and in order that it may
take place without the direct operation of external forces and
couples we may conceive the pressure P to be due, as before,
to some highly idealized mechanism attached to the solid. As
before, the only forces capable of modifying the impulse are
the external forces acting on the solid ; and the equations of
motion are therefore still to be found by equating the
impressed force- and couple-components to the corresponding
variations of the ‘‘ impulse.” Since we know the expressions
for the impulse-components corresponding to a given instan-
taneous motion of the solid and given circulations, we have
only to remember that in these expressions the «’s are
functions of the time, and, just as before, the equations
of motion are directly deducible from Hayward’s formule.
Hquations (19) (20) of Mr. Bryan’s paper will thus be
applicable to the present case, provided that in the value of H
given by (27) the «’s are allowed to vary. 7

An investigation proceeding from a consideration of the
impulse of the whole motion is not so entirely satisfactory, I
think, as the direct method given by Mr. Bryan ; but, at the
same time, this brief attempt to interpret the impulse of the
cyclic motion may not be without interest.—C. V. Burton.

—

Note added by the Author.

Dr. Burton’s note is of much value as showing more
exactly what is meant by the “ impulse ” of the motion in the

Motion of a Perforated Solid in Liquid. 353

ordinary investigations given by Prof. Lamb, and, in a less
intelligible form, by Basset.

The equations of motion under finite forces may be deduced
by equating the change of momentum in a small time-interval
d¢ to the impulse of the impressed forces, taking into account
the fact that in the interval 6¢ the origin has a displacement
of translation (wdz, vdé, wot) and the axes have rotational dis-
placements ( pdt, g6t, 76¢), so that the final momenta are referred
to a different set of axes to the original momenta.

The mode of forming the equations of motion is given by
Prof. Greenhill (Encyclopedia Britannica, art. “ Hydro-
mechanics ’’) for the case of acyclic motion, but it is hardly so
obvious why in thus forming the equations of motion of a
perforated solid, it is necessary to include in the “impulse”
terms representing the components of the wrench applied to
the barriers as well as to the solid. We may, however, sup-
pose the changes which actually occur in the time o¢ to have
been produced as follows :—

1st. Let the solid and fluid be reduced to rest by an impul-
sive wrench applied to the solid, and transmitted to a series of
barriers crossing the perforations. The components of this
~wrench will be found to be

ot or
au + &, SCT ap +r, &c. ...

2nd. The barriers being rigidly connected with the solid, let
the latter receive small displacements whose translational and
rotational components are (wot, vdé, wot, pdt, godt, rdt) and let
the solid come to rest in its new position. The fluid will
evidently also come to rest, and therefore no impulse will be
impressed on the system by this change (as may be otherwise
seen by supposing the change to take place very slowly).

3rd. Let the solid be set in motion with velocity-compo-
nents (w+ Qu/dt.dt,... ptdop/dt.dt...) referred to the
new positions of the axes, and let the circulations « be started
in the new position of the solid by a suitable impulsive wrench
applied to the solid and transmitted from it to the barriers.

Then the impulse of the impressed forces (components
Xdt..., Ldt...) is the resultant of the wrenches required to
stop the whole system in the first process and to start it again
in the third.

It is, therefore, that impulse which must be compounded
with the total impulse in the initial position in order to
obtain the total impulse in the final position.

Whence Hayward’s equations of motion follow at once (as

or

354 Prof. G. M. Minchin on the Magnetic

shown in Greenhill’s article above referred to), and they take
the form of the above equations (14), (15).

If we were merely to stop the solid in the first process
without stopping the liquid, the cyclic motion would cause
the liquid to exert a pressure on the solid in the second pro-
cess, and the impulse of this pressure would not be zero, but
would have to be taken into account in forming the equations
of motion. It would be wrong, therefore, to deduce the
equations of motion from the impulse applied to the solid
alone, as is evident in the analogous case of a solid containing
one or more gyrostats.

XXXV. The Magnetic Field of a Circular Current.
By Professor G. M. Mrycuty, 1.A.*

LERK MAXWELL gives a method of drawing the
lines of magnetic force due to a circular current
(‘ Hlectricity and Magnetism,’ Art. 702) by means of a series
of circles and a series of parallel lines. ‘The object of the
following paper is to show how these curves can be described
by a slightly different method, and to exhibit the geometrical
connexion of the series of circles.
Let AQBQ' be the circular current whose sense is indicated
by the arrows, the plane of the circle being that of the paper;

Fig. 1.

ene,

~

2 fee es Se et ee

let P be any point in space, PN the perpendicular from P on
the plane of the circle, and NAOB the diameter of the circle
drawn through N. We shall calculate the vector potential of
the current at P.

Draw any ordinate, QQ!, of the circle perpendicular to BA;
and consider two equal elements of length of the circle, each
equal to ds, at Q and Q!. Resolving each of these along and
perpendicular to QQ!, we see that the latter components are in
opposite senses, and hence their vector potentials at P cancel

* Communicated by the Physical Society: read March 10, 1893.

Field of a Circular Current. 355
each other, since PQ = PQ’. If Ww is the angle QOA,

a=radius of circle, 1=current strength, the components
of ids along Q’Q being equal and in the same sense, the two
elements of current at Q’ and Q conspire in giving a vector
22 cos
PQ
Hence the total vector potential at P is perpendicular to
the plane PON. -If, therefore, OA is the axis of «x, the
perpendicular at O to the plane of the circle the axis of z,
and the diameter at O perpendicular to AB the axis of y,
the components of the vector potential being, as usual, denoted
by F, G, H, the only component existing is G; but, by
taking the components of the vector potential at a point
indefinitely close to P in the direction of the axis of y, we
easily find that

potential .ds perpendicular to the plane PON.

ae _G
| dy = a"
Hence if X, Y, Z are the components of the force of the
current per unit magnetic pole at P, since this force is the
curl of the vector potential, we have
dG dG G
Sa aa, Yi = (): L=— + oe?
where 2(=ON) and y (=NP) are the coordinates of P.
If along the line of force at P the increments of the co-
ordinates are Aw, Ay, we have

ae
GE VA
Hence along this line we have

AG dG G
Tn At + a + — Aas 0,

i.€., G.e= constant along the line of force.

We shall therefore calculate the vector potential, G, at P.
Hvidently

G = 2i| SON 5
0

PQ
a nd
9 VMat+a+y*?—2aecos p
e 2 "e+e pty?
avian : D —D) dp,

356 Prof. -G. M. Minchin on the Magnetic

denoting the denominator by D. Now let ~p=a—o, and
let p?=(a+a)?+9’, p?=(a—a)?+¥4”’, so that p=PB, p'=PA.

Then
ay o wT p> +p? ie, t
G= 2a‘, 1 ihe 2pA ¢ do,

[2 =
A=A/ 1—(1-§) sin? $.

7
Let o=2¢, and Bal — Gs: then, finally,

where

hia

(res <2 {pK-8)-K},

where K and E are the complete elliptic integrals of the first
and second kinds with modulus &; so that the quantity in

brackets is a function of the ratio — simply. |
27,2

Also, since p?— p”=4aa, we have a= ee

G .« which is constant along the line of force is given by the
equation

,and the quantity

G .a=ip{2(K—E) —#’K}.
It is thus seen that at every point in space G is of the

!
form . if. c ) ; so that at all points on the surface for which

: is a constant, the value of G will vary inversely as p. The

I
surface for which © is constant is a sphere having its centre

on the line BA produced and cutting the sphere having BA
for diameter orthogonally. If we assign a series of values to

!
the ratio f. we obtain a series of spheres having their centres

on BA and cutting the given sphere orthogonally, the radius
of each sphere of the series being, therefore, the length of a
tangent from its centre to the sphere described on BA; for,
given the base, BA, of a triangle, and the ratio of the sides,
the locus of the vertex is a circle whose diameter is the join
of the points which divide BA internally and externally in the
given ratio. The surface locus of the vertex is the sphere
generated by the revolution of this circle. >

Field of a Circular Current. 357

On account of the symmetry of the current round its
axis through O, the lines of force and those of constant
vector potential are the same inall planes through the axis.
We may, then, confine our attention to the plane PON,
and suppose fig. 2 to be in this plane, the current being

Fig, 2.

in this figure represented in projection by the line BA.
Describe a series of circles having their centres on BA pro-
duced and cutting the circle described on BA as diameter
orthogonally. Along each of these circles, then, the ratio ee

es e e e PB
is constant, P being any point on the circle.
Consider first the lines of constant vector potential. For

each of the circles let the value of the quantity 2 (K—E)—K
be calculated. Denote this quantity by Q for any one circle ;
then
Q — AQea
p

so that if we wish to trace out the line of constant vector
potential for which G has any given value, we can find the
point, P,in which it cuts any circle of the series by measuring

358 Prof. G. M. Minchin on the Magnetic

the length PB such that
4

_ 4Q
PB=-G. 4.

Let PT be any circle of the co-orthogonal series cutting BA
at nand m. Then for this circle

i
p Bn mB’
and if this ratio is denoted by s, it is well known that
Or Ue
Cam

where C is the centre of the circle. Now the modulus, &, of
the elliptic integrals which belongs to the circle mPn is
Ag

1 Pe) he Ba1—sts hence
AB

2 AD

a BC’

or the square of the modulus is inversely proportional to the
distance, BC, of the centre of the circle from B.

The circles employed by Clerk Maxwell in drawing the
lines of force can be easily shown to be this co-orthogonal
system whose centres are ranged along BA produced. For,
his rule is to assign a series of values to @, and construct
a series of circles whose centres lie on BA, the radius of

each being 5 (cosec 6—sin @), while the distance of its centre

from O is 5 (cosec 9+sin @) ; the modulus belonging to this

circle is sin 8. For the series of circles he then calculates
the values of the expression (constant for each circle)
sin 6
(K—H)
assigned line of force is found by drawing a certain right
line perpendicular to BA. It is at once found that this
series of circles is precisely the co-orthogonal system above
described ; but Clerk Maxwell’s modulus is not the same

, and the point on each circle which lies on any

!
function of the ratio = or of the radius of the circle selected,

Pp
as that adopted above; for, with Clerk Maxwell, if r is the
radius of any circle of the series and & the corresponding

modulus,
es (z— k),
2 \k

Field of a Circular Current. 359

whereas above we have
_2V71-#

f= je eo.

Of course (as stated in a note by Clerk Maxwell) the elliptic
integrals depending on the one modulus can be transformed
into elliptic integrals depending on the other ; and in this
case the transformation is the well-known one of Lagrange.
But the constructions for the points in which any given line
of force cuts the series of circles will not be the same in both
cases—those of Clerk Maxwell depending on a series of right
lines perpendicular to BA, and those above indicated de-
pending on a series of radial distances from B.

When we propose to draw the line of constant vector
potential through any point, P, which lies on a circle whose
constant is Q,, let PB be p); then the point, R, in which this
line meets any other circle, whose constant is Q,is found from
the relation

men
he Ge
where p= BR.

This latter method has a certain advantage for the eye,
inasmuch as it enables us to see readily those circles of the
series outside which the line of constant vector potential
through any proposed point lies.

Consider now the lines of force. With the above value of ©
Q, the quantity which is constant along a line of force is
p.k’Q, so that on each of the above circles in fig. 2 we must now
mark the number £?Q. Denote this by Q’. Then the above
relation for points on the same line of constant vector potential
becomes for the lines of force

/

p=

and the construction proceeds in the same way. The con-
stants, Q’, for the above series of circles, beginning at the
innermost, are :—

"A841; :4301 ; °3775; °3396; °2782 ; °2376; :1954; °1727.

. The values of the Q’s diminish outwards for the circles; so
that if we consider the line of vector potential at any point,
S, suppose, which is such that SB is greater than the distance
from B of the point along AC in which any circle interior to
that passing through 8 cuts the line BAC, it is at once obvious
that the line of vector potential which belongs to 8 is wholly
outside all such circles. The numerical values of Q for the

360 Prof. G. M. Minchin on the Magnetic

circles in fig. 2 are marked at the circumferences, and as much
of the line of potential belonging to P is drawn as is justified
by the number of circles represented in the figure.

The fundamental proposition of electromagnetism is that
the intensity of magnetic force produced at any point in
presence of electric currents is the curl of the vector potential

Fig. 3.
A P Q B

P
0

at the point. But if in the field there is a current in an in-

finitely long straight wire, AB, we find that at every point in

the field the vector potential due to this current is infinite.
Hence it seems impossible to deduce the magnetic force, and
the lines of magnetic force, from the above fundamental pro-
position. This result is unsatisfactory, and it manifestly points
to some defect in our definition of the vector potential.

We are presented with a similar unsatisfactory result in the
general theory of gravitation potential. Thus, taking the
common definition of gravitation potential, if AB is a limited
uniform bar attracting according to the law of inverse square,
we know that the potential which it produces at any point,

P, is proportional to log (cot > cot =) where A= 7 PAB;

B=ZPBA. Now, if the rod extends to infinity, this ex-
pression becomes infinite. I have shown (‘ Statics,’ vol. ii.
Art. 332) how this difficulty arises, and how it is to be
remedied by mending the definition of potential. The diffi-
culty is avoided in a similar manner with regard to the vector
potential.
Thus, since we are concerned only with differential co-
efficients of the vector potential, the ordinary components,
F, G, H of this vector may have added to them any constant
quantities whatever. This amounts to saying that the vector
potential at any variable point, P, in the field is the vector
potential at any fixed point, O, plus the vector difference
between P and O. It does not matter whether the vector
at O is infinite or not: it is a constant in the field. As in
the general gravitation field we are concerned with dzjerences

Field of a Circular Current. 361

of potential only, so in the electromagnetic field we are
concerned with vector differences only.

Let us, then, calculate for the infinite straight current AB
the vector difference between P and a point O on the per-
pendicular, Pp, at a constant distance Op=a from the line.

Let Pp=r, and let an element, ds, of the line AB be taken
at any point, Q; let 2pPQ=0. Then the vector difference,

Ea hdis ds
due to this element, at P is OP —Q07™

M7 + (a—2") cos’OS * cos 6"

Double the integral of this from 0=0 to 0= 5 is the vector
difference at P due to unit currentin AB. LHxpanding the

Py poe
ge )s we have the

radical in ascending powers of » Cc 3
vector equal to

0. ee ee Lac
2f {an 7g 008 Ot oe ate COW 6 oo Palen)
=—4$n? +40? —FAt+ sirens

and this=log,(1 +) =2 log- . Thus, then, the vector dif-

ference at any point, P, is measured by
C—2 log»,
where C is a constant; and this gives the known value of

the magnetic force at P, viz., — a (where G is the vector

potential), perpendicular to the plane PAB, i.e. where &
i

isa constant. In this way, then, the inconvenience of deal-
ing with an infinite vector potential in presence of an infinitely
long (or very long) straight current is avoided.

e lines of constant magnetic potential, or the loci of
points, P, at which the given circular current subtends a
constant conical (“solid”) angle, are the orthogonal trajec-
tories of the lines of force, and can be drawn when these
lines are drawn.

It is not easy to draw these equipotential curves independ-
ently, or even to deduce their typical equation from that of

362 Prof, G. M. Minchin on the Magnetic

the lines of force by the mathematics of orthogonal trajec-
tories.

The magnitude of the conical angle subtended at any point
by a given circle can be expressed in finite terms by means
of complete elliptic integrals of the third kind. The para-
meter involved in these integrals will depend on the way in
which they are taken.

If a sphere of unit radius is described round P as centre,
and lines are drawn from P to the points on the circum-
ference of the given circle, BMAI, fig. 4, these lines will
intercept on the sphere a spherical ellipse, bmat, whose area
is the conical angle subtended by the circle at P. The minor
axis of this ellipse is the great circular are ab determined by
the lines PA, PB, while the major axis, mi, is determined by
the chord, MI, of the circle which subtends a maximum angle,
MPI, at P. This line is determined by drawing the bisector,

Fig. 4.

PC, of the angle BPA, meeting BA in O; then MI is the
chord through C perpendicular to the plane BAP. The
point cin which PC meets the surface of the sphere is the
centre of the spherical ellipse.

Now, given any curve, mpi, fig. 5, on a sphere of unit

Fig. 5.

radius, its area is ja cos #)dg, where, if o is any point on
the sphere inside the area, @ is the circular measure of the

Field of a Circular Current. 363

spherical radius vector op drawn to any point, p, of the curve,
and ¢ is the angle between the radius op and any fixed arc,
oa, drawn ato. If, as said, the pole o is inside the area,
goes from o to 27; but if o is outsede the curve, the area has
a different expression, viz.:—

if cos Odd,

the longitude angle ¢ obviously starting and ending with a
zero value. If o is on the curve, the expression for the area
is again different.

In calculating the area of the above ellipse it would be
natural to choose for pole (0) the point n in which the sphere
is cut by the line PN; but this leads to difficulties when the
position of P is such that n falls on the ellipse. This will
happen when P is on any perpendicular to the plane of the
circle of the current drawn at any point on its circumference;
and, moreover, the choosing of n for pole will lead to expres-
sions for the conical angle which present its values in forms
which are apparently discontinuous for points P which project
inside and outside the area of the given circle BMAI. Such
discontinuity must not exist, and to get rid of it from the
expressions requires troublesome transformations of elliptic
integrals of the third kind.

We must, then, choose for pole a point which is always
inside the spherical ellipse. The simplest point is the point
o (fig. 4), in which the sphere is cut by the line PO which
joins P to the centre, O, of the given circle. This point is,
of course, always inside the ellipse.

Let, then, Q be any point on the given circuit, and p the
point in which PQ cuts the ellipse. Taking for the fixed
plane of longitude through o the plane baP, or BAP, and
denoting the angle poa by ¢@, the area of the ellipse is

(7d —cos op)dd, i. e., 2a —{ "cos op .dd.

Denoting, as before, the position of Q by. the angle , or
QOA, we easily find, if PN=z, PO=r, ON=a,

v2
d = 6 ° © e d
vo) 27 + at gin” ap Vr,
— —ax cos
cos 00 = aaa
Pr / y+ a — Que COS yp?
Hence

ar ty 2
7” — AL COS
cos op -dp=2e | be CONN Gs EY
0 0 Vp +a’—2arcosy 2 +2° sin“

364 The Magnetic Field of a Circular Current.
Putting ~~=7—y, this becomes

dy ?
2e| Jea/1—Psi?§ — Hsin? X + 75 Paap bs STi aang SPOOR

sin

[2

where, as before, p=PB, p'=PA, and ?=1— ie . If we put

¥=2e, this becomes

if A ; ye — a? da
| naga? pA / 2? +2’ sin? 20’

where A= V 1—F?’ sin’ o.

To reduce this to elliptic integrals, we must resolve the
fraction 1/2? + 2? sin? 2 into two fractions. It is easily found
that

xo)

2+2" sin’ 20=2 +42’ (sin? o—sin* o)
=(V72+0?+a—24 sin? o)(V 2 +2?—a2+4+ 22 sin’ @).
Let v denote the sine of the angle between PO anu

the axis of the current (or PN); then the expression, after
resolution into partial fractions, becomes

vad =D i 1
akc ASN oS eee i itv iyawe)

The aia of this expression which has A in the deno-
minator is at once the sum of two complete elliptic integrals
of the third kind; and the portion which has A in the nume-
rator is easily reduced to the same form. The result is

eae a 0

where N=1—v+ > sin’w, and N! is the value of N when v
is changed to —v. Hence we have two elliptic integrals of

the third kind, one with (= ae , k) for parameter and mo-

dulus, and the other with (—
1l+y

then, we have for the oe expression of the conical
angle subtended by the circuit at P the value

ae crs aha

, #). In the usual notation,

eee eae

pr =

On Hydrolysis in Aqueous Salt-Solutions. 365

Of course it is not pretended that this expression is the
most convenient for the purposes of calculation: the approxi-
mate value of the conical angle which is given by a series of
spherical harmonics is that which should be employed; but
it may be well to give the complete expression in the above
form, which I have not seen published anywhere.

XXXVI. On Hydrolysis in Aqueous Salt-Solutions.
By Joun SHE Ds, B.Sce., Ph.D.*

e)* dissolving potassium cyanide in water it is partially

decomposed into potassium hydrate and hydrogen cya-
nide. This action of the water in producing decomposition is
ealled hydrolysis. Probably all salts are hydrolysed in aqueous
solution to a certain extent, but in the majority of cases the
amount of hydrolysis is so excessively small that the means
which we have at our command are not sufficiently delicate to
enable us to detect it. Besides the salts there is another im-
portant class of compounds, namely the esters, which are sus-
ceptible to hydrolysis on being mixed with water. Methyl
and ethyl acetate, for example, are decomposed by water to a
considerable extent into acetic acid and the corresponding
alcohol. The extent to which hydrolysis takes place is regu-
lated by the law of mass action as enunciated by Guldberg and
Waage. In all cases we are dealing with a state of chemical
eden or balanced action which is usually represented
thus :—

KCN + HOH =— KOH+HCN,

or

CH;,COOC,H; + HOH =— C,H;0H + CH;,COOH,

the sign =—— being substituted for the ordinary sign of
equality as suggested by Van’t Hoff.

Now, a priori, we should expect a substance, for example
potassium cyanide, which is formed from chemically equivalent
quantities of acid and base to be neutral, and we have every
reason to believe potassium cyanide, as such, to be so. Its
solution in water, however, as is well known, has a strongly
alkaline reaction, and the above explanation of hydrolysis
furnishes us with no reason why the solution should react
alkaline rather than acid, since the hydrolysed fraction of the
potassium cyanide still exists in the solution as chemically
equivalent quantities of acid and base. Here Arrhenius’
theory of electrolytic dissociation comes to our aid, and shows
us that although we may have in the solution equivalent

* Read before the Swedish Academy of Science, Stockholm, 11th
January, 1893, Communicated by the Author.

Phil. Mag. 8. 5. Vol. 385. No. 215. April 1893. 2C

Pe ir,

ern dope? 2 TD

366 Dr. J. Shields on Hydrolysis

quantities of potassium hydrate and hydrogen cyanide, yet the
former is very largely dissociated into its ions, and, therefore,
in a particularily favourable state for entering into reaction
with the indicator, whilst the latter is not so. Accordmg to
the same theory, if we add other salts to a solution of hydro-
eyanic acid, which, per se, is only slightly electrolytically
dissociated, then the amount of dissociation is diminished
many thousand times, and this is practically what occurs in
the solution under consideration. The presence of the un-
hydrolysed potassium cyanide causes the dissociation ratio of
the hydrocyanic acid to be vastly decreased. |

‘There are salts, on the other hand, whose solutions have an
acid reaction. This is due to the fact that the acid, which is
one-of the products of hydrolysis, is more highly electrolyti-
eaily dissociated than the base which is formed at the same
time. Usually the above facts are expressed by saying that
the base is stronger than the acid, or vice versa.

if hydrocyanic acid were as nearly completely dissociated
as hydrochloric acid is, at the same dilution of course, then
probably a solution of potassium cyanide would be as nearly
neutral as one of potassium chloride, for Ostwald has pointed
out that all acids when completely dissociated are equally
strong.

In this memoir, salts of strong bases with weak acids only
have been considered. The investigation was undertaken at
the suggestion of Dr. Svante Arrhenius, in Stockholm, and
the main object in view was the determination of the amount
of free alkali in aqueous solutions of such salts as potassium
cyanide, sodium carbonate, &c.; that is, of salts whose solutions -
exhibit an alkaline reaction, or act as mild alkalies.

I should like to avail myself of this opportunity to express
to Dr. Arrhenius my warmest thanks for the help which he se
willingly gave me and for the interest which he all along took
in the work.

A research, “ Zur Affinitiitsbestimmung organischer Basen”
(Zeits. f. physikal. Chemie, vol. iv. p. 19,1889), on somewhat

- similar lines, has already been carried. out by Dr. James

Walker. In it the relative strengths of different organic
bases were measured ; but one of the experimental methods
which he adopted could have served equally well for the
determination of the amount of free acid in aqueous solutions
of salts of the bases.

As a general rule, it will be found that the determination of
the amount of free alkali in solutions of the above salts is
beyond the scope of ordinary analysis. A reaction which
enables us to do so, however, is known. The velocity with
which the salt-solutions saponify methyl or ethyl acetate gives

wn Aqueous Salt-Solutzons. 367

us a measure of the quantity of free alkali which they contain.
The essential condition for saponification to take place is the
presence of hydrogen or hydroxyl ions. Now Walker’s
method was based on the presence of hydrogen ions, whilst
in the experiments about to be described we are dealing with
hydroxylions. This places us, as it were, on vantage ground ;
for, since hydroxyl ions saponify much more rapidly than
hydrogen ions, it is thus possible to work with more dilute
solutions where perturbing influences are reduced to a
minimum.

To return once more to the typical example of the salts
under investigation, potassium cyanide, let us for a moment
consider what takes place when we dissolve this body in water.

+
Besides the undissociated KON we get a great number of K
and CN ions, the water itself, too, is slightly dissociated into
> - +
H and OH ions. Now the H ions coming into contact with

the CN ions unite with them to form HCN which is uncharged,
being practically undissociated, whilst the hydroxyl ions re-
main free and counterbalance the potassium ions.

The water goes on continually supplying hydrogen and
hydroxyl ions, which are disposed of in this way, until equili-
brium takes place. If we now make up a small inventory of
the principal constituents of the solution we get :—

+ a
1 and 2, K and ON ions.
3, KCN undissociated.
4, HOH undissociated (say).
5, po undissociated (say ), and, corresponding to this,

6 and 7, K and OH ions.

6 and.7 taken together represent the quantity of free potash
present in the solution. The task which now lies before us is
comparatively easy, but before proceeding to deduce formule
for the calculations it is as well to point out what will be
proved later on, namely, that potassium cyanide itself is not
an active agent of saponification. Attention may also be
directed to the fact that the dissociation of the hydrogen
cyanide is so excessively slight in presence of the salt, that it
cannot exercise any appreciable influence on the velocity of
saponification: the truth of this will be the more readily ad-
mitted if we bear in mind that hydrogen ions are much less
active than hydroxyl ions. What has already been said
regarding the influence of the salt on the dissociation of the
hydrogen cyanide applies equally well to the water.

When ethyl acetate is saponified by a solution of potassium

2C2

368 Dr. J. Shields on Hydrolysis

hydrate, the velocity of the reaction is represented at every
instant by the general equation

& =hO—n) (C2), « «+ = ee Q)
where k is the coefficient of velocity of reaction, C and C, the
concentrations of the ester and base respectively at the com-
mencement, and 2 the quantity of ester which has undergone
change during the time ¢. .

In the case of the salt-solutions we wish to determine the
concentration of the base, z.e., the amount of active free
alkali at the commencement, the coefficient of velocity for the
various bases being already known. On dissolving potassium
cyanide in water we get

KOH + HENg=— KCN Sale
(quantity KOH x diss. ratio) x (quantity HCN x diss. ratio)
= (quantity KCN x diss. ratio) x (quantity HOH x diss. ratio).

The dissociation ratios of potassium cyanide and potassium
hydrate, water and hydrogen cyanide, do not alter appreciably
with change of concentration in the solution, and may conse-
quently be regarded as constant. (Arrhenius, Zeits. f. physikal.
Chemie, vol. v. p. 17, 1890.)

The quantity of water as compared with the other substances
is supposed to be infinitely great and regarded as a constant
K. The saponification of ethyl acetate by means of aqueous
potash takes place according to the equation :—

CH;COOC,H; + KOH=CH;COOK + C,H;08 ;

and if we represent by C, the initial concentration of the
potassium cyanide, by A the concentration of the free
potassium hydrate, and by 2 that of the potassium acetate
formed, then C,—#2—A will represent the actual concentration
of the potassium cyanide, and A+w that of the hydrocyanic
acid; all of course being expressed in the same unit, namely,
gram-molecules per litre. From the equilibrium,

KOH +HCN =~ KON+ HOH
we now get, using our new symbols, the equation
A(A +a)=K(C,—2—A), ee
which represents what takes place at any stage of the reaction.
After the first few moments, however, when A becomes very
small compared with 2, we may write the equation thus :—

aa Kina), ‘

in Aqueous Salt-Solutions. 369

Now, in the general equation (1) C,;—w the concentration of
the base is what we now call A, so that we may re-write it in
the form

Cp a a
Be a e e e e ° . (4)

Combining (8) and (4) we get

de be K (Ci) (5)
dt °C—a k unis
which on integration gives the solution :
Cy . C,—2, C C—2
oe p= 0, log nat. pean C0 log nat. ae
of k(t,—to) - (6)

k, the specific coefficient of velocity, is known, and for potash
at 24°-2 C.is numerically equal to 6°22. Having got K froin
equation (6) all that remains to be done in order to know how
much free potash is present in the solution at the commence-
ment is the calculation of A from equation (2). At the
beginning, when «=0,

IR (Cpa Baan ie 8 elgg CG)
from which we get A in gram-molecules per litre.

The percentage amount of potassium cyanide which has
been decomposed by the water is therefore

100A
OF :

It is here unnecessary to describe in detail the apparatus
and method which I used to determine the velocity of the
saponification of ethyl acetate by the salt-solutions, as it was
precisely similar to that which has already been employed by
Ostwald (Journ. f. pr. Ch. [2] vol. xxxy. p. 112, 1887),
Arrhenius (Zerts. f. physikal. Chemie, vol. i. p. 110, 1887), and
others. Measured volumes of a known strength of salt-solu-
tion and of ethyl acetate were mixed at the temperature of the
thermostat. (For the construction of the thermostat, c.
see Zeits. f. physikal. Chemie, vol. ii. p. 564, 1888.) From
time to time small fractions of the mixture were withdrawn
by means of a pipette and titrated as expeditiously as possible.

In calculating the concentration of the salt at the com-
mencement, it has been assumed that the volume of the mixed
solutions of salt and ester is the sum of the volumes taken
separately. This is of course, strictly speaking, not true, but
the deviation from the truth is so small as to be entirely
negligible. I shall now proceed to give the experimental

370 Dr. J. Shields on Hydrolysis

results which I obtained. The first column in the tables
contains the time ¢ expressed in minutes since the beginning
of the reaction. The second and fourth columns C,—2 and
C—z contain the concentrations of the salt and ester re-
spectively in hundredths of a gram-molecule per litre. The
third column contains x the quantity of ester which has under-
gone change, also expressed in the same unit. In the last
column will be found the constant expressed in arbitrary units.
Here it may be noticed that the first few values have been
neglected in accordance with the derivation of the formula.
From the mean value of these the characteristic constant K
has been calculated. A represents the amount of free alkali
in gram-molecules per litre, and besides this will be found the
percentage amount of salt which has been hydrolysed in the
solution experimented on and at the temperature at which the
experiment was carried out. It is conceivable that the
addition of ethyl acetate to the solution of salt would disturb
the existing equilibrium, but a discussion of this question is
reserved for a later part of the memoir.

Potassium Cyanide.

Solutions of this salt of four different concentrations were
examined, namely, +, 4, 4, and ~, normal. The tempera-
ture at which the experiments were made was 24°20. The

value of k, the coefficient of velocity for potash at this temper-_

ature, is 6°22. Nitrophenol was found to be the most suitable
indicator, and enabled me when titrating with decinormal

= Potassium Cyanide.

t. O,—2. z. O—x.
0 94°74 0-00 39°34
4 93°40 1°34 38°00
16 92:28 2°46 36°88 (313) x 1077
| 39 91-40 3°34 36°00 324
90 88°72 6:02 33°32 385
210 86°40 8°34 31:00 337
353 84:20 10-54 28°80 342
580 81:20 13°54 25°80 378

-Mean=353 x 1077

K=0:000928.
A=0:00296, or 0°31 per cent. of salt hydrolysed.

hydrochloric acid to observe the end point pretty accurately. _

wn Aqueous Salt-Solutions. St

IN : d
—- Potassium ( vyanide.

4
: i
be | CLs | a. hy eK Cre
| etd ae eSeS INCE clue Aa
| |
0 | 2348 0:00 39:34
Go|. 222s | O96 i. esses 7).
re) 2198s) || 50, saree 1) (117) x 10s!
ef IO) | 1:9 S786 4 TBS
Sheet . 2012. | SOO at |, weonos: 4 219
2) Sd ok s ee 20 |. Bl 216
oem | 144 GO4> 7 ee3s30E" 4) 226
Bee | 1598 | 7:50 Sted, F206
1394 - |. 13°00 10-48 D886 1 | 225
2789 | 9:82 13°65 2568 |° 245

Mean=221 x 10-7)

K=0-00121.
A =0-:00168, or 0°72 per cent. of salt hydrolysed.

N ee:
— Potassium Uyanide.
10
t C,—2. ff C—x
0 9°52 0:00 48°70
2 9°23 0:29 48°41 |
6 8:87 0°65 48:05 (251-5) x 10-6
12°5 8:67 0-85 47°85 123°8
33 815 kes fae 47-33 12671
6Ooioin. 767 1:85 46:85 | 131-2
130 6°78 2°74 45°96 =|: 1451
209 6°25 3°27 45°43 Messy
319 5°56 3°96 44-74 J41°8
1372 | 2°93 6°59 42°11 | 1376

|
i
i

Mean=133'8 x 10-8

K=0:001204.
A =0°00107, or 1:12 per cent. of salt hydrolysed.

Sra

372 Dr. J. Shields on Hydrolysis

N Potassium Cyanide.

AQ)
t. C,—z. Pe | C—z. |
SS |
0 2:38 0:00 48°70
2 2:20 0-18 48°52
45 2-10 0:28 48-42 (449) x 10-6
8:5 2:00 0:38 48-32 782
22 1-83 0°55 48°15 602
44 1-59 0-79 47-91 683
112 117 1-21 47-49 759
191 100° “| “ps8 47°32 634
303 0-72 1-66 47-04 765
1351 0:16 2-22 46°48 742
| Mean=702'4 x 10-§

K =0:001336.
A =0:000557, or 2°34 per cent. of salt hydrolysed.

é
40 Potassium Cyanide (concentrations in 5}5 gram-
molecule per litre).

| t C,—2 | a C—x, |
|
| 0 4-73 0:00 97-40 |
| 2 4-42 031 97-09 |
5 411 0-62 96°78 | (1050) x 10-6
10 3°86 0:87 96:53 (893) |
23 3°57 1:16 96-24 728 |
36 3:26 1-47 95°93 728 |
60 |) 99204 1-79 95°61 686 |
122 2:30 2-43 94-97 720 |
180 2:02 271 94-69 653 |

Mean =703 x 10-5

K = 0-001328.
A =0°000553, or 2°35 per cent. of salt hydrolysed.

Sodium Carbonate.

Experiments were made with 1, +4, 94, and 2, mole-
cular normal solutions of sodium carbonate.

The titrations were made with the aid of phenol phthalein at
the ordinary temperature of the laboratory. In this way the
amount of standard acid added corresponded only to one half of
the real concentration of the salt in hundredths of a gram-mole-
cule per litre, as the solution becomes practically neutral when
the unaltered sodium carbonate has been converted into sodium
hydrogen carbonate. This would necessitate the doubling of

in Aqueous Salt-Solutions. 373

the apparent concentrations ; but since the exact point of
neutrality was difficult to observe, two series of experiments
were made to eliminate as much as possible the experimental
error and the sum of the apparent concentrations taken to
represent C,—2. Consequently, in the tables for sodium car-
bonate there are two extra columns (I. and II.) with the
sum of the numbers contained in them given under the
column C.—.. The temperature at which all the experiments
on sodium carbonate was made was 24°2C., and the co-
etlicient of velocity & for sodium hydrate at this temperature
is taken at 6°23.

_ (mol.) Sodium Carbonate.

t. fe IT. U,— 2. Le C—x.

0 19-00 19-00 38°00 0-00 48-70
2 18-15 18°10 36°25 1-75 46°95
4 17-40 17:27 34°67 33 45°37 | (150) x 10-6
8 16°55 16°65 33°20 4°80 43°90 | 129
2 15°95 15°99 31°94 6:06 42°64 | 138
20 15°15 15°15 30°30 7:70 41:00 | 135
30 14-72 14-74 29 46 854 40-16 | 112
50 13°23 13°26 26°49 11-51 37:19 | 136
85 11:80 11-95 23°75 14:25 34:45 | 136
155 10°10 9:97 20°07 17°93 30°77 | 141

Mean = 132°4 x 10-6

“ (mol.) Sodium Carbonate.

t. ih Ma Osea. | Aaa Coe.

0 9-40 9°40 18-80 0-00 48°70
2 9-07 9:05 18°12 0°68 48:02
4 8°85 8°10 16°95 1-85 46-85 | (625) x10-°
8 7°85 7:60 15°45 3°35 45°35 815
12 7:30 7:25 14°55 4°25 44°45 839
16 6°95 6:90 13°85 4°95 43°75 854
20 6°60 6:62 13°22 5°53 43°12 880
24 6°40 6°35 12°75 6°05 42°65 874
32 5°82 6-08 11:90 6:90 41°80 885
66 5:12 5:10 10°22 8°85 40°12 741

Mean =841 x 10-6
K=0:01954,
=0°00596, or 317 per cent. of salt hydrolysed,

374 Dr. J. Shields on Hydrolysis

ah (mol.) Sodium Carbonate.

Ree ere y ae 2...) Oa

z. : |
are Seals 7 one TA Tce Sia
0 | 477 | 477 | 954 | 0:00 | 48-70 :
2 | 430 | 433 | 863 | 091 | 47-79 |
4 3:84 | 3°90 T74 | 1:80 46:90 278 x 10-*

8 344 | 350 | 694 | 260 | 46:10 | > a7 |
12 0/2301. [83-18 |) 6492] 93-35 | 45-a5 ee |
|
|

16 290 | 2-96 5°86 3°68 | 45:02 255
32 247 | 2:25 4°72 4:82 | 43°88 243

40 209 | 207 4-12 542 | 43-28 266
62 152 | 160 a12 | G42 | 49:98 283
92 1-22 1:24 246° | 7-08 ..| 41-62 269

Mean= 265 x 10-5,

K=0-02383.
A =0°00465, or 4°87 per cent. of salt hydrolysed.
N
0 (mol.) Sodium Carbonate.
l l ; | | |
t, I Il | G,-2.| 2 | Cm~s
Sass eens | ==...
0 2°38 238 | 476 | 000 |) 458
2 | 195 | 225 | 420 | 056 | 4814
4h. STS 180 | 35d 1-21 47-49 634 x 10-5
8 1:35 153 | = 288 1-88 46°82 676
12 1°22 1:23 | 2-45 2°31 46°39 698
16 1:16 ay 2:27 2°49 | 46°21 613
20 1°02 1-07 2°09 267 | 4603 579
28 0-75 0°85 160° | SiG Maes 665
56 0°49 0°41 0-90 3°86 | 44-84 656 .
Mean=646 x 10-5
K=0-02586.
A =0:00838, or 7°10 per cent. of salt hydrolysed.

Potassium Phenate.

Carbolic acid or phenol is another well-known weak acid
which forms a crystalline salt with potash. As an experi-
ment with this salt seemed likely to be interesting, solutions
of it were prepared by mixing equivalent quantities of solu-
tions of potash and phenol of known strength and then diluting
until solutions of the salt of the required concentration were
obtained. Two sets of experiments were made; one with

in Aqueous Salt-Solutions. 375

zo and the other with =, normal solutions. The indicator
used for titration was nitrophenol.

The temperature of the thermostat was 24°1C., and the
coefficient of velocity for potash at this temperature was
taken as 6°19. Each set of experiments was done in duplicate,
the separate results being given in the columns I. and II.
The mean of these is contained in the column C,—wz. In the
case of the =, normal solution the concentrations are ex-
pressed in 5}, instead of ;}5 gram-molecule per litre, as
before.

N Potassium Phenate.

10
t 1 EE C,—2. a. C—xz.
0 9-62 9°62 9-62 0:00 48°70
2 8-80 8:80 8°80 0:82 47°88
4 8°30 8:20 8:25 1:37 47°33 | (1383) x10-5
6 8-03 8:00 8:01 161 47:09 107
8 781 CCT HEU 1°83 46°87 101
10 766 7-60 7°63 1:99 46°71 95
12 TAD 7:43 7:44 2°18 46°52 96
16 7:09 (US a es) 2°53 46:17 99
22 6°75 6°71 6:73 2°89 45°81 97
30 6°20 6:10 6°15 347 45:23 109
Mean=101x10-5
K=0:00925.

A =0:002936, or 3°05 per cent. of salt hydrolysed.

ny Potassium Phenate.

50
t aL II. C,—4 Ai C—z.
0 3°90 3°90 3°90 0:00 97°40
2 3°15 3:10 312 0-78 96°62
4 2°78 2°80 2°79 ei 96:29 | 567x10-5
i) 2°60 2°67 264 | 1:26 96°14 611
6 2°49 2°54 2°52 1-38 96°02 627
8 2:27 2:27 2°27 1:63 95°77 (704)
12 2°10 2°04 2:07 1°83 95°57 596
16 1:88 1-86 1:87 2°03 95°37 578
20 1-66 1-64 1:65 2°25 95°15 613
eR A hiasteee 1:46 1:46 2°44 94-96 616
OD Ue sends 1-29 1:29 2°61 94°79 629
Mean=605 x 10-5
K=0-00939.
A =0°001305, or 6°69 per cent. of salt hydrolysed.

376 Dr. J. Shields on Hydrolysis

Borax.

Several experiments were made with solutions of borax,
but the results were by no means as satisfactory as could be
desired. The chief difficulty seemed to be in the want of a
suitable indicator. After trying about twenty I finally selected
litmus as the one which gave the best results. Next to litmus
came rosolic acid. I first of all prepared a solution of litmus
of a certain purple tint to act as a guide or standard, and
then I added acid to the solution under examination until it
became of the snes tint. I shall only give one series of
experiments with a =4, molecular normal solution of borax, so
that some conception may be formed as to the amount of
hydrolysis in solutions of borax.

The temperature of experiment was 24°-2C., and the co-
efficient of velocity for sodium hydrate corresponding to this
temperature is 6°23,

N
39 (mol.) Borax.
|
t C,-2 L Ca
0 5°85 0.00 48°70
4 5°82 0:03 48°67
8 572 0-13 48-57 (30) x 10-6
30 5°55 0:30 48°40 (22)
188 4:10 1°75 46°95 120
1190 2°73 3°12 45°58 86
2885 1-40 4-45 45°25 95
4375 0-95 4°85 43°85 94 |

Mean = 99x 10-6

K =0:00050.
A =0:000738, or 0°92 per cent. of salt hydrolysed.

The Influence of Dilution on the Amount of Hydrolysis.

The table which follows contains the general results of the
foregoing experiments and shows the effect of dilution on the
amount of hydrolysis.

The first column gives the approximate concentration of
the solution, the second the amount of free alkali in the solu-
tion in gram-molecules per litre, and the last the percentage
amount of salt hydrolysed.

see

in Aqueous Salt-Solutions. 377

- Concentration. A. Hydrolysis.
N
z KON Be i onhee nee 0:00296 0:31 per cent.
2 mere 5 ak lp 0-00168 072 ,,
N
Pe laos Se 0-00107 ae
N : ‘
=. ae 0000557 Danes
B Gaol. )Na,00 0-00804 2-12
im (mo .)Na, Zot eees 0 wiz 9
N 00596
i0 5 Sh ae CR Ate 0:00596 317 a
N 00465
0 et eacties <<’ moe 0:00465 4°87 vs
0:00338 7-10
Fee c
N
BMOMIOR eeeesecee 0-00294 S0b)
N
Bp OMe 0:00131 669
a Gael N 0007 0:92
39 (mol.)Na,B,O, ... 0:00074 56

A glance at the table will show that among the four sub-
stances examined the greatest amount of hydrolysis occurs in
the case of sodium carbonate. The numbers cannot pretend
to a very high degree of accuracy, chiefly on account of the
difficulties in obtaining suitable indicators for the titration of
the solutions, but the following regularity is easily discernible.
The amount of free alkali contained in the salt-solutions is
proportional to the square root of the concentration of the salt.
This is, however, not strictly true, but more nearly expresses
the truth the greater the dilution of the solution. A rough
calculation on the numbers for the two most concentrated
solutions of potassium cyanide shows that there is a deviation
from the law of about 13 per cent., whilst for the less concen-
trated solutions the deviation is reduced to about 4 per cent.
If the dilutions be plotted as ordinates against the percentage
amount of salt hydrolysed as abscisse, curves are obtained.
Fig. 1 represents the curves for potassium cyanide and sodium
carbonate. ‘These curves enable us to see at a glance the per-
centage of salt hydrolysed at any given dilution. For example,

Dilution.

378 Dr. J. Shields on Hydrolysis

Fig. 1.

Percentage of Salt hydrolysed.

reading from the curve, there should be 1°65 per cent. of
the potassium cyanide decomposed in a 34, normal solution

of that salt. If calculated from the above law, the amount of

hydrolysis is 1°58 per cent.

Now if the salt itself were the cause of the saponification of
the ester, the velocity of the reaction which is proportional to
the amount of free base present would have been very nearly
directly proportional to the concentration of the salt; but it
has been found approximately proportional to the square root
of the concentration, consequently the view that the salt itself
produces the saponification is untenable.

The law which has just been enunciated is what we should
expect from the theory ; for if we again take the case of
potassium cyanide, we get, neglecting the dissociation ratios
as formerly, :

KOH+HCN ==> KCN+HOH,
0. Gee) Ne
where C, is the initial concentration of the potassium cyanide,
and the fraction of it which has been hydrolysed. When «
is very small compared with C,, the above equation becomes

C= V7 Cos

wn Aqueous Salt-Solutions. 379

that is to say, the amount of free potash is proportional to the
square root of the concentration of the potassium-cyanide
solution.

Tt has long been known that water decomposed certain salts,
with formation of free acid and free base, but the amount of
such decomposition has up to the present time only been
measured in a few cases. It is true some guesses at it have
occasionally been made, but they have proved rather unsatis-
factory. For example, it has been supposed (see Ostwald’s
Lehrbuch der allgem. Chemie, vol. ii. p. 187, 2nd edit.), from
measurements of the heat of neutralization of hydrocyanic
acid by caustic soda, that a solution of sodium cyanide con-
tains only one fifth of the salt as such, whilst the other four
fifths are decomposed into free acid and free base.

The experiments which I have made on the velocity of
reaction show that in a tenth-normal solution of potassium
cyanide only about one per cent. of the salt is decomposed in
the way indicated. The results which J. Thomsen (Thermo-
chemische Untersuchungen, vol. i. p. 161) obtained on neutra-
lizing one molecule of sodium hydrate with n molecules of
hydrogen cyanide are as follows :—

n. NaOH Aq, nHCN Aq.
i 13°68 heat units.
iL 27°66 i
2 27°92 =

These numbers indicate that the amount of heat which is
‘developed increases in the same proportion as the quantity of
hydrogen cyanide added, until there are equivalent quantities
of acid and base present. An excess of acid, then, produces
only a very slight alteration in the value of the heat of
neutralization.

Now manifestly this small increase in the heat of neutrali-
zation means that the first equivalent of hydrogen cyanide
has almost all combined with the sodium hydrate. The cause
of the incomplete combination is due of course to the mass
action of the water. Inshort, it would seem that only a small
fraction, presumably about one per cent., of the potassium
cyanide is decomposed by the water into free acid and free
base.

This corroborates the result which I have obtained by a
totally different method.

A guess which H. Rose (Jahresbericht, 1852, p. 311)
hazarded as to the amount of hydrolysis in an aqueous solu-
tion of borax is just as unsatisfactory. Rose supposed that

380 Dr. J. Shields on Hydrolysis

this substance in pretty dilute solution was almost entirely
decomposed into acid and base; but the preceding experi-
ments go to prove that in a =; molecular normal solution
rather less than one per cent. is decomposed by the water.
If the statement that the amount of free alkali in the solution
is proportional to the square root of the concentration holds
good for borax, then a solution in which the borax was com-
pletely hydrolysed would be almost infinitely dilute.

Rose has described a very interesting experiment which is
intended to show the decomposition of borax by water. A
tincture of litmus reddened with acetic acid is added to a
concentrated solution of borax until the red colour has almost
but not quite disappeared ; the whole is then diluted with
water, when the red colour changes to blue. I have repeated
this experiment, and find that a solution prepared in the way
Rose has indicated becomes distinctly blue on dilution. Joulin
(Bull. Soc. Chim. de Paris [2] vol. xix. p. 844, 1873), how-
ever, could not observe this change of colour, and moreover
has attempted to show that water exercises no decomposing
influence at all on salts; but there is little doubt that he has
been too hasty in coming to this conclusion, and that Rose,
at least qualitatively speaking, was right.

Trisodium Phosphate.

A preliminary experiment with a X solution of this salt
showed that the velocity of reaction, on saponifying ethyl
acetate, was singularly great when compared with what had
been observed in the case of the other salt-solutions, and in
fact closely approached that for a =, normal solution of
caustic soda itself. This seemed to indicate that the solution
under examination was almost entirely hydrolysed in the
sense of the equation 3

Na;PO,+ HOH =Na,HPO,+ NaOH.

The formulze which have hitherto been employed are of no
use in this case, for they depend on the condition that A
should be very small compared with 2 Here A can in no
case be neglected ; consequently the equation (3)

he K(C, — a)
is inapplicable. eae Ss
The general equation
dx
becomes d:

7G =KG—2)(C-0), 2... 8)

in Aqueous Salt-Solutions. | 381.

when we substitute for the concentration of the base that of
the sodium phosphate.

Instead of K we may write ky, where we is a factor which
expresses the ratio of the amount of free alkali present to’
what would be present if the hydrolysis of one sodium atom
was complete.

Hquation (8), on integration, gives the solution

. Cy—2

S20. log nat. (a G—0, °s nat. en =hu(t;—t),

Gag — log Gap = 04843 ku (—4)(C—C), + @)

from which we can calculate m at the time ¢,.

In order to determine pu at the commencement, the different
values of mw are plotted against the times, and the curve so
obtained prolonged. The point at which it cuts the axis for
the time t=0 gives the value of w at the commencement.

Hixperiments have been made which show that Na,H PQ, is
only slightly hydrolysed ; so if we neglect this and assume
that the equation

Na,PO,+ HOH=Na,HPO,+ NaOH
represents the posszble quantity of caustic soda which can be
formed in the solution, then 100 represents the percentage
amount of the caustic soda which actually eavsts in be solution.

The following experiments were made with a =, molecular
normal solution of trisodium phosphate at 24°-2 C., at which
temperature the coefficient of velocity of reaction for caustic
soda is 6°28. The concentrations are expressed in 3}5 of a
gram-molecule per litre, and the employment of phenol

_ phthalein enabled the titrations to be made pretty accurately.

i

a (mol.) in Phosphate.

t. I. II. C,—2. oR C—x. pe

0 3°81 J81 3°81 0:00 4°87

2 2°93 2°95 2°94 0:87 4:00 0:945
4 2°41 2°45 2°43 1:38 349 0882
6 2:06 2°03 2°04 1-77 3°10 0873

8 182 | 177 | 179 | 202 | 2:85 | 0-831
10 158 | 155 | 156 | 295 | 362 | 0-897
12 135 | 140 | 137 | 944 | 243 | 0-897
16 112 | 114 | 113 | O68 | 219 | o-788
20 091 | 094 | 093 | 288 | 1:99 | o-v780
4 079 | o8 | o7v9 | 302 | 185 | o-v64
| 30 063 | O66 | o64 | 317 | 170 | 0-738

Phil. Mag. 8. 5. Vol. 85. No. 215. April 1893. 2D~

Coefficient wu.

382 Dr. J. Shields on Hydrolysis

If the equation
Na;PO,+ HOH =Na,HPO,+ NaOH

represented accurately the amount of hydrolysis, then mw at
the commencement should be 1:00. A glance at the last
column of the table shows that the equation must be nearly
true. In order to find approximately the initial value of p,
a curve (fig. 2) has been drawn by plotting the values of w as
ordinates against the times ¢ as abscisse. .

Time, in minutes.

By referring to the curve it will be found that the initial
value of w is 0°98 at least ; that is to say, at least 98 per cent.
of one of the sodium atoms in Na;PO, exists as free caustic
soda in a = molecular normal solution of the salt at 24°-2 C.
In other words, although trisodium phosphate exists in the
sclid state, yet in dilute solution it is for the most part
decomposed into hydrogen disodium phosphate and sodium
hydrate. This result is in entire agreement with Berthelot’s
recent researches.

in Aqueous Salt-Solutions. 383

Allusion has already been made to the fact that hydrogen
disodium phosphate is only slightly hydrolysed when dissolved
in water. ‘This salt behaves rather differently from the others.
During the saponification the solution, which is at first
alkaline, becomes neutral and then acid.

For the sake of comparison with trisodium phosphate, the
following set of experiments was made witha 50 (mol.) solu-
tion of hydrogen disodium phosphate at 24°°2 C. The solution
was prepared from a sample of the salt obtained from Kahl-
baum, and had a slightly alkaline reaction.

The titre of the solution during saponification was as
follows :—

N setae
30 (mol.) Hydrogen Disodium Phosphate. |
ee ee
Time. Titre.
min. 7
0 0:06 ado g--mol. per litre (alkaline),
2 0-04 A; Er haes
5 0:00 Neutral.
32 0-06 zdo0 g.-mol. per litre (acid).
120 0-10 2
226 0-15 ” r
380 0°17 . ?
1380 0-30 a ‘
2815 0:41 ‘s x
4500 0-52 j 33

The titrations were made with phenol phthalein.

At the commencement the solution contained 0:0003 gram-
molecule of free soda per litre.

The case is a very complicated one, but possibly the bulk of
this alkalinity is due to the formation in the solution of tri-
sodium phosphate ; there is still, however, a minute amount
of free alkali in the solution, owing to the hydrolysis of
hydrogen disodium phosphate. The following attempt has
been made to measure it, but no stress must be laid on the
results. I give the calculations here merely for the sake of
comparison with trisodium phosphate, and to show that at the
best there is not much free alkali in the solution. The calcu-
lations were made with the help of equations (6) and (7). It
is evident, of course, that what we measure here is the quan-
tity «2. The initial concentrations of the salt and ester,
expressed in hundredths of a gram-molecule per litre, are
4°76 and 48°76.

2D2

384 Dr. J. Shields on Hydrolysis

If we start at the point where the mixture is neutral we
may construct the following table, from which we can calcu-
late the quantity of free alkali in the solution at the point of
apparent neutrality. This quantity, as has already been sug-
gested, is perhaps due to the hydrolysis of hydrogen disodium
phosphate ; whilst the quantity of free alkali determined by
direct titration is due to the presence of trisodium phosphate,
formed according to the equation

2Na,HPO,=Na;PO, + NaH,PQ,.

The influence of the dihydrogen sodium phosphate has been
neglected altogether. :

te C.—«. ap. C—x.
0 4:76 0:00 48°70
27 4-70 0:06 48-64
115 4-66 0:10 48°60 64x 10-8
221 4-61 0-15 48°55 (86)
375 4:59 0-17 48°53 65
1375 4°46 0:30 48°40 59
2810 4°35 0:41 48°29 55
4495 4:24 0:52 48:18 54

Mean = 59x107°

K=0-00000236.
A=0-:000038, or 0°07 per cent. of salt hydrolysed.

The amount of free alkali determined by direct titration is
0°63 per cent., whilst that determined from the velocity of
saponification, starting at the neutral point, is 0°07 per cent. ;
it is therefore evident that the total amount of free alkali in
the solution is very small when compared with what is present
in a solution of trisodium phosphate.

Sodium Acetate.

After having estimated the amount of hydrolysis in salts
of strong bases with some of the weakest acids, it was
thought desirable to extend the experiments a little and
determine the amount of hydrolysis in a salt of a stronger
acid, for example acetic acid. For this purpose a tenth
normal solution of sodium acetate was prepared and investi-
gated in the same manner as the salts of the weaker acids.
The calculation of the results, however, was in this case much
simplified, owing to the fact that the concentrations of the salt
and ester did not alter much during the reaction, consequently

in Aqueous Salt-Solutions. 385

the mean values have been employed in calculating the

rharacteristic constant.

If, in the equation (5),
de 1 1_ K(CG—z)
dig@en bes og be
we substitute for C.—a and C—w their mean values 9°316

and 48°49, which were obtained from a series of experiments
made at 24° 2 ©., where k=6'23, we get:

deel BI IGK
d 4849 623° 4%”
which on integration gives the solution

ay" — x67

6:23 x 48°49 x 9-316 K=
ty— to |

Having got the characteristic constant K, equation (7)
enables us to determine A, the amount of free soda in the
solution at the beginning, expressed in gram-molecules per
litre. The solution was titrated with the help of phenol
phthalein.

In this case of course a, which is expressed in hundredths
of a gram-molecule per litre, was measured directly. The
values of x in the following table are the means of two con-
cordant sets of experiments.

N et
i0 Sodium Acetate.

t. C,—<2. x. C—x2.
0 9-52 0-000 48°70
1224. 9-46 0-060 48-64
3952 9:455 0-065 48-635
6882 9 385 0-135 48:565 2:58 x 10-6
21252 9:20 0-320 48-380 4-98
25550 9:20 0-320 48-380 4-06
34160 9-165 0°355 48-345 3°72
41290 9:14 0380 48°320 3:51
Mean = 9°316. Mean=48'49. Mean=—3°76x10-°.

K=0:0000000668.
A=0:00000798, or 0°008 per cent. of salt hydrolysed.

According to these measurements and calculations, it will
be seen that in a tenth normal solution rather less than +4)
per cent, of sodium acetate is hydrolysed into free acid and

386 Dr. J. Shields on Hydrolysis
free base ; thus, |
- CH,COONa+ HOH === CH,COOH+NaOH.

Tt has already been stated that the presence of free weak
acids has no measurable influence on the velocity with which
the saponification takes place.

This is equally true in the case of sodium acetate, where
acetic acid is one of the products of hydrolysis, and is also
formed on the saponification of ethyl acetate. Arrhenius
(Zeits. f. phystkal. Chemie, vol. v. p. 2, 1890) has thoroughly
investigated the change of the dissociation ratio of acetic acid
on the addition of sodium acetate, and has shown that it may
be regarded as nil in presence of large quantities of its salts.

By referring to the table it will be seen that the experi-
ments on sodium acetate lasted for a considerable time, and it
is conceivable that the water itself may have played an im-
portant part in the saponification of the ester. In order to
test this a blank experiment was made with water and ethyl
acetate under the same conditions as the experiment with the —
sodium acetate, and after the lapse of nearly three weeks the
solution of the ester was only slightly acid. If, then, pure
water, in virtue of its being electrolytically dissociated to a
small extent, produces such an inappreciable effect, we can
easily conjecture how infinitely slight this effect will be in
presence of a strongly dissociated salt like sodium acetate.

The Influence of the Ester on the existing Equilibrium.

A]l the preceding deductions regarding the amount of
hydrolysis in aqueous solutions of salts of strong bases with
‘weak acids are based on the assumption that the equilibrium
in aqueous solutions,

KCN+HOH <> HCN+KOH,

is not disturbed by the presence of small quantities of ethyl
acetate. ‘To justify this assumption, I have made some expe-
riments in which the concentration of the ester was varied,
whilst the concentration of the salt remained nearly the same.
Now, if the presence of the ester produced any change in the
state of equilibrium, we should expect an alteration in the
concentration of the ester to be accompanied by a corre-
sponding variation in the amount of salt hydrolysed.
The following tables contain the results of experiments, on
an approximately 0-1 normal solution of potassium cyanide,
made at 25°-0 C., at which temperature 4=6°54.

in Aqueous Salt-Solutions. 387

I. Concentration of Ester = 0°4870 g.-mol. per litre.

s C,—2x. oD. C—x. |

2
0 10:08 0:00 48°70
2 9-70 0°38 48°32
6 9-46 0°62 48:08 (100) x 10-8
10 9-20 0:88 47°82 143
20 8:81 1:27 47°43 153
40 8:38 1:70 47:00 142
84 7°70 2°38 46°32 141
152 700 3°08 45°62 140
264 6:20 3°88 44°82 137
1484 2°90 718 41°52 139
Mean = 142x10-°
K=0:001305.

A=0-00114, or 1:13 per cent. KCN hydrolysed.
II. Concentration of Ester = 0°2005 g.-mol. per litre.

é C.—2. 2X. C—-x.
eee 1038 000 |. 20:05
2 10:20 0-18 19:87
6 9-99 0:39 19:66 (27) x 10-6
12 9°77 0-61 19:44 (36)
On 9-41 0-97 19:08 39
63 8:90 1-48 18°57 40
131 8:26 2-12 17-93 42
243 7-67 2-71 17°34 39
1463 4-85 553 1452 41
1683 4-56 582 14:23 49
Mean = 40x10-§
K=0:00151.

A =0:00124, or 1:20 per cent. KON hydrolysed.

III. Concentration of Ester =0°1013 g.-mol. per litre.
|

t. Ob hho x. C—x.
0 10-4902 Ae O00 1013
2 10°40 0-09 10-04
10 10:16 0:33 9:80 (103) x 10-8
37 9-66 0:83 9:30 130
104 9°19 1:30 8:83 143 |
215 8:57 1:92 8-21 160 |
1435 6-40 4-09 6-04 164 |
1655 6-26 4-93 5-90 150
Mean = 149x10-8
K — 0:00 148.

A=0:00124, or 1:18 per cent. KCN hydrolysed.

388 On Hydrolysis in Aqueous Salt-Solutions.

The next small table contains the collected results of these
experiments.

Cone. Ester. K. A. KCN hydrolysed.
0:4870 | 000131 0-00114 | 1:13 per cent.
0:2005 0:00151 000124 4 ae2inae

| ie
|

01013 000148 | 0°00124

The numbers show that the concentration of the ester has
no measurable influence on the amount of hydrolysis, since
the figures in the last column do not arrange themselves in a
series which is either gradually ascending or descending.

The differences between them are probably chiefly due to
experimental error. The mean value is 1°17, and the greatest
deviation from it is less than 5 per cent.

Résumé.—The general results of this investigation may
briefly be stated as follows :—

1st. It is shown how the velocity with which salt-solutions
saponify ethyl acetate may be utilized to determine the extent
to which hydrolysis has taken place in aqueous solutions of
salts of strong bases with weak acids.

2nd. The amount of hydrolysis has been measured in solu-
tions of the following salts; and in 4, molecular normal
solutions between 24°-25° C. the amount of salt which is
decomposed by the water is :—

Potassium cyanide 1:12 per cent.
Sodium carbonate . oa
Potassiam phenate ... . . s-Oa eae
Borax (about) ; 0-5 ss
Sodium acetate 0-008

7?

Ath. Trisodium phosphate can scarcely be said to exist in
a 345 molecular normal solution, as it is almost completely
hydrolysed in the sense of the equation ;
Na;PO,+ HOH=Na,HPO,+ NaOH.
5th. The presence of small quantities of ethyl acetate in the
solution does not materially disturb the equilibrium,
KCN + HOH 22— KOH + GR

University College, London,

[ 389 J

XXXVII. Suggestion as to a possible Source of the Energy
required for the Life of Bacilli, and as to the Cause of thew
small Size. By G. Jounstone Stoney, M.A., D.Sce.,
F.R.S., Vice-President, Royal Dublin Society *.

ie that part of the material universe which man’s position in

time and space, and the limitations of his senses, permit
him to investigate, the Dissipation of Energy is so prevalent
that instances of the reverse process can seldom be clearly
traced out, though many such can be dimly seen. Under
these circumstances, even possible instances, such as that dealt
with in this paper, are instructive if they are of a kind to be
fully understood. They are also important, for if the universe
is permanent, there must be, or have been, or be about to
be, parts of the universe where the Concentration of Hnergy
is as largely predominant as its dissipation is within our
experience.

Some bacilli, e. g. some of the nitrifying bacilli of the soil,
are said to be sustained by purely mineral food, while they
furnish ejecta which contain as much potential energy as the
food, or more. If this be the case, they must be supplied
with a considerable amount of energy to enable them to evolve
protoplasm and the other organic compounds of which they
consist, from these materials. Now many bacilli are so
situated that this energy is certainly not obtained from sun-
shine, and it is suggested that it may be derived from the
gases or liquids about them.

The average speed with which the molecules of air dart
about is known to be nearly 500 metres per second—the
velocity of a rifle-bullet ; and the velocity of some of the
molecules must be many times this, probably five, six, or
seven times as swift. We do not know so much about the
velocities of the molecules in liquids as of those in gases, but
the phenomenon of evaporation and some others indicate that
they are at least occasionally comparable with those of a gas.
Accordingly, whether the microbe derive a part of its oxygen
or other nourishment from the gases, or from the liquids about
it, it is conceivable that ONLY THE SWIFTER MOVING MOLECULES
can penetrate the microbe sufficiently far, or from some other
cause are either alone or predominantly fitted to be assimi-
lated by it.

Now if this be what is actually taking place, the adjoining
air or liquid must become cooler through the withdrawal from

* From the Scientific Proceedings of the Royal Dublin Society,
vol. yili, part i. Communicated by the Author,

390 Dr. G. J. Stoney on the Source of the

it of its swiftest molecules ; and, in compensation, an amount
of energy exactly equivalent to this loss of heat is imparted
to the microbes and available for the formation within them of
organic compounds.

It is further evident that if this be the source of energy
upon which bacilli and cocci have to draw, the minuteness of
their narrowest dimension will be of advantage—probably
essential—to them. Presumably it would only be limited by
such other necessary conditions as may forbid the diminution
of size being carried beyond a certain point. The diameter
of a bacillus is frequently as small as half or a third of a
micron, which brings it tolerably well into the neighbourhood
of some molecular magnitudes.

The transference of energy here suggested may be what
occurs notwithstanding that it does not comply with the
Second Law of Thermodynamics, which states that heat will
not pass from a cooler to a warmer body, unless some ade-
quate compensating-event occurs, or has occurred, in con-
nexion with the transference. This law represents what
happens when vast numbers of molecular events (which are
the real events of nature) admit of being treated statistically,
and furnish an average result. It, therefore, has its limits :
and the communication of energy from air to minute organ-
isms which is described above, is an example of a process
which is exempt from its operation ; since this transference
is supposed to be brought about by a discriminating treatment
of the molecules that impinge upon the bacillus of precisely
the same kind as that which Maxwell pictured as made by his
well-known demons. It therefore belongs to the recognized
exception to the Second Law of Thermodynamics, viz., that
which occurs in the few cases in which we can have under
observation the special consequences of selected molecular
events, instead of, as on all ordinary occasions, being only
able to measure an average outcome from all the molecular
events in the portion of matter we are examining.

If some bacilli—those which live on mineral food—obtain
their whole stock of energy in the way here indicated, it may
be presumed that all bacilli get at least a part of what they
require in the same way.

Should the reader have any doubt as to whether the pro-
cess here described is one of those that contradict the Second
Law of Thermodynamics, he may satisfy himself on this head
by the following considerations :— LTE

Imagine a perfect heat-engine within an adiabatic envelope
with some bacilli and an abundance of their mineral food, all

Energy requred for the Life of Bacilli. 391

‘being at one temperature. If events take place as supposed
above, the bacilli receive sufficient energy from the sur-
rounding medium to enable them to assimilate their mineral
food, and thereby to grow and multiply. Meanwhile the
medium becomes cooler. We may then suppose that the new
bacilli which have come into existence, and all the excreta,
are used as fuel in the heat-engine, and that its refrigerator is
as near as we please to being at the temperature to which the
medium has been reduced. The combustion of the fuel may
take the form of resolving the bacilli and excreta back into
the mineral substances from which they had been evolved,
except that these are now at the temperature of the combus-
tion. Let us next reduce this temperature in the heat-engine
to the temperature of the refrigerator. During this process
a portion of the heat may be converted into mechanical energy ;
and at the end of the process everything within the enclosure
is in the same state as at the beginning, with the sole excep-
tions that some of the bodies within the enclosure are now at
a lower temperature than at the beginning, and that the heat
which they have lost has been converted into mechanical
energy.

It thus appears that the contents of the adiabatic envelope
may be regarded asa heat-engine, all the parts of which start
at a certain temperature, and which yields mechanical energy,
while the only other change is that some of its parts are cooled
to a lower temperature. This contradicts the Second Law of
Thermodynamics as formulated by Lord Kelvin, if we leave
the word “inanimate” out of his enunciation. His state-
_ ment of the axiom is :—‘‘ It is impossible by means of inani-
mate material agency, to derive mechanical effect from any
portion of matter by cooling it below the temperature of the
coldest of surrounding objects.” It is legitimate here to
omit the word “inanimate,” as its insertion merely means
that cases of exception to the law may be met with in the
organic world ; and if this be stated it will need to be added
that cases of exception may also be found among inorganic
processes: the correct statement being that the law does not
apply to individual molecular events, and that therefore it
need not be obeyed in the cases, whether organic or inorganic,
in which any observable effect is the outcome of one-sided
molecular events.

- It should be borne in mind that the heat of a given portion
of matter is the energy * of motions of and within its molecules;

* The energy here spoken of may be partly potential: in fact while

motion is going on, the “energy of the motion,” or a part of it, usually
fluctuates between being kinetic and potential.

392 Intelligence and Miscellaneous Articles.

not necessarily of all such motions, but of those among them
which are capable of restoring energy to the parts of the
molecule carrying electra (see Stoney on “ Double Lines in
Spectra,” Scientific Transactions of the Royal Dublin Society,
vol. iv. part xi.) whenever the motion of the electron has
transferred energy from the molecule to the ether. As ful-
filling this criterion we are probably to include all irrotational
motions within the molecules, and we must also include rela-
tive motions of the molecules—all of them indeed if time
enough be allowed for turmoil within a fluid to subside. It
does not include any motion which the molecules have in
common, as in wind, or in the rotation of a wheel.

When these circumstances are taken into account, it is
obvious that the energy of the heat-motions of an individual
molecule undergoes rapid fluctuations, while there may be a
definite average of the energy of these motions, whether esti-
mated by what happens in an individual molecule over a
sufficiently long period of time, or when estimated by what
occurs simultaneously in all the molecules of a body. In
other words, the motions of an individual molecule do not
from instant to instant conform to the Second Law of Thermo-
dynamics, although the law may apply both to the average of
the motions of a single molecule taken over a long period of
time, and to the average of the simultaneous motions of vast
multitudes of associated molecules. As regards molecular
motions (the motions within a solid, or motions within a fluid
that do not produce currents in the fluid), the millionth of
one second is a long period.

XXXVIII. Intelligence and Miscellaneous Articles.

ON THE MAGNETIZATION OF IRON RINGS SLIT IN A RADIAL
DIRECTION. BY H. LEHMANN.

ee chief results of the present research may be summed up in

the following principles, which hold for an imperfectly closed
ferromagnetic ring, the radius of which is large in comparison
with the radius of the section :—

1. The demagnetizing factor, or the factor which, multiplied
by the mean magnetization, gives the mean factor of the demag-
netizing force, is constant up to about half the saturation.

2. The coefficient of dispersion (Strewungs-coefficient), the ratio
of the mean induction to that in the slit, is constant up to half
saturation.

3. The region of the dispersion of the lines of force is limited
essentially to the vicinity of the slit, and is narrower as the
magnetization increases.

4, The coefficient of dispersion is independent of the radius of
the ring; in regard to its constancy (2), it only depends on the

Intelligence and Miscellaneous Articles. 398

relative width of the ring d/r. The empirical expression for this
dependence is a linear one of the form

ete
7

where h is a constant which, for the Swedish iron investigated, has
the value 7, and will presumably have values differing but little
from this in the case of other ferromagnetic metals. This will
probably be the case more especially in the kinds of iron used in
technical processes.

5. When the empirical constant 2 is known, the factor of
demagnetization can be calculated from the geometrical dimensions
of the system by the formula

Ne 2d

d aN?
Pan = Earl

in which p is the radius of the ring, r that of the section, and d
the width of the slit. This formula holds with the same limitation
as (1), (2), and (4), that is, up to demisaturation. In general the
equation holds,

2d

medi 1
ayy
(p—z)

in which y is the factor of dispersion.
6. For high magnetizing values the factor of demagnetization
approaches the limiting value
Nope 5 are me a)
ee:
The previous results may find an approximate application even in

imperfect magnetic circuits of complicated shapes.—Wiedemann’s
Annalen, No. 3, 1893.

N=

THE SPECIFIC HEAT OF LIQUID AMMONIA.
BY C. LUDEKING AND J. E. STARR.

The specific heat of liquid ammonia, though it has often been the
subject of calculation in development of theory and practice, has
not yet been satisfactorily determined experimentally, if we except
the work of Regnault. His results, however, were unfortunately
lost during the Paris Commune. He assumed the specific heat to
be 0°799. Since then the interest in this constant has very
considerably increased through the rapid development of the
artificial ice industry. Generally the specific heat has been taken
at unity. Thus De Volson Wood in his ‘Thermodynamics,’
page 337, recommends this value “ until the experimental value is
determined.” |

It was our good fortune to have ready access to all the means
necessary for executing the somewhat laborious experiments
involved, and we take this opportunity to present briefly the

a94 Intelligence and Miscellaneous Articles.

results of our work. The liquid ammonia used in the experiments
was found on examination to contain 0°3 per cent. of moisture
and on spontaneous evaporation to leave only a trace of residue.
The impurities were therefore of no consequence in influencing the
result to the limit of accuracy intended.

Of this liquid ammonia 10°01 grams were introduced into a
small steel cylinder of 16:122 c.c. capacity, stoppered by a steel
screw. The mode of filling was quite simple. After cooling the
cylinder in a bath of the liquid ammonia itself and while still
immersed, it was possible to pour it brimful by means of a beaker.
The steel screw stopper, also previously cooled, was then inserted
and drawn almost tight. On then removing the cylinder from the
cooling bath, the liquid contents gradually expanded and escaped
in quantity proportional thereto, and besides a very small vapour
space was allowed to form as is indicated in the experimental data.
Then the stopper was driven tight. Thus the error in the result
due to the latent heat of condensation of vapour of ammonia in the
course of the experiments was reduced to a minimum and
rendered, as will be seen, almost inappreciable in its influence.

The cylinder was perfectly free from leakage and remained
constant in weight during each series of determinations. It was
suspended in the drum of a Regnault apparatus heated by the
vapour of carbon disulphide. The entire mode of procedure was
in all details that commonly used in the Regnault method. After
the cylinder had been heated for about six hours, it was dropped
into a brass calorimeter whose water value was 1°36 cal. and which
contained 150 grams of water. In each experiment it required
very nearly two minutes to raise the calorimeter to its maximum
temperature. The influence of loss by radiation was reduced
to a minimum by the Rumford manipulation. The thermometers
used were standardized, carefully compared, and read to hundredths
of a degree by means of a magnifying lens. The experiments were
conducted sufficiently far from the critical temperature, which
according to Vincent and Chappuis is 131° C.

The following are the data of Experiment 1 :—

Weight of steel cylinder and ammonia. .. 81-008 grams.
Weight of steel cylinder ............%. 70°998

9

Weicht of ammonia ..j.e0es52<. . AEG 10-01 25

The specific gravity of liquid ammonia being 0°656, the volume of
10°01 grams is 15:26 c.c.

Total water value of calorimeter, thermometer,

Bit WVAIeE ne. cs SEE A. ss 151°76 cal.
‘Water value of steel cylinder ............ 8°34 cal.
eMmEperavure OF di... eos. s 5 ts ee 25°4 C.
Temperature of steel cylinder ............ 46°51 C.

Temperature of calorimeter after immersion 26°69 C.
Temperature of calorimeter before immersion 24°44 C,

ftsse in temperaburers 1. Aa crew. ss. ys bot 2°25 C.

Intelligence and Miscellaneous Articles. 395

Thus 341:46 cal. were given off by the cylinder in cooling 19°82
or 17:23 cal. for one degree. Of this 8°34 cal. are due to the
steel cylinder itself, leaving 8°89 cal. for 10°01 grams of liquid
ammonia or 0°888 per gram=specific heat. In a second and third
experiment the values 0°897 and 0896 were obtained. The
determination of the specific heat of liquid ammonia would be
influenced, as stated, by the latent heat of condensation of part of
the small quantity of vapour present, when the cylinder cools in
the calorimeter. This would to a degree be neutralized by the
contraction of the liquid ammonia itself in the cooling and the
consequent formation of more vapour space.

It seemed desirable to ascertain the influence of these factors
collectively by experiment. or this purpose specific heat deter-
minations were made in a way somewhat different from the
ordinary. The steel cylinder was cooled in an iron shell in melting
ice, instead of being heated, and then introduced into the warm
calorimeter water. The mode of precedure was in detail similar to
that described above, and we will therefore only give our results.
In three experiments the values 0°878, 0°863, and 0-892 were
obtained. They are a trifle lower in their average than the results
obtained by the ordinary method. It.is reasonable to assume that
they are somewhat low, while as stated the other results are
presumably somewhat high ; and in order to arrive at the specific
heat of this substance nearest the true value from our experimental
evidence, we will take the average of our six values, viz. :

0-888 0-878
0-897 } 1st series, 0-863 $ 2nd series,
0-896 0:892

and state it as being=0°8857.

_ We beg herewith to acknowledge our obligations to Chancellor
W.S. Chaplin and Prof. Wm. B. Potter for kindly placing the
laboratories under their charges at our disposal.—Stlliman’s Journal,
March 1893.

ON THE OFFICIAL TESTING OF THERMOMETERS.
BY H. F. WIEBE.

In the year 1885 the Imperial Standards Commission undertook
on a large scale the official testing of thermometers which is of
such great importance both in science and in practice ; while pre-
viously only a few institutions, such as the Naval Office, had
occupied themselves to a limited extent with the investigation of
thermometers. These official testings were transferred to the
recently established Physical Technical Imperial Institute, to which
since then a great number of thermometers have every year been sent
for investigation. (In Ilmenau there is a branch for these testings.)
Through the great progress which has been made since Jena glass
has been used for thermometers, it has been possible to undertake
a permanent guarantee for the results obtained in such testing ;
and from the uniformity of this glass the thermometric constants,

once determined, may be universally adopted. The testing takes

396 Intelligence and Miscellaneous Articles.

place in two ways—either by comparison with a standard thermo-
meter at different temperatures, or by calibration and determina-
tion of the thermometric constants. The comparison of the thermo-
meters is made between 0° and 50° in water-baths; above 50°
in boiling-point apparatus with reversing condensers, in which
liquids of various boiling-points are used for the determinations.
The following liquids were found to be especially suitable :—

Boiling-point. Boiling-point.
Clvoroform “i262: .-- 60°6° Toluole \.. ..«s<o<24-¢- see 109°4°
Methylic alcohol ............ 64:5 | Isobutylic acetate............ 1141
Methylic ethylic alcohol Paraldehyde ....sc-.sssseea-=8 1246
Re eee an eee 69°8 Amylic alcohol - 2-222 129°8
Methylic ethylic alcohol Xylole*...7. 2c. tecseeeee 139°4
SEW Dap neh epee 5 ae ee 72:4 | Amylic acetate ............-.. 140:0
Hthylic alcohol ............ 73:1 Bromoform ...2522-4ssse-- 148°9
He propylice alcohol Tarperntine....2-.ce- about 160°0
a eae eee 79°8 Aniline .... <.ccecceeseeeeeee 1843
LS) Ce ee 79:9 Dimethylamine ............ 194:0
Ethylic propylie alcohol | Methylic benzoate ......... 1993
(iS eee a ee 82-2 | Doluidine. .::..:22gcse-o see 199°5
Isobutylic bromide ......... 874 | Ethylic benzoate ..........+. 2123
Ethylic propylic alcohol | Chimoline ....2.¢.-2:sscemenee 235°9
LYOte Nera ne ee 91°5 | Amylic benzoate ............ 259°5
Propylic alcohol ............ 96-0 Glycerine 3.3.22... cs-ceee 290°1
Isobutylic alcohol ......... 105°7 | Diphenylamine ............ 301°9

By boiling various liquids under diminished pressure constant
temperatures may be obtained, and this method is also used in the
Imperial Institute between temperatures of 50° and 140° (compare
Beiblitier, vol. xvi. p. 507). The statement as to the correction
refers to thermometers completely immersed, and corrections must
be introduced afterwards for the projecting thread (compare also
Rimbach, Beiblatier, vol. xvi. p. 417). .

The second kind of investigation which is indispensable for
accurate instruments consists in calibrating them, determining the
distance of the fixed points, &e. The methods for this are described
in the Trav. a4 Mem. du Bureau international, &c. The position of
the ee. at ¢°is, according to Bottcher,

Ht = E,,, + 0°0055 (100 —¢) +0°0,8 (L00—#).
The reduction of the data of the mercurial thermometer of Jena

glass 16'" to those of the air-thermometer, according to Wiebe and
Bottcher, are calculated from the formula
6= —0°0,280 (100 —2)—0°0,299 (100—#),

in which ¢ stands for degrees of the mercury-thermometer, 6 the
reduction to the air-thermometer (see Beiblitter, vol. xvi. p. 352).

For testing the thermometers at low temperatures mixtures of
salts are used to—33° ; for still lower temperatures mixtures of solid
carbonic acid with mixtures of alcohol and water in various pro-
portions (to—78°8). Above 300° baths of fused nitre are used ;
the best is a mixture of potassium and sodium nitrates in equal parts
melting at 230°. Thermometers of Jena glass filled with nitrogen
may be used after a previous continuous heating to about 480°
to 450°.—Zeitschrift fur analyt. Chemie, vol. xxx. p. 1 (1891); E
Beiblitier der Physik, vol. xvi. p. 100.

THE

LONDON, EDINBURGH, ano DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

aaa SSS

[FIFTH SERIES.]

WEA YS 1893:

XXXIX. Gratings in Theory and Practice*.
By Henry A. Row ann f.

Parr I.

T is not my object to treat the theory of diffraction in
general, but only to apply the simplest ordinary theory
to gratings made by ruling grooves with a diamond on glass
or metal. This study I at first made with a view of guiding
me in the construction of the dividing-engine for the manu-
facture of gratings, and I have given the present theory for
years in my lectures. As the subject is not generally under-
stood in all its bearings I have written it for publication.
Let p be the virtual distance reduced to vacuo through
which a ray moves. Then the effect at any point will be
found by the summation of the quantity

A cosb(p—Vt) +B sin b(p—Vo),
in which 6= = ¢ being the wave-length, V is the velocity
reduced to vacuo, and ¢ is the time. Making @ = tan =

* Reprinted from a separate copy from the ‘Astronom. and Astero-
Physics’ for February communicated by the Author.

+ Iam much indebted to Dr. J. 8S. Ames for looking over the proofs of
this paper and correcting some errors. In the paper I have, in order to
make it complete, given some results obtained previously by others,
especially by Lord Rayleigh. The treatment is, however, new, as well
as many of the results. My object was originally to obtain some guide
to the effect of errors in gratings, so that in constructing my dividing-
engine I might prevent their appearance if possible.

Phil. Mag. 8. 5. Vol. 35. No. 216. May 1893. 2 i

398 Prof. Henry A. Rowland on Gratings
we can write this
/ A? + B? sin [0+6(p—Vt) |.

The energy or intensity is proportional to (A’+ B’).
Taking the expression 3

OA + iB) Cm:

when 7= V —1, its real part will be the previous expression
for the displacement. Should we use the exponential expres-
sion instead of the circular function in our summation, we
see that we can always obtain the intensity of the light by
multiplying the final result by itself with —z in place of +12,
because we have

(A +iB)e-®0-¥) » (A —iB) e?-VO = A? + B?,

In cases where a ray of light falls on a surface where it is
broken up, it is not necessary to take account of the change
of phase at the surface, but only to sum up the displacement
as given above. |

In all our problems let the grating be rather small com-
pared with the distance of the screen receiving the light, so
that the displacements need not be divided into their com-
ponents before summation.

Let the point a’, y', 2! be the source of light, and at the
point x, y, z let it be broken up and at the same time pass
from a medium of index of refraction I! to one of I. Consider
the disturbance at a point 2", y", 2! in the new medium. It
will be

o—ib(Ip+T’ =)
where
pawl? + of! 424 x 4 2 4 2 —2 (aa! + yy! + 22!"),
paa? ty te? 402 +y4+2—Ava! +yy! +22).

Let the point 2, y, z be near the origin of coordinates as
compared with a’, 7’, 2 or 2”, y", 2", and let «, 8B, y and @!, BI, 9/
be the direction-cosines of p and p. Then, writing

Real V 22+ yee? +] Vo gl? 4 yl? + ZIP,

A=Te +V'e!,
e=IB+ ¥e,
v=ly +I,

we have, for the elementary displacement,

e—i4[R—VE —Ar—py—ve+kKr2].
3

in Theory and Practice. 399

where Can iY I |
; 2 e=4[ Vo? + yf? 4 2P a VS gill? yf? 4. ile
and
r= ty? +2",

This equation applies to light in any direction. In the

special case of parallel light, for which «=0, falling on a
lane grating with lines in the direction of z, one condition

will be that this expression must be the same for all values of z.

Hence eG

If N is the order of the spectrum and a the grating-space,
we shall see further on that we also have the condition

27a

bales

The direction of the diffracted light will then be defined by
the equations

bap=2a4N = ——

a? +4 BP 4/2 =O,

Try + I'y'=0,
18 +1ig'= : N
Whence
[a ee +27 — N@— —
Iip'= - N= Ip,

yi a
In the ordinary case, where the incident and diffracted rays
are perpendicular to the lines of the grating, we can simplify
the equations somewhat.
Let @ be the angle of incidence and w of diffraction as
measured from the positive direction of X.

A=I!'cos¢+I cosy,

“Napalsin g+I sin yy,
Oat |
b=,

where / is the wave-length in vacuo.
In case of the reflecting-grating [=I', and we can write

A=LI{cos H+ cos},
aN =e=Kisin d+ sin py}.
2H 2

400 Prof. Henry A. Rowland on Gratings

This is only a very elementary expression, as the real value
would depend on the nature of the obstacle, the angles, &c.,
but it will be sufficient for our purpose.

The disturbance due to any grating or similar body will
then be very nearly

a ee Goa
where ds isa differential of the surface. For parallel rays,«=0.

PLANE GRATINGS.

In this case the integration can often be neglected in the
direction of z, and we can write for the disturbance in case of

parallel rays,
eg ib(R—VE) \ ) e—ibl—re—-wy] ds,

Case 1.—SimpuLe PERIopIc RULING.

Let the surface be divided up into equal parts, in each of
which one or more lines or grooves are ruled parallel to the
axis of z.

The integration over the surface will then resolve itself into
an integration over one space, and a summation with respect
to the number of spaces. Fr in this case we can replace y
by na+y, where a is the width of a space, and the displace-
ment becomes

e—ib(R—Ve) > ptibuan i \ etbartny) dss
but - bf

BS sin eC
S2—] ptibuan — et? > ben :
e . bap
sin

Multiplying the disturbance by itself with —z in place of +1,
we have for the light intensity,

>= bapx?
sin ees

2

sin cs

The first term indicates spectral lines in positions given by
the equation :
a
7 = 3

with intensities given by the last integral. The intensity of
the spectral lines then depends on the form of the groove as

[ \ eBOz+uy) ds || ( etibrtuy ds].

sin

in Theory and Practice. . A401

given by the equation «=/(y) and upon the angles of inci-
dence and diffraction. The first factor has been often discussed,
and it is only necessary to call attention to a few of its pro-
perties.

When baw=27N, N being any whole number, the expres-
sion becomes n”?, On either side of this value the intensity
decreases until nbay'=2aN, when it becomes 0.

The spectral line then has a width represented by p/—w! = 2F

nearly ; on either side of this line smaller maxima exist too
faintly to be observed. When two spectral lines are nearer
together than half their width they blend and form one line.
The defining power of the spectroscope can be expressed in
terms of the quotient of the wave-length by the difference of
wave-length of two lines that can just be seen as divided,
The defining power is then

nN*=na 3

Now na is the width of the grating. Hence, using a
grating at a given angle, the defining power is independent
of the number of lines to the inch and only depends on the
width of the grating and the wave-length. According to this,
the only object of ruling many lines to the inch in a grating
is to separate the spectra so that, with a yiven angle, the
order of spectrum shall be less.

Practically the gratings with few lines to the inch are
much better than those with many, and hence have better
definition at a given angle than the latter except that the
spectra are more mixed up and more difficult to see.

It is also to be observed that the defining power increases
with shorter wave-lengths, so that it is three times as great in
the ultra-violet as in the red of the spectrum. This is of
course the same with all optical instruments such as telescopes
and microscopes. ,

The second term which determines the strength of the
spectral lines will, however, give us much that is new.

First let us study the effect of the shape of the groove on
the brightness. If N is the order of the spectrum and a the
grating-space, we have
e=Il(singd+sin py) = =~,

ba,
since sin —<" ==())

2

* An expression of Lord Rayleigh’s.

402 Prof. Henry A. Rowland on Gratings
and the intensity of the light becomes proportional to

[ iy il (F242) ds}[ (fe —ion(J2t Sy) ds}.

It is to be noted that this expression is not only a function
of N but also of lJ, the wave-length. This shows that the
intensity in general may vary throughout the spectrum ac-
cording to the wave-length, and that the sum of the light in
any one spectrum is not always white light.

This is a peculiarity often noticed in gratings. Thus one
spectrum may be almost wanting in the green, while another
may contain an excess of this colour; again, there may be
very little blue in one spectrum, while very often the similar
spectrum on the other side may have its own share and that
of the other one also. For this reason I have found it almost
impossible to predict what the ultra-red spectrum may be, for
it is often weak even where the visible spectrum is strong.

The integral may have almost any form, although it will
naturally tend to be such as to make the lower orders the
brightest when the diamond rules a single and simple groove.
When it rules several lines or a compound groove, the higher
orders may exceed the lower in brightness, and it is mathe-
matically possible to have the grooves of such a shape that,
for given angles, all the light may be thrown into one spectrum.

It is not uncommon, indeed very easy, to rule gratings with
immensely bright first spectra, and I have one grating where
it seems as if half the light were in the first spectrum on one
side. In this case there is no reflexion of any account from
the grating held perpendicularly: indeed, to see one’s face the
plate must be held at an angle, in which case the various
features of the face are seen reflected almost as brightly as in
a mirror but drawn out into spectra. In this case all the
other spectra and the central image itself are very weak.

In general it would be easy to prove from the equation
that want of symmetry in the grooves produces want of
symmetry in the spectra—a fact universally observed in all
gratings, and one which I generally utilize so that the light
may be concentrated in a few spectra only.

Example 1.—SQuaRE GROoVEs.

When the light falls nearly perpendicularly on the plate,
we need not take the sides into account but only sum up the
surface of the plate and the bottom of the groove. Let the

depth be X and the width equal to a
m

in Theory and Practice. 403

The intensity then becomes proportional to

ES sin? 7 sin? wy X,
This vanishes when
. N=m, 2m, 3m, &e. ;
l
The intensity of the central light, for which N=0, will be

Tes ho
7s (x7 x

This can be made to vanish for only one angle for a given
wave-length. Therefore, the central image will be coloured
and the colour will change with the angle, an effect often
observed in actual gratings. The colour ought to change,
also, on placing the grating in a liquid of different index of
refraction, since \ contains I, the index of refraction.

It will be instructive to take a special case, such as light
falling perpendicularly on the plate. For this case,

o=0, X=1(1 + cos), and p=lsinp=

Hence

=0, 1, 2, 3, &e.

rat{lea/i -(5 hb

The last term in the intensity will then be

‘ Small 1 N\2
2 as
sin 4X17 + ee,
As an example, let the green of the second order vanish.

In this case, /="00005. N=2. let a=-0002 centim.,.and
b=:

Then —_X[20000 + /(20000)?— (10000)"] =n.
Whence
pre i 8
37300"

where n is any whole number. Make it 1.
Then the intensity, as far as this term is concerned, will be
as follows :—

404 Prof. Henry A. Rowland on Gratings

Minima where Intensity is0.|| Maxima where Intensity is 1.
Wave-lengths. -Wave-lengths.

Ist spec....| *0000526 0000268 | 0001000 | 00003544 | -00002137

2nd ,, ...| °0000500 ‘0000266 0000833 | 00003463 | -00002119
ord ,, ...| *0000462 0000263 =| 0000651 | 00003333 | -00002089
4th ,, ...| °0000416 ‘0000259 | 0000499 | 00003169 | -00002050
thy oaere &e. &e. | &e. &e, &e.

The central light will contain the following wave-lengths as
a maximum :—

"0001072, :00003575, °0000214, &e.

Of course it would be impossible to find a diamond to rule
a rectangular groove as above, and the calculations can onl
be looked upon as a specimen of innumerable light distribu-
tions according to the shape of groove.

Every change in position of the diamond gives a different
light distribution, and hundreds of changes may be made
every day and yet the same distribution will never return,
although one may try for years.

Example 2.—TRIANGULAR GROOVE.

Let the space a be cut into a triangular groove, the
equations of the sides being e=—cy and w=c'(y—a), the
two cuttings coming together at the point y=u. Hence we

have —cu=c(u—a), and ds=dy-V/1+c?, or dyV¥1+c?.
Hence the intensity is proportional to

EN. 1 (Ee. ow 1

V(1+c¢?)(1+e¢?) . mu(u—cr) . m(a—u)(w+er)
aes UN) | sl a

cos [(H+eA)(a—u)—n(u—er)] t

pf 1+¢ <j 9 TU(jL — Cr) 1+c” 9 7(a—u)(wt+ecr)
(

This expression is not symmetrical with respect to the normal
to the grating, unless the groove is symmetrical, in which case

a
exc’ and u= =.

2

in Theory and Practice. 405

In this case, as in the other, the colours of the spectrum
are of variable intensity, and some of them may vanish as in
the first example, but the distribution of intensity is in other
respects quite different.

Case IJ.—MUuLTIPLE PERIODIC RULING.

Instead of having only one groove ruled on the plate in
this space a, let us now suppose that a series of similar lines
are ruled.

We have, then, to obtain the displacement by the same
expression as before, that is

sinn a
— 2 | etontnnds,

Si —=

except that the last integral will extend over the whole number
of lines ruled within the space a.

In the spaces a let a number of equal grooves be ruled
commencing at the points y=0, 41, Yo, yz, &c., and extending
to the points w, y;+w, yotw, &e. The surface integral will
then be divided into portions from w to y,, from y,;+w to yo,
&c., on the original surface of the plate for which e=0, and
from w to 0, from y,+w to y;, &c., for the grooves.

The first series of integrals will be

U 1 1D p.t0 @ U 4
femray= aap i-@ + eH — ePMntw) + eta — Ko,

= ii { — eibuw of (1 we ent) ( eu a CNY, ae &c.) te eeEe) ,

But e”#*=1 since bua=0 for any maximum, and thus the
integral becomes

1 fe. eiouw
aby

{1+ een + e¥2+ Ke}.
The second series of integrals will be

Ont undsS 1 + un + Ke}

0

406 Prof. Henry A. Rowland on Gratings
The total integral will then be

UGE
sin 2 a el 1 —ebnw w
[ : oe i ehArt+ey) | [1 4+ vy 4. etbuye 4 &e. | :
. bap 2b 0 . ;
sin “ome

As before, multiply this by the same with the sign of z
changed to get the intensity.

Example 1.—Hquat DIstTancEs.
The space a contains n’—1 equidistant grooves, so that
W=Ye—Yi= Ke. = - :
ine

Ss

t=)

Nene
ee eee nl” — gibau

. bap
sin —=
2n'

Hence the displacement becomes

Ores
sinn aE

— pibuw w
—al ae +), eres]:
sin —- :

2n/

As the last term is simply the integral over the space = in

a different form from before, this is a return to the form we
previously had except that it is for a grating of nn’ lines

instead of n lines, the grating-space being.

Example 2.—Two GRoovEs.
1+ e"n=2e 2 cos ee :

But lau=2Nz7.. Hence this becomes

pean
Qem™Na cosa@N2!,
a

The square of the last term is a factor in the intensity.
Hence the spectrum will vanish when we have

in Theory and Practice. 407

Ne =4, 3, 3, &e.*
or
_ila 3a da be
2 2 2,

- Thus when 5 =2, the Ist, 3rd, &., spectra will disappear,
1
making a grating of twice the number of lines to the centim.

When ae the 2nd, 6th, 10th, &c., spectra disappear.
fal
When =6, the 3rd, 9th, &., spectra disappear.
1

The case in which” =4, as Lord Rayleigh has shown,
: Mets :

would be very useful,as the second spectrum disappears leaving
the red of the first and the ultra-violet of the third without
contamination by the second. In this case two lines are
ruled and two left out. This would be easy to do, but the
advantages would hardly pay for the trouble owing to the
following reasons :—Suppose the machine was ruling 20,000
lines to the inch. Leaving out two lines and ruling two
would reduce the dispersion down to a grating with 5000
lines to the inch. Again, the above theory assumes that the
grooves do not overlap. Now I believe that in nearly, if not
all, gratings with 20,000 lines to the inch the whole surface is
cut away and the grooves overlap. This would cause the
second spectrum to appear again after all our trouble.

Let the grooves be nearly equidistant, one being slightly

displaced. In this case y;= 5 +.

COs? 7

Nyy ( 7 eNO aN. Nv?
—3- = ( cos-3— cos —— —sin —— sin — }.
2 2 a 2 a

For the even spectra this is very nearly unity, but for the odd

it becomes
v 2
(«N2) :
a

Hence the grating has its principal spectra like a grating of
space : ; but there are still the intermediate spectra due to

the space a, and of intensities depending on the squares of the
order of spectrum, and the squares of the relative displace-

* A theorem of Lord Rayleigh’s.

408 Prof. Henry A. Rowland on Gratings

ment, a law which I shall show applies to the effect of all
errors of the ruling.

This particular effect was brought to my attention by trying
to use a tangent-screw on the head of my dividing-engine to
rule a grating with, say, 28,872 lines to the inch, when a
single tooth gave only 14,436 to the inch. However care-
fully I ground the tangent-screw I never was able to entirely
eliminate the intermediate spectra due to 14,436 lines, and
make a pure spectrum due to 28,872 lines to the inch,
although I could nearly succeed.

Example 3,—ONE GROOVE IN m MISPLACED.

Let the space a contain m grooves equidistant, except one
which is displaced a distance v. The distance is now propor-
tional to

a a m—1l
Bee: eth ibu\ P — +0 ibu —— @
lte *m+e +&c.+e ( m a m
. bua
—e ™m +zbuve Sl
gine
2m

Multiplying this by itself with —z in place of +2, and
adding the factors in the intensity, we have the whole ex-
pression for the intensity. One of the terms entering the
expression will be

pun Wea fs 0GIe
> ea Dg bam 2p—m+1
ey we sin ou : 7
2m 2
Now the first two terms have finite values only around the
points — =mNz, where mN is a whole number. But

2p—m-+1 is also a whole number, and hence the last term
is zero at these points. Hence the term vanishes and leaves
the intensity, omitting the groove factor,

sin? n a sin? n—/
x + (bv) 2
sin fee ‘ sin? bape
2m F 9

|

in Theory and Practice. 409
The first term gives the principal spectra as due to a grating-
space of < and number of lines nm as if the grating were

perfect. The last term gives entirely new spectra due to the
erating-space a, and with lines of breadth due to a grating of
n lines and intensities equal to (duv)?.

Hence, when the tangent-screw is used on my machine for
14,436 lines to the inch, there will still be present weak
spectra due to the 14,436 spacing, although I should rule,
say, 400 lines to the millim. This I have practically observed
also.

The same law holds as before that the relative intensity in
these subsidiary spectra varies as the square of the order of
the spectrum and the square of the deviation of the line or
lines from their true position. |

So sensitive is a dividing-engine to periodic disturbances,
that all the belts driving the machine must never revolve in
periods containing an aliquot number of lines of the grating ;
otherwise they are sure to make spectra due to their period.

As a particular case of this section we have also to consider

Periopic HRRors oF RuLING.—THEORY oF “ GHOSTS.”

In all dividing-engines the errors are apt to be periodic,
due to “drunken” screws, eccentric heads, imperfect bearings,
or other causes. We can then write

Y=Na+ a, sin (en) +a sin (en), + ke.

The quantities ¢,, ¢, &c. give the periods, and a, ay, Ke.
the amplitudes of the errors. We can then divide the integral
into two parts as before, an integral over the groove and
spaces and a summation with respect to the numbers.

UU

y" y"-y
s| e—BAt+Ky) ds = Set | e—tbAntny) ds,
y' 0

It is possible to perform these operations exactly ; but it is
less complicated to make an approximation, and take y!—y'=a,
a constant as it is very nearly in all gratings. Indeed the
error introduced is vanishingly small. The integral which
depends on the shape of the groove will then go outside the
summation sign, and we have to perform the summation

Se—ibu | aon+ a, sin er + asin eyn+ &e.

410 Prof. Henry A. Rowland on Gratings
Let J, be a Bessel’s function. Then
cos (usin 6) =Jo(u) +2[Jo(u) cose p+dy(u) cosyh+ &e.],
sin (usin 6) = 2fJy(w) sind +33(u) sing d+ Xe. |.
Bye e— usin? — cos (usin d) —2 sin (usin d).
Hence the summation becomes
( g-ibpagn
x [J o(buay) + 2(—23 ,(bua,) sin en + Jo(buay) cos 2e;n— Ke.)
Ss x [Jo(buae) + 2(—t3 (buy) sin egn + J 2( buy) cos 2en — Xe.)
x [Jo(buas) + &e.) |
Lx [ &e. ].
Case I.—Si1ncGLE PERIoDIC HRROR.

In this case only ap and a; exist. We have the formula

pine sin”
Seteimag a? 4
ae
sins
Hence the expression for the intensity becomes
2 2
\ sin n wal | sin n ts ot +]
Jo(bua,) ———— 7+ J," (bya
| Pens (+9 OH a |
2 2 2 4
ee 2
| sin pete ta |
4 ee, + &e.
om e1
| sin | J

As n is large, this represents various very narrow spectral
lines whose light does not overlap, and thus the different
terms are independent of each other. Indeed, in obtaining
this expression the products of quantities have been neglected
for this reason because one or the other is zero at all points.
These lines are all alike in relative distribution of light, and

their intensities and positions are given by the following
table :—

in Theory and Practice. 411

Places. Intensities. Designations.
= = ah J0°(bmay). Primary lines.
. 0 .
fe pe ca Jy?(bpey a1). Ghosts of 1st order.
2e
fg=bt a Jo°(bpya2). Ghosts of 2nd order.
p= Pe < J3°(bpras)- Ghosts of 3rd order.
&e. &c. ac.

Hence the light which would have gone into the primary
line now goes to making the ghosts, so that the total light in
the line and its ghosts is the same as in the original without
ghosts.

The relative intensities of the ghosts as compared with the
primary line is

. Jn’ (bya)
Jo” (bua)

This for very weak ghosts of the first, second, third, &c.
order becomes

2 4 6
Ay 2 Ag 6 Ag

The intensity of the ghosts of the first order varies as the
square of the order of the spectrum and as the square of the
relative displacement as compared with the grating-space ap.
This is the same law as we before found for other errors of
ruling; and it is easy to prove that it is general. Hence

The effect of small errors of ruling is to produce diffused
light around the spectral lines. This diffused light is subtracted
from the light of the primary line, and its comparative amount
varies as the square of the relative error of ruling and the
square of the order of the spectrum.

Thus the effect of the periodic error is to diminish the
intensity of the ordinary spectral lines (primary lines) from
the intensity I to Jo*(bua,), and surround it with a sym-
metrical system of lines called ghosts, whose intensities are
given above.

When the ghosts are very near the primary line, as they
nearly always are in ordinary gratings ruled on a dividing-

412 Prof. Henry A. Rowland on Gratings

engine with a large number of teeth in the head of the screw,
we shall have

2 LZ 2 A \ _ oe
J bay (u+ i )+d pha, (1 = 2J,°bayu nearly.
Hence the total light is by a known theorem,

Jo? + 2[J,?+J,.?+ &e. |=1.

Thus, in all gratings, the intensity of the ghosts as well as
the diffused light increases rapidly with the order of the
spectrum. This is often marked in gratings showing too
much crystalline structure. For the ruling brings out the
structure and causes local difference of ruling which is
equivalent to error of ruling as far as diffused light is con-
cerned.

For these reasons it is best to get defining power by using
broad gratings and a low order of spectra, although the
increased perfection of the smaller gratings makes up for this
effect in some respects.

There is seldom advantage in making both the angle of
incidence and diffraction more than 45°, but if the angle of
incidence is 0, the other angle may be 60°, or even 70°, as in
concave gratings. Both theory and practice agree in these
statements.

Ghosts are particularly objectionable in photographic
plates, especially when they are exposed very long. In this
case ghosts may be brought out which would be scarcely
visible to the eye.

As a special case, take the following numerical results :-—

N= 1. 2. 3.
@ gl 1.4. 11 22
a; 25 50? 100 25’ 50° 100, 2555p aumm
(xt) 4 td
TG) 63’ 252? 1008 16 63° 252° = 7? 28? 102"

In a grating with 20,000 lines to the inch, using the third
spectrum, we may suppose that the ghosts corresponding to

“ — = will be visible and those for i

1
a 50 very trouble-

0 25

in Theory and Practice. 413

some. ‘The first error is a;= zo9hp95 in. and the second

=spo000 m. Hence a periodic displacement of one
Set of an inch will produce visible ghosts and one five-
hundredth-thousandth of an inch will produce ghosts which
are seen in the second spectrum and are troublesome in the
third. With very bright spectra these might even be seen
in the first spectrum. Indeed an over-exposed photographic
plate would readily bring them out.

When the error is very great, the primary line may be
very faint or disappear altogether, the ghosts to the number
of twenty or fifty or more being often more prominent than
the original line. Thus, when

bya, = 2°405, 5°52, 8°65, &e. =2nN-,

0

the primary line disappears. When
bjs, =0, 3°83, 7:02, é&e. =20N-,
0

the ghosts of the first order will disappear. Indeed, we can
make any ghosts disappear by the proper amount of error.
Of course, in general

ics toet » Ji, He)

n—2°

Thus a table of ghosts can be formed readily and we can
always tell when the calculation is complete by taking the
sum of the light and finding unity (see p. 414).

This table shows how the primary line weakens and the
ghosts strengthen as the periodic error increases, becoming 0

at InN = 2-405. It then strengthens and weakens periodi-

0
cally, the greatest strength being transferred to one of the
ghosts of higher and higher order as the error increases.

Thus one may obtain an estimate of the error from the
appearance of the ghost.

Some of these wonderful effects with 20 to 50 ghosts
stronger than the primary line I have actually observed in a
grating ruled on one of my machines before the bearing end
of the screw had been smoothed. The effect was very similar
to these calculated results.

Phil, Mag. 8. 5. Vol. 35. No. 216. May 18938. 2F

414

Prof. Henry A. Rowland on Gratings

GGO: | 600: | ITO:
vl “Sip | ool p

TOL. | 40. | GO0-

0cO: | GOI | PIT

€00: | LTO: | T90-

eee . .
° eee see
°
eae ee eee
. eee °
see vee eee
eee eee
eee eee eee
ee ° eee

80:

T10-

eee ee
eee eee
eee .

sein

0.01
* $99.8
CS he
OTOL
ok ina
06a¢
a Ove
oe ae
* ZEB.
Ba (Ns
"* 409%
ee Fie
a

in Theory and Practice. 415

DovusLE Pertopic ERROR.

Supposing as before that there is no overlapping of the
lines, we have the following :—

Places. Intensities.
= = [Jo(dyae) Jo(bazp) |?. Primary order.
0
e ‘
7 taee a [91 (a 41) JoC are) ]?. | Ghosts of Ist
Bs : r order.
M2 = et ba [Jo (basme) Ji (daefe) ]?. |
ete,
M3 = b+ = [Js (bays) J, (Daopes) ]?. 7
aa 2e 5 | hosts ef 2nd
fs, = eat Ta [Jo (ba,p4) Jo (Daopt4) |. G oe 2
; |
s= wtp — [Fo(bams) Fa(daqes)
+2
be = WETS, [Ty (Barge) Ta(Daaue) ). >
2
Pe ai [J o(Daypez) Ja (Deof47) |?.
“ Y \ Ghosts of 3rd
ps = B45 —— [Io(aypts) Js (Baus) }* | ae
Uy
3 :
Hy = wp [3 (betof49) Jp (batopte) ]?.
Ac. ae.

Each term in this table of ghosts simply expresses the fact
that each periodic error produces the same ghosts in the
same place as if it were the only error, while others are added
which are the ghosts of ghosts. The intensities, however,
are modified in the presence of these others.

Writing c,=ba,p and c.=bapy.

The total light is

2357(c,) Jo° (ce)

2517(e1) Jo?(co) 2071 2/., r

Jo (¢,) Jo’ (cg) + | + 2c.) J (co) } i Fone a0) oe
o (C1) Jo (C2

which we can prove to be equal to 1.
2F 2

416 Prof. Henry A. Rowland on Gratings

Hence the sum of all the light is still unity, a general pro-
position which applies to any number of errors.

The positions of the lines when there is any number of
periodic errors can always be found by calculating first the
ghosts due to each error separately; then the ghosts due to
these primary ghosts for it as if it were the primary line, and
so on ad infinitum.

In case the ghosts fall on top of each other the expression
for the intensity fails. Thus when e.=2e,, 3, = 3, uc., the
formula will need modification. The positions are in this
case only those due to a single periodic error, but the inten-
sities are very different.

Places.
2QaN 5
= [Jo(bayw)T y(basu) |.
0
= pt ap [J if (bap) J 0 (bap) —J 3(bayfy) JS 2 (Dae p11) = Ke. | 2
& ~~ bag + [Js (Gap) Ss (42p41) re 3(bayp5) 3; (baopey) + &e. ]?.
‘Ke eG

We have hitherto considered cases in which the error could
not be corrected by any change of focus in the objective. It
is to be noted, however, that for any given angle and focus
every error of ruling can be neutralized by a proper error of
the surface, and that all the results we have hitherto obtained
for errors of ruling can be produced by errors of surface, and
many of them by errors in size of groove cut by the diamond.
Thus ghosts are produced not only by periodic errors of
ruling but by periodic waves in the surface, or even by a
periodic variation in the depth of ruling, In general eee
ever, a given solution will apply only to one angle and
consequently, the several results will not be identical : -
some cases, however, they are perfectly so.

Let us now take up some cases in which change of focus
can occur. ‘The term «7? in the original formula must now
be retained. |

Let the lines of the grating be parallel to each other. We
can then neglect the terms in z and can write r2= 2 ver
nearly. Hence the general expression becomes ered

10(AZ+ py—Ky2
Se ees:

where « depends on the focal length. is i

very (ead aad hence « is small. ; vis 16 oppose
The integral can be divided into two parts—an integral over

the groove and the intervening space, and a summation for

all the grooves. The first integral will slightly vary with

in Theory and Practice. AIT

change in the distance of the grooves apart, but this effect
is vanishingly small compared with the effect on the summa-
tion, and can thus be neglected. ‘The displacement is thus

proportional to
DS eib(uy—Ky?)

Case I.—Lines at VARIABLE DISTANCES.
In this case we can write in general
y=an+a,n? + apn’ + &e.

AS K, %, a, &¢., are small, we have for the displacement,
neglecting the products of small quantities,

Dd etlelant ayn2+ agn3+ &e.)—Ka2n2]

Hence the term an? can be neutralized by a change of
forms expressed by wa,=«xa®. Thus a grating having such
an error will have a different focus according to the angle n,
and the change will be + on one side and — on the other.

This error often appears in gratings and, in fact, few are
without it.

A similar error is produced by the plate being concave,
but it can be distinguished from the above error by its having
the focus at the same angle on the two sides the same instead
of different.

According to this error, a,n?, the spaces between the lines
from one side to the other of the grating, increase uniformly
in the same manner as the lines in the B group of the solar
spectrum are distributed. Fortunately it is the easiest error
to make in ruling, and produces the least damage.

The expression to be summed can be put in the form

See" + tb( wa, — Ka?)n? + ibpagn? + ib [wag + 2b (wa, — Ka?)?] n4
+ &e. |

The summation of the different terms can be obtained as
shown below, but, in general, the best result is usually sought
by changing the focus. This amounts to the same as varying
« until wa,—Kxa?=0 as before. For the summation we can
obtain the following formula from the one already given.

Thus

n—1 1
. sm np .
3h e2tpn P pip(n—1),

in p
Hence
= 1: Ame Chine ae ™sin np
m2ipn — ip(n—1)f rane eA ee
a ane (inn? (z+éln 1)) Tar

418 On Gratings in Theory and Practice.

When 2 is very large, writing = =pn=aNn+q, we

have

a—1 Mon
> nine2tpr — —¢ (2 4 +4) S: Js
g @ dq q
Whence, writing

¢ = b(uay—xe),

i bpoag,
c" = bl pas + tb (pa,—xa’)’],
cl" = &e.,

the summation is

( n’
nti( SHES ee ) |
:
(a pes 1 94. |)
+ (2c0 + aoe + 4c 13+ ia |
ous yn ye & | salleeanen
i(e; + 363 + 6¢ Te a cng
q
_ (et n° )\S |
( Sag ae
5 4
5, ore
+2\ 6 a. |
+ &. }
dsnq_ eos si
dq q q
@ sing _ —2q cos g + (2—¢?) sing
dey q°
anes _ (69) cos g— (6—3¢') sing
dy’ g q |
&e. &e.

These equations serve to calculate the distribution of light
intensity in a grating with any error of line distribution
suitable to this method of expansion and at any focal length.
For this purpose the above summation must be multiplied by
itself with +2 in place of —2.

The result is for the light intensity

On the Differential Equation of Electrical Flow. 419

4

e 3 See
E+ (ach + 205 + ce aa
q t /dq q

n
8
4 5 3 ot Q
—_ (es ieee ke.) a wag + &e. \

{

8 16 dg q
n nt d’ sing
anes a sin g a
(oN + be. ee + &. ¢ -

As might have been anticipated, the effect of the additional
terms is to broaden out the line and convert it into a rather
complicated group of lines, as can sometimes be observed
with a bad grating. At any given angle the same effect can
be produced by variation of the plate from a perfect plane.
Likewise the effect of errors in the ruling may be neutralized
for a given angle by errors of the ruled surface, as noted in
the earlier portions of the paper.

XL. On the Differential Equation of Electrical Flow.
By T. H. Buaxestey, J/..4.*

apes object of this paper is to point out that the theory
of electrical discharge, as exemplified in the mathe-
matical expressions employed to represent the physical facts,
is incompetent to explain all the phenomena observed in
extreme cases; and to show that the admission of certain
properties of matter not usually recognized is the only way of
satisfactorily obviating the imperfection of the existing views.

In some of the investigations I shall not employ exclu-
sively algebraical symbolic methods, but, where it may more
advantageously be adopted, I shall avail inyselt of the geome-
trical method. Such cases most frequently arise where magni-
tudes under consideration are capable of having negative
values. All tidal effects, using the word in its most general
sense, involve such magnitudes.

Hlectrical currents in a given conductor may have all
possible values in one direction or in the opposite direction,
but are otherwise restricted.

The projection of the line joining two points in space
upon a fixed straight line is a geometrical magnitude of this
sort. With respect to the direction in space, sometimes one
of the projected points will be on one side of the other

* Communicated by the Physical Society: read March 24, 1893.

420 Mr. T. H. Blakesley on the Differential

projected point, sometimes on the other. So that sucha line
has all the properties necessary for representing another
magnitude of the same character. .

In this way I shall most generally make the projection
represent Hlectromotive Force, but occasionally Field of
Magnetism at a point. As to matter of nomenclature,
the only scientific term which | shall employ admitting of
any doubtful interpretation, is the Effective Electromotive
Force. By this term I intend to convey the idea of that
eleciromotive force which is numerically equal to the product
of the current and the resistance, at a point of time. Asa
department of State has recently employed the term in a
totally different sense, this statement has appeared to me to
be necessary in the interests of proper explanation. The
effective electromotive force is the algebraical sum of all the
impressed and induced electromotive forces, and is here
represented by E. If V is the sum of all the impressed
electromotive forces and F is the sum of all induced electro-
motive forces, then the equation among their quantities is
V+F=E universally. ?

Geometrically, if AB, BC are lines whose projections on

some one fixed straight line represent the sum of the im-.

pressed and the sum of the induced electromotive forces
respectively, then the projection of AC will represent the
effective electromotive force.

The three lines must form the sides of a triangle, those
corresponding to the impressed and induced electromotive
forces being taken the same way round the triangle, that
corresponding to E being taken in the opposite direction.

Now if the actual changes in the magnitudes are harmonic,
and of the same period, it is clear that the lines A B, BC,
AC must remain of constant length and the triangle must
rotate in its own plane at a uniform rate of such a value as
to perform a complete revolution in the period of the har-
monic change. ‘The triangle thus shows admirably the way
in which these magnitudes succeed one another in phase. It
also foliows from the properties of harmonic motion that if
two magnitudes have the same harmonic period, but differ
in phases by a quarter of the whole period, the corresponding
lines to be projected are at right angles with each other. And
hence the rate of variation of an harmonic magnitude differs
in phase from the magnitude itself by a quarter of the
period. But in the simplest case of a circuit being plied
with an harmonic electromotive force V, it is generally
considered that the induced electromotive force varies as the

Equation of Electrical Flow. 4AQ1

rate of change of the current ; that is

gC > Lidl eG
i> ie > eae for H=RC,
where C is the current, R the resistance, and L is the
coefficient of self-induction.

The equation already given then becomes

yee Lo? =n RC.

Multiplying through by C ee integrating through a com-
plete period,
VeanL foo? ari cat

The first term represents the work done by the source of
the disturbance.

The second term vanishes.

The third term represents work done in heating the
circuit.

Hence the whole work done has gone to heat the circuit.

Now it is admitted on all hands that when the period is
sufficiently short a radiation of energy into space takes place.
A portion of this radiated energy is sometimes caught by
means of a neighbouring circuit and converted into heat.

A coefficient of mutual induction and a corresponding
extra term is then introduced into the equation. But are
we to suppose that radiation would not proceed into space
were there no neighbouring conductor? Itis against proba-
bility, against the electromagnetic theory of light.

If electromagnetic waves are capable of being sent into
space, we can no longer look upon the operation of establish-
ing a current in a circuit as analogous to bending a stiff
spring or displacing rigid wheelwork. The wheelwork must
have indiarubber spokes or teeth.

The above equation takes no account of this radiation whieh j is
expended outside the wire, nor of any other work done else-
where than in the conductor ; and this latter the equation
states to be exactly equal to the ener gy expended in propa-
gating the electromotive force. Hven supposing a portion of
the field is occupied by some material whose passage through
a cycle of magnetization involves the loss of energy, in the
form of heat, this, equally with wave-propagation through
space occupied by perfectly elastic matter, will not be
accounted for by the equation.

Now of such phenomena as radiation of energy in electro-
magnetic waves, or absorption of energy in the field, there is

422 Mr. T. H. Blakesley on the Differential

ample evidence. Therefore an equation will not meet such
eases in which the induced electromotive force is taken as
entirely in quadrature with the current, or when F is wholly

of the form pee .
dt

Hence, in the geometrical representation it is clear that
the induced electromotive-force line must
not be exactly at right angles with that of =
the effective electromotive-force line; 7. e.
the angle BC A is not exactly a right angle;
and it is easy to see that it must be greater
than a right angle, for B C may be resolved
into BD.DC, where BDC is a right =
angle and A C D is one straight line. For C
then the whole work done is equal to
gD yal
7A cell

the conductor is

The work done in heating

J ° A
ea and the differ-

ence, or the work done in the field, is see

Hence, if D lies on the side of C neurer to A, A D would
be less than A C, and the work done by the discharge would
be less than that required to heat the conductor: in other
words, energy would have to be received from space.

Hence the induced electromotive forces may be represented
by two components—one A D in quadrature with the current,
and one D C in opposition to it,

dC
-L& -a¢,

where % may or may not be a constant, but is in kind a
resistance.
The equation among the electromotive forces may be
written
dC

V—L--—’AC=RC.

Multiplying through by Cdt and integrating through a
complete period,

{v Cdt—L jc - dt= R| Cae + facta,

The second term on the left vanishes as before, the first
term representing the whole work dove. On the right the

Equation of Electrical Flow. 423

first term heats the conductor and the second term gives
energy to space.
We may go somewhat further into the causes of such an in-
duced electromotive-force component if we
employ the geometrical mode of symboli- B
zing the electric quantities. BC,the induced
electromotive-force line, should be at right
angles to the induction through the circuit,
for it is the rate of increase of the latter D
which produces the former. Hence if A H
is a perpendicular let fall upon BC pro- C
duced, A E will represent the phase of the
magnetic induction. But AC being in E
phase with the current is in phase with the
field. Hence HAC, or CBD which is
equal to it, is a magnetic phase-lag, and A E may be said to
be in phase with the effectve field, and therefore with the
induction. This suggests that if we employ the lower lines of
the figure to represent fields, we may make up a triangle
A CE such that A Cis the impressed field,
C E an induced field, and A E an effective Cc
field, of course when, as usual, projected on
a fixed line ; C EH being perhaps, though by
no means certainly, at right angles to AE. E
However, whether CHE here has in any a
case two components perpendicular and
parallel respectively to A EK or not, it appears very certain that
the perpendicular component must exist. Assuming at first
that it alone exists,—
If we employ small letters :—

» for impressed field = AC,

f for induced field =CH,

e for effective fied =AH,

1 = coefficient of magnetic self-induction, so that

A

and yw for the permeability, I for the rate of magnetic induction,
1. @. per square centim., we have

To obtain an equation of energy from this we must multiply
(not by I, as analogy would at first sight perhaps dictate) by

dl y :
oe dt x cross section, for the formula for energy is

424 Mr. T. H. Blakesley on the Differential

[?e-*m | = [we ~2t— me || welt ?m? lt
= | Field | ane
ia
i a1 \(F) a = (Fo dt.

Here the term on the right hand oe necessarily,
and the work expended, if any, is equal to (<a) de. Hence

this work vanishes only if /=0, 2. e., if there is no component
field in quadrature with the induction ; a curious antithesis
to the electric problem. If there were a field induced in
phase with the induction, it would not result in the dissipa-
tion of energy. No argument for such a state of things can
be drawn on the score of loss of energy.

If the phases of magnetism in any cycle coincided with the
phases of field, there could be no such thing as hysteresis ;
and, further, no radiation of energy from an alternating
magnet.

But both these phenomena have been for many years recog-
nized. It follows, therefore, that when induction through
any space changes, a magnetic field is induced acting counter
to the change.

Now it may be noticed that the tangents of the angles of
lag, whether electric or magnetic, involve a coefficient in
their numerator and the value of the period in their denomi-
nator. They therefore become larger as the period is made
less. It might therefore happen that extreme rapidity of
change would be necessary before a lag of current or of in-
duction could be detected. Electric lags, or, at all events, the
coefficients of self-induction can readily be measured. Mag-
netic lags have been measured by the author in certain cases
by special artifices, but when we deal with a medium of small
permeability, as air, the period must be extremely minute to
make the lag-angle sensible, and as yet no machines possess
a sufficient frequency to effect it. Recourse has been had to
the rapid oscillations which take place when a Leyden jar is
discharged. In these cases the radiation has been frequently
caught and approximately measured, and it is therefore in

these very cases that the rectification of the formula becomes —

important.

I propose to investigate by geometry and otherwise the —
conditions under which a Leyden jar is discharged. Geo- —

metry especially will afford an excellent and graphic insight
into the question of the oscillatory discharge.

ee

Equation of Electrical Flow. 425

As in the case of the sustained discharge, I shall first take
the usual formula, obtain the geometrical illustration of it,
and, observing where the defect shows itself, pass by an easy
transition to the truer state of things.

In the case of the discharge of a condenser through a simple
circuit removed from proximity with any other, we have the
following equations to deal with :—

Peeeemerlequaion vw b= fe ke fw eG)
sO eee ees -' CHa)
dC Ede
F = Meee eece!) <7 -(ats)
dV
C gen eres ee sae oi oo (iv.)
where

C is the current discharging the condenser ;

K is the capacity of the condenser ;

L is the coefficient of self-induction ;

R is the resistance ;

F is the induced electromotive force ;

E is the effective electromotive force ;

V is the potential difference of the plates of the con-

denser.
Hliminating E and F from (i.) by means of (ii.) and (iii.),
—— Oo ee Fee eal)
Differentiating,

Ge ge wee Se
and substituting for x from ean
C aC dC
=e ae = 1% ai ==)
or
dC PC
C+KR ar + LK; =0,

the differential equation of C.
Since C= - , it follows that the equation

dE PE
H+KR-+LKT =0

is also true, and therefore is the differential equation of FE.

426 Mr. T. H. Blakesley on the Differential

2
Again, from (v.) and (iv.), since s = <——— , obtained
by differentiating (iv.),
dV a7V
if ig SOE J ae
V+RK Ti +LK Te =
This is the differential equation of V.

Thirdly, differentiating twice the equation
V+F—RC=0,

d?V- se d?F a2C
Ge ge de ae

from (iil.) by differentiation it is seen that
d?C 1 dF

Geese i, de
and from (iv.),
ay 1 dC

dime at Kee
which is further reduced to ube by (iii.)
: KL Dy Gili).
Hence me iidientlidl
KL ae oe ae

or

dk ak
Fr +KRT, oa KL 7a

=
the differential equation of F.
It is thus clear that the variables V, F, E, C, all have the
same form of differential equation, viz. :—
di ae
H+KR— +KL—a =.
Of course, to make this equation homogeneous,

KR is of the order (time) ;
Ki; =: p (biniie)2.

Kh may be written KR. : , or still better se s
If we write 2 lis
ee
and a — ts,

t, and ft; are time-constants of the circuit, and the differential

Equation of Electrical Flow. 427

equation may be written
aa
ode
In this expression the two time-constants may be considered
to be independent.
To obtain a geometrical representation of the changes :—
(1) Supposea line, whose length is 7, to shrink logarithmi-
cally so that its change is represented by the equation

K
E+ a. +t; =(),

Gi iat
Cire svbne
where ¢, is a time-constant.
Then ae
r=ae 4,

where a is the value of rat the beginning of the time, and ¢,
appears as the time taken for 7 to shrink to : of itself.

(2) Secondly, suppose a straight line in a plane to con-
stantly change in direction at a uniform rate, in the same
sense. If0 is the angle measured from a fixed direction,

d@ 27
: Qty ta!
where ¢, is a time-constant. Hence
| ge ee
to

Whence ¢, appears as the time required to describe 277.

(3) Suppose a line to undergo both the changes contem-
plated, which is possible, since one is a change of length, the
other a change in direction. “ Then, eliminating the time, we
have be aes

Qnty
ee
)
or r=ae tanB,where tan C= —
2

This is the equation of the equiangular spiral, with the
characteristic angle 8, whose value merely depends upon the
two time-constants ¢, and t.

(4) Now imagine this length * constantly projected cn
some fixed straight line, and for simplicity take this straight
line as at right angles to the direction in which 0=0.

Then the projection under consideration (E) has for its
expression ac
K=a.e tangsin 0;

428 Mr. T. H. Blakesley on the Differential

2. é., 1t consists of a constant factor, a logarithmical factor,
and a rhythmical or harmonic factor.

Substituting for @ its value = be
2
so a
H=a.¢ 7% tame" sin SU
2

D
H=ae taf sin @,

di

pe Q @ =e 6
do 2° tanB COS ~ Ene” tanB sin
in a 1D
= 72 GOS aa ereaict
a? 1 dH = WAC A a anes).
aGammees ine." Sen) = 7a t 68 cos 8
Snes, dE petra il iGtue!}
Saeetanye de) tang td0 tanB
= 2) 0B) Salles
=-a9 B+ meee f
therefore
ie 2tanB dH tan? B PH _o
1+ tan? @ d@ 4 W2\tan’ 6 dG? ee
Now
dH di. dt di, to
ae = dé ade Tae De
therefore
eH 2B tt, a(t
dG? “de? d027* -d? rye
therefore
E 2tanB t dH tan” B (5 1 ee
Maen Oar dt ee aniG or) di?

; ; 2Qat
which, since tan = oe becomes
2

2, . dh i?
Bak (1+ tan?) dé aH (1+ tan? 8) dt? mi
Pet ty
and if ¢3 is written for (@= ane)
di ah
K + 2t, We tbs Te =(0.

An equation which is at once comparable with those obtained
in the Electrical problem.

Equation of Electrical Flow. 429

It thus appears that the variables in the problem of elec-
trical discharge under consideration may be represented by
the projections of three sides of
a triangle, which is constantly
undergoing uniform rotation
and linear logarithmic shrink-
ing. Let the figure represent
a portion of the appropriate
curve whose characteristic angle
is 8, and let O R be some radius
vector. Then the projection of
OR on OY will be a maximum when the tangent at Ris parallel
to OX. let P be such a position, and let PM be the
wucentaie. Then MPO= POX =p.

Now suppose O A the line representing (in its projection)
the effective electromotive force about to change sign through
the value zero. This means that the current is about to change
sign, and the condenser having been receiving current is
about to begin to be discharged, 2. e. its charge and therefore
potential difference is a maximum. Then the line of P.D.
must make the angle POA with the line of effective H. MF.

Again, the E.M.F. of self-induction is zero when the current
is at a maximum, by the nature of the ordinary hypothesis.

Therefore, when the line representing EH makes an angle @
with O X, the line representing induced E.M.F. (F) must be
parallel with it. Hence it also makes an angle 8 with the
line of effective H.M.F.; but in phase lags behind it, whereas
the P.D. is in advance by that angle.

Thus, if on any line taken as base we construct an ésosceles
triangle of appropriate base angles, the sides will represent
the P.D. of the condenser and the induced
H.M.F. of self-induction respectively, and
the base will represent the effective H.M.F.
It only remains to rotate the triangle with
appropriate speed and to allow it to shrink
at the due logarithmic rate.

The properties of the triangle agree exactly
with the electrical properties.

The angle @ is such that tan @= a

2

KR
1 t 2 KR?
e 2 = DSO = “3 = — .__—_—. °*
therefore cos’? B a aio caveaie ie
+ ar bes
( ly R

Phil. Mag. 8. 5. Vol. 35. No. 216. May 1893. 2G

430 Mr. T. H. Blakesley on the Differential

therefore cos B= = es and @ can have a real existence
when a 1 ;—the condition of Oscillatory Discharge.

Al,
The complete period is f, and is obtained in the electrical
quantities thus ;—
2Qrrt, ;

tg

tans =

therefore
eee (277) ati at (277)? ty)?
> tan? B ~ sec? B—1’

and cos? B= : already obtained ;
1
Am tst 40° KL
therefore ea

2 te aa 2
te te 1 (a

therefore
IaV KL

ea

the form usually quoted if we neglect the second term of the
denominator.

I purpose to show that in a discharge of the sort here con-
templated (which has been shown to be the result of the
ordinary premisses given at page 425) there will be no work
done by any electromotive force which lags at an angle 6
behind the current, provided the initial condition is one of
zero-current. And, further, that the source of H.M.F., which
is represented by the side of the isosceles triangle in advance
by the angle 8, of the effective H.M.F., does all the work of
heating the circuit and no more. It will thus be seen that
there is no provision in the theory for expenditure of power in
the field, and hence that the theory does not explain the well
recognized phenomenon of radiation into space.

To establish the above-mentioned propositions, take the —
product of the projections of two lines undergoing variations
corresponding to the two radii vectores of two equiangular
spirals of the same characteristic angle 8 and period, and
differing in phase by the angle 2y.

One of these quantities may be expressed by

Equation of Electrical Flow. 431

EY ou
ae tam8sin O+y.
The other by
Ore
be nb sin @—y.
The product is
26
ab.e ™Bsin O+y SID @—y,
or

20
ab.e tamB (sin? @— sin’y),

This quantity, multiplied into an element of time dt, has to

be integrated through one period. Since = = = the
integral 1 becomes
abt
a e eer (cos 2y— cos 20) dd,
or
mem tanB cos Yy dO — a pp oraces 26 dé.

The first term of the integral is
abt
8a

The second term is

ae ——cos 2y tan Be — =r

20

abt pale DB orcs
3, sin 8 cos B +20 ‘ ee

and therefore the ce ig expressed :—

Abts | =

a Br °
This expression has to be taken between limits. If we con-
template one revolution only the limits will be ®,+27 and @,,
and the Definite Integral becomes

Abts 20,
3 1—sin 8 cos B+ 3+ 20, +tan B cos Qyte™ tus( 1—e ~ ane ).

If the limits are infinity and @, the integral becomes
_. 26,

us af ae Bcos2y—sinBcosB+203¢ me . (a)

aie {sin 8 cos 8 +20—tan @ cos 2y}.

Hither of these expressions becomes zero when

tan 8 cos 2y=sin 8 cosB+ 20;
2G 2

432 Mr. T. H. Blakesley on the Differential

or
cos 2y=cos 8 cos B+ 26,
showing that the condition that no work shall be done in the
electric problem depends on the initial circumstances, 7.e. 0;
-is involved. If 2y= the condition of no work becomes
cos 8+ 26, =1,
which is satisfied when

Hence if the initial condition be that of no current, the line
bisecting the angle between the line of effective H.M.F. and that

of the self-induced E.M.F. makes —§ with the line @=0, and

it is thus proved that on the whole no work
is done in the field.

If, on the other hand, we make
é,=+ B :
1 2 7
and start from a point where the current
is zero, we have in the above expression,

when proper substitutions are made for a and 3, the value of
the work done on the circuit by the discharging condenser.

The integral between infinity and @, becomes, when 6,= C and

ab. ty . F =e
— {1— cos 26} sin 8.e tanB;

or

id Ais ee ORME
? sin®Be tank,

; iD ELIE Eh ecw §
In this case 6= Rand ae tan sin Bis the potential difference

between the plates of the condenser at starting =Vj, say,
=Vsin8. Hence the expression becomes

My ager. fd
R:a,52 iS Ve
(E and V being now the full sides of the triangle, properly
E

interpreted), and Z.y =e B by the geometry of the triangle,
and further,

Equation of Electrical Flow. 433

tan game mad thereiore = =

ty Aq
and the work
pei’ ? i ty or ty sin? B
sR 2cos 6 2tan 6 [ae Ge
which is the expression we should obtain if we integrate the

square of the current multiplied by Rdt, seen as follows :—
In the general expression («) obtained above for the pro-

by
2 tan B’

sin? 8,

duct of the projections make a=H, b= = and 0,=0, y=0

the expression («) becomes

sa {tan 8 —sin B cos 8}
Pegee! an sin 6 cos f5,

or

EK? ty ;

aR a B—sin 8 cos P},
or

[Dee
in t, sin” B, as above.

Thus the whole of the work goes to heat the wire, and,
further, substituting in the equation for E in terms of V, it
may be shown to be entirely derived from the charged con-
denser.

The work may be written, eliminating E,

2V? cos B ty
R Aar

Ne ty O18)
Kae cos B sin’ 8.

sin’,

or

Now V/?=V’sin? @, and thus the work is

t
VR cos? B,
. ry t
or, since cos*B= a
1
V17ts KR
= and é = ——
Pree On oe
VK
— 5) 9

which is the ordinary expression for the energy stored in the
condenser ; and this appears from the investigation to he

434 On the Differential Equation of Electrical Flow.

entirely expended in heating the circuit, and there is no
margin for the exhibition of power elsewhere.

Suppose a line A B to represent (E) the line of effective
E.M.F. At the extremity A set off AC
as the direction of the line representing c
the P.D. of the condenser.

Then, as the condenser contains all
the energy that is going to be expended
on the circuit and on the ether, from
what has been said it is clear that A C
must be rather longer than the side of
the isosceles triangle; for, if not, the
energy stored will not do more than «a £ we
heat the circuit. If therefore a perpen-
dicular be dropped upon A B from GC, it will fall at a point
nearer B than A.

Join C B, and, further, draw C D to meet AB produced in
D, and so that C DA is an isosceles triangle on A D as base,
and therefore CDA=8. Now CB must be the line repre-
senting the resultant of the induced electromotive forces F,
and however complicated the case may be this line CB is
equivalent to two components CD, DB: of which CD results
in no expenditure of power because it is in a phase B behind
the current, and DB is in phase directly opposed to the
current, and therefore resulting in whatever expenditure of
energy takes place outside the circuit, and therefore in the
ether or in magnetic bodies, or in neighbouring or surround-
ing conductors. Asin the former case of sustained oscillations,
it may be shown that BCD isa magnetic lag necessary for
the exhibition of such phenomena.

The electromotive force DB may be expressed by —AC as
before, and the general equation

Vo E—s

takes the form

Vee be! nC
dt

and, as this may be written

V-L& =(R+2)C,

we see that the extra consideration required to express the
actual state of things is simply that the resistance of the
circuit is virtually increased. In the previous work it is
necessary to write (R+)) in all the equations.

Heat of Vaporization of Liquid Hydrochloric Acid. 435

The actual work done altogether is derived from the charged
condenser. This is divided between the circuit and the field
in the ratio R:X.

It may happen, therefore, that if the circumstances of the
discharge are such as to make X very large in comparison
with R, the ordinary heating-effect may be minimized. Among
such causes is frequency, and in this consideration is to be
found the true explanation of some of the experiments of
M. Nikola Tesla. The energy of the discharges which that
physicist encountered was expended in chief part in radiation
which his body did not check, and not in current through his
body. It is here suggested that the best way to measure
radiation would be to measure the defect in the heating of a
_ circuit, taking care to note the P.D. of the condenser at the
moment previous to discharge.

In ordinary sustained oscillations, as derived from a machine,
the alternations are not of sufficient frequency to make the
effect of X perceptible. Hlectromotive forces of induction in-
volve the period in their denominators, and it is reasonable
to suppose that induced magnetic fields do the same; and if
the period of the electromagnetic vibrations becomes com-
parable with that of light, it is conceivable that mere heating
might vanish, as in the solar spectrum light has less heating-
effect than radiation of smaller frequency from the same source.

XLI. Note on the Heat of Vaporization of Liquid Hydro-
chloric Acid. By K. Tsuruta, Rigakush, Tokio, Japan*.

| the thirtieth volume of the Proceedings of the Royal

Society of London Mr. Ansdell gave a full account of
a series of experiments on the condensation of hydrochloric
acid. At the end of the paper he promises another commu-
nication containing his considerations on some thermodyna-
mical quantities relating to that gas, but this, so far as I am
aware, has never appeared. Although his measurements
have often been referred to and used by other physicists, yet
some of the deductions that can be made from them appear
still left untouched, for instance the heat of vaporization,
which forms the subject of this note.

For the sake of convenience of reference I- here reproduce
those measurements as contained in the following Table given

by Ansdell :—

* Communicated by the Author.

436 K. Tsuruta on the Heat of Vaporization

eel B ea |. m E F
| a eS == | oe ip gee eee
1 | 4 [19781 | agp | (755 | Teme) eee
2, | 995 11896 | ges | 790 | 1505 | 939
3, | 188 |10350| soy | 885 | 1239 | 37°76
4 | 11 | or77 | sty | 874 | 1080 | 41-80
2 | eon 910 | 9892 | 45°75
6. | 2675 6969 | a5, 900)
7. | 38:4 | 55°75 }*t | 1019 | B50 loam |
g | 394 | 4485 | ais | 1068 | 419 | 66-95 |
9. | 448 | 3634 | aaa | 1196 | 308 | 520
10, | 48 | 8138) gem | 1200 | 261 | 8080
11. | 494 | 27-64 | arg | 1292 | 218 | 8475
12. | 5056 | 2670 |... 14:30 | 1-79 | 85:33
eon | 346 | |

The column A gives the temperature of the gas.

The column B gives the volume of the saturated vapour at

point of liquefaction.

The column © gives the fractional volume of the gas at
point of liquefaction in relation to the initial volume
under one atmospheric pressure.

The column D gives the volume of the condensed liquid. —

The column E gives the ratio of the volume of the gas
to that of the liquid.

The column F' gives the pressure in atmospheres.

These data alone are incomplete to enable us at once to
deduce by calculation the heat of vaporization in terms of
the usual units (metre and kilogramme). Here are given
only the relative volumes of the saturated vapour and con-
densed liquid, so that their specific volumes at different tem-
peratures, which are wanted, are unknown. it will, however,
be enough for our purpose if we know their densities. Now,
Ansdell gave as results of independent measurements the
densities of the condensed liquid at different temperatures.
An interpolation formula, obtained between those densities

of Liquid Hydrochloric Acid. 437

and those temperatures, when combined with the numbers
given in the second and fourth columns of the above Table,
will enable us to find the corresponding densities of the satu-
rated vapour. The results thus found were not very satis-
factory. Another way to overcome the difficulty is to make
use of the numbers in the third column, which give the
volumes of the saturated vapour just at the point of lique-
faction in relation to the volume occupied by the mass of the
gas at the temperature ¢° (column A*) and under the pressure
of one atmosphere. If the specific volume of the gas under
the normal circumstances be known in terms of the usual
units, this together with the coefficient of expansion under
that pressure will give us the specific volumes of the satu-
rated vapour at different temperatures. Now, Biot and
Arago{ give the density of hydrochloric acid under the
normal circumstances to be 1:2474 in reference toair. There-
fore, the specific volumes under consideration will be given
by the following :—

il i fractional
Bae 1998 1-247: | volume | ree

When a long time ago I began my calculation I was not able to
get any information with respect to the coefficient of expansion,
and I assumed it perhaps not far from the value 0:008665.
Quite recently, however, I have found that it was determined
by Regnault f as long ago as 1843 to be 0:003681, and so I
have proceeded to recalculate. Of course no great differences
were thus wrought in the final values of the heat of vaporiza-
tion. It is, moreover, to be remarked that Regnault himself
did not put much confidence in the accuracy of his value on
account of an unavoidable admixture of air, very small though
it was, with the gas he investigated.

The formula for the heat of vaporization (according to the
notation of Clausius) becomes :-—

—__ 10883 1 di fractional a\ dp ,
TE T393 ‘Toa7 | volume |* (+44) (1-2 au:

in which the ratio o/s is to be supplied by the numbers in
the second and fourth columns of the above Table.

* As it must have been, although it is not explicitly mentioned,
t+ Wiillner, Lehrbuch der Physik, iii. p. 150.
{ Ann. de Chimie et Physique, série 3, tome iv.

IN

438 Heat of Vaporization of Liquid Hydrochloric Acid.

o was calculated from the following interpolation formula

found by the method of least squares :—
p=28'451 + 0°4914 t+ 0:012463 #,

in the evaluation of whose constants the numbers in the
eleventh row in the above Table were omitted, because the
representative point in the p- and ¢-curve was much out of
the general course. p (calculated) in the following Table
are from the above interpolation formula, whose use is amply
justified by the numbers in the difference-column.

| |

}
|
| | iP P ; o P,P
| us || (observed). | (calculated). Tinie =e 5 |
j | atm. atm. calor. |
1. 4 29°8 |), a h061 +0°81 61-02
2. 9:25 | 33°9 34:10 +0°20 64-99 |
3. 138 37°75 3760 —O0°15 65°77
4, 18:1 | 41°8 41°45 —0°37 65°45
dD. 22 | 45°79 | 45°29 —046 || 63°51
Geo, Sen We pd 50°57 —043 | 60:02
7. 30-4 58°85 | 58:76 —009 | 5317 |
8. 39°4 | 66°95 67:15 +020 || 45-18
ae) ASS | 152 7547) | «= 4026 I ae
tO) as 80°8 80°75 | —005 | 30°08
a4 2 494 84:75 8914 | —161 | 20°49
1954) P5056.) || 85°33 85:22 0a
13. 51 |

i | H
| |

The manner of variation of these numbers for 7, as deduced
from the observations of Ansdell, is very remarkable. From
4° to about 14° the heat of vaporization increases, attains
there a maximum value, then decreases in a regular manner,
but from about 45° onwards it diminishes quite rapidly, as if
the gas were preparing for the critical point (51°25), at
which the heat of vaporization is to vanish.

Among those substances whose heat of vaporization was
investigated by MM. Cailletet and Mathias * we have no in-
stance like hydrochloric acid. It is much to be desired that
any one who has proper instruments in his possession will
take the trouble to decide whether the anomaly is real or
whether there were some mistakes in our data.

* Journ. de Physique, tom. v. 2° série, 1886. Also, zbid. tom. ix,
2e série, 1890.

[ 439 7

XLII. Note on the Flow of Water in a Straight Pipe.
By M. P. Rupsx1, Priv. Doe. in the University of Odessa *.

T is a known fact that the law of resistance to the motion
of a liquid in pipes and channels of great size differs much
from that in capillary tubes. It is also known that this differ-
ence is due to the presence of eddies in great pipes, while in
capillary tubes the liquid flows in straight lines. Prof. Osborne
Reynolds + has shown that there exists a certain critical mean
velocity, depending on the diameter of the pipe and on
the temperature (7. e. viscosity) at which the eddies must
appear. He thinks that the appearance of eddies is due to
the instability of rectilineal motion. But Lord Kelvin ¢ has
shown that at least for small disturbances the rectilineal
motion is stable provided the coefficient of viscosity is not zero.
Although Lord Rayleigh § thinks that Lord Kelvin’s proof is
not quite convincing, it seems to me to be so, because the
steady rectilineal motion with zero velocity at the walls
satisfies the condition that the loss of energy shall be the
least possible. This motion belongs to the type which was
shown by Helmholtz to have this property ||. Now itis known
that generally the motions, which in a certain manner satisfy
the minimum or maximum condition, are stable.

The same question was also treated by Mr. Basset 4]. He
has found the rectilineal motion unstable. As far as I can
understand him, from a short communication, it was only
after he had introduced in the expression of resistance a term
depending on the square of relative velocity. In doing so he
has anticipated the law of resistance proper to the eddying
motion. On the other hand, he finds that without this term
the steady rectilineal motion remains always stable. His
results also agree closely with the results of Lord Kelvin.

It seems to me that all this clearly agrees in showing
that it is not the question of stability or instability which
arises here, but another one. In speaking of stability we
mean ¢o ipso the tacit assumption that the eddying motion
may be also expressed with the help of functions satisfying
the common partial differential equations of viscous fluid

* Communicated by the Author.

+ Phil. Trans. 1885, p. 935.

{ Phil. Mag. 5 ser. xxiv. pp. 188 and 272.

§ Phil. Mag. 5 ser. xxxiv. p. 67,

|| Basset, Hydrodynamics, vol. ii. p. 356.

4] Proceedings Roy. Soe. vol. lii, no, 317, p. 273.

440) On the Flow of Water in a Straight Pipe.

motion. Our equations of disturbed motion serving to inves-
tigate the question of stability are the same hydrodynamical
equations with certain terms neglected. These equations, as
Lord Kelvin has proved, show that the undisturbed motion is
stable. But if we introduce something that is not contained
in the hydrodynamical equations, as Mr. Basset has done, we
find the sought instability.

In other words, our hydrodynamical equations, which we
know to be strictly true only for small relative velocities, are
now shown to be, in the case of water, of very limited im-
portance. They are not able to express the eddying motion.

In the motion which they are able to express, any surface
drawn within the liquid is supposed to be strained in a con-
tinuous manner. In the eddying motion these surfaces
are continually breaking and again reforming, an opinion
which seems not to be new to hydraulicians *.

The opinion that it is with a real breaking that we have to
do is strongly supported by a striking fact observed by Prof.
Reynolds. The eddies appear only at a certain distance from
the entrance of the pipe. This distance is diminishing when
the velocity increases, but diminishes asymptotically. Now
it is a known fact that the breaking of bodies, solid, plastic,
or plastico-viscous, depends not only on the amount of the
strain, but also on the velocity of straining. Even hard
bodies sustain a great strain when the straining is slow
enough ; on the other hand, fleazble bodies, when very rapidly
strained, Sreak down.

On the other hand, when the liquid enters the pipe tumul-
tuously, but with small mean velocity, the viscosity begins to
act at advantage, the breaking ceases, and the eddies die out.
Reynolds has shown that this reversal trom tumultuous to
quiet motion occurs at a critical mean velocity, which ceteris
paribus is about 6-3 times smaller than the other mean velocity
which renders the quie* motion impossible.

All other features of the phenomenon—the dependence of
critical mean velocity, z.e. of the critical rate of straining, on
the viscosity and on the size of the tube—are clearly in best
accord with the hypothesis of breaking for a certain critical
rate of straining.

The existence of two critical velocities—a greater which
makes the quiet motion impossible, and a smaller which
makes the tumultuous motion impossible—is very interesting,
and shows similitude to many other physical phenomena.

* See Boussinesq, ‘* Kssai sur la théorie des eaux courantes,” Mém,
Sav, Etr. vol. xxiii. p. 5.

er 44 @ 7

XLIL. Liquid Friction. By Joun Pury, F.R.S., assisted
by J. GRAHAM, B.A., and C. W. Huatu*.

: [Plate VIL]

PIECE of apparatus such as is used in this investi-

gation was designed and partly constructed in Japan
in 1876 ; it is described in my book on Practical Mechanics
(1883). The specimen actually used by us was constructed
at the Finsbury Technical College in 1882, and has been
occasionally used since that time, but no complete sets of
observations were attempted till October 1891.

The simplest hydrodynamical condition of viscous fluid is
that of the fluid bounded by two infinite parallel planes, the
fluid in one boundary being at rest, the velocity in the other
boundary being constant and in the plane. Motions in a
pipe and near a vibrating disk, or even near a steadily
rotating disk, are rather complicated. Our apparatus was
designed to approach as nearly as possible to the conditions
subsisting between the infinite planes. Between two such
planes, if V is the constant velocity of one of them, the other
being at rest, and 0 is their distance asunder, the fluid being
of uniform density, and gravity being neglected, if 2 is
measured at right angles from the fixed plane, the equation of
steady motion is

d?

Vv .
dz’ = 0, SyMeEE Tt 1 eis Mine key sn (1)
a DF NGS By Fem ae ome iaas a (-)

and the tractive force per unit area required at the moving
plane to maintain the motion is «V/b, where mw is the co-
efficient of viscosity. We have used, instead of planes,
concentric cylindric surfaces of as large radii and as small
difference in radii as could be conveniently constructed and
used (see Pl. VII. fig. 2).

EEE is a cylindric trough, of which the curved parts
K and E are brass. The inner and outer radii of this trough
are 10°39 and 12°65 centimetres. C, which forms the bottom,
is of iron; and the whole trough can be rotated about its
vertical axis at any desired speed by driving the pulley P from
a coned pulley D with numerous steps.

G is a hollow brass cylinder supported by a steel wire L,
of 0:037 centim. diameter, 67°78 centim. long, whose axis

coincides with the axis of the trough and the axis of

* Communicated by the Physical Society: read March 24, 1893,

449 Prof. J. Perry on Liquid Friction. -

rotation. G may be raised or lowered relatively to the trough.
The outer radius of G is 11°63 centim., the inner being 11°41
centim. The whole apparatus is supported on a stand, with
three adjustable feet. We exhibit also some photographs of
the apparatus in position, showing how it was driven. —

The trough contains the liquid whose viscosity is to be
measured : when it rotates, G tends to rotate ; and when for
any constant speed G is in equilibrium, the twist in the steel
wire measures the torque due to the tractive forces with which
the liquid acts upon G at its inner and outer surfaces. The
twist was measured by the angular motion of a pointer clamped
on the wire at a distance of 59 centim. from the fixed end.

To test the accuracy of our assumption that the fluid
behaved as if between parallel plane surfaces, let us consider
the actual motion in which the stream-lines are circles.
Consider the motion of a stream-tube of section 6r 6z,
«2 being measured axially and 7 radially. The tangential

? e s e e . du Uv e
force on unit cylindric surface of radius 7 is (Ss Re if

v is the velocity. The moment due to all such forces on
the inner surface of our ring is

The moment tending to increase the velocity of the ring due
to forces on the cylindric parts of it is therefore

Cte AGG
ET + a= — 3) 8r Bars

also, due to the plane faces we have the moment
d?v
Qerpr®—. Sy. Bx.
ie or. 6a
Equating the sum of these to the rate of increase of the
moment of momentum of the ring, we have
i AGGv hi Oe, CO apade
dtd Pp tde ad 7 7

as the equation of motion in co-axial circular stream-lines.
Now the discontinuity at the edge, and also the nearness of

2
the bottom of the trough, cause the term ad to be important;
dx

but the solution seems to be very difficult. Maxwell satisfied

himself (Collected Papers, vol. ii. pp. 16-18) that the dis- —

continuity at the edge of a vibrating disk could be allowed

Prof. J. Perry on Liquid Friction. 443

for as a virtual increase in the radius of his disk, and the
assumption that the behaviour of his fluid was the same as if
his disk were part of an infinite disk. The correction not
being readily obtained for a disk, he assumed it to be the
same as for the straight edge of an infinite plane surface. We
are certainly not less correct in taking the same correction
for the edge of our cylinder*. Following Maxwell, there-
fore, we assumed that when our cylinder G was immersed
to the depth AB or J in the fluid it was really a portion of
length /-++X of an infinite cylinder of the same diameter. We
2

therefore neglect a in (3), and we use

Ge bedtn. 30 2. p

CIE ET Gi Pe ST oe VN ete (4)

When the motion is steady, that is when dv/di=0, the
solution is

. Ey Pa aM wet! LAS A)
If v=v, when r= R,, and v=0 when R=R,, then
v= Ry (7 — R,?/r) /( RY — R,’) °

We must now distinguish between the space outside the
suspended cylinder and the space inside it. The radii of the
inner and outer surfaces of the suspended cylinder are 11°41
and 11°63 centim., and the inner and outer radii of the trough
are 10°39 and 12°65 centim.

Our cylindric surfaces were not perfectly true, although
great care was taken to make them so ; and the radii given
are only average dimensions. But, inasmuch as slightly
tilting the apparatus or otherwise putting the axis of the
suspended cylinder out of coincidence with the axis of the
trough made only small differences in the observations, we
did not think that such inaccuracies of workmanship or mea-
surement as existed could affect our results.

Even when the tilting of the apparatus was quite evident
to the eye, the tractive torque was found to be only slightly
increased by the tilting. Of course, as the suspended cylinder

* It is to be remarked that Maxwell assumed, generally, that there was
no radial motion of his fluid. Now there must have been radial motion,
his disks resembling centrifugal fans in their action, creating a variable
flow always outwards between his fixed and moving disks; and the
energy wasted in producing this flow is neglected by him. We do not
know the amount of this error, and he may have satisfied himself as to its
insignificance. Prof. Maurice FitzGerald in criticizing this proof has
pointed out the fact that on James Thomson’s theory of river bends there
must exist a radial motion of an interesting kind in our apparatus.

444 Prof. J. Perry on Liquid Friction.

got closer and closer to the side of the trough the torque did
increase, and became very large when the suspended cylinder
nearly touched the side of the trough.

Again, it was observed that at our highest speeds the
amount of wetted surface did not perceptibly alter ; and we
are, we think, justified in assuming that the surface of the
liquid was always a plane surface.

It is evident that the tractive forces on the suspended
cylinder are the same whether we assume the trough to
revolve steadily at m radians per second, the suspended
cylinder being at rest, or the suspended cylinder to revolve
steadily at w radians per second and the trough to remain at
rest. We shall therefore, for ease of calculation, always
assume the trough to be at rest and the suspended cylinder
to be revolving at w radians per second. Then the velocities
of its inner and outer surfaces are, in centimetres per second,
11:41 and 11°63.

On any cylindric surface the tractive force per unit area

: B
being p(—) is == @ from (5); so that, whether for
the outer or inner space, if R, is the radius of the suspended
moving cylindric surface, and R, the radius of the fixed
surface, the tractive moment per centim. of length is

+ Arrow Ry /(R?/R?—1).

Taking actual sizes, this is 0°5 per cent. greater than the
value obtained by calculating the forces on the assumption
that the fluid moves in plane layers as in (2), 6 being the
actual thickness of fluid 1:02 centim., and V being the actual
velocity at the mean radius. We may, in fact, imagine the
speeds to be increased by 0°5 per cent., and make all caleu-
lations as to viscosity on the assumption of motion in plane
layers.

The tractive torque per centimetre of length of cylinder is,
in our case, 19010yo, or 1991 ny if the angular velocity
is given as x turns per minute. If / is the wetted length
in centimetres, and A is the virtual additional length repre-
senting the edge effect, the total torque is 1991 nu(l +2).
The total observed motion of the pointer being D degrees,
and the torque per degree being a, the torque due to tractive
forces acting on the cylinder is

aD = 1991 nu(l+A) ;
and if this law is found to be true experimentally, then

p =aD/{1991(1+a)n}. . 2 . . ©)

Prof. J. Perry on Liguid Friction. 445

Two methods of determining the torsional constant of the
wire were employed :—

First Method.—A fine cotton thread was wound round the
outside of the suspended cylinder and passed over a nearly
frictionless pulley (the pulley of an Attwood’s machine) to a
scale-pan. The thread was nearly horizontal as it left the
cylinder. In this way it was found that the twisting moment
required to produce a pointer-rotation of one degree was
1531 dyne-centimetres. In making the measurement as the
weight of the scale-pan and its contents was gradually
increased, the steel wire was drawn away from the vertical,
and therefore from the middle of the scale; but the stand
was tilted to counteract this effect. |

The effects due to solid friction were eliminated by taking
the mean of the limiting weights for equilibrium. When the
weight was 30 grams, one tenth of a gram either added to or
taken from the scale-pan produced a perceptible change in the
position of the pointer ; so that the solid friction was small.

Second Method.—The suspended cylinder was allowed to
vibrate, twisting and untwisting the wire ; and its times of
oscillation were noted. ‘The observations were repeated when
a known moment of inertia had been added. Unloaded, it
made 40 complete oscillations in 583 seconds, or one oscillation
in 14:575 seconds. We then attached to the cylinder an iron
bar of rectangular section, whose own moment of inertia had
been determined accurately by previous experiments (found
to agree with calculation on the assumption that it was homo-
geneous), this moment of inertia being 566°2 (in gram-
centimetre? units). The time of a complete oscillation was
now found to be 21:425 seconds. It follows that the moment
of inertia of the suspended cylinder is 487°72, and the tor-
sional constant of the wire is readily obtained. ‘This constant
being corrected on account of the position of the pointer, it
follows that to produce a rotation of the pointer of one degree
requires a torque of 1552 dyne-centimetres. This is greater
than the constant derived from direct measurement by 13 per
cent. ; but, on the whole, we are rather inclined to accept the
number obtained directly, as we are not quite sure that the
mean position of the iron bar was at right angles to the mag-
netic meridian.

Hight quite independent measurements of the diameter of
the wire were made by men experienced in making such
measurements ; and the mean value was ‘0371 inch, the
greatest and least being "0373 and ‘0369. Using this mean
value, and the directly measured torsional constant, it would
seem that the modulus of rigidity of the steel is 7°71 x 10”.

Phil. Mag. 8. 5. Vol. 35. No. 216. May 18938. 2H

446 Prof. J. Perry on Liquid Friction.

As an error of ‘0004 inch in the diameter measurement leads
to an error of 4 per cent. in the modulus of rigidity, and as
the modulus of rigidity usually taken for steel is 8°19 x10",
we believe that our constant 1531, as directly measured, is
sufficiently correct for practical purposes.

In using (6), then, we take a to be 1581.

The virtual addition \ ought, by Maxwell’s formula, to be
0:52 centim. in our case. But the bottom of the trough H
was only 0°5 centim. from the edge B of the suspended
cylinder in most of our experiments, and we do not know how
to calculate for this. Our experiments have shown that when
this distance is 0°5 centim. the twisting moment at a given
speed is practically the same as when the distance is much
greater ; but we did not know this from any theory, and,
besides, it is always rather dangerous to depend upon a
theoretical calculation of X such as Maxwell was compelled to
use. It is possible, also, that a correction of the same kind
ought to be introduced for capillary and other actions at the
surface of the liquid. The action of the atmosphere was in
any case negligible, because when there was no liquid present
in the trough, so that there was an action of the air several
times greater than ever occurred during the experiments, the
deflexion was quite imperceptible at much higher speeds than
those used in the experiments.

The temperature being kept as nearly as possible constant,
but probably varying between 18°°9 C. and 20° 1 C. (stated
as 19°°5 C.), the following experiments were made with
sperm-oil, beginning with a small quantity in the trough and .
ending with a large quantity. The bottom of the trough was
in every case 0°5 centim. below the edge of the suspended
cylinder.

TasLe I.—June 9th, 1892.

| Defiexion D when
MN, | ) ] |

| ¢=0°O em. | /=2°5 em. | 7=5 em. l=7-d5 em. | /=9-9 em. |

50 24 67 112), 1, tee

49 re hy cs = 196 |
48 | |
40 oo eae 3. ee 163

39 fn, fea ee

23 io: | | |

175 8 k 57 ees

ae RRs. 2 24 39

Ae NE gi ial b> ld 40

115 |

11 | | a a es

Prof. J. Perry on Liquid Friction. 447

As the deflexion is sufficiently nearly proportional to the
speed to allow of corrections by this rule when the cor-
rections are small, we have corrected the above observations
to ene speeds 50, 40, 174, 114; and we obtain the following
results :-—

|

Values of 2.

Values of /. cs
| 50. 40, Mie 114
| 5 24 18 Sms 5
| 25 67 54. | 25 16
5:0 1h 93 40 | 27
| TD 165 132 7 Cie |
| 99 | 200 163 735 | 51 |

D and / were then plotted as the coordinates of points on
squared paper ; and it was obvious that for each value of n
these points lay very nearly in a straight line, and all the
straight lines passed through the point/=—0°8. Itis curious
that the lmear law should hold for such small values of / as
0-5 centim., and for high speeds as well as low speeds. We
shall presently see that some of these speeds are considerably
above the critical speed at which (4) ceases to represent the
motion.

We may take it, then, that »=0°8 centim., which is greater
than the calculated value 0°52. The discrepance cannot be
due to the distance BH being small, for we have altered this
distance and found no perceptibly different results. As
already stated, it may be due to some capillary surface action.
Taking a=1531 and X=0°8, we have (6) becoming

e—0T6Dne@tOSe . . . . @)

Of course our results are consistent with our equations of

motion only so long as D/(¢+0°8) is proportional to n.

Many observations have been made with this apparatus
during the last year on various liquids, under very different
conditions of temperature and speed and depth. We give
here a set made on sperm-oil. In all cases the bottom of the
trough was 0°5 centim. below the edge of the suspended
cylinder.

Keeping the oil at a constant temperature we ran the trough
at a number of speeds, and repeated at other constant tempe-
ratures. The results are given in Tables LV. to XI.

When a temperature had to be taken the rotation was
stopped and a thermometer dipped about halfway down in the
oil, the reading being taken at the end of about half a minute,

2H 2

448 Prof. J. Perry on Ligud Friction.

A small Bunsen flame was applied underneath the trough
when a temperature higher than the room had to be main-
tained for a considerable length of time.

As the temperature varied slightly, and we wished to reduce
our observations to constant temperatures, we afterwards made
two sets of observations at very varying temperatures but
constant speeds. These later observations we shall consider |

first. They are given in Tables II. and III.

TABLE IJ.—March 29th, 1892. (d=8°275 centim.)

pote {a D)
a a OF 1): EN | L. LE peed
= — = = a
Pesoa iss f 189 10> 21-09 | ‘400 | +446
| 395 | 171 | 165 |- 1760 | 834 9) eee
40 195 || 150 | 1653. |- 31877) Gees
40 24-0 | 184 .| 1477 | -Os7) | aan
40 253 | 1965 | 1394 | -268 254 |
40 89 | 1115 | 12:28 236 PS ial
40 32:0 109 11:46
40 42-5 | 88 9-70
i 40 469 81 8-65
40 585 | 67 TU |
40 64.0 | 58 6-39
aor emo | 56 bisa fl | |
| ee Ue a cg | |
40 85:5 | 5:12 | |

The numbers in the column headed av are obviously ;

De
n l+nr
intended to be corrections of D/(/+ 2) for the constant speed
of 40 revolutions per minute.

TABLE II1.—March 380th, 1892. (/=7:78 centim.)

7 ]

: 9a)
| SO ae er | ‘Dea oe Fee HB calculated.
aes —_———_|—- — SS —- —___|_ —=
| 8°75 52) 1160 ©) 19-19 | Sige 2-06
975 | 80 85 9°15 0-78 0:82
92 | 100 57 6:56 0-73 | 062
9-0 108 47 548 | 047 | 9056
9:0 16°6 36:5 | 4:96 | 0363 | — 0-366
9-2 248 26°5 | 3:02 | 0-258 0259
9-0 35-0 19:5 | 2:27 =| 0-194 0196
9-0 47-0 140 1:63 0-139 0:137
9-0 565 10-2 119 | 0-101 0-104.
9-0 67:0 8-0 0-93 0-079 0-081
9-0 89:0 5-4 063 0-060 0-058
9-0 84:5 6-0 070 | 0054 0-054

a

Prof. J. Perry on Liquid Friction. 449

The numbers headed : S are intended to be corrections
of D/(J+2) for the constant speed of 9 revolutions per minute.

We have plotted the numbers in the last columns of these
tables with @ upon a sheet of squared paper; but it is
unnecessary to publish the resulting curves. We exhibit
them to the members of the Society.

Knowing what has been done by Prof. Osborne Reynolds,
it seemed unlikely that one simple formula should satisfy
either of these curves ; that is, it was likely that in the lower
curve there was some temperature for which the speed n=9
was a critical speed, and there was also a temperature for
which n=40 was a critical speed. We therefore used the
curves merely for small temperature-corrections in our other
experiments, in which we kept the temperature nearly
constant.

It was therefore without much interest that, in preparing
this paper for publication, we tried to obtain empirical formulee
for these curves ; and at first we used, not the observations
themselves, but the observations as corrected by curves drawn
upon squared paper.

When log (@—4:2) and log Try are plotted as coordinates

of points on squared paper, we were astonished to find that
when n=9 the points lie in two straight lines. The allinea-
tion of the points is very striking, even when the uncorrected
observations are taken, and leads to the following empirical
formula :—

Letting @ denote @—4:2, and letting y denote D/(/+))
the torque as measured in dégrees deflexion of pointer per
unit length of wetted cylinder ; then, at the constant speed
orn 9,

yo =constant for temperatures above 40° C.

yp =constant for temperatures below 40° C.

On plotting logy and log @¢ for the constant speed n=40,
the points are not found to lie so nicely in straight lines, but
there does seem to be some sort of discontinuity at a tem-
perature of about 45° C.

At first we thought that these temperatures were the tem-
peratures at which the speeds n=9 and n=40 were the
critical speeds, and we were greatly concerned because our
result seemed to be quite out of accord with the reasoning of

450 Prof. J. Perry on Liquid Friction.

Prof. Osborne Reynolds*. As his ingenious theory has been
completely verified by experiments made upon the very
smallest and largest pipes with flowing water, and as it is
simple we had adopted it for the reduction of our experiments.

According to his theory, Tk or, as we shall call it, y,

ought to be proportional to 7 until n exceeds a certain value;
this value being a function of u/p, where p is the density of
the fluid. Now the alteration of p with temperature in such
a liquid as sperm-oil is so small that the error in neglecting
it is small in comparison with our errors of experiment.
Neglecting, then, the alterations in p, the theory of Prof.
Reynolds leads to
y = al?-*n*, . en

where F is a function of the temperature, n the number of
revolutions per inute ; where «=1 until the critical speed
m, 1s reached, n. being proportional to I’, and « having a
higher value than 1 for all speeds above the critical; @ is a
constant. This is on the assumption that Prof. Reynolds’s
theory would lead to the sume result in our case as in his
pipes.

Now, in the first place,it seemed absurd that the temperatures
for which the speeds 9 and 40 were the critica] speeds should
be so near to one another as 40° C. and 45° C. But a much
more serious consideration was this. According to. any rea-
sonable application of the theory to our case, at constant
speed, if yp” is constant when the speed is less than the
critical speed, and if yd* is constant when the speed is
above the critical speed, then s ought to be less than m,
whereas 1°349 is about twice 0°686. We came to the con-
clusion that the point of discontinuity has nothing whatever
to do with the critical speed ; indeed, we subsequently found
it probable that n=9 does not become the critical speed until
the highest temperature of Table III. is reached.

Using the deflexions in Table ITI. to determine « according
to (7), we have the results given in column 5 of the Tables.
The numbers in column 5 of Table I. are calculated for tem-
peratures lower than 26° C., which is about the temperature
at which 40 is the critical speed. In some of the following
tables, giving the results of experiments made at various
constant temperatures, we have also given values of w. There

* “ An Experimental Investigation of the Circumstances which deter-
mine whether the Motion of Water shall be Direct or Sinuous, and of the
Law of Resistance in Parallel Channels,’ by Osborne Reynolds, F.R.S.,
Phil. Trans. pt. iii, (1883), |

Prof. J. Perry on Liquid Friction. 451

is as much consistency in all these results as might have been
expected. We lay most weight upon the results given in

Table ITI., which lead to the laws
ro 2:06(0—4-2)\e 8 below 40° Cy. 22. |. (9)
p= 21-60(G—4-2)-!* above 40° ©. .... . (10)

We have searched in books in vain for a mention of a dis-
continuity in any other physical property of sperm-oil about
this temperature ; but we have already begun to experiment
on its other physical properties, as it is unlikely that there
should be a discontinuity in the law for the viscosity alone.
At the same time, we may say that our chemical friends see
no reason for a confirmation of our belief.

In the tables we give the viscosity as calculated from these
formule ; and it will be seen that they agree well enough
with the observed viscosities.

TasBLe [V.—March 18th, 1892.
(l=6°15 centim. Temperature Constant, 17°°5 C.)

, or
1 _ DU-LA). M
36 114 16-41 351
39 121 17-41 344
54 172 24-75 352
69 245 35:26
80 300 43°16
92 B45 49-64
28 74 10°65 356
16 52 7-48 360 |
13 A ee 500 349
8°75 o7 3:98 349

{

The column headed pw is 0°769D/n(l+ A), and has no
meaning at a speed greater than the critical speed. The
critical speed, 7, is probably about 50. The first three and
last four values are probably measurements of w. The average
value of these seven is w=0°351. Formula (9) would make
pf to be 0°349.

Plotting logy and logn as the coordinates of points on
squared paper, the points lie very nearly in a straight line
indicating yan until the critical speed, about n=50, is
reached, and for all higher speeds the points lie nearly in
another straight line indicating y an’,

452 Prof. J. Perry on Liquid Friction.

Taste V.—March 21st, 1892. (=6°075 centim.)

0° C, Nn. 1D; Y- pi.
22:5 9:25 24°5 3°40 ‘283
232 11 28°0 397 ‘278
22°7 14:2 37 5:16 ‘280
22:0 17-2 45 6°15 ‘279
25:0 27 68 10:19 ‘277
24-5 23 57 8-41 281
24-0 32 “Eh 11-20 ‘269
23:0 90 340 48:00

22°5 102 410 - 56°96

23:0 80 276 38°94

24-0 72 224 32°58

24:5 56 169 24-95

24-0 48 129 18°76

23°5 43 _ 108 15 42 ‘278
230 38 eo 13-69 ‘217

The column headed y is D/(/ +) corrected to the constant
temperature of 24° C. by a correction of about 3 per cent. per
degree. The numbers in the last column have no meaning
for speeds higher than n=about 48. The average value of p,
the viscosity, in the first seven and last two observations is
0-278. Formula (9) would make w for this temperature
0-266.

Plotting logn and logy on squared paper gives points
lying nearly in two straight lines, showing that y an to the
critical speed n=about 43, and above that speed y an'*",

TaBLeE VI.—March 21st, 1892. (J=6:075 centim.) —

| | |
G2. | n 1D), | y

SS ae a a Eee

29°5 | 38 81 | 11-63

30 | 43 95 13°82

31 48 114 16:99

30°5 56 134 19-73

30°5 60 147 | 2165

|

y here means D/(/+ 2) corrected to the constant temperature
of 30° C. by a correction of 24 per cent. per degree. yp as
calculated from (7) would have no meaning, as the critical
speed for this temperature is about 28 revolutions per minute,
and we give no column headed w. y¥ is very nearly an,

Prot. J. Perry on Liquid Friction. 453

TaBLE VIT.—March 22nd, 1892. (/=5°4.25 centim.)

|

g°C n Dp: y HL
56 38 49-5 792
59 42 59 9:20
55 54 125 11°31
56 58 88 14:13
56°5 14 116 18°79
575 108 158 26°32
58°5 29 34 578
56 24 25 4-01 "1282
57 17°95 ll 1-81 ‘0791
57 155 14 2°31 "1148
54 155 12 1-82 ‘0903
55 16 14 2°19 1054

y means D/(/+X) corrected to 56°C. by a correction of
24 per cent. per degree. The critical speed is probably below
n= 24, and for speeds greater than the critical y «n!* nearly.
For speeds less than this the average value of pu is 0°103.
According to (9) the value of mw for 56° C. is 0°1055.

Plotting logy and logn as the coordinates of points on
squared paper gives points which may be said to lie on two
straight lines, but the errors of observation are too great.
For n>24 we might perhaps say that y «n!?5; but it seems
hardly fair to draw conclusions from this set of observations.

TasnE VIIL.—March 24th, 1892. (/=7:025 centim.)

in 0° OC. nN. D. | y. | bh. |
30 100 363 45 24. |
30°8 78 250 31°79
31 115 404 51-64
31 32 62 7:92 ‘1903 |
= 3l 22 47 6:01 ‘2103 |
3} yy 37 Ae 14 |
39 13 29 3:80 49 |
31 ll Dae) 3°00 “2097 |
30 9:2 20 2°50 209

-yis D/(l+X) corrected to 31° C. by a correction of 24 per
cent. per degree. The numbers of the last column have no
meaning for speeds higher than n about=32. The average
value of w is 0°210. According to (9) the value of w for
en CO. is 0°216.

Below n=382, y an,

Above n=382, we may perhaps say
that y an, : .

Prof. J. Perry on Liquid Friction.

TaBLE [X.—March 28th, 1892. (=6°525 centim.)

0° C: n, D. | Yy-
81 38:5 3 | 518
80°5 56 63 | 8-557
80 69 88 | 11-80
79-5 84 112 | 14-70
Bus 104 134 18-29
83 92 116 16-157 |

y means D/(l+2) corrected to 81°C.
The law seems to be 7 «n!? nearly.

TABLE X.—March 23rd, 1892. (/=7:025 centim.)

0°C. n Pp; Y:
82 17°5 16 2°06
82 14 11 1:23 |
82 26 26 3°35 |
81 32 33 4-22
80 11°5 8:5 1:08 |
82 10 Gia 0°84

If it is assumed that n= 10 is not much above the critical
speed, w may be calculated as 0°0646. According to (9)
p=0°062 for 81°C.

y an* may be taken as the law.

Taste XI.—March 24th, 1892. (/=6-7 centim.)

D y. HB.

65 4 8 1:07 091
66 10:8 9 1:21 | -086
65:5 17 16 914. | 2asza
64:5 21 21 279 |
65 23°5 26 3:46 |

ee on65 29 32 426 |

| 65 114 210 28:00. |

| 66 102 162 21-82

| 645 88 156 20:10

| 65 66 112 14-93

[24 66 52 74 9-96
66 44-5 59 7-94
66 38 46 6:19

|

y is D/(1+2) corrected to 65°C, jw has no meaning except
for the first three speeds, and the mean of these three is

0-091. According to (9) the value of w for 65° C. is 0-085.

j

Prof, J. Perry on Ligud Friction. 455

Above the critical speed, which is possibly below n=17,
the law is probably y an’.

lt is not worth while to publish any of the observations
which we have made upon other liquids, nor to publish the
curves we have drawn for sperm-oil, although we exhibit
them before the Society. Hrrors of one degree in obser-
ving temperature were quite possible, and errors of half a
degree in the deflexion of our pointer were also possible.
Small fluctuations in speed were continually taking place, so
that the pointer was never quite still, the motion of the fluid
was therefore not truly steady. It is our determination to
repeat the whole work with improved apparatus. In the
meantime, however, it will be observed from Table III. that
there is fair agreement in the law connecting w with tem-
perature, from all the sets of observations. There is, on the
whole, a very fair agreement with what we venture to call
Prof. Reynolds’s rule,

ie
=a en,

where « has the value 1°33 or 1 according as n is above or
below the critical speed*. The sheet of squared paper on which
we have plotted all our values of log y and log n for the various
constant temperatures shows that the errors of observation are
too great for the establishment of this value of «; but it is the
probable value. It shows, however, in the allineation of the
points of discontinuity, with sufficient accuracy that y, co n,”,
if the rule is taken to be generally true; and although there
is some little vagueness always in one’s observations just about
the critical speed, we may take y-=0°009 n,? without very
ereat error. Indeed, we are satisfied with the substantial
agreement of all our observations with the formula

hee be 2—k P
y=( ae95) ny

* Prof. Reynolds, in criticizing a proof of this paper, has been kind
enough to point out that his rule for pipes does not necessarily apply to
the fluid in our apparatus. We had not seen the reprint of his Royal
Institution lecture, else we should have known that the condition of the
liquid in circular flow is inherently stable or unstable according as » is
greater or less than the radius of the fixed cylindric surface. As he
points out, the liquid in the outer space is inherently stable for velocities
far exceeding the critical velocity (if there is one) for plane surfaces,
whereas the liquid in the inner space is unstable from the first.

We directed the attention of the meeting to the fact that Tables IV.,
V., VI., and VIII. give unmistakable evidence of the truth of what
we have called Prof. Reynolds’s Rule, however difficult we may find it in
explanation.

456 Prof. J. Perry on Liquid Friction.

where a='009 and «=1'33, That is, for low speeds we have
the law

SIE ad
PS
At the critical speed the law suddenly changes to
Ss a( eg s) >

which holds for all higher speeds which we have tried, The
critical speed

= 1444,

1

ea oa
OO a.
and

=O, OF WI WE.

It is to be recollected that p is too nearly constant for us
to say with certainty that a is proportional to p, as the theory
requires. The errors of observation were so great that it was
not worth while finding accurately the most probable values
of « and a.

We wish it to be understood that our apparatus was very
carefully constructed, and great care was taken in making the
observations ; but it is our intention to pursue the investiga-
tion with apparatus much more carefully constructed.

Vibratory Hxperiments.

In designing the apparatus it was our intention to obtain wu
from the damping of the rotational oscillations of the suspended
cylinder about its vertical axis, the trough being at rest. We
meant in this way to obtain w for velocities very much smaller
than those which could be employed in our steady motion ex-
periments. A considerable number of observations were made,
but when we tried to make calculations of ~ we found that our
mathematical difficulties were too great, and after many months
of effort we are forced to say that we are unable to utilize these
observations. In equation (4) assume that v=we'*, and w
may be obtained in Bessel functions. Unfortunately, as there
are two surface conditions, doth particular solutions of the
Bessel equation are necessary, and the work of reduction be-
comes very great. An approximate solution is obtained by
taking r= R-+ 4a, R being the radius of the suspended cylinder,
and taking the equation (4) to be

Oy yk aie 6?

de Rida RO ame

Making this assumption in the case of steady motion, it was |
found that it was sufficiently correct for practical purposes.

(11)

i
4
:
4

Prof. J. Perry on Liquid Friction. A457

The following numbers show the sort of error introduced,
taking R=10, and 1 the greatest value of w.

=
Values of v.

festa OD = =a
Values of x. | On the assump- |

Correct. | Approximate. | tion of motion
| 'in plane layers.

De ee ee es

0 \ l |
2 7914 7914 8
5 4875 4872 5
7 2895 2892 3
1-0 0 | 0 0

)

The solution of (11) for vibratory motion is easy enough ;
but we found it still difficult to calculate w from our observa-
tions. Hven when we assume that the motion is in plane
layers, so that the solution used by Maxwell is employed, we

find that our - is too great for a logarithmic decrement to

exist with such amplitudes and times of oscillation as we had
employed in the experiments, and it was impossible for us to
repeat the experiments under the same conditions again at
slower velocities, because the apparatus had been taken to
pieces and could not be fitted up again in exactly the same
way. When we say that a logarithmic decrement did not
exist, we mean that it was not constant, but varied with the
amount of the oscillation. or the tractive force to be pro-
portional to the velocity of the cylinder it is necessary for 4/p
and the periodic time to be so great that the velocities of the
fluid at all places shall be in the same proportion as if the
motion were steady. .

After this paper was written we asked Mr, J. B. Knight,
of the Chemical Department of the Finsbury 'lechnical College,
to make measurements of the specific gravity of sperm-oil at
different temperatures. His results give a very striking con-
firmation of the views expressed in the paper as to a discon-
tinuity of some kind due to rise of temperature. As all the
authorities whom we have consulted seemed to see no possible
reason for a discontinuity in the rate of change of « with
temperature in sperm-oil at about 40°C., it is possible that
these results may be of importance.

ae

458 Miss Earp on the Effect of the Replacement oj

Temperature Cent. | Specific Gravity.
25 | 831
30 | 8306
35 828
40) | 826
45 8758
50 8753
5d | “OT ET

We are now arranging a piece of apparatus which will give,
not the absolute value of the specific gravity, but with great
accuracy relative rates of the change of specific gravity with
temperature *. We shall make experiments of the same kind
upon other animal oils.

XLIV. Note on the Effect of the Replacement of Oxygen by
Sulphur on the Boiling- and Melting-points of Compounds.
By Miss A. G. Harpf.

N various papers published in the Philosophical Magazine t
Carnelley has called attention to the effect produced on
the boiling-point and melting-point of compounds by replacing
one element in the compound by another belonging to the
same group. He gives numerous examples (mostly organic
compounds) to show that in the case of the halogen com-
pounds, when one halogen is replaced by another of a higher
atomic weight, both the boiling- and melting-point are corre-
spondingly raised.
As a further instance of the same kind of thing he gives the

following series of the ethyl carbonates and sulpho-carbonates

to show that the boiling-point is raised in proportion to the
amount of sulphur introduced in the place of oxygen. He
also points out that the same series shows that a definite effect
is produced by a change in the arrangement of the molecule
without any change in the number of sulphur atoms.

‘ Doe 5) : a VO See
OG E, BP. Zon. Cen H. B.P. 196°.

co B.P. 156° cages
: } Gs fe)
+ 0—C i; SC,H.
Ge ae: s1° OX ee 24
\o--0,H, B:Psi6h; \sc,H, B.P. 240°.

* We described at the Meeting results obtained for other specimens of
sperm-oil, with the new apparatus, which exhibited no discontinuity.
Yet we can find no reason to doubt Mr. Knight’s measurements.

+ Communicated by M. M. Pattison Muir.

t Phil. Mag. Oct. 1879.

j

Oxygen by Sulphur on Boiling-points of Compounds. 459

He does not, however, mention the way in which this eftect
is reversed in the cases in which the oxygen of the hydrowyl
group is replaced by sulphur, and I therefore conclude that
it escaped his notice. By examining the large number of
boiling-point data given by him in his tables I have found
the following rule to be perfectly general :—

The replacement of oxygen by sulphur in a compound always
raises the boiling-point except in those cases in which the oxygen
of the hydroxyl group is replaced by sulphur, and then the re-
verse effect is very marked. |

In obtaining data in proof of this I have been confined
of course mainly to organic compounds, and of these I have
only given the simpler instances, and such of the more com-
plicated compounds as have a known structural formula.
The reason for this is obvious, since Kopp has shown that the
boiling-point of isomeric hydrocarbons is not the same, show-
ing that a mere rearrangement of the atoms in a molecule is
sufficient to affect the boiling-point without any change in
number or kind. The fact is further exemplified in the series
of ethyl-carbonates given above.

In the following list of compounds containing hydroxyl
and their sulphur analogues, it will be seen that the replace-
ment of the OH by the SH group always lowers the boiling-
point, and that in the case of bodies of low molecular weight
the difference is considerable, but decreases as we ascend a
homologous series*.

Diff.

RP oid etocrssussacce- SOIKSE\ Ee Once merase. 100 | 161°8
TEL SU ee oe ORIEL CHOBE. oicdinc ick kha 67 46
Ls SBP | Os OSL, Gees nr oye. 784 | 42
CEL) ere LAG SE (CHLOE WR occ os 197 51
BEUOHOH SH .....0.0.:.. 90 | CH,CHCH,OH............... 96 6
SEMOE-CH SH «.......5.. (igen COHEOE CH ORs. 09o)4.0. 97 30
MEELVOCHSH 1 ......006..0 Sinn OH OOH Gres .sr, 83 26
fo )SOHCH,SH:.........:. Sse (CH) CHO OH 1. 108 20
CH,OH,CHSHCH, ......... 84 | CH,CH,CHOHOH.......... 99 15

OH(CH,).CH,CH,SH ...... 120\ | OH(OH,),CH,CH,OH ... 131:5 | 11:5
WCVCHOHSH ............-.. 137 CCl CHOMOH,.... 1). 149 26
JOS oa NY GCC IECXO)E [Nat Oly eee 180 8
BEI (SEL) 0.0.55 250 lcasesecens DAS ee ON (OED). © hss. vccedons 270 27
OH (CH.),CH,SH. ......... 1450 | OH,(CH,),CH.OM ...... 157 12
ROME OELSH .......ccccasccdes sh Wy /Ol BU XODELCOUSIAN SAA eae lle! 205 11
OPH CH.SH (a) .....50000.- een | Os Ole OF (a) vente 188 0
i, (G) 3. are 188 * (Gis ce emenet 201 13
(yy) a eae 188 rea (Cy) eek. 198 10
CO) 5 ah Coie OH COON aCe tet 17 24
OLE OSH (a)......000cccce BtGw "C,H OHO (e) i i.08. 6. 245; 29)

+ Exception :—C,,H,SH(a) 285 C,,H,(OH)(a)

* The only exception to the rule is that marked +, and isin the case of
a body of high molecular weight and complicated constitution.

460 Miss Earp on the fect of the Replacement of

Again, in the following list of compounds containing
oxygen not in the condition of hydroxyl, it will be seen that
the normal rule is followed. :

Diff,
5 | °
GHIGHS oN eee 205 | CH,CHO Si | 184
(GEORe oo ern: 300:.| (CH,).0.... 138 | 187
(OH So tes 41 | (CH,),0... aoean. 64
(OH OSH Phe... 200 | (CH.),CO, 1... 91 109
(HAC ys ee. 64 | (C,H(CH)O a li | 58
Ce a ee 99 |(C/H.).0 -.... oa 35 | 87
OH(CH OHOHS =... 114 | origi, ) CH, OHO .... ee ae
COR Vu Rel ee Oi 249 | (C,H,),CO, nna 125 | 1b
MESOHGHE We. 1 | mG One a B8 | 96
(GHIOHCH is ap 140 | (CH,CHCH,,0 20m 82 | 58
(GHICHCH an eh... 188 | (CH.CHCH.),0, «1.0... 171 17
(Po SO ae 180 | (Pr),0(«) ....2 s2 | 48
. es i 01 | @... e 60 | 60
CoS Cenc kel he 310 | (RtOCH,)>..... am 193 | 87
CinecGstias aah ia. 204. | 0,H.00,H. a 172 | 32
(GHLOECH.GH,).S .......... 182 | (GH.CH.CH,CH,),0 .. 140 | 42
CREHOIECING oe eee 215 | CAC CHORt am 185 | 30
GEER a 950 | (C.H,.),0 (Iso) eae 175 | 7
(Gao de alee oo: 339 | (CLH 0"... ee 978-288 | 5444
GS. ee. 392.| (CH ).O ae 246 | 46
GHICOSCH, «7 .. 95 | CELCOOCH, aa 56 | 39
beCens: soot ce ee 169 | "CO(OCH,), ©). eam 90 | 79
@HCOSOH Lg es 115 | CH,COOU-H, 4. Gem 77 | 88
PE OOSCH (a) 8 uk 35 | CH{COOCH (a) «+. 102 BB
es 124 ged eee
Carcoods Aus i ir 984 | C,H C0000 ae 276 8
CELLOSC ie ee 249, | G,H,COQU, Hy aaa 212 | 30
CIOCUN Gee 132 | CHLOCN .\. Jem 90 | 49
CHeNCS ee 119 | CH-NCO ... 44 | 75
OH CHGH NOS... 150 | CH.CHCH,NCO ......... 82 | 68
GRAISONI(G) sees 151: | C,H,OCN (B) ... aa 67 | 84
Gi(OH;),CH,NCS...... 162 Ci(CHT,),CH.NCO a 110 | 52
GuOOseO, et 984 | C,H.COOCO,.... ama 276 Wilks
fie sae cies weer oY |
(SONGS eee ee 218 |.C,HNCO ....aaee Coe Be
GaTOHENON eet) 943 | O-H-CH,NOO ce 175-200
ie SObines Meee ee 156-160, CCIO0CL, -..... (about) 100 |

To the above may be added the series of ethyl carbonates
quoted at first, and also the following inorganic compounds:—

OSs Wate css 42°6 GOs.) tieeeeee —782
CSC] ie yee-kes-- 71 COC vs: secre 82
1S) C) eee renee 125 POC, .tocceee 197

By arranging the data rather differently it is easy to see
that the abnormality hes entirely with the hydroxy! group.
Thus, if we take any group of sulphur compounds of one type,
we shall find the boiling-point increases with the molecular
weight as well when the hydrogen of the SH group is
replaced by a hydrocarbon radical as in any other case.

Oxygen by Sulphur on Boiling-points of Compounds. 461

Such, for example, are the following :—

le}
ae ~61°8 H,S......—61'8 Histo 2 e =618
CH,SH ...... 21 Gh USiengs 36 C,H.SH ... 172
me (CH.).S-...... Aiea,” (C.),S... A, O,H.SC,H, 204
VH,.CH,S 64 Pr,S («) .. "130 Poe (CAHBcies o>

Taking in the same way the corresponding oxygen com-
pounds, we find that by replacing OH by OX, where X
stands for any hydrocarbon radical, unless very complex, we
lower the boiling-point of the compound considerably, whereas
when the exchange is simply between different hydrocarbon
radicals the change is in the normal direction.

elec... 100 Te Obs sec. 100 HOVSGRae 100
CH,OH ...... 67 C,H,OH...... 78:4 (C,H,OH_... 180
Beco .. —23 | B, (C,H,),0.... 35 B, O,H,00,H,... 172
eneH.O... 11 (Pr,)O («) .. (C,H,),0...... 246*

From these data it is evident that the fact that water,
which has a lower molecular weight than even any of the
“permanent” gases (except hydrogen) will remain liquid up
to a very high temperature, is only one particular and well-
marked case of the general effect of the hydroxyl group.

It has been objected by Ostwald and others that the com-
parison of boiling-points is unsatisfactory, inasmuch as in
some cases it is possible that the vapour-pressure curves of
different substances may cross one another at some point; and
in that case, if some other than atmospheric pressure were
taken as the standard, the relative position of the boiling-
points would be reversed.

It is difficult to plot the vapour-pressure curves for H,O
and H,S on the same scale, since the pressure of H,S varies
by many atmospheres ; while that of H,O varies through the
same range only by a few inches, so that it has to be repre-
sented on the H.S scale by a line following the zero. The
H.S curve is, however, perfectly normal, and shows no ten-
dency whatever to approach the zero at any point short of
infinity. Hence the objection about the crossing of the
eurves falls to the ground in this case. The same may be
shown by comparing the curves for CO, and CS,; only in
this case, of course, the sulphur compound follows the zero
line, while the other is highly inclined.

With regard to the melting-points of oxygen and sulphur
compounds the same general rule holds ; but exceptions are
not rare, particularly in the cases of more complicated com-
pounds, and naturally it is among these that the larger number

* In this case the destruction of OH is not sufficient to balance the
effect of introducing the second carbon ring.

Phil. Mag. &. 5. Vol. 35. No. 216. May 1893. 21

402-- Notices respecting New Books.

of melting-point data are given. In all probability the ten-
dency to form molecular groupings and other unknown factors
tend to obscure the effect on melting-points due to the change
of constitution alone.

Another point which I think may be noticed with advan-
tage from the series just given on page 461, and which, as far
as | am aware, has been hitherto neglected, is the effect on
the boiling-point of the symmetry of the molecule, unsym-
metrical molecules tending to boil higher than symmetrical
ones.

Consider the series A,, page 461. Between the first and
second members of the series there is a large difference, the
molecular weight beg increased and the symmetry of the
molecule destroyed at the same time. Between 2 and 3 of
the same series, on the other hand, there is a much smaller
difference ; the molecular weight is increased but symmetry
is restored, and the two things act against one another.

Again, consider the series B,. Between 1 and 2 in this
series the destruction of hydroxyl lowers the boiling-point,
the destruction of molecular symmetry tends to raise it, the
result being that the difference only of the two effects is small.
Between 2 and 3 the destruction of hydroxyl and the resto-
ration of symmetry act together, and the resultant effect is
large.

The same effects may be noticed by comparing A, and By
in the same way, and also by comparing the first, second, and
fourth members in the series A; and B; respectively.

XLV. Notices respecting New Books.

An Elementary Treatise on Modern Pure Geometry.
By R. Lacutan. (London: Macmillan. 1893. Pp. x+288.)

N R. LACHLAN is a recognized master of the Geometrical

craft, and the work before us well maintains his reputation.
His primary object is to meet the new Cambridge Tripos regula-
tions, in which provision is made for the introduction of a paper
on “ Pure Geometry.” All that could fairly be looked for in such
a paper is given by the writer, or is led up to by him. He has not,
however, contented himself with such a limited supply as this
would require, but he has written with a view to allure students
on to the arcana of the science. After a careful perusal we have
detected very few errata. On page 53, Ex. 4 is obviously a slip,
and in line 3 from bottom for Bw read By, for Cw read Cz.
Page 55 line 13 contains a small clerical error: the opening

Notices respecting New Books. 463

sentence of §116 is not sufficiently guarded to be accurate. In
Ex. 3, page 70, it is not stated what point S’is. On page 161
line 11, for “polar” read “ poles.” Two or three clerical errors
are easily corrected. The following historical one occurs on
page 78, Ex. 6: “ Mr. H. M. Taylor’s paper was read before the
London Mathematical Society on Feb. 14th, 1884,” whereas he
had previously published his Note, “ On a six-point circle con-
nected with a triangle,” in the ‘ Messenger of Mathematics,’ vol. xi.
(May 1881—April 1882). If we mistake not, the “circle” had
previously been given by him ina Trinity paper. In conclusion
we are glad to say that the text is not overburdened with corol-
laries and superfluous matter, the figures are excellent, and there
is a most judicious and varied selection of exercises.

Revue Semestrielle des Publications Mathématiques rédigée sous les
auspices de la Société Mathématique d Amsterdam. Tome L.,
1* partie. (Amsterdam. 1893. 104 pp.)

THE object which the Mathematical Society of Amsterdam has in
view in putting forth this Revue is * de faciliter l’étude des sciences
mathématiques en faisant connaitre, sans délai de quelque import-
ance, le titre et le contenu principal des mémoires mathématiques
publies dans les principaux journaux scientifiques.” Primarily it
is intended for the use of its own Members, but the Society has
rightly judged that such a publication, if well conducted, will be
of service to a much larger circle of readers. This opening number
contains titles of papers printed in about 120 journals, 19 of which
are British and 8 American. A careful list of the titles is drawn
up with various particulars of interest (pp. 87-104).

The title of each communication is preceded by a system of
notation adopted at the recent Congres International de Biblio-
eraphie des Sciences Mathematiques, and is followed by a very
concise Compte-rendu of the contents. We may say that the
Revue, though its objects are similar to those of the well-known
Fortschritte der Mathematik (Berlin), does not aim so high, for in
the generality of instances the insight into any paper given by the
notices here is little more than a student would inter from the bare
title. Its merit is that a much earlier record, if the editors keep
up to date, will be available for authors and readers. The papers
tabulated from this Journal are comprised in Vol. xxxiv. (Nos. 206—
209) and are seven in number. ‘Twoare given by the titles only :
of the others a fair abstract is given. Lord Rayleigh’s papers are
assigned to “J. W. S. Rayleigh.’ We wish the Society good
success and a large clienteéle.

-f 1464.)

XLVI. Proceedings of Learned Societies.

GEOLOGICAL SOCIETY.
[Continued from p. 313.]

January 25th, 1893.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.

ae following communications were read :—

1. “On Inclusions of Tertiary Granite in the Gabbro of the
Cuilin Hills, Skye; and on the Products resulting from the Partial
Fusion of the Acid by the Basic Rock.” By Prof. J. W. Judd,
F.RS., V.P.G.S.

The author first calls attention to previous literature bearing on
the subject of the extreme metamorphism of fragments of one
igneous rock which have been caught up and enveloped in the
products of a latereruption. The observations of Fischer, Lehmann,
Phillips, Werveke, Sandberger, Lacroix, Hussak, Graeff, Bonney,
Sauer, and others show that, while the porphyritic crystals of such
altered rocks exhibit characteristic modifications, the fused ground-
mass may have developed in it striking spherulitic structures.

On the north-east side of Loch Coruiskh, in Skye, there may be
seen on a ridge known as Druim-an-Eidhne, which rises to a little
over 1000 feet above the sea, a very interesting junction of the
granitic rocks of the Red Mountains with the gabbros of the Cuilin
Hills. At this place, inclusions of the granitic rock, sometimes
having an area of several square yards, are found to be com-
pletely enveloped in the mass of the gabbro. ‘The basic rock here
exhibits all its ordinary characters, being a gabbro passing into a
norite, traversed by numerous segregation-veins ; the acid rock is an
augite-granite, exhibiting the micropegmatitic (‘ granophyrie ’) and
the drusy (‘ miarolitic’) structures, and it passes in places into an
ordinary quartz-felsite {‘ quartz-porphyry ’).

Within the inclusions, however, the acid rock is seen to have
undergone great alteration from partial fusion, and it has aequired
the compact texture and splintery fracture of a rhyolite; weathered
surfaces of this rock are found to exhibit the most remarkable
banded and spherulitic structures.

Microscopic study of the rock of these inclusions shows that the
phenocrysts of quartz and felspar remain intact, but exhibit all the
well-known effects of the action of a molten glassy magma upon
them. The pyroxene, however, has been more profoundly affected,
and has broken up into magnetite and other secondary minerals.
The micropegmatitic groundmass, which was the last portion of
the rock to consolidate, has for the most part been completely
fused, and in some places has actually flowed. In the glassy
mass thus formed, the most beautiful spherulitic growths have
been developed, the individual spherulites varying in size from
a pin’s head to a small orange. These spherulites are often

Geological Society. 465

composite in character, consisting of minute examples of the
‘common type enclosed in larger arborescent growths (‘ porous-
spherulites’) of felspar microlites, with silica, originally in the
form of opal and tridymite, but now converted into quartz, lying
between them. All the interesting forms of spherulitic growth
which have been so well described by Mr. Iddings from the Obsi-
dian Cliff in the Yellowstone Park, and by Mr. Whitman Crossfrom
the Silver Cliff, Colorado, are most admirably illustrated in these
inclusions of the Cuilin Hills. It is interesting to note that the
nuclei of some of these large spherulites consist of fragments of the
micropegmatitic granite which have escaped fusion. Among the new
minerals developed in these inclusions, by the action on them of
the enveloping magma, are pyrites and fayalite (the iron-olivine).

The phenomena now described are of interest as setting at rest

all doubts as to the order of eruption of the several igneous masses
of the Western Isles of Scotland. That the gabbros are younger
than the granites was maintained by Macculloch in 1819, by J. D.
Forbes in 1846, by Zirkel in 1871, and by the author in 1874. In
1888, however, Sir A. Geikie asserted that these conclusions were
erroneous ; he insisted that the granites were erupted after the
gabbros and basalts, and that they are, indeed, later than all the
voleanic rocks of the district except a few basic dykes which are
seen to traverse them. The occurrence of the remarkable inclusions
of granite within the gabbro now removes all possibility of doubt on
the subject, and proves conclusively that the granite was not only
erupted but had consolidated in its present form before the outburst
through it of the gabbro.

2. “ Anthracite and Bituminous Coal-beds. An Attempt to
throw some light upon the manner in which Anthracite was formed ;
or Contributions towards the Controversy regarding the Formation
of Anthracite.” By W.S. Gresley, Esq., F.GS.

The author does not seek to advance any new theory in this
communication, nor to proclaim new facts of any importance, but to
put old facts in something of a new light, in order to aid the inves-
tigations of others. His main object is to establish two facts, viz.:—
that the associated strata of anthracite-beds are more arenaceous
than those containing so-called bituminous coal-beds, and that the
prevailing colours of the sandstones, grits, etc., of anthracite regions
are greyer and darker than those of regions of bituminous coal. To
these facts may perhaps be added a third, that the more anthracitic
the coal-beds, and the more siliceous the enclosing strata, the harder
and tougher these associated strata are.

While recognizing that the rocks of many anthracite regions have
undergone great disturbance, he cites other areas where coal-basins
have been much folded, without any corresponding production of
anthracite in considerable quantity.

The modes of occurrence of anthracite are illustrated by many
instances observed by the author in the Old and New Worlds.

ie pe I

466 Geological Society :—

February 8th.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.

The following communications were read :—
1. “‘ Notes on some Coast-Sections at the Lizard.” By Howard
Fox, Esq., F.G.8., and J. J. H. Teall, Esq., M.A., F.B.S., F.G-S.

In the first part of the paper the authors describe a small portion
of the west coast near Ogo Dour, where hornblende-schist and
serpentine are exposed. As a result of the detailed mapping of the
sloping face of the cliff, coupled with a microscopic examination of
the rocks, they have arrived at the conclusion that the serpentine 1s
part and. parcel of the foliated series to which the hornblende-
schists belong, and that the apparent evidences of intrusion of

_ serpentine into schist in that district are consequences of the folding

and faulting to which the rocks have been subjected since the
banding was produced. The interlamination of serpentine and
schist is described, and also the effects of folding and faulting.
Basic dykes, cutting both serpentine and schists, are clearly repre-
sented in the portion of the coast which has been mapped, and these
locally pass into hornblende-schists, which can, however, be clearly
distinguished from the schists of the country. The origin of the
foliation in the dykes is discussed.

The second part of the paper deals with a small portion of the
coast east of the Lion Rock, Kynance. Here a small portion of the
‘oranulitic series’ is seen in juxtaposition with serpentine. The

phenomena appear to indicate that the granulitic complex was

intruded into the serpentine ; but they may possibly be due to the
fact that the two sets of rocks have been folded together while the
granulitic complex was in a plastic condition, or to the intrusion of
the serpentine into the complex while the latter was plastic.

2. “ On a Radiolarian Chert from Mullion Island.” By Howard
Fox, Esq., F.G.8., and J. J. H. Teall, Hsq., M.A., EUR SineG a:

The main mass of Mullion Island is composed of a fine-grained
‘oreenstone,’ which shows a peculiar globular or ellipsoidal structure,
due to the presence of numerous curvilinear joints. Flat surfaces
of this rock, such as are exposed in many places at the base of the
cliff, remind one somewhat of the appearance of a lava of the
‘ pahoehoe’ type.

The stratified rocks, which form only a very small portion of the
island, consist of cherts, shales, and limestone. They occur as thin
strips or sheets, and sometimes as detached lenticles within the
igneous mass. The chert occurs in bands varying from a quarter of
an inch to several inches in thickness, and is of radiolarian origin.
The radiolaria are often clearly recognizable on the weathered
surfaces of some of the beds, and the reticulated nature of the test
may be observed by simply placing a portion of the weathered
surface under the microscope.

The authors describe the relations between the sedimentary and

Remarks on certain Islands in the New Hebrides. 467

igneous rocks, and suggest that the peculiar phenomena may be due
either to the injection of igneous material between the layers of the
stratified series near the surface of the sea-bed while deposition was
going on, or possibly to the flow of a submarine lava.

The forms of the radiolaria observed in the deposit, and also their
mode of preservation, are described in an Appendix by Dr. G. J.
Hinde.

3. “* Note on a Radiolarian Rock from Fannay Bay, Port Darwin,
Australia.” By G. J. Hinde, Ph.D., V.P.G.8.

4, “ Notes on the Geology of the District west of Caermarthen.”
Compiled from the Notes of the late T. Roberts, Esq., M.A., F.G.S.

To the east of the district around Haverfordwest, formerly de-
scribed by the author and another, an anticlinal is found extending
towards Caermarthen. The lowest beds discovered in this anticline
are the Tetragraptus-beds of Arenig age, which have not hitherto
been detected south of the St. David’s area. They have yielded
eight forms of graptolite, which have been determined by Prof.
Lapworth. The higher beds correspond with those previously
noticed in the district to the west; they are, in ascending order:
(1) Beds with ‘ tuning-fork’ Didymograpti, (2) Llandeilo limestone,
(3) Dicranograptus-shales, (4) Robeston Wathen and Sholeshook
Limestones.

Details of the geographical distribution of these and of theic
lithological and paleeontological characters are given in the paper.

February 22nd.—W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.

The following communications were read :—

1. “On the Microscopic Structure of the Wenlock Limestone,
with Remarks on the Formation generally.” By Edward Wethered,
F.G.S., F.R.MS.

2. “On the Affinities (1) of Anthr He a, (2) of Anthracomya.”
By Dr. Wheelton Hind, B.S., F.G.S.

3. ‘ Geological Remarks on certain Islands in the New Hebrides.”
By Lieut. G. C. Frederick, R.N.

As far as can be judged from the soundings obtained, the New
Hebrides are probably situated on a bank lying from 350 to 400
fathoms below the surface of the ocean and running in a N.N.W.
and §.8.E. direction, with a deep valley between it and New Cale-
donia. The only two soundings obtained between these two groups
are 2375 and 2730 fathoms, the former within a short distance of
the New Hebrides.

Of the islands, Tanna is voleanic—an active volcano, apparently
consisting entirely of fragmental material, being situate on its
eastern side. Kfaté has some volcanic rock, but is chiefly of coral
formation. It rises to a height of 2203 feet, and in some parts has’
a terraced appearance, the terraces denoting distinet periods of

468 Geological Society.

upheaval. Coral was found to the height of 1500 feet above sea-
level. To the north of Efaté are Nguna, Pele, and Mau, of volcanic |
origin, and no coral has been found on them above sea-level; whilst |
Moso, Protection, and Errataka, to the west of Efaté, are of coral |
formation and similar in character to the adjoining coast of Efaté. |
In the vicinity of the coral isles is very little coral-reef, especially
when the shores are steep. Delicate live corals were brought up
from depths of 28, 39, and 42 fathoms off Moso, 37 fathoms near
Mau, and 40 fathoms off Mataso. Mataso is a volcanic island with
a narrow fringing-reef. Makura (6 miles N. of Mataso) and Mai
are also volcanic, with narrow fringing-reefs partly surrounding the
former and entirely encircling the latter island. A short distance
west of Mai is Cook’s Reef, of atoll formation. The Shepherd Isles
are all of volcanic formation, apparently recent, and no coral was
found growing around their shores. Mallicolo Island is of volcanic
and coral formation. At one place in this island coral was found at
a height of about 500 feet above sea-level.

March 8th.—W. H. Hudleston, Esq., M.A., F.BS.,
President, in the Chair.

The following communications were read :—

1. “On the Occurrence of Boulders and Pebbles from the Glacial
Drift in Gravels south of the Thames.” by Horace W. Monckton,
Esq., F.L.S., F.G.S.

North of the Thames near London, the Glacial Drift consists largely
of gravel, which is characterized by an abundance of pebbles of red
quartzite and boulders of quartz and igneous rock. With the ex-
ception of very rare boulders of quartz, the hill and vailey-gravels of
the greater part of Kent, Surrey, and Berkshire are entirely free
from these materials. The author points out that the River Thames
is not, however, the actual southern boundary of the distribution of
these Glacial Drift pebbles and boulders, though the number of
localities where they are found in gravels south of that river is few.
The author describes or mentions several, of which the foilowing
are the most important :—Tilehurst, Reading, Sonning, Bisham at
351 feet above the sea, Maidenhead, Kingston, Wimbledon, and
Dartford Heath.

2. “‘Onthe Plateau-Gravel south of Reading.” By O. A. Shrub-
sole, Esq., F.G.S.

This paper contains observations on the gravel of the Easthamp-
stead-Yately plateau.

The constituent elements of the gravel are described, and the
author notes pebbles of non-local material near Czsar’s Camp,
Easthampstead, on the Finchampstead Ridges, and at Gallows
Tree Pit at the summit of the Chobham Ridges plateau. He
mentions instances of stones from the gravel of the plateau (described
in the paper) which may bear marks of human workmanship. He
furthermore argues that the inclusion of pebbles of non-local origin

Inéelligence and Miscellaneous Articles. 469

in the gravels may be due to submergence of the plateau up to a
height of at least 400 feet above present sea-level, and cites other
facts in support of this suggestion. He concludes that the precise
age of the gravel can only be more or less of a guess, until the mode
of its formation has been definitely ascertained.

3. “A Fossiliferous Pleistocene Deposit at Stone, on the Hamp-
shire Coast.” By Clement Reid, Esq., F.L.S., F.G.S.

This is practically a supplement to a paper, ‘On the Pleistocene
Deposits of the Sussex Coast,’ that appeared in the last volume of
the Quarterly Journal. An equivalent of the mud-deposit of Selsey
has now been discovered about 20 miles farther west, and from it
have been obtained elephant-remains, and some mollusca and plants
like those found at Selsey. Among the plants is a South European
maple.

XLVII. Intelligence and Miscellaneous Articles.

ON VILLARI’S CRITICAL POINT IN NICKEL.
BY PROF. HEYDWEILLER.

eS magnetism of iron, nickel, and cobalt changes under the

influence of stretching forces. Villari first observed a special
behaviour of iron in reference to this attribute, namely that with
moderately strong magnetization small stretching forces increase
the magnetism, while larger forces diminish it; thus the strength
of the magnetism is graphically represented as a function of the
load, the ordinates of the curve firstincrease up to a maximum and
then diminish to far below the original values. The point of the
curve at which the ordinate again reaches the original value is
named Villari’s critical point.

In nickel this property has not been observed up to the present ;
in this case, so far as hitherto known, the magnetism steadily
decreases with increasing load. But with strongly magnetized
soft iron also, with small load, the original increase of the mag-
netism vanishes, and it was thought probable that with sufficiently
weak magnetization nickel also possesses a Villari’s critical point.
Experiments have confirmed this expectation. In observing the
changes in the very feeble magnetizations, it was found necessary
to work with a very sensitive arrangement.

A chemically pure nicke) wire, 46 cm. long and 0°15 em. thick,
was suspended vertically with its lower end very near (3°5 em.
distant) the upper magnetic needle of an astatic system, and so
that small longitudinal displacements caused no perceptible altera-
tion in the direction of the needle. An intensity of magnetization
I=1 C.G.S. unit corresponded to about 90 p throw with 110 p
scale distance.

The reduction of the observed numbers to absolute measure was
effected by comparison with an auxiliary magnetometer with single
needle.

Phil. Mag. 8. 5. Vol. 35. No. 216. May 1893. 2 K

470 Intelligence and Miscellaneous Articles.

The observations were conducted with alternate leading and
unloading, the strength of field remaining constant. The load
never exceeded 1 kilog. per sq. mm. cross section of the wire.

With small strength of magnetization under 2 ©.G.S. units and
with the smallest loads, soft annealed nickel shows a small decrease
of magnetism, with somewhat larger an increase, which may rise
to 26 per cent. of the total magnetism, and finally again a decrease
with increasing load.

Thus, for example, for the intensity of magnetization I=0-97
C.G.S. units with a load of p gr. per sq. millim. cross section, there
were obtained the following respective variations of magnetization
él

I
| let é1/I. D. “SUE
28 —0:006 347 +0:067
46 —0-011 490 +0042
63 0014 7138 +0257
102 —0:019 904 +0162
165 =0029 || 977 +0155
| 246 +0015 ||
|

With stronger magnetization the increase becomes continually
smaller; moreover after-effects of the preceding loading and phe-
nomena of hysteresis show themselves to a considerable degree.

Hard-drawn nickel presents the same phenomena with much
stronger magnetization still, even though in feebler degree.

Thus with a hard-drawn nickel wire, for 155-5 C.G.S. units
the variations of magnetization with a load of p gr. per sq. mm.
were :—

D. é1/I. p. 61/1.

9 —0:0034 84 +0187
18 —0:0052 113 +0:0180
27 —0-0054 246 +0-0122
33 —0-0062 360 +0-0080
42 +0°0081 490 —0:0304
56 +0:0186 740 — 00682

‘We may therefore assert that, with reference to the above=
discussed phenomena, the behaviour of nickel agrees well with that
of iron quantitatively but not qualitatively.

The detailed communication of the method of experimenting and
~ the results will be given in another place.—Svtzb. Wirz. Phys.-med.
Ges. March 11, 18938.

Intelligence and Miscellaneous Articles. 471

ON THE INTERFERENCE-BANDS OF GRATING-SPECTRA ON
GELATINE. BY M. CROVA.

Photographed gratings applied on bichromated gelatine by
M. Izarn’s* method may give rise to straight or curved inter-
ference-bands, sometimes very irregular, in the spectra which they
produce ; similar bands have been produced by Brewster f in other
circumstances. These phenomena are obtained with great beauty
on the spectra obtained by reflexion on gelatine-gratings on
silvered glass.

M. Izarn, in mentioning these interference-bands, expresses the
opinion that they are connated with the interference phenomena
by parallel gratings which I formerly investigated ¢.

Sunlight reflected from a heliostat 1s caught on a very narrow
slit the image cf which is projected upon a screen ; a very small
image of the sun is produced at the focus of this lens, which is
received on the striated surface of a grating photographed on
gelatine on silvered glass; the real images of the slit and of the
diffracted spectra are received on a screen placed in the conjugate
focus of the slit in respect of the lens.

The diffraction spectra are furrowed with large rectilinear black
bands parallel to the rays, and which are almost absolute minima,
the intensity of the rays reflected on the silvered surface being
very little less than that of the rays which fall on the gelatine.

With a copy of a fine Brunner’s grating, which I owe to the
kindness of M. Izarn, the spectra of the first order present a large ©
dark band in the green when the grating is very dry; if the
surface is breathed on the band is displaced towards the violet ;
other and closer ones enter at the red end, and their number rises
to three when the deposit of moisture confuses the projection.
The same phenomena are produced but in the opposite direction
during drying, and the displacement. of the bands becomes very
rapid if the evaporation is accelerated by blowing air over the
grating.

If the incident light extends over the whole height of the
erating instead of only to a small portion of the surface which is
obtained by varying the distance from the lens, the fringes are
curved, become irregular, and are sometimes serrated.

The phenomenon is due to the interference of two parallel
gratings; the one real, situated at the surface of the gelatine in
the points in which the incident wave meets its discontinuous
part; the other virtual, which is its image in the silvered mirror.
Their distance, which is virtually constant, is the optical path, 2 ne,
e being the thickness, and » the index of the gelatine. At the focus
of the lens, since the light only affects a small part of its surface,
the thickness of the gelatine is virtually constant.

* Comptes Rendus, vol. exvi. p. 506.
t+ Phil. Mag. [4] vol, Xxxi. pp. 22 and 98 (1866).
t Comptes Rendus, vol, Ixxu, p. 855, and vol. Ixxiv. (1871-1873).

472 Intelligence and Miscellaneous Articles.

lf, on the contrary, the light extends over a considerable sur-
tace, the thickness of the gelatine varies at different parts,
especially if the plate has been placed vertically while drying ; the
bands are then bent while diverging, and their greatest divergence
is at the part where the layer is thinnest.

When the grating has been prepared, the distortion of the bands
is very irregular ; but after a great number of hydratations followed
by dryings the phenomenon becomes more regular. After fixing
the grating in water and drying, the gelatine possesses, as is known,
i kind of temper which is manifested by its accidental double
refraction; but when it has been hydrated and dried slowly a
great number of times its structure becomes more homogeneous,
aud the bands no longer possess serrations. It is possible that
such alternations injure the good keeping of the gratings, and it
is thus desirable to keep them in a dry place.

Observing the band-spectra in the goniometer they appear like
broad and very dark spaces, but if sun-light is used condensed on
the slit, by a cylindrical lens, the pivot lines of the spectrum are
defined in these spaces with marvellous precision. ‘The production
of these parasitical bands does not affect the accuracy of measure-
ments made with these gratings.

With gratings in gelatine on transparent glass these phenomena
are scarcely perceptible by reflexion or by transmission, owing to
the almost total identity of the refractive indices of gelatine and
glass.

If the mdex of gelatine is taken at 1°52, it is easy to calculate
the thickness of the layer of gelatine as a function of the number
of bands contained in the spectrum reflected on silver; I have thus
found that in the copy which I use the thickness of the layer is
0-04 millim. when it is dry, and about 0°16 millim. when it is at its
maximum hydratation; this number is only approximate, as the
index varies with the quantity of water it contains.

M. Izarn’s gratings are of admirable sharpness, and examined
in the microscope they do not differ from the original ; in a Fro-
ment’s grating, a hundred one, which I possess, the opaque interval
is virtually equal to a fifth of the transparent interval: this is also
the case with M. Izarn’s copy; this is not a negative but a posi-
tive. The transparent intervals are the bands of insoluble gelatine,
while the opaque intervals are the places where the soluble gelatine
has been dissolved away by the water; but owing to the extreme
fineness of the intervals, the water by capillary action has hollowed
out cylindrical grooves which to a plane wave behave like an opaque
body. When the opaque interval is very great compared with the
transparent one, the opposite might take place; but it is easy to see
that even when the two intervals are transparent, the difference of
the refractive indices of gelatine and air is sufficient to produce
phenomena identical with those of the grating. This question calls
tor new investigations.—Comptes Rendus, March 27, 1893.

LH E

LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FIFTH SERIES.]

JUNE 1898.

ALVIN. Electrochemical Effects due to Magnetization.
By GHoRGE OWEN Squier, PA.D., Lieut. U.S. Army *.

INTRODUCTION.

H# infiuence of magnetism on chemical action was the
subject of experiment by numerous investigators during
he first half of the present century t. Up to 1847 we find
by no means a uniformity of statement in regard to this
subject, and secondary effects were often interpreted as a true
chemical influence. Among the earlier writers who main-
tained that such an influence exists may be mentioned Ritter,
Schweigger, Débereiner, Fresnel, and Ampére; while those of
opposite view were Wartmann, Otto-Linné Hrdmann, Ber-
zelius, Robert Hunt, and the Chevalier Nobili.

Professor Remsen’s discovery, in 1881, of the remarkable
influence of magnetism on the deposition of copper from one
of its solutions on an iron plate, again attracted attention to
the subject, and since then considerable work has been done
directly or indirectly bearing on the question.

Among other experiments by Professor Remsen { were the
action in the magnetic field of copper on zinc, silver on zinc,
copper on tin, and silver on iron, in all of which cases the
magnet evidently exerted some influence. With copper sul-
phate on an iron plate the effects were best exhibited, the

* Communicated by the Author.

+ Wartmann, Philosophical Magazine, 1847, (8) xxx. p. 264.

t American Chemical Journal, vol. iii. p. 157, vol. vi. p. 480; ‘Science,’
vol. i. no. 2 (1883).

Phil. Mag. 8. 5. Vol. 35. No. 217. June 18938. 21

FFE en ee Re

474 Lieut. G. O. Squier on the Electrochemical

copper being deposited in lines approximating to the equipo-
tential lines of the magnet, and the outlines of the pole being
distinctly marked by the absence of deposit.

Messrs. Nichols and Franklin * were the next to conduct
experiments bearing on this subject. They found that finely
divided iron which has become “ passive ” through the action
of strong nitric acid suddenly regains its activity when intro-
duced in a magnetic field, and also that when one of the two
electrodes immersed in any liquid capable of chemically
acting upon them is placed in a magnetic field, a new
difference of potential is developed between them due to this
magnetization. ‘They ascribe these effects to electric currents
in the liquid produced indirectly by the magnet, which
currents go in the liquid from the magnetized to the neutral
electrode.

Professor Rowland and Dr. Louis Bell ft were the first to
note the “‘ protective action”’ of points and ends of magnetic
electrodes, and to give the exact mathematical theory of this
action. Their results were directly opposite to those of
Messrs. Nichols and Franklin, who found, as stated above,
that points and ends of bars in a magnetic field acted like
zines to the other portions, or were more easily dissolved by
the liquid.

The method of experiment adopted by Professor Rowland
was to expose portions of bars of the magnetic metals placed
in a magnetic field to reagents which would act upon them
chemically, and study the changes in the electro-chemical
nature of the exposed parts by fluctuations in a delicate
galvanometer connected with the two bars. Iron, nickel, and
cobalt were experimented upon, and nearly thirty reagents
were examined in this manner. The results are summed up
in the following statement :—“ When the magnetic metals
are exposed to chemical action in a magnetic field, such
action is decreased or arrested at any points where the rate of
variation of the square of the magnetic force tends towards a -
maximum.” |

Other investigations in this field are those of Andrews f,
who employed iron and steel bars from eight to ten inches
long with their ends immersed in various solutions, and one
bar magnetized by means of a solenoid. The protective
action was not noted, but, on the contrary, the magnetized

#* American Journal of Science, vol. xxxi. p. 272, vol. xxxiy. p. 419,
vol. xxxv. p. 290.

+ Phil. Mag. vol. xxvi. p. 105.

{ Proceedings of the Royal Society, no. 44, pp. 152-168, and no. 46,
pp. 176-198.

Liffects due to Magnetization. 475

bars acted as zincs to the neutral bars, thus indicating that
they were more easily attacked.

Practically the same results were obtained by Dr. Theodor
Gross * ; soft iron wires, 8 cm. long and 3 cm. in diameter,
coated with sealing-wax except at the ends were exposed to
various liquids. When one electrode was magnetized, a cur-
rent was obtained going in the liquid from the magnetized
electrode to the non-magnetized electrode.

It thus appears that there is at least an apparent incon-
sistency between the protective results of Professor Rowland
and Professor Remsen, and those of Nichols, Andrews, Gross,
and others, who find the more strongly magnetized parts of iron
electrodes more easily attacked than the neutral parts; and it
was with the object of endeavouring to reconcile these results,
and of studying the exact nature of the influence exerted by
the magnet, that the experiments recorded in this paper were
undertaken.

APPARATUS AND MEruop oF INVESTIGATION.

The method of investigation was that adopted by Professor
- Rowland in his previous work on the subject, since its facility
and delicacy permitted the effects of the magnet to be
observed whenever there was the slightest action on the
electrodes by the solution examined, and the investigation
- could thus be carried over a wide range of material.

A large electromagnet was employed to furnish the mag-
netic field, and, at a distance sufficient to prevent any direct
influence due to the magnet, a delicate galvanometer of the
Rowland type was set up. Small cells were made with iron
electrodes of special forms, coated with sealing-wax except at
certain parts, and immersed in a liquid capable of acting
chemically on iron. The whole was contained in a 50 cubic
centim. glass beaker, and when joined to the connecting wires
of the distant galvanometer was firmly clamped between the
poles of the electromagnet.

In the course of the examination of anumber of substances
it was found necessary to use two galvanometers—one
specially made by the University instrument-maker and very
sensitive, which was employed with acids which evolve hydro-
gen; the other, much less sensitive, was best suited to the
violent “ throws” with nitric acid and iron. The samples of
iron used throughout the experiments were obtained from

* “Ueber eine neue Entstehungsweise galvanischer Strome durch
Magnetismus,” Stizwngsberichte der Wiener Akademie, 1885, vol. xcii.
(1885) p. 1873.

2152

a ae versio tare ast
2 aad Bae a

476 Lieut. G. O. Squter on the Electrochemical

Carnegie, Phipps, and Co., of Pittsburg, and were practically
pure.

In order to insure a uniform density of surface, the elec-
trodes were turned from the same piece and polished equally
with fine emery-cloth. The magnet could be made or
reversed at the galvanometer, and its strength varied at will
by a non-inductive resistance. The electrochemical effects
due to the magnetic field could thus be studied with facility
by the fluctuations of the galvanometer-needle. The original
difference of potential, which always existed between the
electrodes, was compensated by a fraction of a Daniell cell,
so the effects of a variation of the magnetic field could be ob-
served when no original current was passing between the
electrodes.

The standard cells were made with care, and under
uniform treatment possessed at 20° C. an electromotive force
of 1:105 volt. The connexions with the compensating cir-
cuit, which contained a finely-divided bridge, were so
arranged that from its readings the difference of potential
between the distant electrodes became known at once without
involving the resistance of the cell or of the galvanometer.

Since quantitative measurements of the effects observed
were desired, a preliminary step was to calibrate the electro-
magnet for a given distance apart of the pole-pieces. The
method employed was the well-known one of comparing the
galvanometer deflexions produced by a test-coil in the 4eld
with those of an earth inductor in series in the circuit.
Since the effect of the sudden addition of a certain strength
of field was wanted instead of its absolute value, the de-
flexions with the test-coil were taken for simple “make”
or “ break ’”’ and not for reversed field, thus eliminating the
residual magnetism of the pole-pieces.

In the formula applicable, viz.,

H amnwv d
EY mga a! ee
in which d and d’ represent the deflexions due to the
inductor and test-coil respectively, H and H’ the earth’s
field and the field to be measured, n and n’ the number of
turns, and a and a’ the radii of the coils, the particular values
were :—
mna’ =20716 square centim.
ma” =6'788 square centim.

Distance between pole-pieces 3°5 centim.

Effects due to Magnetization. 477

H’=1299:48 d'H, and as d’ varied from 3), to 16, the range
of field employed was from 65 to 20,800 H.

A curve was constructed so that from accurate ammeter
readings in the field circuit the strength in absolute measure
could be read off at once.

EXPERIMENTAL RESULTS.

Preliminary.—The first experiments were made with very
dilute nitric acid and iron electrodes—one a circular disk of
5 millim. radius, and the other a small wire 1 centim. long
and 1 millim. in diameter, turned te a sharp point at one end.
The peint was placed opposite the centre of the disk, at a dis-
tance of 1 centim. from it, and the whole placed so that the
cylindrical electrode coincided with the direction of the lines
of force. When the minute point and the centre of the disk
were exposed to the liquid, and the magnet excited, a momen-
tary “throw” of the galvanometer was observed in the
direction indicating the point as being protected or acting as
the copper of the cell.

When the pointed pole was slightly flattened at the end,
and the insulation so cut away that the surfaces of exposure
on the two electrodes were exactiy the same, the throw of the
galvanometer on making the field was very much diminished,
although still perceptible, since the disposition of lines of
force would still be very different over the two plane surfaces
of exposure.

With ball-and-point electrodes precisely similar pheno-
mena were observed as with a disk and point, except to a less
degree.

The gradual reversal of the current shortly after exciting
the field, the independence of the throw of the direction of
the current through the magnet, the disappearance of the
throw when the nature of the magnetic field at the exposed
parts became the same, and the effects of artificially stirring
the liquid, were observed exactly as described by Messrs.
Rowland and Bell.

In the course of a large number of preliminary experi-
ments with nitric acid, it was soon observed that under
certain conditions the effect of suddenly putting on the
magnetic field was to produce a less rapid deflexion of the
galvanometer in the opposite direction, or indicating the
point as acting asa zinc. Plainly this irregular behaviour,
due to the magnet, required a more systematic study than it
had yet received. It had been found that the reversal of the
current, which regularly followed the “ protective throw,”
was decreased or destroyed by anything which prevented free

478 Lieut. G. O. Squier on the Electrochemical

circulation in the liquid, and that an acidulated gelatine,
which was allowed to harden around the poles, was best
suited for this purpose. The great irregularity observed in
any one experiment made it necessary to eliminate everything
possible which might mask the true phenomenon, if any ac-
curate comparisons were to be drawn between the effects
observed in the different cases; accordingly a standard form
of experiment was adopted, which was carefully repeated
many times. The cell found best suited for this purpose was
composed as follows :—

Disk electrode, diameter.................. 14:4 millim.
thickness! .)..c. 4 ae Dib ito tig
Point electr ode, total length ............ L524, Se
RA _ diameter, oso weee 44,
ss length of point......... D2 sug
Distance of point from centre of disk... 10 5

The same electrodes were used aacianeen any set of experi-
ments, being carefully cleaned and polished each time.

With nitric acid the liquid was finally made up as
follows :—

Distilled water ............... 10 grammes.
Flardscelatine ace. 245.2 1 gramme.
C. P. nitric acid (sp. gravity 1°415) 0533 gramme.

‘The gelatine and water were allowed to stand until the
former had dissolved without the application of heat, when
the acid was added and the whole thoroughly mixed. Too
strongly acidulated gelatine would not harden at all.

In some cases, in order to protect the point from the
‘beginning, the electrodes, secured as usual at the ends of two
small glass tubes containing the connecting wires, were
tirmly clamped in the proper position between the poles of
the magnet, and the magnetic field put on before the cell was
completed, by pushing the beaker containing the solution up
in position round the electrodes.

With this cell a series of parallel experiments were con-
ducted to obtain the variation of the effects with time, the
amount of iron salts present, the fluidity of the solution, and
with constant and variable magnetic fields.

A. Behaviour of the Cell with Time, in the Earth’s Field.

The cell was placed entirely outside the magnetic field, and
galvanometer-readings taken at intervals of one minute for
three hours. The curve fig. 1 (I.) shows these results. Posi-
tive ordinates indicate a current from the point to the disk,

Hifects due to Magnetization. 479

and negative ordinates the reverse current. Other experi-
ments with fresh solutions, same electrodes, same exposed
area, and every condition as nearly as possible the same, gave
curves of practically the same character, and the one given is
selected to illustrate.

The curve indicates that the original current was to the
point electrode; this gradually decreased, owing to polarization,
until after a hour and five minutes it reversed slightly, but
again reversed thirty-five minutes later, and after a little
more than two hours the deflexion became perfectly constant,
remaining so indefinitely. .

The iron salts formed could not move with facility from the
exposed surfaces through the hardened gelatine, and were
easily outlined from their brown colour, as the whole appa-
ratus was placed in a strong light.

B. In a Uniform Magnetic Field.

The cell was next placed in the magnetic field, which was
kept practically uniform (about 15,650 H) for three hours,
and galvanometer-readings taken as before.

The electrodes were magnetized before being introduced
into the solution, so as to protect the point from the begin-
ning. In order to prevent the influence of the rise of
temperature due to the heating of the field coils of the
electromagnet, the whole cell was packed with cotton-wool
between the poles. As Gross and Andrews observed, the
temperature effect was small, the solution rising but 0°°7 C.
in half an hour.

The curve fig. 1 (I1.) shows the results of these observa-
tions. It is seen that the original current was, as before, to
the point electrode, and about the same in value. ‘This
reversed after forty-five minutes, and rapidly increased to
approximately twice its original value at the end of one hour
and twenty minutes, and, instead of again reversing, remained
indefinitely with the point electrode as a zinc. ‘The distri-
bution of the iron salts in this case was quite unlike the
former. Notwithstanding the gelatine, the powerful magne-
tization of the exposed point gradually drew the iron salts
from the disk as fast as they were formed, and concentrated
them symmetrically about the point, giving the solution in
this region an almost black appearance.

After waiting a sufficient time to be assured that further
presence of iron salts would not effect the permanency of the
existing electromotive force, the magnetic field was gradually
decreased without ever breaking circuit, by increasing the

480

5
i
| ba
Pe
H
i
: ee
i
4
H
bi
ee
i
i
H
uJ
i
| ee

000% 1 i () ; i ;

Lieut. G. O. Squier on the Electrochemical

PT ee ee eT
HEEEBSS0E (a> cSRREEe
ze eS pes te]

ENE

.
:
ig
i
Klee

Fill
Ateteceen (loatat

GARR Rei

ae sate SClNGEaaa
JSNeRBea ee gers es he eee ee
LPS fee Eee cle
Ae sf

| a8 SEE Ee E
ACERE CEE EEC
ee ee eee

Fake
AEE
CAEP CED EE I) ar
Pest tes TNE a Ear yin

eb HBR a
}
= 3 5 i

Fig.3

Effects due to Magnetization: 481

liquid resistance in the field current. This change of resist-
ance was necessarily made more or less suddenly, and the
deflexion experienced at each increase of resistance a not
very sudden throw toward reversal, in every respect the
same as had been repeatedly observed in the preliminary
experiments, and very different from the characteristic “ pro-
tective throw,” which is always sudden and in one direction.

By simply varying the field current with care, as explained
above, the deflexion could be reversed again and again at
will, and could also be held at the zero of the scale, indicating
no current at all, as long as desired. When once the field
was entirely broken, the iron salts were released from the
control of the exposed pole, seriously disturbed by gravity,
and putting on the field again failed to reproduce the results
noted above.

The only elements of difference in the two cases are, (a)
the magnetized condition of the metal, (0) the distribution of
the iron salts formed by the reaction.

Although, as the curves indicate, the average electromotive
force with the magnetic field was much greater than in the
former case, yet this electromotive force is due to the difference
of action at the two exposed surfaces, and, as will be pointed
out later, the total amount of iron dissolved and passing into
solution in the two cases is probably not very different *.
Quantitative experiments are wanting on this point.

The influence of the magnetized condition of the metal and
its magnitude is exhibited in the phenomenon of the “ pro-
tective throw,” which is always observed with apparatus
sufficiently delicate unless itis masked by other secondary
phenomena.

Since the electrodes were embedded in hardened gelatine,
there could be no convection-currents in the liquid, and this
can be eliminated. Hvidently the great difference in the
behaviour of the cell in the two experiments described is
principally due, either directly or indirectly, to the distribu-
tion of the iron salts formed by the reaction in the two cases.

The principal t¢me effects of the magnet were :—

(a) To produce a higher potential at the point of greater
magnetization.

(b) To increase the rate of change of the potential between
the electrodes and the absolute value of this potential dif-
ference.

(c) It also appears from both curves that after a certain
distribution of iron salts is reached, further presence of the
same does not affect the permanency of the current established.

* Fossati, Bolletino dell’ Elettrictsta, 1890.

482 Lieut. G. O. Squier on the Electrochemical

Since the time effects of the magnet were so marked, it
was thought possible that a “ cumulative ” effect, due to the
earth’s field alone, might be detected after a sufficient time
had elapsed. The apparatus was made as delicate as possible,
and parallel experiments conducted, the electrodes first being
placed in the magnetic meridian, and afterwards perpen-
dicular thereto. No positive difference could be detected.

C. Convection-Currents in the Liquid.

As has already been stated, the reversal of the current
which regularly followed the “ protective throw ” was found
by Messrs. Rowland and Bell to wholly disappear when har-
dened acidulated gelatine was substituted for the dilute acid
solution, so that when the magnet was put on a permanent
deflexion of much less magnitude was obtained instead of a
transitory throw. ‘This indicated that currents in the liquid
cannot be neglected, and their study was next undertaken.
Since hardened gelatine completely prevented the reversal of
the current, and with no gelatine it regularly appeared after
a short time, a large number of experiments were made, in
which the amount of gelatine was varied continuously between
these limits. As expected, the effects also varied—the greater
the fluidity of the solution, the more quickly the reversal
occurred.

In the light of what was already known concerning the
presence of iron salts, some of the experiments were continued
over a considerable time, and in others iron salts were intro-
duced artificially, to increase the effects. It was soon found
that by starting with a fresh hardened gelatine, with which
the “ protective throw” was the only feature, and gradually
increasing the fluidity of the solution and the amount of iron
salts present, both effects were exhibited at the.making of the
field—first, the sudden throw of the needle always in the
direction to protect the point, and immediately thereafter the
comparatively slow “ concentration throw” in the opposite
direction. By making the conditions still more unfavourable
for the “ protective throw,” it gradually diminished until en-
tirely masked by the second effect, so that making the field
produced a deflexion in the direction indicating a current
from the point.

With the proper conditions, both of these effects could be
studied with the greatest ease: first, one made prominent,
then both equal, then the other made prominent at will. The
“protective throw’ could be traced until it became a mere

Liffects due to Magnetization. 483

stationary tremor of the needle at the instant of its starting
on the “concentration throw.” This latter, though called
a “throw,” can be made to vary from an extremely slow
continuous movement of the galvanometer deflexion, as in
experiment B already described, to a comparatively rapid
deflexion at the instant of making the magnet.

By using simply a dilute nitric-acid solution with no gela-
tine, and inserting a thick piece of glass between the
electrodes, the concentration effect was delayed enough to
allow the ‘protective throw” to first appear, with consider-
able iron salts in the solution; and on making the field both
effects were observed as described above.

It now appears that the reversal of the current, uniformly
observed in the experiments of Messrs. Rowland and Bell,
was but a form of the “‘concentration throw” mentioned
above, and that we can regard the substitution of the hardened
acidulated gelatine for the dilute acid as merely separating these
effects, so that the former can be studied by itself; in other
words, the reversal of the current would have occurred just
the same after a sufficient time had elapsed.

Turning to the experiments of Drs. Gross and Andrews,
they employed but one magnetized electrode, which was not
pointed. In this case the nature of the magnetic field at the
two exposed surfaces would be very much more nearly the
same than when a pointed electrode is employed. This
arrangement is not, therefore, suited to bring out the delicate
“‘»rotective throw,” and it is not surprising that the concen-
tration effect was the prominent feature observed.

We have now a complete reconciliation of the directly
opposite results referred to in the introduction. The “ pro-
tective throw ” is due to the actual attraction of the magnet
for the iron, and is always in the direction to protect the
more strongly magnetized parts; while the “concentration
throw ” is always in the opposite direction, and depends upon
the distribution of the iron salts present in the solution, and
the convection-currents in the liquid. The concentration of
the products of the reaction about the point would tend to
produce a ferrous reaction instead of a ferric, and experiment
shows that a higher electromotive force is obtained with cells
in which a ferrous reaction takes place than with those in
which a ferric reaction occurs; and this change in the
character of the reaction produced by the concentration prob-
ably accounts, at least in part, for the increased electro-
motive force at the point.

ee a ne ee

484 Lieut. G. O. Squier on the Electrochemical

D. The Iron Salts about the Point Electrode.

The effect of artificially stirring the liquid, and the direct
influence of the fluid condition of the solution on the de-
flexions observed, at once suggested movements of the liquid,
produced indirectly by the magnet. In order to locate these
currents and determine their potence, a small cell was made
of two rectangular pieces of glass held by stout rubber bands
to thick rubber sides. Perforations in the sides admitted the
electrodes, which were point and disk as before. The cell,
between the poles of the electromagnet, was in a strong light,
and the movements in the liquid were easily perceptible from
the displacements of suspended particles introduced for the
purpose. When very dilute nitric acid was placed in the cell
and the magnet excited, some interesting phenomena were
observed.

The liquid, at first colourless, almost immediately assumed
a pale brown colour about the point, but nothing appeared at
the disk electrode. The iron salts were drawn as soon as
formed towards the point electrode, since here the rate of
variation of the square of the magnetic force is a maximum.

As more iron was dissolved, a surface approximating to an
equipotential surface of the pointed pole, and enveloping the
coloured iron salts, was observed enclosing the point and at
some distance from it. The outline of the surface became
darker in a short time, and finally two or more dark contours,
separated by lighter portions and symmetrical with the outer
one, appeared between it and the point, indicating maxima
and minima of density. When the magnetic field was gra-
dually increased, this surface usually enlarged without breaking
up and holding the iron salts within it. On further strength-
ening the magnetic field to about 16,000 H, the ridges merged
into one thick black envelope around the point.

This phenomenon is best studied with but little iron salts
present, and by watching the point electrode with a micro-
scope while the strength of the magnetic field is increased
and decreased continuously. The sections (fig. 3) show the
general form of these contours with different strengths of
field.

Upon breaking the field everything dropped from the point
suddenly to the bottom of the cell, and on making the field
again it required a few seconds for the salts to reappear at the

oint.
‘ This, at least partially, accounted for the sudden effects
often noticed at breaking the field circuit, and the compara-

a
ne

Hffecis due to Magnetization. 485

tively smali ones at ‘‘make,” especially with certain salt-
solutions, such as copper sulphate.

The outer envelope which held the iron salts together, and
limited the immediate influence of the magnetized point, was
distinctly defined within the liquid, and easily observed by
the reflexion of the light from its convex surface.

The persistency with which the iron salts were held about
the point was shown by moving the cell with respect to the
electrodes, when the contour remained approximately intact,

passing bodily through the liquid without being broken up.

H. Electromagnetic Rotations.

The small dust particles present in the liquid were drawn
radially toward the point until they reached the surface
described, when they pierced it and began to revolve rapidly
about the point inside this surface, in the opposite direction to
the currents of Ampere. Reversing the poles of the magnet
produced surfaces of the same appearance but opposite rotations.

When the current from a Daniell ceil was sent through it.
seemed to have very little effect upon the rotations, showing
them to be controlled by the powerfully magnetized point.

The electromagnet was arranged with its field vertical, and
the point electrode along the lines of force as before. This
arrangement gave better control of the surfaces formed,
since gravity now acted symmetrically about the point.

When a single iron rod about 3 millim. in diameter, and
placed vertically in the cell, was substituted for the two elec-
trodes, two rotations were observed which were uniformly
dextro about the north-seeking pole of the rod, and levo
about the south-seeking pole. About the central neutral
portion no rotations were observed. When the rod was covered
with a thin coating of vaseline the rotations entirely disappeared
as expected. Wartmann™ observed similar rotations about
soft-iron cylinders adhering to the poles of a magnet, and he
ascribed them to electric currents in the liquid which proceed
from the periphery of the cell radially to the surface of the rod.

The explanation of these rotations follows at once from
what we know of the time-effects produced by the magnet.
A higher potential is always produced at points of greater
magnetization, causing electric currents in the liquid from
the more strongly magnetized to the weaker parts of the iron.

Applying this fact to the exposed conical point electrode,
we see that local electric currents exist from its vertex to the
other parts of the surface, returning by way of the metal. In
the case of the vertical rod, these currents pass from the poles

* Philosophical Magazine, xxx. p. 268 (1847).

‘
Fi
5
iy
4
¢
!

ot

er
ih RRS AE
pe we

486 Lieut. G. O. Squier on the Electrochemical

at its ends, through the liquid, to the neutral portions, returning
as before.

These currents*, under the influence of the poles themselves,
would cause electromagnetic rotations of the liquid, as we find
them. The mere mechanical influence of these rotations, as
in the case when the liquid is artificially stirred, is to increase
the chemical action upon the point, causing it to tend to act
more like a zinc, which experiment confirms.

F’. Acids which attack Iron with the Evolution of Hydrogen.

Professor Rowland had observed the ‘ protective throw ”’
with such acids to be extremely small, and difficult to detect
except by very sensitive apparatus. The sensitive galvano-
meter was set up and every precaution taken against inductive
effects. A telescope and scale were used in this part of the
work.

Several substances were first examined, among them being
hydrochloric acid, acetic acid, perchloric acid, chlorine water,
copper sulphate, ferric chloride, sulphuric acid, &e., but as
these observations added nothing to the results already
obtained they are not given here.

After several trials a standard sulphuric-acid solution was
made up as follows :—

Distilled water faces ee eee eee 10 grammes.
Grelatame: ghee WA an ee 1 gramme.
O.P. Sulphuric acid, sp. gr. 1°826 ... 1:062 gramme.

More strongly acidulated gelatine would not harden, and
weaker solutions gave too small effects.

The “ protective throw ” was detected, but the point very
soon became completely covered with minute bubbles of
hydrogen, so that the electrodes had to be cleaned constantly.

The effect of adding hydrogen dioxide to the solution was
next tried, since this would facilitate the removal of the
hydrogen as soon as formed, which was thought to act
merely mechanically.

When about 1 cubic centim. of H,O, was added to the
solution the ‘ protective throw” became much more promi-
nent, and the gas bubbles only appeared in small quantities
aftera considerable time. Further addition of small quantities

* The rotations produced in liquids by axial currents, e. g. currents
coinciding with the direction of the magnetic lines of force as distinct
from radial currents, have been studied by Dr. Gore (Proceedings of the
Royal Society, xxxiil. p. 151).

J. M. Weeren, Berichte der Deutschen Chemischen Gesellschaft,
No. 11 (1891).

Effects due to Magnetization. 487

of the dioxide showed the “ protective throw” to be very
decided with sulphuric acid when the hydrogen 1s removed
from the surface of the electrodes in this manner.

G. The Electromotive Force.

Several attempts were made to obtain the relation between
the strength of field and the electromotive force developed in
the “protective throw”; but it was difficult to obtain con-
sistent readings owing to the trouble of balancing the original
deflexion, and the small absolute values of this electromotive
force when hardened gelatine was employed.

A curve was constructed, however, showing the variation
of the galvanometer deflexion with the strength of field, using
nitric-acid solution without gelatine. This is shown in fig. 2.

The readings were taken one after another as rapidly as
possible, to eliminate the damping effects of the iron salts
formed.

The curve exhibits the general character of the variation.
In the regicn from about 3500 H to 8000 H the greatest rate
of change occurred, and beyond 10,000 H the curve became
nearly horizontal for the particular electrodes used. Curves
were also constructed for the “concentration throw” on
making the field under different conditions, and they were
approximately right lines, more or less inclined according to
the amount of iron salts present.

With the sulphuric-acid solution already given the electro-
motive force varied from 0:°0033 to 0:0078 of a volt, while
with the nitric-acid solution it became as great as 0°036 of a
volt. In making all the solutions used with the different
substances amounts were taken proportional to their particular
molecular weights, and then halved or doubled until of suit-
able strength to give results with the galvanometer. It was
thought possible at the beginning that this might lead to
some relations between the protective results and the strengths
of the particular solutions ; but the general irregular cha-
racter of the whole phenomenon prevented comparisons in
this respect, and all that can be stated is, that both the
“protective throw” and the concentration effect in general
increased rapidly with the strength of the solution.

H. Influence of a Periodic Magnetic Field upon the Cell.

An experiment was made to determine the behaviour of the
standard nitric-acid cell when the magnetic field was made
and broken at regular intervals over a considerable time, and
curves were drawn showing the variation of the “ throw ” with

488 Lieut. G. O. Squier on the Electrochemical

time, and the fluctuation of the original deflexion caused by
this treatment. The strength of field was about 11,000 H.,
and the experiment was conducted without compensating the
original deflexion, and by making the field for one minute,
then breaking for one minute, and so on.

One of the curves is shown in fig. 1 (III.), in which posi-
tive ordinates are values of the concentration throw at “ make,”
and negative ordinates the values of the “ protective throw.”’

Experimenting was not begun until the gelatine had com-
pletely hardened, and since the electrodes would tend to
become polarized while the gelatine was hardening, the “ pro-
tective throw” was very small, and soon masked by the
concentration effects.

After about five minutes, making the field had very little
effect at all, but began to show decided “ concentration
throws ”’ ten minutes later, and these rapidly increased with
time, as the curve indicates.

Considering the fluctuation of the original deflexion, the
effect of this periodic field was to tend to reverse it, just as in
the case of the uniform field in experiment B, but much more
slowly, since the field was on but half the time in this case.

The cell also showed the iron salts almost entirely about the
point, forming a thick black envelope.

i Summary.

The principal results of this investigation may be sum-
marized as follows :—

Whenever iron is exposed to chemical action in a magnetic
field, there are two directly opposite influences exerted.

(a) The direct influence of the magnetized condition of the
metal, causing the more strongly magnetized parts to be
protected from chemical action.

This is exhibited in the phenomenon of the “ protective
throw,’ which is always in the direction to protect the more
strongly magnetized parts of magnetic electrodes.

The “ protective throw ” is small, often requiring delicate
apparatus to detect it, and is soon masked by the secondary
concentration effects.

As to the absence of the “protective throw” with acids
which attack iron with the evolution of hydrogen, the
hydrogen acts merely mechanically, and when removed by
adding to the solution small quantities of hydrogen dioxide,
the ‘“ protective throw ”’ becomes very decided.

In the curve, fig. 2, representing the variations of the
“protective throw’ with the strength of the magnetic field,

Effects due to Magnetization. 489

we trace at once the magnetization of the point-electrode.
Since only the minute point was exposed to the liquid, it
would become saturated for comparatively small magnetizing
forces, and the curve indicates that this occurred at about
10,000 H., beyond which the curve becomes practically hori-
zontal. ‘This further establishes the direct connexion between
this “ throw” and the variation of the magnetization of the
exposed point, and confirms the explanation of Professor
Rowland, that it is due to the actual attraction of the magnet
for the iron, and not to any molecular change produced by
magnetization. :

(6) The indirect influence of the magnet caused by the
concentration of the products of the reaction about the more
strongly magnetized parts of the iron.

This tends to produce a higher potential at the more
strongly magnetized parts, and finally establishes permanent
electric currents, which go in the liquid from the more
strongly magnetized to the neutral parts of the iron.

This concentration-effect increases rapidly with the amount
of iron salts present and the fluidity of the solution.

The convection-currents in the liquid are themselves a
consequence of this same concentration, being electromagnetic
rotations produced by the action of the magnet upon the local
electric currents between different parts of the iron.

As to the permanent current due to the magnet which is
finally set up between the electrodes, as shown in fig. 1 (II.), it
is probably owing to a change in the character of the reaction
produced by the concentration of the iron salts about the more
strongly magnetized parts, which would tend to cause a
ferrous instead of a ferric reaction to take place, and thus
increase the electromotive force.

Physical Laboratory, Johns Hopkins University,
May 1892.

Note.—Since the completion of the above investigation, a
number of experiments have been performed similar to those
of Professor Remsen. Starting with the known existence
and direction of the electric currents in the liquid, it was
thought that these might lead to some explanation of the
peculiar form of deposit in equipotential lines. A number of
interesting facts have been noted, but they are withheld for
further experiments. Go OS:

Phil. Mag. 8. 5. Vol. 35. No. 217. June 1893. 2M

f 490 ]

XLIX. Onthe Applicability of Lagrange’s Equations of Motion
ina General Class of Problems; with especial reference to
the Motion of a Perforated Solid in a Liquid. By CHARLES
V. Burton, D.Se.*

i | ee wr, p,... be some only of the coordinates of a

material system, so that when the values of W, ¢,...
are given the whole configuration is not completely determi-
nate. But suppose it known that the kinetic energy T can

be expressed as a homogeneous quadratic function of ab, d, sig’
only ; so that we may write

OT = (rb) W242 (bb p+... 3
(br), (d),... are functions of W, d,... only Nag:

We also suppose it known that (1) continues to hold good so
long as the only (generalezed) forces and impulses acting are of
types corresponding to

UW, dese. 5).

2. Suppose, now, that such impulses of these types were to

act on the system that yr, ¢,.. were all reduced to zero; the
expression for the kinetic energy would accordingly vanish,
and the system would be at rest. By supposing the last
operation to be reversed, we see that the motion at any instant
could be produced from rest by impulses of the types corre-

sponding to
aby by.» only... Ee can

3. Let 2, y, z be the Cartesian coordinates at time 7 of a
mass-element m referred to fixed axes, and let T be the kinetic
energy of the system at the same instant. Further, let A be
the “action” when the system moves without additional con-
straint from one configuration to another, and A+6A the
action when by workless constraints the path is slightly
modified, so that in place of the coordinates z, y, z we have
w+6e2, ytoy,z+6z. Then ft

SA ={Im(aéba + Ysy + 26z) | —[ Xm(ada + yoy + 262) |

: + aterm which necessarily vanishes; . . (4)
where [ | and {} denote the values of the quantities enclosed
at the beginning and end of the motion considered.

Suppose further that, both at the beginning and at the end,
the values of Wy, $,... are the same for the one motion as for

* Communicated by the Physical Society: read March 10, 1893.
+ Thomson and Tait’s ‘ Natural Philosophy,’ 2nd edit. Part I. § 327.

On Lagrange’s Equations of Motion. 491

the other, so that initially and finally dw, 5¢,... are all zero.
Jt does not follow that all the dx, dy, 5z’s are zero ; but

Lm( toa + ydy + 282)

is the so-called “ virtual moment” of the actual momenta in

the hypothetical displacement 62, dy, dz; that is, the virtual
moment, in the same displacement, of the impulse necessary

to produce the actual motion from rest. In virtue of °),
therefore, and of the initial and final vanishing of dy, d¢,..

he see that the bracketed terms of (4) must both be zero ;
ence

The inerement 5A vanishes and A has a stationary value for
all worklessly effected variations of path which leave the
initial and final values of Ww, ¢,.... unaltered. . (3)

4. Lagrange’s equations for the coordinates yp, $,... may
now be written down at once, since the investigation of
Thomson and Tait* becomes applicable to the present case
without modification. It will be noticed that in their equa-
tions (10) and (10)%, § 327, the sign of OV/d¥ should be
reversed.

We have thus a perfectly general proof of the proposition :
If the kinetic energy of a material system can be expressed as a
homogeneous quadratic function of certain generalized velocities

wr, b,... only, the coefficients being functions of Wr, b, ... only,
and if ifs remains always true so long as the only forces and
impulses acting are of types corresponding to Ww, h,..., the
equations of motion for the coordinates Yr, d,... may be written
down from this expression for the energy, in accordance with
the Lagrangian rule. Provided only that the stated conditions
are satisfied, we need not consider whether the whole confiqura-
tzon zs determined by the values of vf, 25 On what is the
nature of the cqgnored coordinates. . . HAE | Suaaa tee ty (HAN)

5. Passing over the known spottenicd of this result to the
motion of solids through an irrotationally and acyclically
moving liquid, we come to the more general case of a perfo-
rated solid, with liquid irrotationally circulating through the
apertures. Take as coordinates any six 6, 6’,... which deter-
mine the position of the solid, together with y, y’,... equal
in number (m) to the apertures; each y being the volume
of liquid which, starting from a given configuration, has flowed
across some one of the m geometrical surfaces, required to
close the apertures, these surfaces being supposed to move
along with the solid.

Of course the coordinates 0, 6’,... v. x’,... are insufficient

* Loe. cit.

2M 2

492 Dr. C. V. Burton on the Motion of a

to determine the entire configuration of the system (including
the positions of all the particles of liquid); but we shall see
immediately how, in virtue of the proposition (A), Lagrange’s
equations may be written down.

6. Since an increment dy in one of the coordinates y is the
volume of liquid which flows across a barrier-surface (1. é.,
which flows through an aperture relatively to the solid), the
generalized force corresponding to y must be conceived of as
a uniform pressure exerted over the said geometrical surface,
by means of some immaterial mechanism attached to the solid;
while the impulse corresponding to y is of course a uniform
impulsive pressure applied in the same manner. [rom hydro-
dynamical considerations we know that the measure of such an
impulsive pressure is pdx, where p is the density of the fluid,
and 6« the change produced in the circulation through the
corresponding aperture.

Hence the impulses corresponding to y, y’,... are

Kp, p, . «2 2 aio

where x, «’,... are the circulations through the various
apertures.
7. Now when the motion of the liquid is irrotational, we
have
T =a homogeneous quadratic function of 0, 0’,...«,«’...
only ; coefficients functions of 4, 6’... only;

X,X ++. = homogeneous linear functions of 6, 6’,...
x, «',... only ; coefficients functions of 6, 6’,... only.

Since the y’s are equal in number to the «’s, let us suppose
the last-written system of linear equations to be solved for
the «’s in terms of the ¥’s ; we then have

x, ’,...= homogeneous linear functions of 6, 6’,... XX’; only.
coefficients functions of 0, 0’,... only.

Substituting in the expression for T we get

T = a homogeneous quadratic function of 6, Oa ¥, x, .. only;
coefficients functions of 0, 0’,... only.

This, then, remains true so long as the motion of the liquid is
irrotational; in other words, so long as the only forces and
impulses acting are of types corresponding to 6, 6’,... (since
these are applied to the solid), y,7’,... (since these are
uniform over the barriers, by § 6).

If we identify Wy, $,... with the coordinates 0,0’,...4,%',--.
of the present example, we see that the proposition (A) of § 4
is immediately applicable to this case. We may therefore

oe.

Perforated Solid in a Liquid. 493

ignore all other coordinates, and from the kinetic energy

expressed as a function of 0, 0’,...y, x’,... write down the
Lagrangian equations for 0,6’,... and, if we wish, for y, x’,...
also. These latter, however, are less directly intelligible,
since in general they involve finite pressures continuously
acting over geometrical surfaces drawn through the liquid.

8. If we wish to picture the application of the principle of
least action (§ 3) to the present case, we may proceed as
follows: —Let the system start from the configuration (1.)
and move without additional constraint or influence to the
configuration (II.). Then let it start again from the confi-
guration (1.) with the same velocities as before, and durin
the motion let infinitesimal additional forces act on the solid,

_while infinitesimal pressures, uniform over each barrier-

surface, are impressed on the liquid ; the total rate at which
the additional influences do work being at each instant zero.
Further, let the additional influences be so adjusted that the
system, after following a slightly different path, passes through
a configuration such that 0, 6’,... x, x’,... are all the same
as for (II.). Then, to pass from the configuration (II.) to the
present configuration requires no displacement of the solid,
and only such displacement of the liquid that the total volume
which crosses any barrier-surface is zero. In such a change
of configuration impulses of the types 0, 6',... y, x’,... would
have no “virtual moment,” just as forces applied to the solid
and uniform pressures applied to the barrier-surfaces would
give rise to no virtual work. aia

9. At this stage it will be convenient to replace 6, 6',...

by the components u,v, w of linear velocity and p, g, r of

angular velocity, which determine the instantaneous motion
of the solid along and about axes fixed in itself. The Lagran-
gian equations for the six coordinates 0, 6’,... must accord-
ingly be replaced by the forms suitable to moving axes. The
expression for the energy in terms of the velocities now
becomes a homogeneous quadratic function of w, v,; w, p, 9; 7;

¥, x',... in which all the coefficients are known to be
constants.

Let us apply the method due to Routh*, and modzfy this
function with respect to the coordinates y, y',... If T be the
value of the kinetic energy in terms of the velocities alone, the
modified function (@.e. the kinetic part of Routh’s modified
Lagrangian function)

Ce a = T—Kpy—x'py! — nat CO)

* Rigid Dynamics,’ vol. i, chap. viii.

494 Dr. C. V. Burton on the Motion of a

from (6). Itis further known that the whole energy of the
system

=H-+K, . . =o!

where Eis a function of u..., p..., only, and K is a function
of the momenta xp only. Suppose, now, that the solid were
brought to rest by forces applied to it alone: HE would vanish
along with u, v, w, p, g, 7, while the circulations «, and con-
sequently also K, would remain unaltered. The generalized

velocities x, y',... would in general have changed, becoming,

let us suppose x%, Xo,--- and the kinetic energy would
accordingly have become

K=Lpyy ti pyl + ...): 2a re
Now let

V=NVotX V=NItx' ~ . » . . (0)

so that each x1 is that part of the flux of liquid (volume per
unit time) which takes place across a barrier-surface owing to
the motion of the solid itself.

Having regard to (8), (9), and (10) our equation (7) for
T’ becomes
T’=(H+K)—2K—x«pyi—epy. . . . (1d)
Let us write for the velocity-potential of the acyclze motion
P=ud,+ vd, + wh, + ph, +qP, +7, + - (12)
and for the value of x, across the barrier-surface « we have
¥1 =\\{% —[ul+vm+ wnt p(ry—mz)
+ 9(lz—nz) +r(ma—ly)] bdo, peters ke
where 2, ¥, z are the coordinates of the element do and 1, m,n
are the dircction-cosines of its normal y, all referred to the

system of axes fixed in the solid. From (12) and (18) sub-
stitute in (11); thus

T’=E-K+ uSap|| [— ono + similar terms in v, w,

+ pnp | (ny —mz— oer \aa +similar terms in g, 7, . (14)

where the summation refers to the m barriers.
_ Remembering (8) it will be seen that T’ is now expressed
in the proper form, namely as a function of u, », w, Ps, 7, and

Perforated Solid in a Liquid. 495

the momenta xp, «’p,... only. By means of the relations

-
Be je ae ne

= Oe es

dap dv "aw "dg ©! a
the equations of motion of the solid can at once be written
down. X,..., L,..., are of course impressed force-and couple-
constituents.

10. Since the kinetic energy due to any number of per-
forated solids, moving in circulating liquid, can be divided
into two parts, of which one is a function of the component
velocities of the solids alone, and the other a function of the
circulation-momenta alone, the above method may obviously be
extended ; in fact a slight change in (14) will-render it at
once applicable to the more general case. We shall have,
evidently,

VY=H-K+ Sniep {| (1 oo a0 +similar terms in v, w,

Ze SpBep| | (ny—me— oo ria+ similar terms in g, 7, (15)

where H is still the energy due to the motion of the solids and
the acyclic motion of the liquid, and K the energy due to the
circulations. In each barrier-term the first } denotes sum-
mation with respect to all the solids, and for each u or p, &c.,
the second > denotes summation with respect to all the barriers
of the system.

These hydrodynamical results are not new, but the method
of proof is in some respects different from anything that has
yet been given, and will, I hope, be found intelligible and fairly
simple. In an admirable memoir, just communicated to the
Physical Society, Mr. Bryan has given a direct hydrodynamical
proof of the equations holding good for the motion of the
system in question ; but it seemed to me also desirable that
the problem should be rigorously treated by the method of
generalized coordinates, avoiding any assumption as to the
impulse of the cyclic motion, and proceeding entirely from the
principles established by Lagrange, and extended by Hamilton,
Routh, and Hayward.

When this paper was in proof it contained some remarks
on the ignoration of coordinates, as treated in Thomson and
Tait’s ‘ Natural Philosophy’*. Calling y, x’,... the inde-

* Part I. § 319, example G.

496 Mr. A. B. Basset on the Finite

pendent coordinates which, together with Wy, ¢,... determine
the whole configuration of the system in §§ ],..., it was
suggested that, in hydrodynamical and kindred applications,
there was a difficulty in proving that OT/dx, dT/dx’,---
were all zero.

But the difficulty, if indeed it should exist, is easily removed.
For since the actual motion at any instant could be generated
from rest by impulses of types corresponding to W, ?,... only,
we have throughout the motion

olfoxy—0, dT/ox'=0,233
and by the Lagrangian equations for y, y’,..., since all the
generalized forces are of types corresponding to W, @¢,...,
we get

egtyor dol. al

=e. a — > — =, =9,...
dt ox Ox bE ON 2 HOM :
whence
or or
—— =(), — =0 =e sie
Ox Oe

L. Note on the Finite Bending of Thin Shells.
By A. B. Basset, IA., F RS

ie HEN a thin shell of any form is bent in any manner,

the most convenient way of obtaining the equations of
equilibrium is to consider the stresses which act on a small
element of the shell bounded by four lines of curvature on the
deformed middle surface. If OAD B be a small curvilinear

Fig. 1.
Cc

rectangle bounded by the four lines of curvature OA,

AD, DB, and BO, the stresses across the section A D (as

pointed out in my previous papers{) consist of the following
* Communicated by the Author.

+ Proc. Lond. Math. Soe. vol. xxi. pp. 33 and 53; Phil. Trans. 1890,
p. 433.

Bending of Thin Shells. 497

quantities, viz.:

T, = a tension across A D parallel to OA;

M,= a tangential shearing-stress along A D;

No =a normal shearing-stress parallel to OC;

G,= a flexural couple from C to A, whose axis is parallel
to A Ds

ya torsional couple from B to C, whose axis is parallel
to OA.

Similarly the stresses which act across the section BD
consist of :—

T, = a tension across B D parallel to OB;

M,= a tangential shearing-stress along B D:

N, = a normal shearing-stress parallel to O Ol;

G, = a flexural couple from B to C, whose axis is parallel
to BD;

l= (cs torsional couple from C to A, whose axis is parallel

to O B.

By resolving the stresses and bodily forces (such as gravity
and the like), which act upon the element, parallel to the axes
OA, OB, and OC, and by taking moments about these lines,
we obtain the six equations of equilibrium of the element ;
but as these six equations connect ten unknown quantities,
namely the ten stresses which act across the sides of the
element, they are insufficient for the solution of the problem.

2. In the case of a bell, or of a railway bridge which is
thrown into a state of oscillation by a passing train, the
displacements are all small quantities, and under these cir-
cumstances the ten sectional stresses can be expressed in
terms of the displacements of a point on the middle surface
and their differential coefficients ; and owing to the fact that
these displacements are small, we may neglect their squares
and products when determining the stresses, and their cubes
&c. when determining the potential energy due to strain.
There is, however, another class of problems of considerable
importance in which the deformation is finite instead of
infinitesimal ; and to such problems the theory of thin shells
is inapplicable.

3. An ordinary clock-spring is one of the most familiar
examples of the finite bending of a thin plate or shell. Such
springs consist of a naturally curved steel strip whose thick-
ness is somewhere about one thirtieth of an inch, and whose
breadth is from an eighth to a quarter of an inch according
to the size of the clock ; and when the clock is wound up
an amount of bending takes place which it would be unsate
to treat as infinitesimal. ‘The hair-spring of a watch also

498 Mr. A. B. Basset on the Finite

involves a case of finite bending; but as its cross section is
approximately square, the theory of the bending of wires*
would be more applicable. Similar examples, such as spring
balances and other mechanical appliances where springs are
employed, will readily suggest themselves; and the question
whether the theory of wires or the theory of thin shells is
most appropriate depends upon the nature of the spring. If
the cross section does not differ much from a circle or a
square, the former theory would appear to be the most applic-
able; if, on the other hand, the breadth of the spring is
considerable compared with its thickness, it would be better
to regard it as a thin shell.

When the natural form of a spring is a plane curve, and
the spring is bent into another plane curve, the problem may
be completely solved by the methods explained in chapter viil.
of my ‘ Elementary Treatise on Hydrodynamics and Sound.’
The mathematical treatment is the same whether the spring
be regarded as a wire or as a thin strip of metal like a clock-
spring; the only difference being that the flexural rigidity is
different in the two cases. If, however, a piece of clock-
spring is twisted as well as bent, or a thin plate or shell is
deformed in a finite manner, the solution of the problem pre-
sents difficulties of a rather formidable character.

4, Whenever the deformation is finite, the displacements of
a point on the middle surface are not small quantities whose
squares and higher powers may be neglected, and therefore it
is useless to attempt to express the stresses in terms of these
quantities; but since any deformation involves a change in
the values of certain geometrical quantities, such as the cur-
vature and torsion of certain lines drawn on the middle surface,
the most appropriate course to pursue would be to endeavour
to express the stresses in terms of such geometrical quantities.

There is one class of problems which can often be solved
without much difficulty, which occurs when a plane surface
is bent without extension into a developable surface ; or when
a developable surface is bent into a plane, or into some other
developable surface such that the lines of curvature on the
old surface are lines of curvature on the deformed surface.
This method can generally be applied when a plane plate is
bent into a conical or cylindrical surface ; but it could not be
applied in the case.of a right circular cone which is bent into
a cone whose lines of curvature are not identical with those
of the former cone.

The success of this method, in cases where it can be applied,
depends upon the circumstance that the flexural couples Gy,

* See Proc. Lond. Math. Soc. vol. xxiii. p. 105.

es

Bending of Thin Shells. 499

G, can be expressed in terms of the changes of curvature,
and also that in the special cases alluded to a sufficient
number of the ten stresses are zero to enable the remainder
to be determined by means of the general equations of equi-
librium.

5. We shall now determine these couples, using Thomson
and Tait’s notation for stresses and elastic constants, and
Love’s notation for strains. Fie o

Let O A, OB be two lines of curvature on ‘
the middle surface of the undeformed shell ;
O,, O, the centres of principal curvature ;
let oa, ob be the curves in which the
planes OA O,, OBO, meet any layer of
the shell. Let p,, p. be the principal radii
of curvature at O, let Oo=7, and let 2h be
the thickness of the shell. Also let accented
letters denote the strained positions of the
various points.

If P denote the traction along oa, and R
the normal traction along Oo,

P=(m+n)o,+ (m—n) (a, +03)
=%n{(1+H)o,+Ho,}+EHR,. . . . (1)

where |
EH=(m—n)/(m+n).
Now
__ dal —oa
and ai ee
OG ENS | SUI ee ne eee
OA Times OW aa oe n' =(1 +43).

Since we neglect the extension of the middle surface,

O'A'=OA, whence
Uh
pee UPL =m (— ~) 4 1

1+%/p; P1 Pi Pi
Tira! 1 n R
=n ( et a + pi! | magn Mates) | e e (2)
Similarly,
ae seg yf RK 1 "
a=n(o at pe! | men ~Blaite) f° e (3)

The value of Gy is
h
G.=| Pains, la tetidiees @ (/(4)
—h

500 Mr. A. B. Basset on the Finite

Now, according to the fundamental hypothesis of my
former papers it follows that, provided there is no eaternal
pressure, R must be a quadratic function of h and n, and con-
sequently the retention of R will lead on integration to
terms in Ge» of a higher order than h?, which are to be
neglected, since the solution we require is an approximate
one which does not contain higher powers of h than the cube.
Accordingly if we substitute the values of o,, a2 from (2) and
(3) in (1), and the resulting value of P in (4) and integrate,
we shall obtain |

= 4 3 f = a a (= as ~) :
Similarly,

h
G)= =) Qn dn,
—h
which gives

an oe ee (i 2 ,
a git {0+ (S ele ae ae
Equations which are equivalent to (5) and (6) have been
given by more than one writer on elasticity ; but attention
has not always been called to the fact that they depend upon
the express conditions that the surfaces of the shell are free
normal pressures, and also that the extension of the middle
surface may be neglected.
When a plane plate is bent into a developable surface
Pi=p,=; also one of the quantities p,', or ps! (say pe’) is
infinite ; whence (5) and (6) become

Gy= $nl3(1-+E) /p/! >
Gy = —$nh*H/p,' }

where G, is the couple about a generating line of the develop-
able.

Since the extension of the middle surface is neglected,
equations (5) and (6) would not apply to the case of a plane
plate deformed into a surface such as a portion of a sphere.

7. Asan example of the preceding method, we shall con-
sider the case of a plane plate of thickness 2h, which is
bounded by two radii CA, CD, and two ares OB, AD of
concentric circles ; and we shall inquire whether it is possible
to bend this plate into a portion of a right circular cone in ~
which OA, BD are generators, and OB, AD are circular
sections.

We shall assume for trial that the bending may be effected
by means of tensions, normal shearing stresses, and flexural

Bending of Thin Shells. 001

couples applied to the edges ; so that the tangential shearing
stresses and the torsional couples are zero.

Fig. 3.

o)

B D

Let « be the semi-vertical angle of the cone, r the distance
of any point on OADB from ©, Then
pi =p =; p2=0; p/=r tana;
whence
| G,=4nh? Hr! cota,
Gy = —$nh3(1+ B)r— cota.

The equations of equilibrium are

d
qn (hit) T=,

a)

dT,
as, +N,cos a=0,
d dN
q,p Nz") sin «+ oat —T.,cosa=0, > (8)
dG,
AE + Ny sine=0,
d
£ (Gor) —Nor + Gy=0. |
Let
4nh3 (1 + E) cota=h,
then
Ci. —k/r,
whence
No=—hk/r*, N,=0,
whence

T,=4& tan a/72,
and therefore

A ktane
h= fie ee
, ?

where A is the constant of integration.
From these equations we see that all the stresses are per-

502 Prof. Angstrém on the Intensity of

fectly determinate except T,. If CO=a, CA=8, and T,, To
denote the tensions along OB, AD, we have

7 A ktan @ |
Za ae :
PA hime (? + | al eee)
Cee: ae

from which it appears that either T, or T, may, if we please,
be made zero, provided the other be properly determined.

The above results would also apply to a belt of a complete
cone, bounded by two circular sections.

LI. Bolometric Investigations on the Intensity of Radiation
by Rarefied Gases under the Influence of Electric Discharge.
By Kyvr Ayestrou*.

()* E of the peculiar difficulties attending the quantitative
determination of the amount of energy radiated by gases
in vacuum-tubes is the extreme feebleness of its intensity.
In his recent work in this field, executed at the Hochschule
at Stockholm, Prof. Angstrém attacked the problem by the
bolometric method, which, although leaving something to be
desired as regards sensitiveness, led to some important results.
Another obstacle lay in the well-known difficulty of obtaining
the gases in a state of such purity that the spectrum exhibited
by the discharge through them in a vacuum-tube showed no
foreign admixture, such as the carbon-bands seen whenever
grease is used for joining surfaces, or where the flame touches
in the process of soldering.

The discharge-tube used for the most careful experiments
was thoroughly cleaned after soldering-in two electrometer-
terminals, and attaching two short lengths of tubing at right
angles near each end. The latter were to receive the elec-
trodes, whose construction required particular care. Into a
short capillary tube a piece of platinum wire was introduced
from one end and a piece of thoroughly cleaned aluminium
wire from the other. The tube was then heated so as to form
an air-tight junction between the two wires, and was then
fitted into a glass plate. After removing all grease the tube
covering the aluminium wire was cut off, so that the latter
acted as a perfectly clean electrode, and the glass plate hold-
ing it was fitted on to the short tube attached to the discharge-

* Abstract from Wiedemann’s Annalen, No. 3, 1893, by E. E. Fournier
d’Albe, B.Sc., Royal College of Science.

Radiation by Rarefied Gases. 503

tube. The joints were made air-tight by means of sodium
silicate, which proved to be a highly useful cement, and did
not give rise to any impurities. Short lengths of tubing
containing mercury were placed round the platinum wires to
convey the current to the electrodes.

The behaviour of four gases only was investigated, viz.
hydrogen, oxygen, nitrogen, and carbonic oxide. Hydrogen
and oxygen were prepared by electrolysis of pure newly-
distilled water acidulated with phosphoric acid. The nitrogen
was obtained by passing pure air over heated copper-turnings
reduced by hydrogen. Carbonic oxide was prepared by the
reaction of sulphuric and oxalic acids, and purified by passing
through caustic potash. In producing these gases all rubber
tubes were dispensed with, and the different parts of the
generating apparatus were soldered together.

The discharge-tube was connected through a Kundt glass
spring and a set of cleaning-tubes to the tube used for intro-
ducing the gas, a mercury-valve, and the air-pump. © The
mercury-valve consisted of a U-tube communicating at the
bottom with a long tube full of mercury. By varying the
level of the mercury by means of a reservoir the valve could
be opened and closed. The tube for introducing the gases
corresponded in the main to Cornu’s arrangement. A vertical
glass tube is filled with mercury whose level can be varied by
means of a reservoir connected through a flexible tube, as in
the case of the mercury-valve. At a point some distance
from the bottom is attached a capillary U-tube, the end of
which, in the process of filling, is introduced into a small
reservoir containing the gas. Lowering the mercury esta-
blishes a connexion with the discharge-tube through the
drying-tubes, and on raising the level the gas is shut off
from the atmosphere. |

The current was furnished by a battery of 800 small Planté
accumulators, regulated by means of a liquid resistance con-
sisting of cadmium iodide dissolved in amyl alcohol, and
measured by a dead-beat reflecting-galvanometer. The fall
of potential in the discharge-tube was measured by a Mascart
quadrant-electrometer.

The bolometer used for the experiments consisted of two
gratings cut out of tinfoil mounted in ebonite frames. These
frames were placed one behind the other in a tube with
double walls, the posterior one being protected from radiation
by a small double screen. Four diaphragms were mounted
in the tube in front of the gratings, to diminish air-currents.
The grating absorbing the radiation occupied a circular space
of 16 millim. diameter. It was blackened by precipitated

504 Prof. Angstrém on the Intensity of

platinum and smoke. The four branches of the Wheatstone-
bridge arrangement, of which the gratings formed two, had
each a resistance of about 5 ohms. In order to be able to
rapidly test the sensitiveness of the combination, a constant
resistance was introduced as a secondary circuit into one of
the branches. The opening or closing of this circuit usually
made a difference of 75 scale-divisions. If not, the reading
was reduced to that standard sensitiveness.

The bolometer was separated from the end of the discharge-
tube by a double screen with a perforation, inside which was
suspended a small screen. This was quickly pulled up to
expose the bolometer. The strength of current through the
discharge-tube was measured by the galvanometer, the diffe-
rence of potential within it by the electrometer, and the
deflexion of the galvanometer in the bolometer circuit was
read from minute to minute. ‘The latter gradually increased,
owing to the warming of the walls of the discharge-tube. By
suddenly breaking the current and again observing the
bolometer the radiation of the tube-walls was eliminated.
Another method of elimination was by interposing a plate of
alum about 4 millim. thick, which totally absorbed the radia-
tion from the glass. Another source of error was the reflexion
from the walls of the tube. The end of the tube opposite the
bolometer was closed by a plane-parallel plate of rock-salt.
This occasioned a loss by reflexion, whereas the other surfaces
entailed a gain. Both were corrected by introducing a small
copper box heated by steam circulation into a tube of the
same construction as the discharge-tube, observing the
bolometer deflexions, and repeating with the box alone.

Prof. Angstrém states his main results as follows :—

1. For a given gas and a given pressure the radiation of
the positive light is proportional to the intensity of the electric
current.

2. For a given gas and pressure the composition of the
radiation is constant and independent of the strength of
current.

3. On increasing the pressure of the gas, the total radiation
for a given strength of current increases as a rule, slowly at
low, more rapidly at high pressures. At the same time the
composition of the radiation changes, inasmuch as the ratio
of the intensity of the shorter waves to the total radiation
decreases. Thus the distribution of the intensity in the
spectrum changes in such a manner that with diminishing
pressure the intensity of radiation increases for the shorter

wave-lengths.
4, The ratio between the intensity of total radiation and

Radiation by Rarefied Gases. 505

the current-work increases continuously with diminishing
pressure of gas.

5. The useful optical effect of the radiation (here given by
the ratio of the intensities of the radiation passing through
the alum plate and the total radiation respectively) is very
high for some of the gases at low pressure (about 90 per
cent. for nitrogen). But the useful optical effect of the
work spent is not very great (about 8 per cent. for nitrogen
of 0-1 millim. pressure).

6. The intensity of total radiation must be considered as a
secondary effect of the discharge, and depends upon the mole-
cular constitution of the gas.

7. Whatever views we hold concerning the nature of the
gaseous discharge, this investigation appears to confirm the
hypothesis of Hittorf, E. Wiedemann, and others, that the
radiation is not a pure function of the temperature of the
gases, but must be regarded as anomalous (“ irregular,”
“* luminescence ”’),

If we call “irregular” a radiation in which the spectro-
scopic distribution of the energy is anomalous, there are
certain facts observed by Prof. Angstrém which lead to the
conclusion that the radiation in question is irregular. The
radiation did not show any relation to the absorptive power
of the gas at ordinary temperatures. Again, the radiation,—
which in nitrogen at 2 millim. pressure is still rich in dark
rays,—rapidly changes in quality when the pressure de-
creases, and at 1 millim. consists almost exclusively of light
radiation. Prof. Angstrém supposes that the radiation of the
gas during electric discharge consists of two parts, one of
them regular, the other irregular. With decreasing pressure
the former decreases, whilst the irregular radiation increases in
proportion as the motions are less obstructed by the mass of
the gas. At constant pressure a certain portion of the energy
in each molecule is converted into radiation ; as the strength
of the current increases, the number of active molecules, and
hence also the radiation, increases in the same proportion as
the current. The number of active molecules being relatively
small, the damping effect of the rest may be taken as constant,
and the composition of the radiation remains practically
unaltered as the current increases. On increasing the pres-
sure, however, the damping effect changes, the anomalous
dispersion is more easily transfermed into a normal one, and
the radiation becomes richer in infra-red rays. A greater
proportion of the energy supplied is spent in heating, and
for the same current-work the total radiation decreases with
increasing pressure.

Phil. Mag. 8. 5. Vol. 35. No. 217. June 1893. 2N

506 Mr. E. C. Rimington on Luminous

But in view of the difficulties of the investigation, the
paucity of available material, and the approximate nature of
the results in this almost unexplored field, no final decision
can as yet be arrived at. A tabulation and a graphic repre-
sentation of the results, with diagrams of the apparatus and a
full discussion of methods and corrections, will be found in
the original paper.

LIT. Luminous Discharges in Electrodeless Vacuum-Tubes.
By HE. C. Rimineron*.

See reading a paper in conjunction with Mr. E. W.

Smith on November 25th, 1892, before this Society, on
“ Experiments in Electric and Magnetic Fields, Constant and
Varying,” the Author’s attention has been drawn to a paper
contributed by Mr. Tesla to the ‘ Hlectrical Hngineer’ of
New York, July 1st, 1891, in which the luminous ring-
shaped discharge obtained when a Leyden jar is discharged
through a coil of wire surrounding an exhausted bulb is
attributed to the electrostatic action of the surrounding wire,
and not to the electric stress set up in the rarefied dielectric
in consequence of the rapidly oscillating magnetic induction
through the bulb.

As one experimental proof of this assertion Mr. Tesla
gives the following experiment :—“ An ordinary lamp-bulb
was surrounded by one or two turns of thick copper wire,
and a luminous circle excited by discharging the jar through
this primary. The lamp-bulb was provided with a tinfoil
coating on the side opposite to the primary, and each time
the tinfoil coating was connected to the ground, or to a large
object, the luminosity of the circle was
considerably increased.”’

The author repeated this experi-
ment with two Leyden jars arranged
as in fig. 1, and found that when the
spark-gap was sufficiently large to
produce a bright ring when the tin-
foil was not connected to earth, doing
so produced no noticeable difference
in the brilliancy ; but that, if the
discharge were faint, it was ren-
rendered considerably brighter on
making the earth connexion. Better
results were, however, obtained on

* Communicated by the Physical Society: read April 28, 1893.
+ Ante, p. 98.

yy Bie

Discharges in Electrodeless Vacuum- Tubes. WENO

connecting the tinfoil to either of the outside coatings, A or
B, of the jars instead of to earth. This result led the author
to try a series of experiments to endeavour to determine
the cause of the effect, of which the typical ones are here given.
Hzperiment 1 (videfig. 2). A Fig. 2.

S

and B are the outside coatings
of a pair of Leyden jars (those
employed were about pint size).
Cand D two vertical and paral-
lel metal plates, at a distance of
about one foot from the jars. The
spark-gap, 8, is adjusted by a
screw, so that the spark-length
can be varied by small amounts
when necessary. A single turn
of wire, a , encloses an exhausted
bulb, and its ends are connected
to A and B, as shown in the
figure, so that a the part nearest
to C is connected to A, and 6 to
B. Two loose wires, e and /, are
also connected to A and B.

The spark-gap is now shortened until there is just no
luminous ring in the bulb.

The plates C and D are then connected to the outer
coatings A and B by means of the two loose wires, with the
following results :—

(1) Ato C. Bright ring.

(2) Bto D. Bright ring.

(3) A to C and B to D simultaneously. Bright ring.

(4) A to D. ; :

(5) B to ©. ; No luminous ring.

(6) A to D and B to C.

Expt. 2.—The wire turn ab is removed from the bulb,
given a half twist, and then replaced ; so that a is now
nearest to D, and 6 to C. Plates not connected, no luminous
ring.

(1) Ato C.

(2) B to D. fs luminous ring.

(3) A to C and B to D.

(4) A to D.

(5) B to C. trig ring.

(6) A to D and B to C.

Hapt. 3.—Arranged as in Expt. 1, case (1) or (2). Cis
then connected to D, and the ring becomes less bright.

Expt. 4.—Arranged as in Expt. 1, case (1). © and D
2N 2

ee a ma WS

PT ee

OY oa

jae x EE ate ok 2. =
es aso ~

508 Mr. E. C. Rimington on Luminous

connected. On approaching C to the bulb, ring becomes
brighter.

On approaching D less bright.

If arranged as Expt. 1, case (2), the reverse happens.

All the above four experiments give the same effects if the
turn of wire be larger than the bulb, as in fig. 3, only a longer
spark-gap has to be used.

Eept. 5—A single turn of
wire (fig. 3), a 6, larger than
the bulbis employed, and between
the bulb and the ring a semicir-
cular strip of tinfoil or metal T is
placed. The wire is connected as
in Expt. 1. The spark-gap is
arranged to give no ring. Con-
necting T to B bright ring, T
to Anoring. The reverse hap-
pens if the tinfoil is placed in
position T’ as shown by the dotted
line.

Haupt. 6.—A piece of gutta-
percha covered wire is bent into
shapes shown in figs. 4 and 5. On placing either of these
over bulb as in fig. 6, a figure of eight-shaped luminous

Fig. 38.

Fig. 4.
Z 6

h c

discharge is obtained, and there is no noticeable difference
between the two.

Fig. 5.
7 6

h c

Expt. 7—Putting the wire (fig. 4) on bulb as in fig. 7, a

Discharges in Electrodeless Vacuum- Tubes. 509

single broad band-ring is obtained, as the two turns will help
one another with respect to magnetizing effect.

Doing the same with the wire (fig. 5) a discharge is
obtained shaped like the sector of an orange, as shown by the
dotted lines, fig. 7.

Fig. 6. Fig. 7.

Expt. 8.—Bending a wire as shown in fig. 8, and placing a
bulb in the loop 6 ¢, there is no effect even with a long spark-
gap, although the potential difference between the sides

Fig. 8.

cand } would be much greater than in the case of a single
turn.

Putting a bulb in the loop, be, of fig. 4 at once gives a
bright ring.

a

510 Mr. Ki. C. Rimington on Luminous

Hxperiments 6, 7, and 8 seem to show that ring, or other
shaped, sharp luminous discharges can only be obtained with
the wire so wound as to give magnetic induction through the
bulb, while the first five experiments show that an electro-
static field in the bulb may help the effect. ‘The theory the
author has come to after consideration of the above and
other experiments is:—That if the H.M.F. due to rate of
change of magnetic induction acting in the dielectric of
rarefied gas be insufficient to break it down and produce a
luminous discharge (owing to the spark-gap being too short),
the electrostatic field between the plates C and D, or between
one of the plates and part of the wire, if correctly timed with
respect to the rate of change of current in the wire, will
commence the breakdown of the gas, thus allowing a less
H.M.F. due to the magnetic induction to complete it.

To put this to the test, a single turn of wire was put round
a bulb and the spark-gap adjusted so as to give a very faint
or no luminous ring ; on the top of the bulb was laid a piece
of tinfoil connected to one pole of a + in. spark induction-
coil ; when the coil is worked the tube is filled with a faint
glow: if now the Leyden jars are charged and discharged
there will be sometimes a ring in the bulb which will be
occasionally quite bright. The reason it cannot be always
bright is of course that the discharges of the induction-coil
are periodic, as are also those of the jars, and it is only when
the two are properly timed (i.e. the P.D. due to the coil
coming either just before or simultaneously with the spark)
that there will be a bright ring.

This experiment seems to settle the question and show
conclusively that a properly timed electric stress in the bulb
due to an electrostatic field will allow an E.M.F. due to the
alternating current in the wire to produce a breakdown of
the rarefied gas, which the latter is too small to effect without
the aid of the former™*.

In Expt. 1, when A and C are connected this field will
exist between © and 0 the side of the turn of wire remote
from C, and must therefore pass through the bulb. When A

* To prevent misconception, it had better be definitely stated that this
electrostatic stress does not necessarily act in the same direction as the
E.M.F. due to the rate of change of magnetic induction. In experiments
(1) to (5) the direction of the former will be through the bulb from side
to side, while that of the latter is a circle coplanar with the wire. As
the discharge in a gas is of a nature more or less electrolytic, being
accompanied by the splitting up of the molecules, it seems reasonable to
suppose that anything which increases the number of dissociated molecules
will enable a smaller stress to produce a breakdown in the form of a
luminous discharge.

Discharges in EHlectrodeless Vacuum- Tubes. bit

is connected to D, as the strongest field is between 6 and D,
where thé P.D. is greatest, it does not pass through the bulb ;
in fact the field in the bulb willsimply be that due to the P.D.
between a and 0, or the same as it is if the wires e and / are
disconnected. ‘The results of Experiments 2, 3, 4, and 5 are
also obviously explained by this theory.

To treat the subject mathematically. We have the well-
known equations for the discharge of a condenser :

Lo +Re=- = where K is the capacity,
and Pa dq
dt

Combining these,
&q , Rdg 1
see, © Kid

To obtain an oscillatory discharge 4L must be greater than

Oe
Putting a for == and b for ee emo 5 the solution
ig
pee wees oa ee
where @ =eun'| ~-) and @ is the initial charge.

This may be more conveniently written

p= Qe EFF os un,
where
ay) or tang=—+ = _ KR
ae) eee 4L—KR*

Eas i oe
If the oscillations are to be rapid, RP must be large compared
4

R2
to 42
Therefore 7 will be some small angle.

Instead of quantity we may write P.D. of the condenser,
or

ares)
5 Vee Va +P cos (e—n). ig ogee}

i oe

512 Mr. E. C. Rimington on Luminous

The current
C= dq — Q — ~p
ae biG Ol

Now the electric stress acting in the bulb is proportional to

et sin bt=

asindt.. . . (3)

de
the rate of change of current, or to — ;

“ile
and Oe TING Gi OS
——— Ss bt). scare C2
ee (asin bt + 6 cos Jt) (4)
The current itself will be a maximum or minimum when
de fe
ioe 3
?,é. when asin bt+b cos bt=0, :
or when a eee — Als tae :
a KR?

Therefore l¢=0, and is in general nearly equal tol 5

The maximum values of the current occur when
bi=0, 27+0, 474+, &e.,
and the minimum values when
bt=7r+6, 3874+0, 57+4+8, Ke.

This is shown in the curve (fig. 9), the points M,, M., M3,
&c., representing the maximum and minimum values of the

. 7
current. The distance O A represents 0, and A B= °) =P 9
It is now necessary to consider when the rate of change of

. ae A
the current is greatest. Ai will be a maximum or minimum
C4
2

when ne —(),
dt?

Now

iE V + he

a = ope (a? —L*) sin bt + 2ab cos bt} = 0.
Hence |

in a = 2. 2 RY Ka Sg
on 2L—-KR?

Let

2L—KIi?

y will be in general a small angle.

Discharges in Electrodeless Vacuum- Tubes. 513

The rate of change of current will be greatest (either a maxi-
mum or a minimum) when

bt=—y, w—-y, 27—y, Ke.

Obviously 0¢ cannot equal —y, so that the rate of change
of current is greatest for values 7—y, 27—y, d&c.; or at
points “44, M2, #3, &e. in the curve (fig. 9), and HF=y. If

Fig. 9.

R
ty,
Dotted curves are values of the exponential 77 ° 21

é =
Sc
Se Z
e

YA LUES OF CURRENT

M,, M,, M;, M, are the maximum values of the current. p,, m2, us are
the points where the rate of change of current is greatest.

the oscillations are to be very rapid KI? must be negligible
compared to 4L ; in which case

tan y= He

tan yn = Wo

we

also

he! Mr. E. C. Rimington on Luminous

and they are both very-small angles, hence y=2” approxi-
mately, or HEF =2AB.
When bt=7—y,

Ue

== ie
de vy e fy 25

we 6
or if the oscillations are very rapid,
de = eB ye
pee
If, however, ¢=0,
re
Cpe NU:

so that the greatest rate of change of current occurs at the
first instant of discharge, although this is not a mathematical
maximum.

HKiquation (4) may also be written

de _ V Ve+E
dt bL
n being the same angle as before.
It is now necessary to consider the values of the P.D.
between the outside coatings A and B of the Leyden jars.
Let / and r be the inductance and resistance of the coil
connected to the outer coatings, and L and R the same for
the whole circuit. Let v,—v,=« be the P.D. bevmeen the
outer coatings at any instant t. Then

e cos (bt-+9); ae)

Vice
c= e@ sin bt,

bL

and 2=0,—v. er +1,
dt
Ve, :
ware {(r+la) sin bt + lb cos bt}
Vee Dy Oey Seay Ea I
=a, V Pb +(r+ la)? cos (bial) ee
where ” ae
tan 7! = !
USER PGD

7! will be in general a small angle not very different from ;

Discharges in Electrodeless Vacuwm-Tubes. 515

and if : = nor the time-constant of the coil equals the time-

constant of the whole circuit,
; =~ =—2a,

a
., tang = j = tan n, or y' =n.

That is # is in phase with v the P.D. at the inner coatings of

the jars.
To find the maxima and minima of x we have

ee: ae [ {ar + l(a? —b7)} sin bt+ b(r + 2la) cos bt] =0.

ut b(r + 2la)
a tame = ar+Ua2—2)

_ (rL—Rl) VK(4L—KR)
S L(KRr +21)

= tano.

Then « has its greatest positive or negative values when
bi=5, +8, 27+56, Kc. Sis in general a small angle, and

is positive if

L l
ane
and negative if
he
(Pers
If eae ;
ar ae 60;

If = be not greater than : the first largest value of a will

occur at t=0, and as the rate of change of current is also
greatest at this instant the two will occur simultaneously.
The next greatest value of 2 occurs when

pees (itz 2 -),

th
and the next greatest rate of change of current when

bt=7 —¥.

Sa a ee

516 Mr. KH. C. Rimington on Luminous

6 will be less than y, if be nearly equal to so that the

de
dt’
but the value of z will not differ very much from its maximum

maximum value of x will occur after the maximum of

de . ; ; :
when a is A maximum®*. This bears out the results obtained

in experiments 1 and 2, though, of course, the electric field in
the bulb will be that due to the P.D. between one of the
plates, C or D, and the opposite side of the turn of wire, and
this will only be about half that between the outer coatings
A and B. Moreover, the phase of the potential of C will
not be quite the same as that of A, on account of the
inductance of the connecting wire e. Experiments 1 and 2
were, however, tried with the plates C and D, and the con-
necting wires removed, the turn of wire ab being moved so
as to bring either a or b nearest to A or to B, and the results

obtained were practically the same as those of experiments
1 and 2.

Effect of Size of Surs.

When different-sized Leyden jars are employed with the
same length of spark-gap the luminous ring is more brilliant

* The above investigation into the value of the P.D. between the
outer coatings will only give correctly the state of things when a steady
swing has been set up in the circuit; as evidently when ¢=0 the value
of w also equals zero, so that 2 must start in phase with the current; it
will, however, rapidly get out of phase with the latter, and finally be
nearly in quadrature with it, This is due to an initial wave starting
from the spark-gap which runs round the circuit. Possibly the value of
x can be empirically represented by one of the two subjoined formule :-—

AEN emerge
£= VPP (tla)? sin {(bt-+p)(1—e-P4)t,

Ne Veat = :
* w= Ty NPG (r-Hla)? sin {Bt + y (1—e-Pe)},

=

where P= = —yn', and p some constant. Dr. Lodge, in his researches on

the A'and B sparks, approximately represents the initial values of 2 by
the current multiplied by the impedance of the conductor 7, or makes

Veut
t= — (?b?-+r* sin bt.

The initial maximum of z will consequently roughly coincide with the
maximum of the current, or be near the point M, of fig. 9, and will thus
come about a quarter of a period before the second maximum rate of
change of current, point p, (fig. 9).

Discharges in Electrodeless Vacuum- Tubes. Dali

with larger jars. Now the E.M.F, acting in the rarefied gas,
and producing the breakdown of the same, is proportional to
de

di’
Also the greatest value of de ta first occurs is when ¢=0,

dt
and then
de V

a yk
and the next is for very rapid oscillations
VS as
Ai = ey 2 Ibg

So that the first value of the E.M.F. acting in the gas is
independent of the capacity, and the next and succeeding
values are less the greater the capacity.

The effect on the eye, however, of the luminous ring will
be the time-integral of the discharge or approximately depend
on |

The whole limits of ¢, viz., from 0 to «©, cannot be taken at

once, as < keeps reversing, and this reversal will not affect

the luminous discharge. Referring to the curve (fig. 9) it
will be seen that the first reversal must take place at M,, when
bt=80, and subsequent ones for values 7 +0, 277+ 0, KXc., of bt.
It is therefore necessary to take first the limits 6 and 0, then
a+6 and 6; 27+0 and r+40, and so on, alternately writing
the integrals plus and minus.

* de =e We eae “t sin Ot |
\ a = aL le sin b¢ | le sin bt

2r+0
+ ee sin ot | — &e.ad inf. :

7+
Remembering that

sin ( 7+0)=—sin 0,
sin (27+0)= sin @,

sin (37 + 0) = —sin 9, and so on,

518 Mr. E. C. Rimington on Luminous

this gives
” de ae a) Gero) © (On + 6)
i, a = zy, sine Ga + e2 +e6 +e. \,

The series in the bracket is a geometrical progression, in

a
which the constant factor is e@"; and, since a is negative,
this is less than unity.

Hence
“6
* dc Gps 2V sin 0 eb
nade 6L 7
and
tan 0= ee oie or sin@= We KR’,
also
4L—KR sin @
— — 4/7 kale
e tenner age
re) => 46
{ eo = 2V oe aad
» at a
1—e

RY ee) =
eV W—=KR?—e J 4L—KR?

et Ogg Sa _=eand ra /_KRE_ =
4L— — 41,--KR?

Then the denominator =e*—e?-9, and

ealtet 5 + 3 ea

2ay y? 3u7y

ig
omer ih ia

oa B - + &e.,

. 2xy eo 3n*y __ 3ay? y
oot tt ee. 38>

+ terms of the 4th, 5th, &. powers.

Discharges in Electrodeless Vacuum- Tubes. 519

Now wz and y will in general be small fractions, since KR?
is usually much less than 4L.
If the oscillations are very rapid, @ is very nearly equal to

y Hence y=2x approximately. Then e’—e*’ becomes
9a ig
6 = 2a (1 ae =) approx.

Therefore the time-integral

) ap prox.,

av4/8 = 4/*(1- =)
~ 2e(14 ©) =) e
and

c= ty / KR? aoe Ee sien
meoN/ (bk 4 eke

so time-inte or

approx.

mw RK
au (I~ “55,

Now from this it is seen that the effect of increasing the
capacity would be to slightly diminish the time-integral, and
consequently probably make the brillianey of the laminous
discharge less, if it were not that increasing the capacity
diminishes the real resistance of the circuit, since it makes
the oscillations slower, and the resistance R for copper for
rapid oscillations approximately equals /46/ Ry; where / is
the length of the wire, and R, its resistance for steady cur-

approximately.

rents. Now b= VEL

- Therefore

so that the time-integral is very roughly proportional to the
fourth root of capacity.

There is also another reason why larger jars might produce
a brighter discharge, even though the ae integr al were less.
With larger jars ines time foleen for the amplitude of the cur-
rent to sink to a value at which it becomes insignificant will

LR ——

520 Mr. E. C. Rimington on Luminous

be longer than in the case of small ones. Now, as the initial
value of 2 is the same whatever the size of the jars, the after

values (although their time-integral is less and their actual
values less also) last longer in the case of larger jars.
When the breakdown of the dielectric of rarefied gas is once

ees See de
begun by the initial ai the values of 7 necessary to keep it

up may probably be very much less, and consequently the

smaller values of = lasting longer, as given by the larger

jars, may produce a luminous discharge more brilliant to the

eye than the larger values of = lasting a shorter time, as given

by the smaller jars.

The actual results obtained with a ring of four turns of wire
containiny an exhausted bulb about 24 inches in diameter
were that the differences in brilliancy, obtained by using

half-gallon jars, pint jars, or very small jars made from spe-
cimen glasses, were not so very great.

Other Effects. Apparently unclosed Discharges.

A closed luminous discharge is not the only one that can
be obtained. Mr. Tesla, in 1891, pointed out that by wrap-
ping a wire round an exhausted tube so as to form a coarse-
pitched spiral, a luminous spiral discharge is obtained. He
was apparently only able to obtain a very feebly luminous
spiral, but the author has succeeded in getting one quite as

brilliant as in the case of the ring-shaped discharge obtained,
with a bulb.

Fig. 10.

In fig. 10 two half-gallon jars have their outer coatings
connected by a wire, A B, bent as shown in the figure. Over

J *~

Discharges in WB icopradeless Vacuum- Tubes. Sb DY

-the wire is laid an exhausted tube, C, with a tinfoil cap*, T,

at one end; T is connected to the outer coating of the jar

nearest to it. The object of this is to utilize the electrostatic

effect and make the tube more sensitive to breakdown by the

electromagnetic one. When the jars discharge, a straight

luminous band is observed in the tube directly over A B.
If the tube C be now moved towards the jars, even by a
very small amount, a closed circuit discharge will be obtained.

_There is apparently, then, a tendency for the luminous dis-
.charge to form a closed circuit whenever possible ; and it
.seems probable that even when the discharge is apparently

not closed, as in the case of the spiral or the straight line,

_the electric stress acting in the rarefied gas takes the form
of a closed circuit, but is only intense enough to produce

sharp luminosity close to the wiret. To further test the ques-
tion an unclosed ring tube was made, and when it was placed
inside a coil of wire no trace of a single luminous band could
be seent. A small glass tube was also bent so as to form a
spiral of four turns, and exhausted. A wire following the
spiral was attached to it, but this also gave no trace - of
luminous discharge.

Magnetic Kffects of Discharge.

The ring discharge in a bulb or closed circular tube acts
like a metallic circuit as far as magnetic effects are concerned.
This may easily be shown by the following experiment.

A coil of three or four turns of wire has a similar one wound
with it to form a secondary ; the latter is connected to a
third coil, in which is placed an exhausted bulb. The first

‘coil is connected to the outside coatings of the jars (fig. 1).
‘The spark-gap can be adjusted so that a fairly bright ring is

* Tt is not always necessary to use this cap, as, if the exhaustion is
high enough to give green phosphorescence of the glass, with the two
half-gallon jars in series, the discharge can be obtained without the cap.
With another tube of lower vacuum the author finds the cap necessary.

+ That is, the return part of the discharge is so diffused and feebly
luminous as to easily pass unnoticed in comparison with the sharp and

brilliant luminosity close over the conductor. The same applies to the

spiral discharge, each turn of the spiral probably forming a closed circuit

by itself.

t On afterwards repeating this experiment the author obtained a dis-
charge in parts of the tube, and with half-gallon jars in the whole tube.
The discharge, however, was a closed one, as there were two distinct

bands in the tube, one on the side next to the coil and the other on the

side farthest away from it. This is what might be expected if the
magnetic induction be sufficiently strong.

Phil. Mag. 8. 5. Vol. 35. No. 217. June 1893. 20

LGPL TOC ATTEN IALTEOA E

522 Mr. E. C. Rimington on Luminous

produced in the bulb. If now a second bulb is placed within
the first coil a luminous ring will be formed in it, and the
ring in the other bulb will be much weakened or altogether
extinguished. Exactly the same effect is produced if a metal
plate or closed coil be brought near the first coil in lieu of the

bulb.

Sensitive State of Discharge.

If a single turn of insulated wire surround one of the
exhausted bulbs as in fig. 1, and the spark-gap be adjusted so
as to produce a rather faint luminous ring (the fainter the
better); on approaching the finger and touching the wire at
any point the discharge appears to be repelled, and takes the
shape shown in fig. 11. Instead of touching the wire with
the finger a small piece of tinfoil may Fel
be laid between the wire and the bulb, Pen.
as at A (fig. 11), and this may be touched
by the finger or connected to any large
object, insulated or otherwise ; the effect
produced is the same. Connecting the
tinfoil to one of the outer coatings of the
jars does not produce this effect, and
it is scarcely, if at all, visible when
the luminous ring is brilliant, due to
a longer spark-gap. With a wire ring
of several turns the author has not been
able to obtain it. If a turn of bare
wire be employed the effect is produced
when the finger is brought very near to the wire, but if it be
brought into actual contact the effect is no longer visible.
This apparently shows that it is due to the capacity between
the finger or tinfoil and the wire; it is probably of the

same nature as the “ sensitive state’ in an ordinary vacuum
tube,

ADDENDUM, May Ist, 1893.

Since writing the above the author has made a further
experiment* which at first sight appears to contradict the

one{ given in the paragraph on ‘‘ Magnetic Effects of Dis-
charge,”’

* Called hereafter the second experiment.
shown when the paper was read.
+ Called hereafter the first experiment.

This experiment was

Discharges in Electrodeless Vacuum- Tubes. 523

A ring (R) of four turns of wire is joined in series with a
single turn, and the two are connected to the outside coatings
of the jars. In the single turn a bulb is placed and the spark-
gap adjusted until a fairly bright ring is produced in it at
every discharge. If now a closed ring of thick copper-wire,
a metal plate, or a ring of several turns, similar to R, and
with its ends joined, be laid on R to act as a secondary, the
luminous ring in the bulb is brighter ; on substituting for this
an exhausted bulb and placing it in R, there will be a brilliant
ring-discharge in it, while the discharge in the other bulb
will be rendered fainter or altogether extinguished. In this
experiment the exhausted bulb secondary appears to act in
the reverse way to a metallic secondary.

The author then made the following experiments :—

(a) A ring of four turns of guttapercha-covered wire pre-
cisely similar to R was made, its ends were connected to an
ordinary Geissler tube. When this was used as secondary it
acted exactly in the same manner as the exhausted bulb both
in the first and second experiments, the Geissler tube being
brilliantly illuminated.

(6) The Geissler tube was then removed, and the ends of
the secondary coil connected to the coatings of a small Leyden
jar. The effects produced by this secondary were the same as
those produced by the exhausted bulb in both experiments.

(c) The ends of the secondary were connected to the loops
of a glow-lamp to act as a resistance (about 100 ohms). This
acted similarly to the exhausted bulb in both experiments.

(d) A disk of gilt paper (imitation) and also a ring of the
same were used as secondaries; these acted similarly to the
bulb in both experiments. When the discharge took place
there were brilliant sparks produced at various spots on the
paper, wherever there was any flaw in the gilding, showing
that considerable energy was dissipated there.

(e) The secondary coil of four turns had its ends joined by
a strip of gilt paper about 6 inches in length, with a con-
siderable number of flaws in the gilding (produced purposely,
by bending the paper sharply in several places, so as to
obtain considerable sparking). This acted similarly to the
bulb and dimmed the discharge in the bulb surrounded by the
single turn. On shortening the length of gilt paper between
the ends of the secondary, the discharge in the bulb was less
dimmed.

The results of these five experiments are, that any of tho
above secondaries are able to reduce the mutual induction
between the primary and secondary in the first experiment
sufficiently to render faint or altogether extinguish the

202

FE ay ee BEL Se <I>. +6 Te

ALM aa OE + i LOE ICDL EN PIE PRED AP

oem

LS SN

524 Luminous Discharges in Electrodeless Vacuum- Tubes.

discharge in the bulb, and act similarly to an exhausted bulb
secondary. In the second experiment a low resistance se-
condary behaves in the reverse manner to an exhausted bulb
secondary, while (c) and (e) show that a high resistance put
externally into the secondary circuit, and (d) that a secondary
having a high resistance in itself, act in a similar manner to
an exhausted bulb secondary. (6) shows that if the ends of
the secondary be attached to a capacity it behaves like the
bulb.

' The most probable explanation seems to be the following:—
The amount of energy in the jars when charged is a fixed
quantity for a given spark-gap; this energy will be mostly
expended in the coil R and the single turn and bulb (the
second experiment). If, now, we can make energy be ex-
pended elsewhere, as in a secondary, we shall have diminished
the energy received by the bulb, and this will in general dim
it or altogether extinguish it. This will explain what happens
when an exhausted bulb secondary is used ; also experiments
(a), (c), (d), and (e). With regard to experiment (6), energy
may have been expended in heating the glass of the jar on
account of electric hysteresis. Moreover, this secondary did
not dim the bulb so much as the others, but was found to be
capable of improvement in this respect by including some
resistance (in the shape of the glow-lamp or a strip of gilt
paper) in its circuit.

In the case of a low-resistance secondary the energy dissi-
pated in it will be small, since its impedance will not be much
lessened by its being of low resistance on account of the high
frequency. This does not explain, however, why the dis-
charge in the bulb is brighter when a low-resistance secondary
is used*,

A further experiment was then made. The coil R in the
second experiment had a similar secondary 8 placed in it;
this was connected 1c another similar coil T. The spark-gap
was lengthened until a brilliant luminous ring was produced
in a bulb placed in T. The bulb in A was then moved away
from A until there was a very faint luminous ring init. On
removing the bulb from Ta very slight brightening of the

* Tnis energy explanation is probably not a complete one. Working
out the frequency in the cases of no secondary, a secondary of four turns
short-circuited, and the same with its ends joined through 100;
the author finds that the damping-term is increased when either secondary
is used, but more so with the 100 in circuit. The frequency is much
the same with the 100 in circuit as when there is no secondary, but
with the secondary short-circuited the frequency is about doubled. This
may account for the increase in brightness of the discharge in the bulb.

On the Psychrometer and Chemical Hygrometer. 525

_ faint ring of the bulb in A was observed. Instead of placing
an exhausted bulb in T, a coil of four turns with its ends

joined through 100 was laid on T, and the bulb in A adjusted

A one turn; S, R, and T each four turns.

to give a very faint ring; on removing the coil from T a
decided brightening of the discharge in the bulb was observed.
This experiment seems to show fairly conclusively that in-
creasing the energy in the circuit of the secondary S dimi-
nishes the brightness of the discharge in the bulb placed in A*.

LIL. Comparative Experiments with the Dry- and Wet-Bulb
Psychrometer and an improved Chemical Hygrometer. By
M. 8. Pemsrey, W.A., WB., Radcliffe Travelling Fellow ;
late Fell Hxhibitioner of Christ Church, Oxford. ne vom the
Radcliffe Observatory, Oxford.)

URING the late winter it seemed desirable to make a
series of comparative experiments with the Dry- and
Wet-Bulb Psychrometer and an improved Chemical Hygro-
meter, in order to ascertain the accuracy of the results given
by the Psychrometer for temperatures below the freezing-
oint.

: A series of comparative experiments, made by me in the
summer of 1889, had shown that the amounts of moisture
calculated from the psychrometric readings varied by +6 per
cent. to —9d per cent.from the amounts actually found by the

* Since writing the above the author finds that Prof. J. J. Thomson
has observed the effects noticed in the second experiment, and gives an

explanation practically identical with the above.
+ Communicated by Mr. E. J. Stone, #.R.S., Radcliffe Observer,

226 Mr. Pembrey on Comparative Haperiments

chemical method. The mean difference, however, in the
above series was insensible*.

The Chemical Hygrometer employed in both series was
that introduced by Dr. Haldane and the author f.

The absorption-tubes were placed in a small wooden box
with wire partitions to prevent them from knocking against
each other. The entrance-tube, by which the air to be
examined passed into the hygrometer, was fixed through a
small perforation in a rubber partition covering a hole in
the box. In this way any possibility of air being taken from
the inside of the box was avoided. }

The comparative experiments were made in the following
manner. ‘The weighed absorption-tubes were placed in the
shed containing the psychrometer about ten inches below the
bulbs of the thermometers. The wet- and dry-bulbs were
then read off; the absorption-tubes were connected by a long
piece of rubber-tubing with the aspirator. Air was now
drawn through the tubes at a rate of 1500 cub. centim. per
minute, until about 11,500 cub. centim. of the air had been
taken. Five readings of the temperature of the water and of
the air in the aspirator were taken during each period of
observation. When the aspiration was finished, the readings
of the wet- and dry-bulbs were again taken, and the absorption-
tubes disconnected and stoppered. The period of observation
generally lasted about ten minutes.

Simultaneous determinations with two chemical hygro-
meters were made in the previous, but not in the present
series of observations. In order, however, to check the com-
pleteness of the absorption and any errors in weighing, a
second pair of absorption-tubes was connected up with the
first pair.

The results for the psychrometer were calculated, not from
my own readings, but from the mean of three other readings
—one at the beginning, one at the middle, and one at the end
of each period of aspiration. These readings were obtained
from the continuous photographic record of the wet- and dry-
bulbs taken at the Radcliffe Observatory. It is possible to
read off this record to two minutes and to one-tenth of a
degree Fahrenheit. The accuracy of the readings has been
proved by years of use and comparison with eye-readings.

In every case care was taken to have the wet-bulb properly
moistened about a quarter of an hour before the observations.

* Phil. Mag. April 1890, p. 314. |
t ‘An Improved Method of Determining Moisture and Carbonic Acid
in Air,” Haldane and Pembrey, Phil. Mag. April 1890.

527

with the Psychrometer and Chemical Hygrometer.

TABLE I.
CS i Ete Ee we NEE a eel Sle we > I OE Ses eR Re ee

Weight of

Time during which Gain in weight] Variation in |vapour calcu- ITE: Dry-bulb | Wet-bulb

Experi- Dates air was aspirated eee ee of absorption- weight of test- lated from beat S : (mean of | (mean of
ment. through absorption- a vial tubes, first [pair of absorp-|psychrometer von CHOATE three three
tubes. Fe ees air. tion-tubes. | by Glaisher’s readings). | readings).
P y method
Tables. ;
cub. centim. erm. erm. erm. per cent. wie 5
1.......| 8 Jan. 1893.| 2.26 — 2.31 p.m. 5,802 "0209 + -0002 0198 —5 311 29:0
Dette’ 3 10.15 -10.19% a.m. 5,630 "0154 +0002 ‘0164 +7 20°1 20:0
Sh actiocel| a2) A 10.43 -10.14 _,, 11,552 ‘0289 +:0003 0288 —0 20°0 196
Acces geal a59 3 10.41 -10.51 ,, 11,278 0303 +0001 0297 —2 21-0 20°5
Disnegsa|c0 iy 10.20 -10.29 __,, 11,358 ‘0445 +0001 0470 +5 30°7 29'9
Ooocee alloc 3 11.2% -11.12 _,, 11,396 0481 — ‘0002 0480 —0 30°9 30°4
The ss Sy 3 10.45 -10.54 ,, 11,174 0431 +0005 0427 —1 28°6 28:1
Sie sel 9) ” 11.213-11.83 _,, 11,202 0439 +0002 ‘0448 +2 28°5 28°2
Ot line, 5 10.14 -10.23 _,, 11,302 ‘0576 — ‘0002 "0589 +2 341 33'8
WO ecesat |e ‘5 10.45 -10.54_,, 11,320 ‘0587 +0003 0583 —0 343 33°9
Acc ag LO. ‘5 10°7 -10.16 ,, 11,370 "0574. + 0004 0575 +0 347 34:2
Dees texe saelis9 ) 10.39 -10.48 __,, 11,410 0578 +:0001 ‘0603 +4 352 347
WSs coxcae( LL i 10.14 -10.23 _,, 11,428 0481 +0002 0476 —1 32'3 30°9

Lee NET at

528 Mr. Pembrey on Comparative Experiments

The aspirator used was that described in the paper pre-
viously mentioned*. The aspirating-bottles were covered
with felt, so that the temperature of the water generally
varied only a tenth or two.of a degree Centigrade, never
more than half a degree, during the period of observation.

The volume of air aspirated has always been corrected for
temperature, aqueous vapour, and barometric height.

In calculating the tension of aqueous vapour from the
chemical determinations the table given by Shawf has proved
very valuable.

The preceding Table (I.) shows that the amounts of moisture
calculated from the psychrometric readings by Glaisher’s
Tables vary, when compared with the gravimetric determina-
tions, from —5 per cent. to +7 per cent. The mean, how-
ever, is ‘0430 to ‘0426 grm., or less than +1 per cent. for
the psychrometer.

The tensions given by the chemical determinations have
been calculated, and are compared in Table II. with those
obtained from the psychrometer by means of Glaisher’s,

Haeghens’, Guyot’s, and Wild’s tables.

Nae tree Ee
Psychrometer.
Experiment Chemical 9
‘| method.
Glaisher. | Haeghens.| Guyot. Wild.
millim. millim. millim. millim. millim.
| a eee 3°45 3°20 3°44 3°45 3°47
De there i. 2-60 2-67 2°73 ORD a ee
Desctiowec way 2-49 2°36 2:58 2°56 2
7 a oe Sie 2°56 2°36 2-70 2:64 26
De Mee ose acres a1 3°83 4:01 3°98 3:93 2
Giraieseccu net 4-03 4:06 4°20 4-16 AT
Tae ae = Be 3°70 3°63 3°80 3°78 S48
eee 3°75 378 3°84 ool 3°83
es iin 2 4-87 4-85 4-84 4-82 4°83
MOR aerate at 4°95 4°85 4-84 4:82 | 4:80
1B sey Se Se ae 4°85 4-87 4°86 4-82 4°80.
DA Sees ee 4°86 4-98 4-97 4:92 5°00
WS ates ae 4°05 3°86 4°23 3°96 | 4°17
WMisanves. cone: 3°84 3°80 3°93 3°88 | 3°89

In order to make this paper more complete, the cor-
responding tables of the previous experiments are here
reproduced.

* Phil. Mag, April 1890, p. 309.
tT On Hygrometric Methods,” Phil. Trans. 1888, A. ~~

529

with the Psychrometer and Chemical Hygrometer.

e . e

CONDAAA Fw DH

oh
a

Date.

ites a
om her
We a
20 Le
Za 5;
5 Aug. 1889.
Ot
al %
oy
Des
cham

* The rubber of one of the stoppers

16 July 1889.

‘TasueE EID,

Time during
which air was
aspirated.

11.39-11.48 a.m.
11.39-11.45 a.m.
11.10-11.16 a.m.
11.6 -11.12 a.m.
11.45-11.52

12.13-12.16 p.m.
11.52-11.58 a.m.
11.48-11.54 a.m.
11.21-11.27 a.m.
WO) SIDIEAG/ AN
11.24-11,80 aa.
1L.é

52-11. 39 A.M.

Corrected
volume of
air aspirated
through
each pair.

cub. centim.

07123
5722
5723
5780
5681
5732
5707
5709
5756
5776
5731
5755

Gain in
weight of

pair I,
determina-

tion A.

0510
‘0575
‘0678
‘0583

{

Gain in
weight of
pair 2,
determina-
tion B.

erm.

‘0430*
0524
0512
0508
‘0610
0435
‘0687
‘0564
0510
‘0572
‘0675
0585

Weight of
vapour caleu-
lated from
readings of
psychrometer
by Glaisher’s
Tables, 7th ed.

erm

Percent-
age diffe-
rence of
pyschro-
meter
over
chemical
method.

per cent.

0450
0552
0520
0519
‘0600
(0452
0668
0548
0495
0552
0678
0553

+54

Dry-
bulb
(mean of
3 read-
ings).

pike
61:6

58'3
61:3
63°7
d7°9
61:5
65°6
625
63:0
64:1
61:0
64:6

Wet-
bulb
(mean of
3 read-
ings).

Variations of
test pair 3,
showing that
carrying the
tubes about
introduced no
error of

weighing.

grm.

+0001
+0002
— ‘0002
+0002
+0003
— ‘0002
— 0003
+0000
+0002
+-0001
+0002
— 0001

was found to be split on reaching the Observatory, and bei accounts for sire slight excess in
weight of this pair of tubes,

’

530 On the Psychrometer and Chemical Hygrometer.

TaBeE LV.
Psychrometer. |
; Chemical |
Experiment. | method.
Glaisher. | Haeghens.| Guyot. | Wild. |
nee Le | as ee. |
millim. millim. millim. millim. millim.
| eee ae ae 743 776 737 731 74
Bias ae hc 3 915 9°55 9 54 9°51 9°5
Ou, de acueee 8:99 9-00 8:88 8°87 89
a a 8-78 8:99 8°74 877 88
Dg ceeeencee 10°70 10°72 10°75 10°76 10:7
Coit 7:63 778 739 7:34 74
Les desea 12°15 11-72 11°78 11-80 Grd
co eer on 9-91 965 9:57 9°57 96
OS ae enes 8-90 8:68 8°45 8:43 85
LON eee 10:00 9°52 9°38 9°41 94 |
Da eae 11°82 11°84 11:93 11:93 1 eS ae
LAR sa ee 10:23 9°67 S95 9°57 9°5
pe hee ee ih | ee a
Means: 9-64 SRD 9°44 9°44 9°44

Regnault*, during his comparative experiments with the _
psychrometer and his chemical hygrometer, made a series of
determinations in which the temperature of the air was below
the freezing-point. The experiments were made in December
1846 and January 1847. The lowest temperatures during
the sixteen determinations were —6°°89 C. for the dry-bulb
and —7°:74 for the wet-bulb ; the highest —0°13 and —0%69
respectively. The chemical determination lasted from three-
quarters of an hour to one hour ; readings of the psychrometer
were taken every five minutes. 7

The results showed variations of the psychrometer over
the chemical method ranging from +11 per cent. to —3 per
cent., the mean being about +4 per cent.

In conclusion | must express my hearty thanks to Mr.
Stone, the Radcliffe Observer, who has given me every facility
to make these and the previous experiments, and has always
aided me with his advice. I must also thank his assistants,
Messrs. Wickham, Robinson, and Maclean.

* Annales de Chimie et de Physique, t. xxxvii. 1853, p. 274.

sel |

LIV. Water as a Catalyst. By R. E. Hucuss, B.A., B.Sc.,
F.CS., late Scholar of Jesus College, Oxford, Natural
Science Master, Eastbourne College *.

Ss further chemical changes have been investigated,

and the influence of the absence or presence of water on
the progress of the change has been determined. Last year
the author showed (Phil. Mag. xxxilil. p. 471) that dried
hydrogen-sulphide gas has no action on the dried salts of
lead, cadmium, arsenic, &c.; and, in conjunction with Mr. F.
Wilson, it was shown that dried hydrogen-chloride gas is
without action on calcium or barium carbonates (Phil. Mag.
poecnvep.. 117).

Silver chloride prepared in the dark, dried perfectly in an
air-bath, and then placed on a watch-glass in a desiccator
partially exhausted, was found to be not perceptibly darkened
in sunlight even after an exposure of some hours ; whereas a
rapid darkening takes place if moisture is introduced.

It isa well-known fact that paper, especially ordinary glazed
writing-paper, when moistened with a solution of potassium
iodide and exposed to the light, becomes of a brownish-violet
tint—due doubtless to the decomposition of the KI and libe-
ration of the iodine.

The author finds that the progress of this change is subject
to several conditions. A solution of potassium iodide placed
on glass or porcelain becomes brown only after an exposure
of some days. ‘This change, it is suggested, is due to either
the organic matter or the ozone in the atmosphere.

A piece of ordinary filter-paper soaked with a saturated
solution of KI was dried in the dark. When placed ona
watch-glass under a desiccator, no change took place on ex-
posure even after some days; although crystals of the salt
were formed on the paper. Moreover, generally speaking,
the wetter the paper the deeper was the tint produced. In
fact the tint was proportional to the quantity of water present.
When no water was present, then no change took place.
Further, a strip of filter-paper floated on the top of a solution
of KI for quite two hours in bright sunlight before any per-
ceptible darkening occurred, although the underside had
assumed a deep brown tint.

But this change also depends on the kind of paper used ;

* Communicated by the Author. [As some of Mr. Hughes’ results

have been anticipated by Mr. Baker (Proc. Chem. Soc. May 4, 1893,
. 129), he wishes it to be stated that the MS. was received by us on

April 21st.—Ebs. |

532 Mr. R. E. Hughes on Water as a Catalyst.

thus strips of highly glazed note-paper, ordinary filter-paper,
Swedish filter-paper, and vegetable parchment were cut,
soaked in the same KI solution, and exposed side by side to
bright sunlight. It was found that after some hours a grada-
tion of tints was thus obtained, the deepest being that on the
glazed paper, whereas the tint of the parchment was almost
imperceptible. Hence this change is perhaps due to the
traces of chlorine invariably present in glazed paper. The
depth of tint in the same paper was affected by the surface on
which the paper lies. Thus, if lying on blotting-paper the
change was very minute, slightly more perceptible on glass or
polished surfaces, and most evident when on wood or other
rough surface. ‘This chemical decomposition also took piace
in the dark but more slowly; further, once the paper was
quite dry, no perceptible deepening in tint was observed. A
solution of potassium iodide may be kept in sunlight for an
indefinite period, provided it is not exposed to the atmo-
sphere. ‘This change is doubtless due to organic matter or
ozone present in the atmosphere, but is dependent on the
presence of moisture; whereas the staining of paper by this
solution is due to the chlorine present or other constituent of
the glaze, and is also dependent on the presence of moisture.

Silver nitrate behaves closely similarly, as also to a lesser
degree does platinum chloride.

Some experiments were then made to determine the
question whether dried hydrochloric-acid gas has any action
on dry silver nitrate.

The gas was passed through a tube containing copper
filings (to remove chlorine), then through a series of drying-
tubes containing strong H,8Q,, and finally over P,O; con-

tained ina tube. This dried gas had no action on dried blue ~

litmus-paper. The silver nitrate was contained in a porcelain
boat, and had been previously heated to incipient fusion.
The gas was allowed to pass slowly through for about two
hours. <A very slight change of colour was produced in the
silver salt, and a shght change did take place. By weighing
before and after, the amount of change was determined and
found to be 1:7 per cent. of the theoretical amount of change.
This experiment was conducted at the temperature of the
laboratory. An experiment conducted at 100° showed. that
1:0 per cent. of the theoretical amount of change had taken
lace.
: The action of dried HCl gas on dried manganese dioxide

was next investigated. This MnO, was prepared from a pure —

manganous sulphate by treatment with bromine and caustic
soda. It was thoroughly washed and dried.

Mr. R. E. Hughes on Water as a Catalyst. 533

- In this instance a decided change undoubtedly takes place,
which appears to be totally independent of the absence or
presence of water. In one experiment the change observed
was 20 per cent. of the theoretical amount, this particular ex-
periment being conducted at the temperature of the laboratory.
In an experiment conducted at 100° the change was 13 per
cent., whereas in another experiment conducted at the ordi-
nary temperature, as much as 42:7 per cent. of the theoretical
amount of change took place. In all these experiments the
gas was allowed to pass for about three hours.

. Experiments of a different character were then undertaken.

An “inactive” solvent, such as anhydrous ether in one
case and benzene in another, was taken, and silver nitrate
dissolved in it by warming. Through the solution a current
of dried HCl gas was passed.

- For some time no change could be observed, and even
after one hour only a very slight turbidity was produced.

Using absolute alcohol as the solvent, a more decided pre-
cipitate was obtained at the end of one hour ; but the change
was still only very partial, as was shown by the remarkahle.
increase in the precipitate on the addition of a minute
quantity of water.

_ Mereuric chloride was dissolved in absolute alcohol, and
thréugh this solution a current of dried hydrogen sulphide
gas (dried according to the method described in Phil. Mag.
Xxxill. p. 471) was passed. For about a quarter of an hour
or even longer no change was noticed, then a slight turbidity
which became more perceptible, very slowly assuming a pale
yellow colour, then a darker yellow, and finally a greenish
yellow precipitate was obtained. No further change was
observed even after one hour and a half—the change is in
fact a limited one, and the green insoluble compound pro-
duced is doubtless a double chloride and sulphide of mercury.

The addition of a little water instantly changed this green
precipitate to a black one. It is intended to repeat these
experiments quantitatively.

An experiment was conducted to determine whether dried
HCl gas and dried ammonia gas combine when mixed.

The method was as follows :-~Two equally-sized U-shaped
glass tubes, with their limbs sealed, and having narrow side
delivery-tubes capable of being drawn out and sealed, were
taken. One of these tubes, in the bend of which was placed
some freshly heated lime, was filled with dried ammonia gas
and sealed. ‘The other tube, containing phosphorous pent-
oxide in the bend, was filled with dried hydrochloric-acid gas,

534 Notices respecting New Books.

and the side tube similarly drawn out and sealed. These
two tubes were then allowed to stand for three days. The
drawn-out ends were then joined by a piece of india-rubber
tubing, previously soaked in melted paraffin, and the ends
broken off.

The contents of the two tubes being thus placed in con-
nexion with each other, were allowed to remain so for 24
hours.

No deposition of a solid on the clean sides of either tube
was noticed. On passing a current of air through the two
tubes the contents were driven out, a white fume being evi-
dent, however, only on the mixed gases reaching the outside
air, while simultaneously a strong odour of ammonia was
perceptible.

A similarly conducted experiment gave a similar result, so
that it seems certain that dried HCl and dried NH, when
mixed do not combine.

Eastbourne College.

LV. Notices respecting New Books.

Alternating Currents. By FREDERICK BEDELL, Ph.D., and ALBERT
C. Crrnore, Ph.D., of Cornell University. (Whittaker and Co.)

pee I., of 207 pages, is an analytical treatment of the sub-
ject, and Part II., of 104 pages, is graphical.

The book is intended for students and engineers. Self-induc-
tion is regarded as constant and nothing is said of mutual induction
between circuits. The transformer is not touched upon. Simple
harmonic functions of the time are dealt with almost exclusively,
but there are two short references to periodic functions in general.
In Part II. the same problems are considered in the same order as
in Part I.

The first eleven chapters, of 175 pages, deal with the following
problem :—Given e¢ the electromotive force in a circuit, of re-
sistance R, self-induction L, and containing a condenser of capacity
C, to find the current. The solution of this problem for all cases
may be given in one page or in a thousand, depending upon the
previous knowledge of the reader. The authors of this book seem
at some places to assume a considerable amount of mathematical
knowledge; where, as in chapters ii. and v. for example, they dis-
cuss very unnecessarily the conditions for Pdv+Qdy+Sdz being
a complete differential. At other places, however, the whole
working-out of an easy integral is given, seeming to be copied
from a beginner’s rough note-book. Regarded as exercise-work
on the application of the Calculus to alternating current problems,

Notices respecting New Books. 539

the book may be recommended to beginners, particularly as some
‘numerical exercises are given, and some curves are given to illus-
trate the answers ; and the most general case is led up to gradually.
We feel, however, that the authors have not taken advantage of
their good opportunity. Surely it would have been better to begin
by showing the student that in most practical problems d/dt enters
in a linear fashion, and if we indicate it by 6 this symbol may be
used like an algebraic quantity. Self-induction means a resistance
L@; a condenser is represented by a resistance 1/C@; and the
problem of these eleven chapters is to find

1
iS (R+Le+ a)

We are sorry to think that the authors mention so very few of
the interesting exercises which may be given to students on this
subject.

Chapters xi. and xiii. are devoted to a subject which is rather
remote from the previous one; it is one on which they seem to
have written original scientific papers,—“ circuits containing dis-
tributed capacity and self-induction.” It is unfortunate that a
very serious mistake should be made at the beginning. The mis-
take leads to the equation

Now a very little consideration ought to have shown the authors
that the self-induction term must be of the same sign as the re-
sistance term. If they had used the symbolical method already
referred to, they must have seen that they had only to use R+ L@,
instead of Ri in the equation as given by Lord Kelvin originally.
We have no time to investigate the amount of error which is
introduced by this negative self-induction into the results of the
authors, nor even to test their results by those given by Mr.
Heaviside (Phil. Mag. January 1887).

In Part II. there is no attempt to give new matter; students
who care for the graphical treatment of this subject will find it
sufficiently easy to understand.

Discussion of the Preasion of Measurements, with Examples taken
mainly from Physics and Electrical Engineering. By Stas W.
Houman, S.B. (176 pages). (Kegan Paul, Trench, Triibner,
& Co., Limited.)

WE understand that this is a publication of Prof. Holman’s notes
of a regular course of lectures delivered by him at the Massa-
chusetts Institute of Technology. What is the probable accuracy
of an experimental result? What accuracy is essential ? How

536 Notices respecting New Books.

may a. sufficiently accurate result be obtained with the least
trouble? All experimenters ask themselves these questions, and
often answer in an off-hand, unscientific way. Prof. Holman is
impressed with the importance of establishing a course of proce-
dure easily understood and fairly general, and Taal too laborious in
its application. As he says in his preface :—“ In venturing to
urge the importance of the subject as a course of study for
engineers and for students of physics, or other pure sciences, the
author would suggest the value of the attitude of mind produced
by it. One who has in any reasonable degree mastered its methods,
although he may never apply them directly, will not only have
increased his power to intelligently scrutinize experimental results,
but will have acquired a tendency to do so. And it is, perhaps,
not too much to hope that he may acquire a notion of a judicious
distribution of effort which, with the best of results to himself, he
may carry into quite other matters.” The course of procedure
seems to us to be one which is practised by every experienced
laboratory worker, and whether one ought to adopt it instinctively
and because it is natural to exercise some common sense even in a
physical laboratory, or whether the inexperienced laboratory worker
should study it by listening to lectures on it as a new science are
questions which Prof. Holman’s old pupils can best answer. An
experienced man who already follows the course of procedure will,
we think, read the book with greater pleasure and benefit than the
students for whom it has been written. In the planning of direct
measurement the method of procedure is summarized as follows :—

(a) Obtain a general idea of the proposed ee. apparatus,
and conditions of work, or of several methods, , from which
selection may be made.

(6) Make a thorough study of all discoverable sources of error,
taking preliminary observations if necessary.

(c) Plan the sufficient removal of all determinate sources s of
error or determine corrections for them.

(@) Take the final series of observations.

Of course this summary gives only a one-sided view of the

teaching, but still the book is intended to be read by students who
need to be taught these things. We should have thought that
work in the laboratory and attendance at a few meetings of a
Scientific Society would have better effected the author’s purpose.
We can hardly forgive the author for ignoring altogether the use
of squared paper by experimenters.
_ Prof. Holman would, probably, deliver an interesting course of
lectures to babies to teach them how to walk; but after all the
babies will learn better through falling and crawling and general
experience. So a student will learn more in a good laboratory,
under an experienced demonstrator, than from this course of
lectures. It is the experienced demonstrator who will enjoy
reading the book.

Pasar.
LVI. Intelligence and Miscellaneous Articles.

ON THE DISENGAGEMENT OF HEAT OCCURRING WHEN ELECTRICAL
VIBRATIONS ARE TRANSMITTED THROUGH WIRES. BY DR. I.
Vv
KLEMENCIC.

je present research is concerned in the first place with the
disengagement of heat which occurs when electrical vibrations
are transmitted throagh wires. Vor the experimental invest gation
a method was used which consisted in placing close to the wire to
be heated the junction of a thermo-element constructed of fine wires,
and measuring the heating of the wire due to the radiation against
the junction by the thermo-current produced. The primary cir-
cuit furnished waves 3°3 m. in length, and consisted of two
brass disks 30 cm. in diameter, which were connected by a linear
conductor with a spark-gap in the middle. An exactly similar
body constituted the secondary inductor, except that it had no
spark-gap, but the middle part of the linear conductor was formed
of the wires to be investigated. Two experimental wires were
interposed ; the length of both together was at most 12.cm., while
the whole linear part of the secondary inductors had a length of
89 cm. Experiments on the development of heat in wires led
thus to the question of the division of the electrical current in
vibrations. With regard to the circumstance that the disengage-
ment of heat in very rapid electrical oscillations takes place almost
exclusively in the surface-layer, it seemed to the author not
unimportant to observe how in this case the intensity of the
radiation is related to the change of resistance of the heated wire,
and then further to investigate what is the value of this ratio with
constant current. Measurements have shown that with wires of
the thickness here examined (0-037 cm.) there is no appreciable
difference in this respect. The heat disengaged on the surface is
rapidly conducted to the interior of the wire. It follows from the
experiments on the disengagement of heat that the resistance to
the passage of very rapid electrical vibrations depends on the
magnetizability of the wire in question, and on the kind of wire;
yet as regards the latter in a way differing from the constant
current. For several wires of different material 6 cm. in length
and 0:037 cm. in thickness, a heat is found in vibrations which is
approximately expressed by the following ratio :—
Iron : german silver : brass : copper = 10°5 : 1°75: 1:1.

The number for copper is probably too large, as it was inserted
in the series after a correction which was only .approximately
correct.

If the formule of Stefan are applied to these observations,
theory and experiment agree well in the combination german silver-
brass. The combination german silver-copper did not give con-
cordant values, which is partially due to the fact that in these
experiments all the conditions were not fulfilled which theory
requires.

Taking Stefan’s formula the number 111 was obtained for the
magnetic permeability of iron, and in another 73. The observations

Pit, Mags S.owV ol. 30, No. 217, June 1893. 2 P

er i RE” PEE Te EEE

a mes
~ eenesceshnatt ii aaa TC aes eae EL MADE

in. eaten d

a ae a

inna —
pene enna nacre cece

Li
LORIE A OLE OC A
a ini

A IEEE IOS AES

perme

538 Intelligence and Miscellaneous Articles.

showed further that in the branching of electrical vibrations
the coetficient of self-induction is almost entirely of dominant
influence and not the resistance.— Wrener Berichte, March 16,1893.

ON THE POTENTIAL OF ELECTRICAL DISCHARGE.
BY PROF. HEYDWEILLER. .

The author, at the conclusion of a paper on this subject, gives
the following table for the values of the potential of discharge, v,
between equal spherical electrodes of radius 7, for sparking-distances
dcm.; the experiments were made by means of a spark-micro-
meter of suitable construction, so that no appreciable mductive
actions were to be feared. The experiments were made at a pressure
of 745 mm. and ata temperature of 18°C.; for an increase of
pressure of 8 mm. or for a diminution of temperature of 3°, these
values are to be raised 1 per cent. in either case.

r= 2°5 cm. r= 1:0 cm.

dem. e d em. v.
0:5 61:2 0-1 $77
06 72:0 0-2 27:0
Oi 818 0:3 379
08 91-1 04 48°3
0-9 100°3 0°5 58°3
LO 109°5 06 67°9
11 1186 07 (yee
12 1277 | 08 86'8
Ls 136°7 1:0 104°3
14 145-6 i-2 118°3
1-5 154-1 1-4 128°8
16 162-2 16 137°6

r=0°5 cm. r= 0:25 em.

d em. v. d em. v.
Ol 16°0 0-1 161
0:2 279 0:2 279
0:3 aro 0:3 378
0-4 485 0-4 459
0-5 inn TOA 0:5 52-4
0°6 66°4 06 by des
0-7 735 | 0-7 61:0
0:8 80°3 08 63:4
0:9 85°3 1-0 67-3
1:0 90:0 1) 74:4

With the accuracy of 1 per cent. which these values possess
as derived both from Paschen’s observations and my own, they
will be sufficient in most cases for practical purposes, and will
probably have attained the limit of accuracy possible in such
cases.— Wiedemann’s Annalen, xlviii. p. 213, 1893.

ON A PROPERTY OF THE ANODES OF GEISSLER’S TUBES.

BY E. GOLDSTEIN. .

While a great number of properties of the kathode of induced
discharges in rarefied spaces have been made out, only a few pro-
perties of anodes are known. ‘The following communication
describes a new property of the anode. If a vessel in which the
discharge takes place, one for instance with electrodes at the ends

Intelligence and Miscellaneous Articles. 539

opposite each other, exceeds a certain width, as the rarefaction
proceeds the positive light, if it does not wholly disappear, is re-
duced to a thin layer on the surface of the anode, and the anode
“slows.” In rarefied air, which is assumed to be the medium of
these experiments, the colour is peach-blossom. If an electrode is
made of pieces of different metals, for instance if a disk is used
half of aluminium and half of silver, the kathode light is generally
distributed over both halves of such an electrode, but shows far
greater brightness oa the aluminium half. This probably depends,
as has already been observed by Hittorf, cn the fact that the re-
sistance to passage is considerably greater on a silver kathode than
on an aluminium one. If such an electrode, hitherto unused,
having a perfectly fresh surface is used as the anode, the glow
covers the whole of the anode side facing the kathode; and assu-
ming that both halves are symmetrical with respect to the kathode,
they show more or less approximately equal intensity. ‘This
extension of the glow is also maintained if the discharge is
allowed to pass in the same direction, and occurs also if the
passage of the current is broken and then re-established in the
same direction. But if the current is reversed for a few seconds,
so that the compound electrode acts as a kathode, and then the
former direction is restored, the glow is bright on the silver half of
the anode, but on the aluminium half it is either quite destitute
of light, or so pale that special attention is necessary to see
the light. The boundary of light exactly corresponds to the line
of separation of the two surfaces. The discharge light at the
anode accordingly despises that metal which is favoured by the
kathode light, and occurs with brightness on that surface on which
the kathode light shows the least intensity.

The phenomenon was also demonstrated also with a series of
other electrode surfaces. In an aluminium circular disk of 4 centim.
diameter, a star-shaped surface of silver was let in. The glow at
the anode was limited to the silver star, the whole surrounding
surface being destitute of light.

If in an aluminium disk, several centimetres in diameter, nume-
rous detached silver points are inlaid in circles of # millim. to 24
millim. in diameter, the anode luminosity occurs at all the silver
points, while the intermediate aluminium parts remain dark. By
arranging the silver points, any given luminous figures can be ob-
tained, stars, arabesques, &c.

If, on the other hand, aluminium parts are let in a silver disk,
the whole of the disk is luminous except the aluminium, which re-
mains dark. If the anode consists of a chain of alternate links of
aluminium and silver, only the silver ones are luminous. Silver
when used as kathode in rarefied air soon tarnishes, becoming
steel-yellow to steel-blue.

The author will elsewhere enter more minutely on the pheno-
menon described, especially as to the behaviour of other metals and
in other gases.—Verhandl. der Phys. Gesellschaft Berlin, Dec. 16,
13892; Wiedemann’s Annalen, May 1893.

POL TIS a a a Se >

IT IE Oe a

Pe Ta OE.

ee i en ie ae Dah a Ne
Crew NES i i a EES

[ 540 ]

INDEX tro VOL. XXXV.

ACTINOMETER, on a chemical,
ee

Ammonia, on the specific heat of

, liquid, 393.

Angstrom (Prof.) on the intensity of
radiation by rarefied gases under
the influence of electric discharge,
502.

Anthracite and bituminous coal-beds,
on, 465.

Averages, on a new method of

treating correlated, 63.

Bacilli, on a possible source of the
energy required for the life of,
389.

Baily (W.) on the construction of a
colour map, 46.

Baly (KE. C. C.) on the separation
and striation of rarefied gases by
the electric discharge, 200.

Barus (Dr. C.) on the fusion con-
stants of igneous rock, 173, 296;
on the colours of cloudy conden-
sation, 315.

Basset (A. B.) on the finite bending
-of thin shells, 496.

Becher (H. M.) on the gold-quartz
deposits of Pahang, 75.

Bictite, on a secondary development
of, in crystalline schists, 150,

Blakesley (T. H.) on the differential
equation of electrical flow, 419.

Boiling-points of compounds, on the
elfect of the replacement of oxygen
by sulphur on the, 458.

Boltzmann (Prof. L.) on the equili-
brium of ws viva, 153.

Bonney (Prof. T. G.) on the Nufenen-
stock, 148; on some _ schistose
‘“‘oreenstones” and allied horn-
blendic schists from the Pennine
Alps, 149 ; on asecondary develop-
ment of biotite and of hornblende
in crystalline schists from the
Binnenthal, 150.

Books, new :—Sawer’s Odorographia,
73; Blake's Annals of British
Geology, 145; Alexander’s Treatise
on Thermodynamics, 307 ; Barus’s
Die physikalische Behandlung und
die Messung hoher Temperaturen,
310; Heydweiller’s Hulfsbuch fur
die Ausfuhrung elektrischer Mess-
ungen, 311; Lachlan’s Ele-
mentary Treatise on Modern Pure
Geometry, 462; Revue Semestri-
elle des Publications Mathéma-
tiques, 463; Bedell and Crehore’s
Alternating Currents, 534; Hol-
man’s Discussion of the Precision
of Measurements, 539.

Boron, on the properties of amor-
phous, 80.
Bosanquet (R. H. M.) on mountain-
sickness, and power and endurance,

47.

Breissig (F.) on the action of light
upon electrical discharges, 151.
Bryan (G. H.) on a hydrodynamical
proof of the equations of motion

of a perforated solid, 338.

Burton (Dr. C. V.) on plane and
spherical sound-waves of finite.
amplitude, 317 ; on the motion of
a perforated solid in a liquid, 351,
490.

Catalyst, on water as a, 531.

Chattock (A. P.) on an electrolytic
theory of dielectrics, 76.

Collins (J. H.) on the geology of the
Bridgewater district, 150.

Colour-blindness, on, 52.

Colour map, on the construction of a,

Condensation, on the eolours of
cloudy, 316.

Contact-action and the conservation
of energy, on, 134,

Cooke (J. 1.) on the mals and clays
of the Maltese Islands, 148.

INDEX. 541

Crova (M.) on the interference-
bands of grating-spectra on gela-
tine, 471.

Current, on the magnetic field of a
circular, 354.

D’Arsonval galvanometer, on high
resistances used in connexion with
the, 210.

Dielectric, on the attraction of two
plates separated by a, 78.

Dielectrics, on an electrolytic theory
of, 76.

Diffusion of substances in solution,
on the, 127.

Dispersion, on some recent determi-
nations of molecular, 204.

Dyuic equivalent of a substance,
definition of the, 267.

Karp (Miss A. G.) on the effect of

the replacement of oxygen by
sulphur on the boiling- and melt-
ing-points of compounds, 458.

Edgeworth (Prof. F. Y.) on a new
method of treating correlated
averages, 63.

Electric discharge, on the separation
and striation of rarefied gases by
the, 200; on the intensity of radi-
ation by rarefied gases under the
influence of, 502.

discharges, experiments with

high frequency, 142; on the

action of ight upon, 151.

fields, constant and varying,
experiments in, 68.

Electrical discharge, on the potential
of, 538.

flow, on the differential equa-

tion of, 419.

furnace, on a new, 313.

properties of pure nitrogen, on

the, 1

vibrations, on the disengage-
ment of heat occurring when, are
transmitted through wires, 537.

Electrochemical effects due to mag-
netization, on, 473.

Electromotive force, on the relation
of volta, to pressure, &e., 97.

Emmons (H.) on the petrography of
the island of Capraja, 312.

Energy, on radiant, 113; on contact
action and the conservation of,
134; on the distribution of kinetic,
among Kelyin’s doublets, 160; on

a possible source of the, required
for the life of bacilli, 389.

Equations of motion of a perforated
solidin liquid, on the, 338, 490.

Kquipotential lines in plates tra-
versed by currents, on a visible
representation of the, 151.

Everett (Prof. J. D.) on a new and
handy focometer, 333.

Fluorite, on the refraction of rays of
ereat wave-length in, 44.

Focometer, on a new, 333.

Foote (A. E.) on a meteoric stone
seen to fall in South Dakota, 152.

Force, on the laws of molecular,
211.

Fox (H.) on some coast-sections at
the Lizard, 466; on a radiolarian
chert from Mullion Island, 466.

Frederick (Lieut. G. C.) on the
geology of certain islands in the
New Hebrides, 467.

Friction, on liquid, 441.

Furnace, on a new electrical, 315.

Fusion constants of igneous rock, on
the, 173, 296.

Galitzine (B.) on radiant energy, 118.

Galvanometer, on high resistances
used in connexion with the
D’Arsonval, 210.

Gases, on the separation and stria-
tion of rarefied, by the electric dis-
charge, 200; on the intensity of
radiation by rarefied, under the
influence of electric discharge,
502.

Geissler’s tubes, on a property of the
anodes of, 538.

Gelatine, on the interference-bands
of grating-spectra on, 471.

Geological Society, proceedings of
the, 74, 146, 312, 464.

Glacial Drift, on the occurrence of
boulders and pebbles from the, in
oravels south of the Thames, 468.

Gladstone (Dr. J. H.) on some
recent determinations of molecular
refraction and dispersion, 204.

Gold-deposits, on the Pambula, 76;
of Pahang, on the, 75.

Goldstein (11.) on a property of the
anodes of Geissler’s tubes, 558.

Gore (Dr. G.) on the relation of
volta electromotive force to pres-
sure &e., 97.

” a a I a lt ae all Dell

542 INDEX.

Gratings, on a certain asymmetry in
Prof. Rowland’s concave, 190; in
theory and practice, on, 397.

Grating-spectra on gelatine, on the
interference-bands of, 471.

Gravity, on the daily variations of,
314,

Greenstones, on some schistose, from
the Pennine Alps, 149.

Gresley (W. S.) on anthracite and
bituminous coal-beds, 465,

Hall’s phenomenon, explanation of,
151.

Heat of vaporization of liquid hydro-
chloric acid, on the, 435.

, on the disengagement of, when
electrical vibrations are transmit-
ted through wires, 537.

Helmholtz (Prof.) on colour-blind-
ness, 52.

Heydweiller (Prof.) on Villari’s
critical point in nickel, 469; on
the potential of electrical dis-
charge, 538.

Hornblende, on a secondary develop-
ment of, in crystalline schists, 150.

Hughes (R. E.) on water as a
catalyst, 531.

Hull (Prof. E.) on the geology of
Arabia Petrea and Palestine,
146.

Hydrochloric acid, on the heat of
vaporization of liquid, 455.

Hydrolysis in aqueous salt-solutions,
on, 365 c¥,

Hygrometer, comparative experi-
ments with the dry- and wet-
bulb psychrometer and an im-
proved, 525.

Interference-bands of grating-spectra
on gelatine, on the, 471.

Tron rings split in a radial direction,
on the magnetization of, 592.

Irving (Rev. A.) on the base of the
Keuper formation in Devon, 147.

Judd (Prof. J. W.) on inclusions of
Tertiary granite in the gabbro of
Skye, 464.

Kinetic energy, on the distribution
of, among Kelvin’s doublets, 160.

Klemenéic (Dr. 1.) on the disen-
gagement of heat occurring when
electrical vibrations are trans-
mitted through wires, 537.

Lagrange’s equations of motion, on,
345, 490.

Lefevre (J.) on the attraction of two
plates separated by a dielectric, 78.

Lehmann (H.) on the magnetization
of iron rings split in a radial
direction, 592.

Light, on the diffusion of, 81; on
the action of, upon electrical dis-
charges, 151.

Liquid, motion of a perforated solid
in, 358, 490.

Lommel (E.) on a visible represen-
tation of the equipotential lines in
plates traversed by currents, 151.

Ludeking (C.) on the specific heat of
liquid ammonia, 393.

Luminons discharges in electrodeless
vacuum-tubes, on, 506.

MacGregor (Prof. J. G.) on econtact-
action and the conservation of
energy, 134.

Madsen (V.) on Scandinavian boul-
ders at Cromer, 312.

Magnetic field of a circular current,
on the, 354.

fields, constant and yarying,
experiments in, 68. 4

Magnetization of iron rings split
in a radial direction, on the, 392.

, on electrochemical effects due
to, 4738.

Mascart (M.) on the daily variations
of gravity, 314.

Melting-points of compounds, on the
effect of the replacement of oxy-
gen by sulphur on the, 458.

Meteoric stone seen to fall in South
Dakota, on a, 152.

Michigan, on the geology of the iron,
gold, and copper districts of, 74.
Minchin (Prof. G. M.) on the mag-
netic field of a circular current,

354.

Moissan (H.) on the properties of
amorphous boron, 60; on a new
electrical furnace, 513.

Molecular force, on the laws of, 211.

refraction and dispersion, on
some recent determinations of,
204.

Monckton (H. W.) on the occurrence
of boulders and pebbles from the
Glacial Drift in gravels south of
the Thames, 468.

Motion of a perforated solid in
liquid, on the, 338, 490.

Mountain-sickness, remarks on, 47.

IN DEX.

Nickel, on Villari’s critical point in,
469.

Nitrogen, on the preparation of pure,
1

Ohm’s law, on a necessary modifica-
tion of, 65,

Oxygen, on the effect of the re-
placement of, by sulphur on the
boiling- and melting-points of
compounds, 458.

Pembrey (M. S8.), comparative ex-
periments with the dry- and wet-
bulb psychrometer and an im-
proved chemical hygrometer, 525.

Perry (Prof. J.) on liquid friction,
441.

Pickering (S. U.) on the diffusion of
substances in solution, 127.

he (Dr. W.) on colour-blindness,

ae (F. D.) onthe Pambula gold-
deposits, 76.

Pressure, on the relation of volta
electromotive force to, 97.

Psychrometer, comparative experi-
ments with the dry- and wet-bulhb,
and an improved chemical hygro-
meter, 525,

Radiant energy, on, 115.

Radiation by rarefied gases under the
influence of electric discharge, on
the intensity of, 502.

Raisin (Miss C. A.) on the variolite
of the Lleyn, 312.

Refraction of rays of great wave-
length in rock-salt, sylvite, and
fluorite, on the, 35.

, on some recent determinations
of molecular, 204, 270.

Reid (C.) on a fossiliferous Pleisto-
cene oi at Stone, 469.

Rigollot (H.) on a chemical actino-
meter, 77.

Rimington (E. ©.), experiments in
electric and magnetic fields, con-
stant and varying, 68; on lumi-
nous discharges in electrodeless
vacuum-tubes, 506.

Roberts (T.) on the geology of the
district west of Caermarthen, 467.

Rock, on the fusion constants of
igneous, 173, 296.

Rock-salt, on the refraction of rays
of ereat wave-length in, 35.

Rowland (Prof. H. A.) on gratings
in theory and practice, 397.

543

Rubens (H.) on the refraction of
rays of great wave-length in rock-
salt, sylvite, and fluorite, 35.

Rudski (M. P.) on the flow of water
in a straight pipe, 439.

Rydberg (Dr. J. R.) on a certain
asymmetry - in Prof. Rowland’s
concave gratings, 190.

Salt-solutions, on hydrolysis in aque-
ous, 365.

Sanford (f.) on a necessary modifi-
cation of Ohm’s law, 65.

Shells, on the finite bending of thin,
496.

Shields (Dr. J.) on hydrolysis in
aqueous salt-solutions, 365.

Shrubsole (O. A.) on the plateau-
gravel south of Reading, 468.

Smith (F. J.) on high resistances
used in connexion with the D’Ar-
sonval galvanometer, 210.

Smith (W.), experiments in electric
and magnetic fields, constant and
varying, 68.

Snow (B. W.) on the refraction of
rays of great wave-length in rock-
salt, sylvite, and fluorite, 35.

Solid, on the motion of a perforated,
in liquid, 338, 490.

Solution, on the diffusion of sub-
stances ria Ae

Sound-waves, on plane and spherical,
of finite amplitude, 317.

Squier (Lieut. G. O.) on electro-
chemical effects due to magnetiza-
tion, 473.

Starr (J. E,) on the specific heat of
liquid ammonia, 393.

Stoney (Dr. G. J.) on a possible
source of the energy required for
the life of bacilli, 389.

Sulphur, on the effect of the re-
placement of oxygen by, on the
boiling- and melting-points of
compounds, 458.

Sumpner (Dr. W. E.) on the dif-
fusion of light, 81,

Sutherland (W.) on the laws of
molecular foree, 211.

Swinton (A. A. €.) on high
frequency electric discharges,
142,

Sylvite, on the refraction of rays of
ereat wave-length in, 43.

Teall (J. J. H.) on some coast-
sections at the Lizard, 466; on a

MRE ee ee

bn Sos ULE

IN RB EMA I ATEN SOE EAE OT | CITE EE EOI LIONEL EN 4 OI 8 MELE ETE NY LITTON SIE GE IO
en SE eapat ieaciey tee anaheim ners Serpents wees atone : 6

JA pee es

=

544 = INDEX.

radiolarian chert from Mullion
Island, 466.

Thermodynamics, on the signa of
the second law of, 124.

Thermometers, on the official testing
of, 595.

Threlfall (Prof. R.) on the electrical
properties of pure nitrogen, 1.

Tsuruta (K.) on the heat of vapo-
rization of liquid hydrochloric
acid, 435.

Vacuum-tube in a varying and in a
constant electric field, theory of a,
COT.

Vacuum-tubes, on luminous dis-
charges in electrodeless, 506.

Variolite of the Lleyn, on the, 312.

Villari’s critical point in nickel, on,
469.

Vis viva, on the equilibrium of, 153.

Volta electromotive force, on the re-
lation of, to pressure &e., 97.

Wadsworth (Prof. M. E.) on the
geology of the iron, gold, and
copper districts of Michigan, 74.

Water, on the flow of, in a str aight
pipe, 489.

—- as a catalyst, 531.

Waves, on plane and _ spherical
sound-, of finite amplitude, 317.
Wiebe (HL. F’.) on the official testing

of thermometers, 395.

END OF THE THIRTY-FIFTH VOLUME.

Printed by Jaytor and Francis, Red Lion Court, Fleet Street.

Elana SoSW Val, 66 Mek ie

Mintern Bros :

| 5
00
iS
|
}
|
}
|
|
|

DIAGRAM OF APPARATUS

tor the Continuous Preparation

OF

PURE NITROGEN.

|
|
|
| Mintern Bros. lith.

Seeeieniaes imeem inane ee =

Pilll., Wid®-.-O.U-VOL-ou -Fi-il

+O
Lf +O
uve c) nel, dito

| pea
| C
O
ye
. .
O €
re ‘
5K GE 72 at
> "SULY() 2D PUNIS ISO * =
o2 aS
2 So

S Vol parr

e

aod

to

|

Phil. Ma

a

nel,

+

Roch -salt (ove ©) teal, Slee

Svlvcte

\

(ehkove b) nda]

llaorite

(eurve ec)

400

500

100

SYOLW NE

ROCK-SALT.

10

2b

Mintern Bros lith

: UAT 2 Sodg Uta TUTyAy,
apouibya) sxaibay uw aunpouaduey apoubyuay saatboqud anne diay

a Cig Ci = SA eee ig (aps rH al LI 21 So 41 e4e1

Te) NEO +

(OD

We Oeeco

a

LD

W °

00 a)

oa S =

Aa 18

fate 5
N om.
. >
¢ S

. ~
3 3
S &
: :
®
OPEO:

OO:

vo es a . r A pet nn a cet me eee ae tia
penal f at so" ; ; F , ‘ oe .

Phil. Mag.$.5.Vol.85.PLIV.

S

OSCTpLILATOIR «

RESONATOR

Phil.Mag.S.5 Vol 35.PLIV. _
S

| | OSCILLATOR.
»
RESONATOR
»

Pig. 5.

i

Fig.7.

b 1

Mintern Bros. lith- = : : 5

Pll. Mas. 5.6. Vol.3o0. PI. V.

LOCK

Appoar nt Contractrow

~--==p5~--
20 a Sal
he,
ie
an
He

y 1 ve, elu a (bef)

u
net

ar

owt

)
Same. Sectional
at right angles 4
prece dug :

PN LET IT TEL
Sy SA HE A A A Z77

s
° h DS
A | ea | us
+ oO N . \
° o ee ° es

Verticad micrometer and
. yy
| APU LENCE S. Seale Ma

YB

Pars es
oS)

k
d
B)

WO

(AL IUAD SLELYDS SLI SPLLEPLSLELLD,

|
|
|
|
|

|
Secltonal pla oF fasauce

T7777

HS

Yi}

the finsion lube, the sight tule, he bumers,

|
|
Seglicnal elevation of the liirmace, showtuy
ele. Seale Yq .

Same. Sectional ¢
c

devation
» the

FN NF

Hel

) Arm te hold the

Tinsion lihe.

Perforated ving,

Minterms ros Jit

Fig.G.
Clay envelope of the platinum
finsion Ube

i

Melual Contraction

Appar né Contraction

Plul.Mag.S.5.Vol.35 Pl V.

is
= S
I ~ G)
S =
~
k
F\ re
\
q rary
| na
wi
| Z|
\
i
7
1F <
: S
5 5)
= IL
=
= ll
a i

Sess

Phil.Mag. S.5.Vol.35. Pl. VI.

aha
ili)

i coe.
Gucble, showy the solid

charge & aaaal platuum
tuhe. Scale "4.

E

ek.
gectzonal elevatum cf the ZY
Thanace & appurtemances yy,
SS showing the cucablei place. a]
a ;

NN

rir WOO Nis

RRs KKK SSS iG ji RN “
ie P
N
N Yi LA
N

Y a=.
NS QOS UN SKY AL AK LS, ASNSgys MM ELH Ww
ASSN SSS bE WzzZz7 ee PASO scat
WORSE oT Sete 7 SS SS

g
Pee 2,
Sectonal plan of furnace & cruchle.
Scale cale Vy.

400

tT clo

Chart, showurg the relation of thermal cupacuy, solid &
ligrad , to temperwiure,
Sertres I].

=) ae < .
Vantern bros. hth

Pic. 4s,

Phil.Mag.S.5 Vol. 35. PL. VIL.

Phil.Mag.S 5 Vol 35. Fl

f .
NSS

—-

ee ee Soe oe ns er een ee Re ne ae nS nT ae eny

Vol. fh - JANUA

RY 1893. | No. 212.

Published the First Day of every Month.—Price 28> 6d.

P ,
; 2

Ly

THE ee 2
LONDON, EDINBURGH, ano DUBLIN Ss.

|
|
|
PHILOSOPHICAL MAGAZINE, |
|

AND |
JOURNAL OF SCIENCE. |

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson’s ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’

LORD KELVIN, LL.D. P.R.S. &c.

GEORGE FRANCIS FITZGERALD, M.A. Sc.D. F.R.S.
-AND

WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S.

{
|
|
|
CONDUCTED BY |
i

FIFTH SERIES.

Ne 212,—JANUARY 1893.

WITH FOUR PLATES. '
Illustrative of Professor THRELFALL’s Paper on the Electrical Properties
| of Pure Nitrogen; Messrs. RtBpENs and SNnow’s on the Refraction
of Rays of Great Wave-length in Rock-salt, Sylvite, and Fluorite ;
Mr. F. Sanrorp’s on a necessary Modification of Ohm’s Law; and
Messrs. Rimineron and WytHE Smiru’s on Experiments in Electric
and Magnetic Fields, Constant and Varying.

LONDON:

PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.

Sold by Simpkin, Marshall, Hamilton, Kent, and Co., Ld.; Whittaker and Co. ;
and by A. and C. Black ;—T. and T. Clark, Edinburgh; Smith and Son,
Glasgow :—Hodges, Figyis, and Co., Dublin:—Putnam, New York:—Veuve J.

Boyveau, Paris :—and Asher and Co., Berlin.

ODOROGRAPHIA,

A NATURAL HISTORY OF RAW MATERIALS AND DRUGS USED IN
THE PERFUME INDUSTRY, INTENDED TO SERVE GROWERS,
MANUFACTURERS, AND CONSUMERS.

BY

J. Cx. SAWER, F.1.8.

GURNEY anp JACKSON, 1 PatrrnostER Row, Lonpon.
(Successors to Mr. Van Voorst.)

rice 12s.
CATALOGUE
OF THE SPECIMENS ILLUSTRATING THE

OSTEOLOGY OF VERTEBRATE ANIMALS

IN THE
MUSEUM OF THE ROYAL COLLEGE OF SURGEONS OF ENGLAND.
Part 3.—AVES.

By Rk..B. SHARPH, LL.D., &e.

S23 " Daes Os cach,
ApprEnpicus 5 and 6 to the Second Edition of the
DESCRIPTIVE CATALOGUE
OF THE

PATHOLOGICAL SPECIMENS

CONTAINED IN THE
MUSEUM OF THE ROYAL COLLEGE OF SURGEONS OF ENGLAND.
By J. H. TARGETT.

_ Taytor and Francis, Red Lion Court, Fleet Street, E.C.

Medium 8vo. Vol. I. Part I., 4s.; Part II., 7s. 6d.; Part IIL. 6s.

PHYSICAL MEMOIRS, 7
SELECTED AND TRANSLATED FROM FOREIGN SOURCES ©

‘UNDER THE DIRECTION OF THE —
PHYSICAL SOCIETY OF LONDON.

Demy 8vo, price 12s., with numerous Woodcuts, three Plates.

JOINT SCIENTIFIC PAPERS
OF THE LATE
J. P. JOULE, DCL, F.RBS. |
Volume II., published by the Physical Society of London. |
Dniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait.

Vol, - THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

TayLok and FRANCIS, Red Eien Court, Fleet Street, E.C.

THE
LONDON, EDINBURGH, anp DUBLIN

PHILOSOPHICAL MAGAZINE,

AND

JOURNAL OF SCIENCE.

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’

Nicholson’ s ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’

CONDUCTED BY

LORD KELVIN, LL.D. P.R.S. &e.

GEORGE FRANCIS FITZGHRALD, M.A. Sc.D. F.R.S.
AND
WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S8.

es
d

FIFTH SERAES.o°
Ne 213, FEBRUARY 1893”: Bk

Wreoc cs
rice SNe
—~ 4lVom,

i

_

LONDON:

PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.

Sold by Simpkin, Marshall, Hamilton, Kent, and Co., Ld.; Whittaker and Co.;
and by A. and C, Black ;—T. and T. Clark, Edinburgh; Smith and Son,
Glascow :—-Hodges, Figgis, and Co., Dublin:—Putnam, New York:—Veuve J.
Boyveau, Paris :—and Asher and Co., Berlin.

Pp. xi, 8361; Demy 8vo. With 2 Plates and 65 Woodeuts. Price 10s.
TELESCOPIC WORK FOR STARLIGHT EVENINGS.

BY

WILLIAM F. DENNING, F.R.AS.
(Formerly President of the Liverpool Astronomical Society.)

This work is intended as a useful companion for amateur observers, and
contains many facts and references likely to stimulate their interest in the
sublime science of Astronomy.

Chapters are given on the Invention of the Telescope, on Large and Small
Telescopes, and copious notes on Telescopic work. Then follow descriptions
of the Sun, Moon, Planets, Comets, Meteors, Stars, and Nebule. ‘The methods
and requirements of modern observation are alluded to, and the information has
been carefully brought up to date.

TAYLor and Francis, Red Lion Court, Fleet Street, H.C.

Medium 8vo. Vol. I. Part L, 4s.; Part I1., 7s. 6d.; Part IIL, 6s.

PHYSICAL MEMOIRS,
SELECTED AND TRANSLATED FROM FOREIGN SOURCES

UNDER THE DIRECTION OF THE

PHYSICAL SOCIETY OF LONDON.

Demy 8vo, price 12s., with numerous Woodcuts, three Plates.

JOINT SCIENTIFIC PAPERS

OF THE LATE

Af P. JOULE, D.C.L., F.R.S.
Volume EI., published by the Physical Society of London.

Uniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait. |

Vol. I. THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

Tayior and Francis, Red Lion Court, Fleet Street, E.C.

Demy 8vo, price ls.

THE OBSERVATORY,
A MONTHLY REVIEW OF ASTRONOMY.
Edited by
H. H. TURNER, M.A., BSc., Suc. R.AS.,
AND
A. A. COMMON, LL.D., F.R.S., Taras. R.A.S.

THE COMPANION TO THE OBSERVATORY FOR 1893.
Price 1s. 6d.

TayLor and Francis, Red Lion Court, Fleet Street, E.C.

si 33, MARCH 1893. No. 214.

| Published the First Day of every Month.

praice
THE / ,

LONDON, EDINBURGH, anno DUBLIN

PHILOSOPHICAL MAGAZINE,

AND
JOURNAL OF SCIENCE.

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson's ‘Journal, and Thomson’s ‘Annals of Philosophy.’

PRT SST AT OORT IY BN NE TH TS

CONDUCTED BY

LORD KELVIN, LL.D. P.R.S. &e.

GEORGH FRANCIS FITZGERALD, M.A. 8o.D. F.R.S.
AND

WILLIAM FRANCIS, Pe. De t.L.8.: F:B.A.8. ECS.

N° 214.—MARCH 1893.

WITH TWO PLATES.

Illustrative of Mr. Cart Barvus’s Papers on the Fusion Constants of
Jeneous Rock.

|
|
FIFTH SERIES. |

PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREED,

| |
LONDON:

Sold by Simpxin, Marshall, Hamilton, Kent, and Oo., Ld.; Whittaker and Co.;

and by A. and C. Black ;—T. and ‘TI. Clark, Edinburgh ; Smith and Son,

Giasgow :—-Hodges, Figgis, and Co., Dublin. —Putn: am, New York:—Veuve J.
Boyveau, Paris :—and Asher and Co., Berlin,

Pp. xi, 361; Demy 8vo. With 2 Plates and 65 Woodeuts. Price 10s.
TELESCOPIC WORK FOR STARLIGHT EVENINGS.

BY
WILLIAM F. DENNING, F.R.AS.

(Formerly President of the Liverpool Astronomical Society.)

This work is intended as a useful companion for amateur observers, and
contains many facts and references likely to stimulate their interest in the
sublime science of Astronomy.

Chapters are given on the Invention of the Telescope, on Large and Small
Telescopes, and copious notes on Telescopic work. Then follow descriptions
of the Sun, Moon, Planets, Comets, Meteors, Stars, and Nebule. The methods
and requirements of modern observation are alluded to, and the information has
been carefully brought up to date.

Taytor and Francis, Red Lion Court, Fleet Street, H.C.

Medium 8vo. Vol. I. Part L., 4s.; Part IL., 7s. Gd.5 Pach Elis.
PHYSICAL MEMOIRS,
SELECTED AND TRANSLATED FROM FOREIGN SOURCES

UNDER THE DIRECTION OF THE

PHYSICAL SOCIETY OF LONDON.

Demy 8vo, price 12s., with numerous Woodcuts, three Plates.

JOINT SCIENTIFIC PAPERS

OF THE LATE

J. P. JOULE, DOL, FBS.
Volume IL., published by the Physical Society of London.

Uniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait.

Vol. I. THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

Taytor and Francis, Red Lion Court, Fleet Street, E.C.

Demy 8vo, price Is.

THE OBSEBVATORY,
A MONTHLY REVIEW OF ASTRONOMY.
Edited by
H. H. TURNER, M.A., B.Sc., Sxc. R.A.S.,
AND
A. A. COMMON, LL.D., F.R.S., Treas. R.A.S.

THE COMPANION TO THE OBSERVATORY FOR 1893.
Price 1s. 6d.
TayLor and Francis, Red Lion Court, Fleet Street, H.C.

THE Bay
LONDON, EDINBURGH, anno DUBLIN

PHILOSOPHICAL MAGAZINE,

AND
JOURNAL OF SCIENCE.

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson’s ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’

CONDUCTED BY

LORD KELVIN, LL.D. P.R.S. &e.

GEORGH FRANCOIS FITZGERALD, M.A. Sc.D. F.R.S.
AND

WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S.

FIFTH SERIES.
N° 215.—APRIL 1893.

LONDON:
PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET.

|'Sold by Simpkin, Marshall, Hamilton, Kent, and Oo., Ld.; Whittaker and Co. ;

| and by A. and C. Black ;—T. and T. Clark, Edinburgh; Smith and Son,
Glasgow :—Hodges, Figgis, and Co., Dublin:—Putnam, New York:—Veuve J.
Boyveau, Paris:—and Asher and Co., Berlin,

|

|

Pp. xi, 361; Demy 8vo. With 2 Plates and 65 Woodcuts. Price 10s.
TELESCOPIC WORK FOR STARLIGHT EVENINGS.

BY
WILLIAM F. DENNING, F.RB.A.S.
(Formerly President of the Liverpool Astronomical Society.)

This work is intended as a useful companion for amateur observers, and
contains many facts and references likely to stimulate their interest in the
sublime science of Astronomy.

Chapters are given on the Invention of the Telescope, on Large and Smail
Telescopes, and copious notes on Telescopic work. Then follow descriptions
of the Sun, Moon, Planets, Comets, Meteors, Stars, and Nebule. The methods
and requirements of modern observation are alluded to, and the information has
been carefully brought up to date.

TayLor and Francis, Red Lion Court, Fleet Street, E.C.

Medium 8vo. Vol. I. Part I., 4s.; Part II., 7s. 6d.; Part IIL, 6s.

PHYSICAL MEMOIRS,
SELECTED AND TRANSLATED FROM FOREIGN SOURCES

UNDER THE DIRECTION OF THE

PHYSICAL SOCIETY OF LONDON.

Demy 8vo, price 12s., with numerous Woodcuts, three Plates.
JOINT SCIENTIFIC PAPERS

OF THE LATE

J. P. JOULE, DCL, F.RS.
Volume II., published by the Physical Society of London.

Uniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait.

Vol. I. THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

TAYLoR and Francis, Red Lion Court, Fleet Street, E.C.

Demy 8vo, price Is.

THE OBSERVATORY,
A MONTHLY REVIEW OF ASTRONOMY.
Edited by
H. H. TURNER, M.A., BSc., Sc. R.A.S.,
AND
A. A. COMMON, LL.D., F.R.S., Treas. R.A.S.

THE COMPANION TO THE OBSERVATORY FOR 1893.
Price 1s. 6d.
Taytor ard Francis Red Lion Court, Fleet Street, E.C.

1-36. | MAY 1893. | No. 216.

Published the First Day of every Month.—Price 2s. 6d.

mah, 8% ¥o

| LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE,
AND

JOURNAL OF SCIENCE.

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson's ‘Journal,’ and Thomson’s ‘Annals of Philosophy.’

*

LORD KELVIN, LL.D. P.R.S. &e.

GHORGE FRANCIS FITZGERALD, M.A. Sc.D. F.R.S.
AND |

WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S.

CONDUCTED BY

FIFTH SERIES.
Ne 216,—MAY 1893.
WITH ONE PLATE.
j

Illustrative of Prof. J. Perry’s Article on Liquid Friction.

ay

LONDON:

: PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,

"Sold by Simpkin, Marshall, Hamilton, Kent, and Qo, Ld.; Whittaker and Co. ;

' and by A. and C. Black ;—T. and T. Clark, Edinburgh; Smith and Son,

Glasgow :—Hodges, Figyis, and Co., Dublin:—Putnam, New York:—Veuve J.
Boyveau, Paris :—and Asher and Co., Berlin,

~ Lp, Al, VUL, Welly OVO. Wilh 2 flates and 0o VW oodcuts. F£rice 1Us.
TELESCOPIC WORK FOR STARLIGHT EVENINGS.
BY
WILLIAM F. DENNING, F-.R.A.S.
(Formerly President of the Liverpool Astronomical Society.)

This work is intended as a useful companion for amateur observers, and
contains many facts and references likely to stimulate their interest in the
sublime science of Astronomy.

Chapters are given on the Invention of the Telescope, on Large and Small
Telescopes, and copious notes on Telescopic work. Then follow descriptions
of the Sun, Moon, Planets, Comets, Meteors, Stars, and Nebule. The methods
and requirements of modern observation are alluded to, and the information has
been carefully brought up to date.

Taytor and Francis, Red Lion Court, Fleet Street, E.C.

Medium 8vo. Vol. I. Part I., 4s.; Part IL, 7s. 6d3; Parke os
PHYSICAL MEMOIRS,
SELECTED AND TRANSLATED FROM FOREIGN SOURCES

UNDER THE DIRECTION OF THE

PHYSICAL SOCIETY OF LONDON:

Demy 8vo, price 12s., with numerous Woodcuts, three Plates.

JOINT SCIENTIFIC PAPERS

OF THE LATE

J. P. JOULE, DCL, F.RBS.
Volume II., published by the Physical Society of London.

Uniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait.

Vol. Il. THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

Tayior and Francis, Red Lion Court, Fleet Street, H.C.

Demy 8vo, price Ls.

THE OBSERVATORY,
A MONTHLY REVIEW OF ASTRONOMY.
Edited by

H. H. TURNER, M.A., BSc., Szc. R.AS.,
T. LEWIS, F.B.AS.,
H. P. HOLLIS, B.A., F.B.AS.

THE COMPANION TO THE CBSERVATORY FOR 18983.
Price 1s. 6d.

TayLor and Francis Red Lion Court, Fleet Street, E.C. —

ol. 35. JUNE 1893. ( © fo32-~No. 217.

: Published the First Day of ever ae Month. Pred 282, sa :
THE
LONDON, EDINBURGH, anno DUBLIN

PHILOSOPHICAL MAGAZINE,

AND
JOURNAL OF SCIENCE.

Being a Continuation of Tilloch’s ‘Philosophical Magazine,’
Nicholson’s ‘Journal, and Thomson's ‘Annals of Philosophy.’

CONDUCTED BY

LORD KELVIN, LL.D. P.R.S. &e.

GEORGH FRANCIS FITZGERALD, M.A. So.D. F.R.S.
AND

WILLIAM FRANCIS, Pa.D. F.L.S. F.R.A.S. F.C.S.

FIFTH SERIES.
Ne 217.—JUNE 1893.

LONDON:

PRINTED BY TAYLOR ching FRANCIS, RED LION COURT, FLEET STREET.

Sold by Simpkin, Marshall, ‘Hamilton, Kent, and Oo., Ld.; Whittaker and Co. ;
and by A. and C. Black ;—T. and T. Clark, Edinburgh ; Smith and Son,
inact, —Hodges, Figgis, and Co., Dublin:—Putnam, New York:—Veuve J
Boyveau, Paris:—and Asher and Co., Berlin.

i

DUBLIN UNIVERSITY PRESS SERIES.

A TREATISE ON THE ANALYTICAL GEOMETRY OF TH |
POINT, LINE, CIRCLE, AND CONIC SECTIONS:

!
CONTAINING AN ACCOUNT OF ITS MOST RECENT EXTENSIONS, ||
WITH NUMEROUS EXAMPLES.

BY .
JOHN CASEY, LL.D., F.R.S. |
Second. Edition, Revised aud Enlarged. Crown 8vo, 12s.

London: LONGMANS, GREEN & CO.

Medium 8vo. Vol. I. Part I., 4s.; Part II., 7s. 6d.; Part III, 6s. .
PHYSICAL MEMOIRS, iH
SELECTED AND TRANSLATED FROM FOREIGN SOURCES f

UNDER THE DIRECTION OF THE

PHYSICAL SOCIETY OF LONDON.

Demy 8vo, price 12s., with numerous Woodeuts, three Plates.

JOINT SCIENTIFIC PAPERS

OF THE LATE .

J. P. JOULE, DCL, FBS.
Volume I1., published by the Physical Society of London.

Uniform with the above, price £1, with numerous Woodcuts, four Plates,
and Portrait.

Vol. I. THE SCIENTIFIC PAPERS OF THE LATE J. P. JOULE,
D.C.L., F.R.S.

TayLor and Francis, Red Lion Court, Fleet Street, H.C.

Demy 8vo, price 1s.

THE OBSERVATORY,
A MONTHLY REVIEW OF ASTRONOMY.
Edited by i
H. H. TURNER, M.A., BSc., Sc. R.A.S., [

T. LEWIS, F.R.AS.,
H. P. HOLLIS, B.A., F.R.AS.

THE COMPANION TO, THE OBSERVATORY FOR i893.
fa 4 a 5/4 - Price ls. 6d.

TAYLOR and FRANCIS Red Lion Court, Fleet Street, E.C.

RD
& LS a
2
1
j
}
=|
BI XY z
ra » 5
Ng
if a ~ af aks
x
a 4
‘ SU era
i ‘4 ty Lana
a Jays nh
e z : , ar, d
7 ‘i ies
Ae : a at
' ah
3 ee
ie 7

ts

; ‘ ‘ vena) —_— oe" e ae a
Eto, - ¢ 1 Apt te OAR MO Mala iene oe eT aR RNARAT ONE . CE TT BT *
B — —_— ne se deat aR LISLE .
— > I a a
= rahe ae 1 oS a

.

i

ik