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RAIOQRIQRAGIAIRVRAG LNAI IIR IOI RIRAIZIRIOANIOION

UNITED STATES PATENT OFFICE

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GOVERNMENT PREVTING OFFIOL

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THE TS.

LONDON, EDINBURGH, anv DUBLIN

PHILOSOPHICAL MAGAZINE

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CONDUCTED BY °

LORD KELVIN, G.C.V.O. D.C.L. LL.D. F.R.S. &e.
2OnN JOLY, M.A. D.Sc. F.R.So2.G:S.

AND

WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.0.8. ;

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

VOL. V.—SIXTH SERIES.
‘JANUARY—JUNE 1903.

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

SOLD BY SIMPKIN, MARSHALL, HAMILTON, KENT, AND CO., LD.—T. AND T. CLARK,
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“ Meditationis est. perscrutam: <eeoulta ; conterhplationis est admirari
perspicue, ey. Adaiiratio: genétag ‘Guestionem, quzestio investigationem,
investiga tio inyentionem,’ *__ Hug go de WS. Vietar é ec

“ Cur spirent venti, cur terra dehiscat,
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Pheebus ferrugine condat,
Quid toties diros cogat flagrare cometas,

Quid pariat nubes, veniant cur fulmina ccelo,
Quo micet igne Iris, superos quis conciat orbes

Tam yario motu.”
J. B. Pinelli ad Mazonium.

—

CONTENTS OF VOL: V.
(SIXTH SERIES).

NUMBER XXV.—JANUARY 1903.

Prof. A. Battelli and Mr. L. Magri on Oscillatory Discharges.
Dr. Harold Pender on the Magnetic Effect of Electrical Con-
BO ee ee i ay Se eee Ee OR i i ae dun Sc soe eee
Prof. H. L. Callendar on the Thermodynamical Correction of
elem henmMameben’s . ms ees ae pir oe tb ek ae
Prof. E. Rutherford on Excited Radioactivity and the Method of
Ee MMOS MNSSIOM eo, cae. so ss eae ts sees yg os 4 ee
Mr. R. L. Wills on the Effect of Temperature on the Hys-
RISSUS JL OVS AT ue 0) aA ae ma ey as aA ena ae
Mr. 8. H. Burbury on the Conditions necessary for Equipar-

FECT MOMP LOL, (5 scare dee ts stop ayaeet ts ch a ds de en ee
Lord Rayleigh on the Theory of the Fortnightly Tide......
Dr. Louis Lownds on the Thermomaenetic and Related

Paoperbies oF Crystalline Bismuth 2.2.0 2: te. ey ee es
Prof. John Trowbridge on the Spectra of Hydrogen, and Re-

Remsen Hines an the Spectra of Gases ....5. 500... i. wae

Dr. E. W. Marchant on a Graphical Method of Determining
the Nature of the Oscillatory Discharge from a Condenser
through a Coil of Variable Inductance ................

Prof. D. B. Brace on a Sensitive-strip Spectropolariscope

Notices respecting New Books :—

Dr. Alois Lanner’s Naturlehre.....

Proceedings of the Geological Society :—

Prot. W. B. Dawkins on the Red Sandstone-Rocks of
Peel (1. of Man), and on the Carboniferous, Permian,
and Triassic Rocks under the Glacial Drift in the
North of the Isle of Man ... pies

Dr. J. §. Flett on the Ash that fell on n Barbados, “after

thesErUpMOMah St. VINCCMb sf tela sm ec yt ces wee

Dr. C. Callaway on the Plutonic Complex of Central
BRP Ron enya reac’ y Waa wi CEM a cv wtye ase wig eye. euscal
Prof. T. G. Bonney on Alpine Valleys in Relation to
eg ACIOUS EER as yer Pac U te Ma aie yf ours uk Saleh ts
Prof. E. J. Garwood on the Origin of some “ Hanging
Valleys in the Alps and Himalaya ........,....-

Page
it

34
48

lv CONTENTS OF VOL. V.—SIXTH SERIES.

Page

Dr. H. M. Ami on the Great Saint-Lawrence-Champlain-
Appalachian Fault of America 7.2222). ~..) aoe 174

Mr. A. K. Coomaraswamy on the Point-de-Galle Group
(Ceylon): Wollastonite-Scapolite Gneisses ........ 174

Prof. 8S. H. Reynolds and Mr. A. Vaughan on the Jurassic

Strata cut through by the South Wales Direct Line
between Filton and Wootton Bassett .............. 175

Intelligence and Miscellaneous Articles :—

Hodekins'Medal . oc... 32... oR eee 176

NUMBER XXVI.—FEBRUARY.
Prof. E. Rutherford on the Magnetic and Electric Deviation

of the easily absorbed Rays from Radium .............-. 177
Mr. F. L: Hitcheock on Vector Differentials ............ 187
Lord KelvinzAnimal Thernidstat <2... .....) 20. oe 198

Dr. Marshall Watts on the Existence of a Relationship
between the Spectra of some Elements and the Squares of
them Atomie Weights“... 4... : 0... von pee ee 203

Dr. Meyer Wilderman on the Theory of the Connexion be-
tween the Energy of Electrical Waves or of Light intro-
duced into a System and Chemical Energy, Heat Energy,
Mechanical Energy, &c. of the. same .......... 3a 208

Mr. Walter Makower on a Determination of the Ratio of the
Specific Heats at Constant Pressure and at Constant Volume
for Air and Steam. (Plate I)) ...... ‘3... 462 226

Lord Rayleigh on the Spectrum of an Irregular Disturbance . 238

Prof. A. Schuster on the Influence of Radiation on the
Transmission of Heat... (Plate 11))......:.).25 eee 243

Prof. R. W. Wood on Screens Trausparent only to Ultra-
Violet Light, and their Use in Spectrum Photography.
(Plates LIL. & TV.) pHs tS el aniG «+ eee eee 257

Dr. G. Johnstone Stoney: How to apply the Resolution of

Light into Uniform Undulations of Flat Wavelets to the

Investigation of Optical Phenomena ................25 264
Mr. W. GC. D. Whetham on the Theory of Electrolytic Dis-

SOGIAION 6.0 leu oad swe eee ene ee ene 279

Notices respecting New Books :— |

Annuaire:pour ’An 1903. ..... 24. Ja. - ss =. 290
Compte Rendu du deuxiéme Congres International des

Mathematiciens ... -.. <5 20 2eee eee: ee ee 290

Prof. L. Boltzmann’s Lecons sur la Théorie des Gaz .. 291

Prof. P. Drude’s The Theory of Optics .............. 292

CONTENTS OF VOL. V.——-SIXTH SERIES. ¥

NUMBER XXVIL—MARCH.

Page
Lord Rayleigh on the Free Vibrations of Systems affected ;
emma simiall) Hotabary Derm Sie) 0 2.ti iste lorh sod ab hdd leg Bel 293
Lord Rayleigh on the Vibrations of a Rectangular Sheet of
SURAT CPUC RT Ye eran crs OR oP PEN EM tr 297
Dr. W. W. Taylor and Mr. J. K. H. Inglis: A Suggested
iiheoryot the Aluminium Anode (Ate cep saisre Silo eovel 301
Mr. George A. Campbell on Loaded Lines in Telephonic
Mramsmissions. (relates V...d¢. VE) emer 2h es tas 313
Mr. C. A. Chant on the Variation of Potential along a Wire
transmitting Electric Waves. (Plate VII.) ............ 331
Prof. A. Schuster on the Spectrum of an Irregular Dis-
EE URGED yin Stee Nigel ae sa A ok de hanaicedcecaWasoebesia'ls age: oy ltaee a tele 344
Prof. J. J. Thomson on the Charge of Electricity carried by a
EraSeOUS ROT, vi eure MM PTS loa! Savafae tale. 346

Prof. F. L. O. Wadsworth on the Effect of Absorption on
the Resolving Power of Prism Trains, and on Methods of
Mechanically Compensating this Effect. (Plate VIII.) .. 355
Prof. H. 8. Carslaw on the Use of Contour Integration in the
Problem of Diffraction by a Wedge of any Angle........ O74
Notices respecting New Books :—
The Meteorology of the Ben Nevis Observatories :

aries POSS S92) ast eke eet ate hyet den tio Da 379
J. Macé de Lépinay’s Franges d’Interférence et leurs

applications! Meétrologiqtes!tin Aeon 4 aac a. 382
M.-H. Carvallo’s L’Electricité Déduite de l’Expérience

et Ramenée au Principe des Trauvaux Virtuels...... 382
L. A. Bauer’s United States Magnetic Declination Tables

aundelisoconic Chartsifor li G02 Ge, eel eee 382

Proceedings of the Geological Society :—
Mr. H. Preston on a new Boring at Caythorpe (Lincs.).. 384
Dr. J. Ball on the Semna Cataract or Rapid of the Nile.. 384
Mr. F. J. Stephens’s Geological Notes on the North-
Ries erovincespoimindial s\s fo.) 62 esa wee es 385
Mr. D. A. MacAlister on Tin and Tourmaline ........ 386
Mr. W. Whitaker on some Well-sections in Suffolk.... 386
Mr. G. Abbott on the Cellular Magnesian Limestone of
IY ura enn Mea es cose a en hee w Cal Cake Seta ak Se G- 387
Prof. T. G. Bonney on the Magnetite-Mines near Cogne
GGA Nera eAU DSN Ip ciara FES. hoe tM R LP ale us Bees, 3
Mr. A. KK. Coomaraswamy on the Tiree Marble ...... 3

vi CONTENTS OF VOL. V.—SIXTH SERIES.

NUMBER XXVIII.—APRIL.

Page
Prof. J. 8. Townsend on the Conductivity produced in Gases ;
by the Aid of Ultra-Violet Light. (Plate 1X.).......... 389
Mr. $8. W. J. Smith on a Portable Capillary Electrometer.
MP late XK.) es be. ee Ses ale acre aks oe 398
Dr. Meyer Wilderman on the Connexion between Freezing-
points, Boiling-points, and Solubilities ................ 405
Prof. J. C. McLennan on Induced Radioactivity Excited in
Air at the Foot of Waterfalls 2. 7. . 6.2530" ") .50.seeee 419
Mr. H. A. Wilson: Determination of the Charge on the
Tons produced in Air by Rontgen Rays ................ 429
Prof. E. Rutherford and Mr. F. Soddy on the Radioactivity
ot Uranium: 0 eo. cca Secs 'c Bape bebe eee Oo eee 44]
Prof. E. Rutherford and Mr. F. Soddy: Comparative Study
of the Radioactivity of Radium and Thorium .......... 445

Mr. H. W. Chapman on the Problem of Columbus. (Plate XI.) 458
Messrs. C. Runge and J. Precht on the Position of Radium

| in the Periodic System according to its Spectrum........ 476

, « Prof, H.. Rutherford on: Radioactivity ¥ . |...) 3.2 see eee 481
i Dr. Quirino Majorana on New Magneto-Optic Phenomena

exhibited by Magnetic Solutions.................0.;75. 486
Prof. L. R. Wilberforce on an Elementary Treatment of

Conducting Networks) 22 a0. wa ee soe eee 489

Notices respecting New Books :—

Kavasji Dadabhai Naegamyala’s Report on the Total
Solar Eclipse of January 21-22, 1898, as observed at
Jeur:in Western India... ... 21. 26. 490

Dr. A. von Waltenhofen’s Die Internationalen Absoluten
Masze Iusbesondere die Electrischen Masze, fiir Studi-

rence der Electrotechnik . 7.22524)... 32: / 2a ee 491
EF. M: Raoult’s Cryoseopieps . 42%: 2 3). See 492
Bericht tiber die Internationale Experten-Conferenz fiir

Wetterschiessen,in Graz ) 20... ’aeeeou ie ye eee 492

NUMBER XXIX.—MAY.

Prof. J. A. Fleming and Mr. W. C. Clinton on the Measure-
ment of Small Capacities and Inductances. (Plate XII.) . 493
Mr. J. W. Peck on the Special Epochs in Vibrating Systems. 511
Dr. G. J. Parks on the Thickness of the Liquid Film formed
by Condensation at the Surface of a Solid............:. 517
Prof. J. Trowbridge on the Gaseous Constitution of the H
and K lines of the Solar Spectrum, together with a Dis-
cussion of Reversed Gaseous Lines. (Plate Doli) < ose 524
Mr. V. J. Blyth on the Influence of Magnetic Field on
Mhermal Conductivity... 2: gaa Gee ebanines ss + 2 oe 529

aR es a

CONTENTS OF VOL. V.—SIXTH SERIES.

Dr. R. T. Glazebrook: Theoretical Optics since 1840.—A
SRE EE oe LC een Iole oy elon cin d ANOS aces oly, 9 is
Dr. E. J. Mills on the Numerics of the Elements.—Part ILI.
Mr. J. J. E. Durack on the Specific Ionization produced by the
Borpuscles given outby Radium...............20+2 +++
Prof. E. Rutherford and Mr. I’. Soddy on Condensation of
the Radioactive Emanations. (Plate XIV.)............
Prof. E. Rutherford and Mr. F. Soddy on Radioactive Change.
Mr. J. Brown on Removal of the Voltaic Potential-Difference
pop [Shear coer OE aaa Ree energie en
Notices respecting New Books :—
Dr. W. L. Hooper and Mr. R. T. Wells’s Electrical
Problems for Engineering Students ..............
Intelligence and Miscellaneous Articles :—
On the Heat evolved when a Liquid is brought into Con-
tact with a finely-divided Solid, by Tito Martini .

NUMBER XXX.—-JUNE.

Mr. J. H. Jeans on the Kinetic Theory of Gases developed
Menta NEW, OvaN@POMMIby 2). 2 Say Pe Pola jyncg ss fod t se
Prof. A. Battelli and Mr. L. Magri on Oscillatory Discharges.
Pra ONEE) Pee Mca Ma SE Se uke To
Prof. W. B. Morton on the Connexion between Speed of
Propagation and Actbenmi on of Electric Waves along
P's. 7e5 ll VARIES Scale at gee rea atte 12 6 he
Mr. W. H. Derriman on an Oscillating Table for Deter-
mamma Niamemts. OF LMertias jas oe As oh ols 4c aed vi cide
Messrs. K. Honda and 8. Shimizu on the Wiedemann Effect
in Ferromagnetic Substances. (Plate XVI.)............
Prof. Karl Pearson on a General Theory of the Method of
RRS me OSIUIOMY + Sees ochre Mea eS ek NL, Pe) 0 PR ORAS
Dr. R. A. Lehfeldt on a Potentiometer for Thermocouple
DPM TAMIRGINEMUS) “sina au eee ae eles oicle nese Gains Bees
Dr. R. A. Lehfeldt on a Resistance Comparator ...:......

_ Prof. S. P. Langley on “ Good Seeing.” (Plate XVII.) ....

Lord Rayleigh on the Proportion of Argon in the Vapour
Bas PMN Oge TOMA MAC MANE 2014 Sree Ale Sobel en ab tess
Hon. R. J. Strutt on Radioactivity of Ordinary Materials ..
Mr. C. G. Barkla on Secondary Radiation from Gases subject
TOM MAINA SUSE aster vars tas Palas no. si cys xcane MDa we BR Caecs
Prof. J. 8. Townsend on the Specific Ionization produced by
POs ClasnO ama. 26! eye ch fe we'd we aneie fee oe aagele eames
Messrs. J. C. McLennan and KE. F. Burton: Experiments
on the Electrical Conductivity of Atmospheric Air ......
Notices respecting New Books :—
Prof. 8S. Arrhenius’s ‘Text-Book of Electrochemistry
Prof. J. M. Pernter’s Meteorlogische Optik ..........
Mr. J. Castell-Evans’s Physico-Chemical Tables ......

vil
Page

Dat
543

500
O61
576
591

595

. o9d

PLATES.

I. Illustrative of Mr. W. Makower’s Paper on a Determination of the
Ratio of the Specific Heats at Constant Pressure and at Constant
Volume for Air and Steam.

II. Illustrative of Prof. A. Schuster’s Paper on the Influence of
Radiation on the Transmission of Heat.

II. & IV. Illustrative of Prof. R. W. Wood’s Paper on Screens Trans-
parent only to Ultra-Violet Light, and their Use in Spectrum
Photography.

V. & VI. Illustrative of Mr. G. A. Campbell’s Paper on Loaded Lines in
Telephonic ian.

VIL. Illustrative of Mr.C. A. Chant’s Paper on the Variation of Patera
along a Wire transmitting Electric Waves.

VIIL. Illustrative of Prof. F. L. 0. Wadsworth’s Paper on the Effect of
Absorption on the Resolving Power of Prism Trains, and on
Methods of Mechanically Compensating this Effect.

IX. Illustrative of Prof. J. 3. Townsend’s Paper on the Conductivity
produced in Gases by the Aid of Ultra-Violet Light.

X. Illustrative of Mr. S. W. J. Smith’s Paper on a Por rtable Capillary
Hlectrometer.

XI. Illustrative of Mr. H. W. Chapman’s Paper on the Problem of
Columbus.
XII. Illustrative of Prof. J. A. Fleming and Mr. W.C. Clinton’s Paper
on the Measurement of Small Capacities and Inductances.

XIII. Illustrative of Prof. J. Trowbridge’s Paper on the Gaseous Con-
stitution of the H and K lines of the Solar Spectrum.

XIV. Illustrative of Prof. E. Rutherford and Mr. F. Soddy’s Paper on
Condensation of the Radioactive Emanations.

XV. Illustrative of Prof. A. Battelli and Mr. L. Magri’s Paper on
Oscillatory Discharges.

XVI. Illustrative of Messrs. K. Honda and 8. Shimizu’s Paper on the
Wiedemann Effect in Ferromagnetic Substances.

XVII. Illustrative of Prof. S. P. Langley’s Paper on “ Good Seeing.”

ERRATUM IN VOL. IV. (Sept. 1902).

Page 329
For og WW athe a eee 1000 approx.,
tines MBAS WN Se 14
read BN Ne 100 approx.
KE, IG Xr, a4

Later 1/100 instead of 1/1000.

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LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[SIXTH SERIES. ]
JANUARY 1903.

I. On Oscillatory Didar "es.
By A. Batrecxi and L.¥ 4

PARTOe AD

General Description of Method.

d. HOUGH experiments have been made for some time

in order to test Thomson’st theory of condenser
discharges, no systematic and simultaneous study has, so far,
been effected of the influences capable of modifying in the
case of those discharges the period of oscillation, as the expe-
rimental disposition hitherto employed failed to prove adequate
for researches extending over any considerable ranges, and

did not allow of taking account of—if not all—even the

principal elements.
Nor has the importance of the spark ever been carefully

considered ; notwithstanding Cardani’s and Heydweiller’s re-

searches, no exact value of its resistance has been obtained,

according to the most considerable mutability of the spark

from one case to another, and the variability of its resistance,
from the moment of its beginning to the moment of its a

appearing. Moreover, in the case of oscillating discharges

the current is not uniformly distributed over the whole section

-of the conductor.

This complication—modifying, as was first shown by

Maxwell, and afterwards more fully by Lord Rayleigh,

* Communicated by the Authors.
+ Phil. Mag. [4] v. p. 3893 (1853).

Phil. Mag. 8. 6. Vol. 5. No. 25. Jan. 1903. B

2 Prof. A. Battelli and Mr. L. Magri on

Stefan, and Barton, the value of the resistance and the self-
inductior aken into account only in the case of
discharges along rectilinear wires, the true resistance and the
true self-induction for rapidly oscillating currents having
been calculated in this special case only.

Finally, to treat this argument ina complete manner there
would be required the knowledge of the energy spent in the
different parts of the circuit, including the spark; and, asa
matter of fact, a study of this distribution has formed the
object of important researches, such as those of Riess, Paalzow,
Villari, and more recently of Heydweiiler and of Cardani;
but in all the experiments above mentioned, though the
relation between the measured quantities and the capacity,
self-induction, and resistance of the circuit is allowed for, yet
it is not ascertained how the distribution of energy may be in-
fluenced by the period of discharge. In the case of oscillating
discharges, in fact, measurements have been made either for
a single value of the period of oscillation only, or those made
for different periods, by different experimenters, are difficult
to compare with each other. A general and systematic study
of such elements as may have a t bearing on the oscillatory
discharge phenomenon is therefore wanting. This we intended
to undertake.

2. In this paper we give an account of the first part of
our researches, the results arrived at being already worthy
of notice. For these experiments we connected in the same
apparatus :

(1) A device for measuring the period of oscillation;

(2) Condensers free from the defect of delay of polarization,
and circuits with exactly known coefficients of self-induction;

(3) Special calorimeters to determine the amount of heat
evolved by the discharges, either in the spark or in the
metallic circuit traversed by them;

(4) An electrometer enabling the potential of discharge to
be exactly measured;

(5) A device for determining the residual discharge ;

2. é., such apparatus as might enable us to know the period
of oscillation, energy disposable at the beginning of the dis-
charge, quantity of electricity effectively dischar ‘eed, and the
energy dissipated in the form of heat in the different parts of
the circuit.

I, MEASUREMENT OF PERIOD OF OSCILLATION.

A. Anterior Researches,

3. Since Feddersen’s beautiful experiments, calling the
attention of pbysicists to the phenomenon of condenser

oer

Oscillatory Discharges. 4

discharges, numerous researches have been performed, either
to show. experimentally the existence of electric oscillations,
or to test the well-known theoretical formula

l= tees e ° ° ° ° ° (1)
LO 41?

established by W. Thomson [Lord Kelvin] for the period of
oscillation.

These experiments—which we think useful to record briefly
—may be divided into two groups, according as they were
made in order to ascertain the value of T by Heddersen’s
method, or with a view to determine the curve representing
the time variations of the intensity of the charge or discharge
current of a condenser.

4, Heperiments performed with Spark-Photographs.—
H. Feddersen* was the first to measure the period of the
oscillatory discharge of a condenser, by photographing the
spark after its reflexion by a rotating mirror; but as he
did not make any absolute measurements of the capacity and
self-induction, he only obtained qualitative laws, which we do
not think worth while recording here.

Feddersen’s experiments were then repeated by Lorenzt,
who stated that the values calculated for the duration of
oscillation of the discharge, though corresponding to those
observed as regards order of magnitude, were always somewhat
higher, probably on account of the too small value ascribed
to the dielectrical constant of the glass forming the insulating
medium of the condensers used.

In order to eliminate this cause of uncertainty, Trowbridge
and Sabine ¢ tested the discharge of an air-condenser by pho-
tographing the spark by means of Feddersen’s method. They
found the formula

T=Irv LC,

to which (1) is reduced for small values of R—as was the case
in their experiments—to be fairly well verified, provided
the value of L as calculated by Rayleigh’s formula for
rapidly alternating currents be adopted. The values of T
obtained are of the order of 0:00000381 sec., in most satis-
factory agreement with theoretical values.

* Pogo. Ann. ciil. p. 69 (1858) ; cviii. p. 497 (1859) ; exiil. p, 487 (1861)
CXV1. p. 132 (1862).

+ Wied. Ann. vii. p. 161 (1879).

{ Phil. Mag. xxx. p. 323 (1890).

4 Prof. A. Battelli and Mr. L. Magri on

Without discussing at length Boys’s* experiments (their
main object being a didactical one), where the spark was
photographed by means of a rapidly turning objective, we
rather wish to point out those undertaken by Miesler+, with
a view to test Thomson’s formula. He photographed the
spark due to the discharge of some leyden-jars by means of a
lens and of a plane mirror set rotating by clockwork, using
a circuit formed by several brass spirals: the periods found
ranged from 0:000016 to 0:0000052 sec., which agrees well
with theoretical values,

But specially remarkable on account of the favourable ex-
perimental conditions and the accuracy of the measurements
are the researches carried on by Lodge and Glazebrook f,
who, using an air-condenser and an induction-coil of great
self-induction but small resistance, photographed the spark
of discharge on a rotating plate, the velocity being capable
of being maintained constant and being measured with great
accuracy. Though Lodge and Glazebrook’s measurements
are relative to very slow oscillations only (from g., to jy 8ec.)>
yet their results are of special importance, as the single
determinations exceed in accuracy those of all previous
experimenters.

In order only to show the rapidity of oscillations so far
reached in those spark photographs, He will mention that
much shorter periods (of the order — agp 8eC-) thave “been
investigated by Decombe §, who photographed the spark of
a Hertz resonator by combining a lens and a rotating mirror;
and Trowbridge and Duane ||, in a paper where the velocity
of transmission of electrical oscillations in metallic wires was
tested, photographed, by the usual method of the rotating
mirror, sparks of a period of about 2 xX 10~“ see.

dD. Feeper ements performed by the method of charge and
discharge curves.—The values of the period of oscillation may
conveniently be derived from the form of the curves repre-
senting the behaviour of the charge or discharge of a con-
denser, both of them taking place thr ough a circuit containing
a resistance and a self-induction.

Among the most accurate researches made with this method
there are to be quoted Hiecke’s'f measurements, whose results
agree perfectly with theoretical deductions.

* Phil. Mag. xxx, p. 248 (1890).
+ Wien. Ber. xcix. Ila, p. 979 (1890).

* ¢ Cambr. Phil. Trans. xviii. p. 186 (1899).
§ Compt. Rend. cxxvi. p. 518 (1898).

|; Phil. Mag. x1. p. 211 (1895).
q Wren. Ber. xevi. Il. a, p. 134 (1887).

Oscillatory Discharges. D

More recent experiments are those of Robb*, who kept the
condenser in communication with the source of electricity for
intervals gradually increasing from very small values, deter-
mined by the duration of the contact established by two
steel spheres striking against one another ; but the uncertainty
attending this method of evaluating the duration of the time
of charge imparts to those experiments a merely qualitative
character.

Similarly Wulf +, in an investigation on the dissipation of
energy in dielectrics, determined by means of an interrupter
moved by a falling weight the curve of residual discharge ;
and whereas for condensers not subject to the phenomenon of
charge-penetration he obtained values agreeing well with
those caleulated from the formula T=2m7V/LC, he found
notable departures in the case of two paraffin-paper con-
densers.

Tallqvist’s t experiments afford more adequate arrangements
for quantitative verifications. By means of a pendulum
interrupter, he obtained a satisfactory verification of the
formule expressing the charge of a condenser as a function
of time, for periods of about five-thousandths of a second ;
and so do Seiler’s similar researches, equally carried on with
a pendulum interrupter allowing of still more exact measure-
ments of the time of charge.

Seiler first found the formula T=2aW/ LC to be verified
for periods ranging from 0:0012 to 0:0045 sec., L being
maintained constant and CO taking variable values; but he
failed to state a satisfactory agreement between the experi-
mental values of the logarithmical decrement of oscillations
and those derived from theory.

Similar investigations, based upon Helmholtz and Schiller’s§
classical method, have recently been made—for periods
between 0:0000246 and 0:0000586 sec.—by Webster ||, using
an air-condenser and two spirals wound in a suitable way, so
as to cause their capacity to be negligible. The interruption
of contacts was effected, instead of by the pendulum, by
means of a weight falling down from different heights (of
about 75 cm.); by starting successively two levers, this device
enabled—according to Webster’s statements—measurements
of time intervals as small as 0°0000005857 sec. to be made.

* Phil. Mag. xxxiv. p. 389 a

+ Wren. Ber. cv. Il. a, p. 667 (1896).
t Ibid. lx. p. 248 (1897).
§ Ibid. \xi. p. 30 (1897).

|| Phys. Rev. vi. p. 297 (1898).

6 Prof, A. Battelli and Mr. L. Magri on

6. In the table given below the values of periods, as so far
observed, are recorded :—

Periods of oscillation of discharges.
a. Determinations by spark photographs.

iBeddersent(U GAS) 2..:ches-a ere reeee from 4:46 to 1°56 x 10-5 sec.
Trowbridge and Sabine (1890) ... .......:....... ol xtc
Bove; USOO) ov. «ic cues Uohceies cece meme eee 3.» x0
Niesler (1S90),: a0. ces nk es from 5 to 13. x ORE se
Trowbridge and Duane (1896) Salat elas aerate 2. >< 10 ioe

Lodge and Glazebrook (1899) ... from 1:2 to 06x10-3 ,,

b. Determinations by curves of charge and discharge currents.

Wallqvish (USOM) Lea s77. 4s. eee from 2:18 to 9°65 10—3% sec.
Seiler ( LAS. cBisatewscsebidcaceee from - 4 to 447x10-—3 ,,
Wrebsberi(l Soe ae cn cdicc.cetines ones: from 24 to 5:3 x10—o

It should, however, be borne in mind that only Trowbridge
and Sabine’s, Miesler’s, and Lodge and Glazebrook’s investi-
gations are really oscillation measurements by method (a).
Now the investigations of Trowbridge and Sabine, as well
as of Lodge and Glazebrook, though important on account of
their being made with great accuracy, are each of them re-
lative to one particular case only, and de not, therefore, afford
a complete verification of this theory. As regards Miesler’s
researches, made in more variable conditions, it will be shown
below that the values derived from them cannot be said to
be reliable, on account of the uncertainties attending the
measurements of time and of spark-photographs. The in-
vestigations made by method (6) are, on the other hand,
fairly satisfactory ; but the periods reached there are not
very short ones.

lt was therefore desirable to undertake new and more
extensive researches on so important a question.

Of the two methods used in those researches that of the
curves of condenser charges and discharges—no sparks being
comprised in the cireuit—will most approach the theoretical
conditions which served to establish the above formula ; but
in addition to the imperfections proper to this method, it does
not refer to the cases of greatest practical importance, a spark
being always produced in those cases.

As regards such imperfections as attend this method the
pr incipal one is that relative to the measurements of the time
passing between the breaks of contacts, effected either by a
pendulum or a falling weight. In fact, though theoretical
considerations may lead us to y regard extr emely small fractions
ot a second as capable of being measured, those ten-millionths
of a second are hardly to be relied upon, as Webster assumes

Oscillatory Discharges. 7

(see above), except in the case of the weight determining the
openings of contacts having a very great velocity (15 mm. i sec.
at the least), and special devices being employed enabling
the action of the opening spark to be rendered either negligible
or, at the least, constant.

In addition to what has been said it should be borne in
mind that those indirect methods cannot be used in the case
of very short periods, they being, at the most, capable of
ascertaining with security periods not inferior to some ten-
millionths of a second.

The method of spark-photographs, on the other hand, in
addition to its allowing very short periods to be measured,
is capable of affording also an idea of the importance of such
modifications as the spark produces in the movement of
electricity.

Among the forms of apparatus used with this method
(e.g. the classical rotating mirror arrangement, Boys’ ro-
tating objective, Lodge and Glazebrook’s rotating photo-
graphical films), the two latter ones do not afford a means of
reaching very high angular velocities, in addition to their
being inadequate for periods of some millionths of a second.

The turning-mirror arrangement is, without any doubt, the
one enabling even very small periods to be measured, pro-
vided all those special precautions enumerated below be taken
in effecting them.

B. Method and Apparatus used in our Heperimental
Measurement of the Pertod.

7. On account of the reasons above quoted we adopted the
rotating-mirror method.

In this method the necessary condition for exact measure-
ments is that the distance between the different luminous
intervals composing the image of the discharge may be of
sufficient magnitude with respect to the width of those in-
tervals, Within certain limits this may be obtained by
diminishing the magnitude of the image of the spark, and
employing “high velocities of this image on the film; this
velocity being given by

v=A7ra,
ry being the distance of the film from the mirror, and @ the
number of turns effected in a second by the latter.

For practical use it proves more convenient, as a rule, to
take r as great as possible and to chose moderate values of a
(from 60 to 200 turns per second). But in order not to com-
plicate the apparatus by adding rotating arms (similar to

8 Prof. A. Battelli and Mr. L. Magri on

those used by Feddersen and by Trowbridge and Sabine to
enable the spark to be produced at the very “moment of the
mirror being in convenient position for reflecting its image
on the photographic film), we preferred adopting a form ae
apparatus capable of imparting to the image an extremely
great angular velocity and of making 7 very small. This
arrangement, moreover, allowed of fairly luminous i images of
the spark being piel photographic films of moderate
size being employed.

During the first part of our investigations we employed
a Froment clockwork, whose last axis could effect about 450
turns per second, but not even this velocity was sufficient in all
our researches. Moreover, as is always the case with those
instruments. where only the friction and resistance of the
medium is made use of to reculate the velocity, we found it
impossible to maintain the movement constant. ,

This defect, inevitable in the case of rotating instruments
driven by clockwork, may arouse some doubt as to the
accuracy ‘of the results obtained by Miesler.

For the same reason we rejected our first sets of observa-
tions, adopting, for the definite investigations, to produce
the rotation of the mirror, a special turbine whose action
we found to be perfectly regular.

8. This turbine, constructed by the mechanician of our
Institute, Mr. Giuseppe Pierucci, as represented by fig. 1, is
in its essential parts similar to that of Foucault.

The steam enters the chamber PP, and leaving it by two
openings strikes against the wreath of vanes C, fixed on the
spindle A, together with the steel mirror 8 and the toothed

wheel R.
This latter gears into another perfectly similar wheel R’,

Oscillatory Discharges. G

secured to the spindle A’, where in the ordinary manner
the mirror §" is fixed, The spindles are kept in position
by the screws VV, V’V’. These screws are pierced through
their whole length, and they carry sapphire pillows, also
ierced in order to allow of an abundant oiling, which has
to be made all the time the turbine is working.

At the beginning we availed ourselves of a much over-
heated jet of aqueous vapour to start the apparatus, but later
on we found it more convenient and suitable to make use of
a jet of air compressed to 6 atm., taken from a large
reservoir,

The regularity of speed of the turbine depends very much
on the oiling of the spindles, which should be continuous but
not excessive. The rotation of the axis becomes in fact very
irregular by lack of oil, the friction being then too great, as
well as by an excess of it, as in this case some oil will enter
between the moving disk and the distribution box.

It is, moreover, absolutely necessary that the air injected
into the turbine should not carry any oil-drops on to the
pump, nor dust particles of any considerable size, as the
turning and the fixed parts are distant from one another only
7p Of a millimetre. To ensure this the air was admitted
through a large recipient fitted with a long filter formed by
several sheets of straight metallic nets.

To ascertain the velocity of rotation a small and light
aluminium disk, to whose edge a short hair was attached,
was fixed on the axis A of the turbine. Next to this disk :
rotating brass cylinder covered with smoked paper was
disposed, the hair making a mark on the paper at each turn of
the axis of the turbine.

The time interval corresponding to the interval between
two marks made by the hair, and hence the number of turns
effected per second by the rotating axis, was deduced in the
usual manner from a comparison with the oscillation curve
of an electromagnetic tuning-fork (whose period of oscillation

was accurately known), recorded on the same cylinder.

A conveniently regulated clockwork was fitted with a
contrivance enabling the cylinder to effect one turn only,
with suitable velocity, so that the cylinder, after a small
fraction of a turn (say about 4), reached a fairly constant
speed.

Fig. 2 (p. 10) represents a general view of the turbine, the
rotating cylinder, and the tuning-fork.

Two solid iron rods, fastened on the turbine columns,
carried a small frame with the photographic plate, whose
dimensions were 3 x 12 em.

10 Prof. A. Battelli and Mr. L. Magri on

Fie. 2.

sa
==
—=

9. The spark to be photographed was produced in A (fig. 3)
within Qa large wooden box, intercepting any irradiation of
light by the spark.

aed

ay || Care 1s

This box, ©, had a hole O capable of being opened and
closed by means of an ordinary pneumatic shutter, as used
in photography.

A card-paper tube reaching as far as the objective L (an
astigmatic Zeiss objective) projected from O. The image
formed by L was reflected by the rotating mirror 8 on to the
photographic plate F,if the mirror was in the proper position.

Oscillatory Discharges. 11

A suitable screen prevented the light emitted by the
opening sparks of the electromagnetic tuning-fork falling on
the photographic plate (so as to avoid any ghosts prejudicial
to the clearness of images).

10. Experiments were carried on in the following way :—
The pressure of air in the reservoir having reached 5 to 6
atmospheres, the photographic plate was placed in position ;
then, after starting the electromagnetic tuning-fork, the
compressed air was led into the turbine, the rate of its
entering the turbine being regulated by means of a con-
venient screw-cock, enabling the velocity to be augmented
slowly and regularly until the suitable value was reached ;
comparison of the note produced by the movement of the axis
with that given by the electromagnetic tuning-fork, afforded a
means of ascertaining approximately whether this velocity
had been reached.

As a rule, this was so considerable that the proper sound of
the turbine had already exceeded the limit of perceptibility,
and the sound of the axis was alone to be heard. The con-
stancy of this latter sound, and hence the uniformity of speed,
could be stated with certainty from a comparison with the
sound produced by the electromagnetic tuning-fork maintained
in vibration during the experiments. Those two sounds, in the
ease of most of our experiments, were nearly in unison.

After having, in the above manner, ascertained the uni-
formity of speed of the turbine, the discharge between the
spheres of the spark-gap was produced, and immediately on
detecting on the photographic plate the reflected image of
the mirror, the shutter of the objective was closed, and the
rotating cylinder was started, the axis of the turbine and
the point of the tuning-fork tracing the respective curves on
it. Accordingly we had but to develop and to fix the film
by the usual processes.

As arule 6 or 7 photographs per period of oscillation were
taken for each explosive distance.

11. The experiments being finished the velocity of the
image was easily deduced from that of the mirror and the
distance between this latter and the plate; a measure of
the speed of the mirror was next obtained directly from the
formula ed 517-2. n!

ae F TEES ?

n
n being the number of vibrations included in a certain part
of the curve, and x! the number of lines traced on the cor-
responding part of the curve by the hair connected to the axis
of the turbine, 517-2 being the number of complete oscillations
made by the tuning-fork in a second at 25°.

Ale 2 Prof. A. Battelli and Mr. L. Magri on

In this first part of our experiments (where we always made
use only of one axis of the turbine) the velocity of the image
on the photographic plate was

V=A4ndN,
d being the distance between the mirror and the plate, this
distance being in our case equal to 19°4 cm.

In order to determine the distances between the images of
the different partial sparks, special care and a certain amount
of practice was found to be necessary. With our preliminary
experiments this determination was effected by making use of
a Froment comparator divided in half-millimetres, the vernier
giving one-hundredth of a millimetre. On the moving
part of this comparator, carrying the vernier, an eyepiece
of small magnifying-power with a cross hair was fixed.
Measurements on the plate were made four times, twice
in either direction, the mean value being adopted.

We never found any noticeable differences in the value of
the distances comprised between the single sparks corre-
sponding to complete periods.

But as these measurements will often be attended by too
great uncertainty towards the end of the discharge owing
to the feeble luminosity, we took care to reject those last sparks
in our determinations.

In all cases, however, we made measurements for one
and the same discharge as well for such sparks as exhibited a
maximum luminosity at the upper electrode, as for those that
showed it at the inferior electrode.

The reading of those distances (N A, N B, fig. 4), as deter-
mined directly on tne plates, was rent
then reduced to the are of the ee A B
circle. The “are = aia wall
afford the value of T by means
of the formula

n
Am OLT 2am ap
this formula being very suitable
for numerical calculations.

12. We give in the annexed
tables some examples relating to
the measurements of period of
oscillation, D and D’ are the
distances NB and NA respec-
tively of fig. 4, n and x’ the numbers of vibrations of the
tuning-fork and of the turns of the turbine counted on corre-
sponding parts of the respective graphs, p is the number of
periods comprised on the measured part of the plate.

Hxperiments with the large spiral wound on marble.

Oscillatory Discharges.

Self-

induction of the spiral 4546000 ems. Capacity of condenser
C=14175 ems.

Ai
T= : VY LC=0:00005317. Explosive distance 2 mm.
Number
of order | 1. ' , 1D): Dr Dp. Ne
of Plate.
14 148 24 5:0495| 0:5205 4 | 0:00005404
{ Sa aee Al ee eee 4:4705| 0:0015 4 0:00005374
hails 15 188 21:8 2818 4°748 7 000005339
SPIN Ie Nea Ny a 3-423 | 5-280 8 0 00005363
16 ee, 18°9 5°326 2°031 3 0:00005417
| [hcl aehataen a eae 4°706 | 1:481 3 0:00005434
17 { 151 30 2:1675| 4°7525 +) 0:00005444 |
bes. shea) | eine sin 1°4875| 53945 5) 0:00005386
18 156 395 5433 0:712 3 0:00005403 |
Arie en leone 4:605 0-021 3 0:00005303
19 i | 133 23°9 2°54 4°84 6 0:00005347
lL) dodebie q) edunce 1:97 4:096 5 0:00005296

Experiments with the small spiral wound on ebonite.

Theoretical value 0:00005317. Mean value 0:00005376.

Total

self-induction of circuit 57797 ems. Capacity of condenser
C=3568 cms.

Peek | ee ai: :
— i VLC =0:00003008. Explosive distance 2 mm.

Number
of order
of Plate.

; Or
——<—__ oa vw"). 8 SS

129

144

n', D. D’. Dp.
. 12656 15-005 | 6
122 |5-807 |5-996| 6
(3365 11682 | 13
149°2 | 3.349 03451 9
«| 1297 5:2485| 10
14431-1545 4-3095| 8
4-683 |1-077 | 9
9/4934 1-300! 9
129°8 | 6.965 |3:721 | 10
0-056 13-462] 9
3:517 | 5:062 4

IO \e-6e5 /6316 | 4
0-611 |4:976 | 14
(0791 |4-718 | 14
147°3 | 9.997 |4-300 | 5
210 4998 | 7

Remarks.

Theoretical value 0°000003008.

0000002986
0 0000038037

0:000003011

0:000003173 (2)

0:000003032
0:000003053
0000003011
0:0000038022

0:0000080384

0:000002981

0:000002904 (?)

0:000003039

0:000003036
0-00C003001

0:0000038042

0:000003021

Not distinct.

Two

sparks following |
one another in short |
intervals on the plate

were measured.

Mean yalue O°00Q0U38024.

14 Prof. A. Battelli and Mr. L. Magri on

Experiments with circle-shaped circuit of copper wire. Total
self-induction of circuit for T=0-00000120, 9242 em.
Capacity of condenser (=3568 ems.

cf ay / LC=0:000001201. Explosive distance 5 mm.

|
Number |
of erder| 2. n'. D. 1, p By
of Plate.
a7 {| 1845) 188 | 4941 | 2585 15 | 0000001213
pape Sill ROR A ayes | 4863 | 2526 | 15. | 0000001205 |
| nq {| 158 | 157 | 5202 | 0634 | 29 | 0-000001224 |
| TEL] Seeeee dd eee | 5296 |] 10398.) . 30. 1 OnRemtaTEES
| go {| 122 | 120 | 2580 | 2451 | 33 | 0-000001220
ee | 2521 | 0834 |. 22 | 0-000001282
9) {| 143 | 140 | 2347 | 5378 | 19 | 0000001194
RPE SAL RCE o, | 2275 | 522 19 | 0000001205
| go {| 74 | 76 | 1818 | 5-493 | 23 | O-000001189
EW a 1742 | 5438 23 | 0000001197
93 | 162 162 | 2966 | 3:050 39 | 0-:000001210
Gare ars | 2893 2843 37 | 0000001221
| ts { 158 | 153 | 3147 1153 | 28 | 0-:000001210
Bia nl | 8080 0959 26 | 0-000001224

Theoretical value 0:000001201. Mean value 0:000001212.

From the tables above given it may be seen that even when
the difficulties of measurements are greatest the possible error
in evaluating the period will not reach 2 per cent.; whereas
for not very short periods a still greater accuracy may be
attained. We believe that in the actual state an accuracy
superior to that reached by us cannot be obtained, the reason
of which will be given below.

Now in order to compare the experimental value with the
value of the period as derived from Thomson’s theory, it was
necessary to obtain the values of the elements entering into
Thomson’s formula, 7. e. capacity, resistance, and self-indue-
tion of the discharge-circuit, with an accuracy not inferior
to that pointed out above. It is thus necessary to explain
briefly the method and the precautions used in measuring
those elements of the circuit.

C. Capacity, Resistance, and Self-Induction of Circuit.
(a) Condenser.

13. In order to know the capacity with due accuracy, as
well for measuring the period as for measuring the dis-
posable energy, which we had to determine when studying

Oscillatory Discharges. 15

the distribution of the discharge over the different parts of the
circuit, it was first of all necessary that the condenser should
not offer such difficulties as would arise from the penetration
of the charge and from a delay of polarization, which always
occur with condensers having solid dielectrics.

This could be obtained only by adopting an air-condenser
constructed especially for this investigation.

It was made up of 70 plates of mirror-glass, plane, coated
with tinfoil on both sides and separated from one another by
small glass prisms.

The mirror-glass plates are rectangular ; their surface is
70 x 35 ems., with a thickness variable from one plate to
another, and ranging from 7 to 10 mm. On each of them,
as has been mentioned, there is extended on both faces a thin
sheet of tinfoil of one piece, caused to adhere to the glass by
special precautions, so as to prevent folds as well as any air-
bubbles being formed. The tinfoils, after being extended
on the glass, were all cut to the exact dimensions 63 x 28 cms.,
so as to leave free around them a margin of glass 3°5 cms. in
breadth. The two tinfoils of each plate were connected to
each other by means of a thin brass strip (about 4 mm. in
breadth), which at the same time served to establish convenient
communications.

These 70 plates were arranged in two piles of 35 each,the first
and last plates of either pile having tinfoil on the internal face
only. As the interval between two successive plates should
remain unaltered and well known, each couple was separated
by six small glass prisms, chosen equal among themselves to
a hundredth of a millimetre by means of a spherometer.

The prisms of the pile of condensers No. 1 we found to be
of a mean thickness of 0°743 cm., those of the pile No. 2
being of a mean thickness of 0°738 cm. In both of these two
condensers the even-numbered and the uneven-numbered
plates respectively were put in connexion with each other,
the respective brass strips being then gathered in two clusters,
which were connected to two terminals carried by glass rods.

Hach condenser was placed on a solid wooden bench,
the respective plates being carried laterally by six glass
angles, so as to secure absolute stability. The apparatus. was
finally protected by a glass jacket, in the interior of which the
air was kept dry by means of sulphuric acid.

(b) ALeaswrements of Capacity.
14. As the dimensions of our condenser are known with

accuracy, its capacity could be derived from the well-known
formula of Maxwell (‘ Treatise, vol. i. § 196).

16 Prof, A. Battelli and Mr. L. Magri on

But we did not limit ourselves to this theoretical value in
calculating the results of our investigations, as it results
from experiments (not yet published) made for this purpose
in our Institute by Dr. Gragnani, that the above formula does
not hold for condensers of the dimensions used by us; and
as, moreover, in this condenser each armature is formed by
two sheets of tinfoil separated by a plate of glass from 7 to
10 mm. in thickness, the departures from the theoretical
conditions this formula holds for are still greater.

in addition, it is impossible to calculate with certainty
what influence the neighbourhood either of conductive masses
or of the walls and the floor may have on the effective
capacity.

Moreover, though the plates as used with our experiments
are of mirror-glass and well worked, one cannot warrant their

being perfectly plane and accurately parallel among one

another.

We therefore measured the capacity of our condenser,
either by comparison with a standard condenser or by deter-
mining experimentally the absolute value.

Experimental Value.

15. (1) By comparison with a Standard Condenser.—The
standard, kindly lent by Prof. Roiti, bears the number
1099 of the firm Latimer Clark, Muirhead, & Co. (West-
minster), and is made up of plates of tinfoil separated by
sheets of mica. The value of the capacity as assigned by the
constructing firm is 4 microfar.; that found by Prof. Roiti*
by means of special determinations is 0°3359 microfar., very
nearly the same as the value 0°3336 found by Glazebrook T
for another standard forwarded by the same firm.

It should be borne in mind, however, that in calculating
the absolute value of the capacity, Roiti adopted for the B.A.
unit of resistance the value 0°9883 legal ohms; whereas in
the Chicago Congress of the year 1893 it was established that
1 B.A. should be equal to 0°98703 international ohms; the
value as given by Roiti should hence be multiplied by
pe enos =1-:0013, in order to reduce it to the absolute units

0°98703

now adopted.
It thus becomes
0°3359 x 1:0013=0°3363 microfarad.
The comparison between this standard and our air-condenser

* Nuovo Cimento [3] xxi, p. 187 (1887),
+ Phil. Mag. [5] xviii. p. 98 (1884).

Oscallatory Discharges. 17.

was made by discharging them successively through a ballisti
galvanometer, after bringing their armatures to potential-
differences whose ratio was known, and which were chosen
so as to have deflexions of the galvanometer-needle of the
same order of magnitude in both cases.

The charging current was given by three Tudor accumu-
lators, whose circuit was kept permanently closed through a
thick argentan spiral, of a total resistance 51°14 B.A.

Tocharge the standard condenser a deviation of the current
between one terminal A of the spiral and a point B distant
about 515 of the length of the spiral was taken ; to charge the
air-condenser the deviation was taken at the two terminals
of the spiral.

The ballistic galvanometer was of the Du Bois and Rubens
type, the duration of a complete oscillation of its needle being
13 seconds. The charge of the condenser was kept on 1 second.

From this comparison we obtained for our condenser the
value C=0-016001 microf., this value agreeing very well
with the value C=0:015972 microf. obtained by substituting
for the resistances AB and AC of the rheostat above mentioned
two other far greater resistances, composed of two Edelmann
resistance-boxes of 530 and 9690 units respectively.

The average of those two values gives for the capacity in
question

C= O05 9S 0 mieror..

2. €. 14388 electrostatic C.G.s. units.

16. (2) Absolute Measurements of the Capacity.—In order
to have more reliable values for the capacity of our air-
condenser we decided to make, as above stated, determinations
in absolute measure also by the bridge method, as suggested

by J. J. Thomson*.

ae a{(a-+d+g) (a+b-+p)—a]
— nl (@+b+p)(a+d)—a(atb) || (at+d+g)(a+e) —u\utd)])
As an interrupter we made use of an electromagnetic

tuning-fork run by another tuning-fork in unison. These
tuning-forks, kindly lent by Prof. Roiti, are constructed in

* Phil. Trans. of tae R. Soc. part iii- p. 707 (1883).

+ Nuovo Cimento, [3] xxi. p. 137 (1887).
Pihil, Mag. 3. 6. Vol, 5, No. 25. Jan, 1903. C

18 Prof. A. Battelli and Mr. L. Magri on

a manner perfectly similar to that described in the above
quoted article. The number » of complete oscillations was
about 126 per second. The very regular speed of the
tuning-forks—the duration of whose oscillations was obtained
by comparison with a Graham pendulum regulated by means
of a chronometer of the Royal Nay y—facilitated the execu-
tion of these measurements, from which we derived the
following values :-—

’

Condensers J. and II. in parallel...... 0°015750 microf.
Condenser No: Ai yt ae see 0-0079763° >
ms EN oP aa iy sn ek ee 0:0078849 _ ,,

17. Resuming, we may write in the following table the >

values of the capacities as obtained by the various methods:—

Electro-
A. The two condensers in parallel. static Units.
[c.e.s.] >» Miezor
derived from comparison with
Latimer-Clark standard ... 14388 0°015987
derived from bridge measure-
TELUS ort het Ne OR Ree tt oes 14175. O-O15%5

B. Condenser No. 1 only.
Capacity derived from bridge measure-
IOVS) OSes Spans Piped 8 rt ane ee Ra 7178 =0°007376

Capacity

C. Condenser No. 2 only.
Capacity derived from bridge measure-
DOYS) 04 PS le ee ARE sd CRT adh ath aces 7096 0:007885

The sum of the capacities of condensers No. 1 and No. 2
thus agrees fairly well with that of these two condensers
when connected in parallel, the more so as measurements of
the capacity of each condenser apart will present less cer-
tainty on account of their small value, and as the neighbour-
hood of the other condenser will have a slight influence on
the capacity of either of them.

The smallness of the difference between the absolute value
-as found by us by the bridge method and the one derived
from a comparison with the Latimer-Clark standard may be
considered as an evidence of the accuracy of our measure-
ments. This difference is probably due to the fact that the
standard may have undergone a slight variation in the fifteen
years passed since Prof. Roiti made his experiments, and that
with the comparative experiments the charge lasted 1 sec.,

a oe : o 3 6

Oscillatory Discharges. 19

whereas with those performed with the bridge it lasted only
about <4, of a sec.

With the latter ones a greater approximation to the con-
ditions of action of the condenser during the measurements
of the period of oscillation is thus secured.

We will therefore presume that the value most suitable
for our calculations is the one derived from our absolute

determinations, 2. é. Capacity.
[C.G.s. | Microf.
For condenser No. 1...... 7178 ():007976
as Noe 228 7096 0:007885
For both condensers in
prAONE a: ech Nae ce TAT 5 001575
For both condensers in
BeOS ess, ites) tae ee ee 3568 0:008965

18. To these values for the capacity of the condenser there
are to be added those of the capacity of the remaining
portions of the circuit; but within the limits of accuracy of
our determinations in most cases this additional amount may
simply be neglected.

The case, in fact, where in our experiments this supple-
mentary capacity had its maximum value, was the one of
the discharge-circuit being made up of a wire 1594 em. in
length, 0°08 cm. in diameter, and arranged in the form of a
square at 85 cm. from the walls of the room where experiments
were made,

The capacity of this wire, as calculated in electrostatic
measure by the formula

ja!

2 log Be

(7 being the radius of the wire, / its length, and d its distance
from the walls) was found to be equal to 97 cm. In this
case we took this correction into account, whereas in all other
cases it was found to be quite negligible as compared with
the capacity of the condenser, which for no experimental

arrangement was below 3568 cm.

D. Resistance of Metallic Circuit and of Spark.
a. Principle of Method,

19. With these first researches the value of the resistance
of the circuits used by us was negligible in calculating the
period of oscillation by Thomson’s formula. But on the
other hand, the knowledge of the true value of the resistance

20 Prof. A. Battelli and Mr. L. Magri on

offered by the metallic parts to the oscillatory discharge was
indispensable to us as an element of comparison, in order to
derive from it the effective resistance of the spark.

This comparison was made by measuring the amount
of heat evolved by the same discharge either in the single
metallic portions of the circuit or in 1 the spark, and for this
purpose we made use of special calorimeters.

B. Calorimeters.

20. Calorimeters for metallic circuit.—TVhose adopted by
us for measuring the energy evolved in the
metallic por tions of the circuit had the form
shown in fig. 5.

The Teceitineanr wire or the spir: al thr ough
which the condenser was discharged. termi-
nated in two short platinum wires fused to
both ends of a glass tube. To this tube
there was connected in a vertical position
the uniform capillary tube C, conveniently
divided and soldered by its lawies part to a
wider tube, to which the cock R was con-
nected, ine latter being, by means of a
rubber tube, put into connexion with the
small mercury reservoir M. The whole of
the tube T, the interior of the tube on
which the spiral was wound, and part of
the capillary tube C were filled up with
toluol. .

The mercury reached at least one centi-
metre above the cock R, allowing thus of
the height of toluol in the capillary tube C
being regulated, and preventing its leaving
by the cock R. Round the calorimeter thus
formed a glass jacket was placed, in order
to regularize the interchange of heat with
the atmosphere.

21. Calorimeter for spark.—This was
made up of two ovoidal recipients RR’ (fig. 6),
one of which was interior to the other, the in-
terval being filled up with toluol oceupying
also the capillary tube T.

The latter was, on the other hand, connected to a reservoir
P containing mercury by a tube furnished with a cock
and a rubber tube. By raising or lowering P, the height
of mercury in the tube, and thus that of the toluol in
the tube T could be eared:

Oscillatory Discharges. 21

Round the exterior recipient R there was wound a
sufficient layer of wool cloth, the whole being placed within
a wooden box ©, and being capable of moving by means of
the arm NO, to which it was attached, along the brass rod A,
and being thus raised to different heights.

We had to make use of the arrangement above described
in order to cause the spark to pass freely when taking the
photographs.

When photographs had to be taken, the box was fixed
at the level shown in fig. 6. Im order next to insert the
spark into the calorimeter it sufficed to raise the arm NO.

Fig. 6.

fire “alt \ =
YE A TTA
wD

A good closing of the two openings aa! of the calorimetric
recipient R was obtained by passing the brass rods D, D! of
the spark-gap through rubber tubes at the part near the inter-
ruption where the spark occurred. This method of closing
allowed of placing the calorimeter in position with all de-
sirable facility and speed when the heat evolved in the
spark was to be determined.

This form of calorimeter seemed more adequate than those
previously used by other experimenters, as we avoided the
trouble due to the explosive and electrostatic effects of the
spark. Moreover, we avoided the difficulties. met with in
the case of air-calorimeters being used, in the accurate deter-
mination of the part played by the expansion of the gas in

14658

Zips Prof. A. Battelli and Mr. L. Magri on

the displacement of the liquid column in a capillary tube.
If the tube be not of perfectly constant calibre, this displace-
ment is influenced to a notable degree by the capillary
action.

y. Standardizing of Calorimeters.

22. In order to obtain in absolute measure from the dis-
placement of the meniscus in the capillary tube of the calori-
meters the energy evolved within them we ettected their
standardizing in the following manner :—

(a) In the case of the metallic spiral calorimeters there
was kept on during a given time a continuous current of
known intensity, from whose value, together with the value
of the resistance offered by the spiral to continuous currents
(this resistance being measured by an Elliott bridge), the
energy spent in the spiral was calculated, and hence the
relation between this energy and the displacement of the toluol
column in the calorimeter was obtained.

(>) In the case of the spark calorimeter we proceeded in
-the same manner, after, however, connecting the two ter-
minals of the spark-gap with a small constantan spiral of
known resistance.

The readings of the calorimeters—made at a distance with
a telescope—were effected in both cases by determining from
minute to minute the displacements presented by the top of
the toluol column five minutes before beginning experiments,
during experiments, and five minutes after wards,

The passage of the continuous current during the standar-
dizing experiments, as well as the passage of discharges
duri ing those of definitive measurements, did not last beyond
40 seconds. Readings were always taken by night, in order
to have as small variations as pos ssible of temperature in the
room, and heat changes with the exterior were taken account
of by calculations analogous to those made in pyrheliometrie

researches.

In the table below the data relative to the five calorimeters
we made use of during our researches are recorded.

Spiral Calorimeter.

Extern.
Diam. of Diameter of No. of Length
Wire, cm. spiral, cm. turns. of spiral.
PaloraNosd:::./) 0-078 1-521 220°25 36°3
Le Reise. (ODS 1-78 423 69

ue LAE Be BOOTS 164 102 15°6

Oscillatory Discharges. 23

Rectilinear Wire Calorimeter.

Diameter Length,
of wire, cm, em.
CaloreNon 4.2. 0:078 100
a 0-078 147

The constant of the spark calorimeter was found equal to
C;=0°0429 ecal./gr. For the remaining calorimeters we
found

C,=0:0668 cal./er.
Ch =0-0Stior ss:
C3 = 0O-O871 39
C=0039o)

6. Resistance of Metallic portions of Cirewt and its Dependence
on Nature of Discharge.

23. We have already pointed out the importance that
an exact knowledge of the metallic portions of the discharge-
circuit had for our researches.

In the case of common copper wires stretched out into a
straight line, the resistance R” opposed by a conductor of
length Z to an oscillating current is given, according to Lord

Rayleigh*, by
ip ep. E ee
ire ——s
R=R(1+45 Re i830 Rt +0), ae

R being the resistance of the same wire for continuous cur-
rents, # its magnetic permeability, and p=27n, n being the
frequency of current.

For the highest values of frequency, Lord Rayleigh’s
theory shows that this resistance R‘ has a limiting value as
follows :—

ny ES aay peda anaes

a ’=—7aR ee

a being the diameter and o the specific resisiance of the
conductor.

This formula is equal to the one deduced for very high
values of » from the theory of electric oscillations in rectili-
near conductors developed by Stefan f.

* Phil. Mag. [5] xxi. p. 781 (1886).
t Wied. Ann. xii. p. 400 (1890).

24 Prof. A. Battelli and Mr. L. Magri on

In the case, however, of circuits wound into a spiral we
cannot say, a prior?, that the same formule will hold which
give the true resistance for rectilinear wires, and as a
theoretical investigation of this problem is wanting, we had
to undertake experimental researches in order to compare
the resistance presented by a spiral with the resistance opposed
to the same discharge by a wire drawn out into a straight
line, |

We determined the heat evolved in two successive parts of
the same circuit made up of two wires of the same diameter
and of the same substance—the one drawn out into a straight
line, the other wound into a spiral—first in the case of both
being traversed by a continuous current, next both being
traversed by an oscillatory discharge.

For this purpose we used the calorimeters Nos. 1, 2, 3, 4, 5,
previously described.

Let n and n’ denote the displacements of the meniscus in
the capillary tubes of the spiral calorimeter and in the
rectilinear-wire calorimeter respectively, in the case of the
same continuous current traversing both of them ; let mr and
n>’ denote the displacements produced in the same calori-
meters by the passage of a certain number of discharges.

Accordingly, let Q, Q!, Q;, Q-’ denote the amounts of heat
evolved in the four cases above mentioned respectively.

From the relations

() mt” Se naa

Qe ae Qe ae

we have in the first place

n _Q Q

ie eee Cs

On’ the other hand, denoting by J, /’ the lengths of the
spiral wire and the rectilinear wire respectively, by R and R’
their resistances, we have for the current with the period 7

Q' Say! ; Q,’ = R/ >
hence we may write :
Nr Nn Ea gate
fe aD eee Ls

Oscillatory Discharges. 95

. R : is dee
Now, as ee and Te represent the resistance per unit of
length of two wires, one of them wound into a spiral, the

other drawn out into a straight line, we may write, denoting
them for brevity’s sake by p ¢ sand p. respectiv ely

Pp Nr nr
a nas
We may say also that the quotient
p
p!

represents the ratio between the resistance of a wire wound
into a spiral and the resistance of the same wire drawn into
a straight line for discharges of period t.

24. Before undertaking the experiments for determining
this ratio, we made up our minds to test whether the calori-
metric method, as used by us, was adequate for affording
reliable indications.

There may, in fact, arise the suspicion that within the toluol
dielectric viscosity phenomena may take place, these pheno-
mena, owing to the heat they ev olve in the insulator, being
capable of disguising to a considerable degree the evolution
of heat in the spiral due to the Joule effect.

But two series of measurements made with special calori-
meters perfectly warranted our rejecting this suspicion.

The first series, performed with two calorimeters in which
the spiral and the wire were immersed in air, gave results
identical with those obtained with toluol calorimeters.

The second series was made with a calorimeter of the
usual form, where in the place of the spiral there was
immersed in toluol a condenser made up of two cylin-
drical armatures. Having placed this calorimeter in par rallel
with one of the spirals traversed by the discharge, we
were not able to ascertain in it any “sensible evolution of
heat.

On the other hand, the objection could be raised that, as a
rule, the displacement of the toluol meniscus, in addition to
its depending upon the amount of heat evolved in the wire,
will depend upon the rate of this amount being given oft to
the surrounding medium ; since in the case of a “calorimeter

co)

containing a rectilinear wire the radiating surface is greater

than in the ease of a calorimeter containing the same wire
wound into a spiral, one would expect ‘haa on this account

26 Prof. A. Battelli and Mr. L. Magri en

the discharges were capable of producing greater effects in
the former calorimeter than in the latter.

We performed some new experiments, however, using
continuous currents, sent through the calorimeters ai long
intervals,

The arrangement adopted for this purpose consisted in
closing the accumulator circuit by means of a pendulum

which carried a point entering a mercury beaker placed
Beton, in the pane corresponding to the position of rest.
This pendulum was 2°50 m. in length and accomplished an
oscillation of 1°80 m. in 1°6 see.

The length of the mercury beaker was 1 em., 2 that the
duration of the passage of the current was about sts of the
interval separating two successive passages.

With these currents so markedly intermittent we obtained
also between the amounts of heat evolved in the two portions
of circuit, the same ratio as obtained in the case of a con-
tinuous passage of current.

We may therefore conclude that the indications of our
calorimeters are really due to the heat evolved in tbe metallic
wire.

As we do not think it necessary to give here the tables
containing the results of the measurements made to ascertain

the value of the ratio —, we record the final values derived

from them, 7z.¢., the means of three series agreeing well
with one another (p. 27).

From an inspection of the table opposite it results that
the effective resistance of a spiral (ratio between the calorific
energy absorbed by the latter and the mean square of the
intensity of current) is greater than the effective resistance
offered by the same wire when drawn out into a straight
hne.

25. In order to test the possible influence of the neighbour-
hood of the spiral on this increase of resistance, we made
some experiments with four other spirals, a, >, c, d, and, by the
method above mentioned, determined the ratio ES The
copper wires the spirals a, 6, ¢ were constructed with had
equal length and Sage whereas the spiral d contained a
greater length of wire

Simultaneously we inve estigated the possible influence of
the frequency of current, owing to the more or less con-
siderable capacities it inserts into the discharge circuit.

Oscillatory Discharges.

Mean of Deviations Observed.

With Continuous Current in the With Oscillatory Discharge in
Calorimeter No. the Calorimeter No.
2 5) 2 5
(spiral). (rectil. wire). (spiral). (rectil. wire).
ook 10°23 24°28 4°32
Ratio=p’=3'14 Ratio=p—5°62
3 e =e Ohtor 7 — 0) ( <lOnes
p
1 | 5 1 5
(spiral) | (rectil. wire). (spiral). (vectil. wire).
168 | 899 | 17:89 £87
: p’=1°878. p= 3°67.
a =1:96 for r= 43 x 10-6.
; 39 | 99 | 20°60 | 11
; p.=1:878. p=4-08.
. =215 for T=3 x 10-°.
if | * | 20:60 } 5:05
p=lsis | p=£08.
ie for T=22x 107%,
3 |
anh | Beil wire). (spiral). | (rectil. wire).
| |
oe 3°01 drow | 3°30
=1'9 | p20
yal 84 for r=1°7 x 10-8

N.B. Calorimeters are placed in series,

28 Prof. A. Battelli and Mr. L. Magri on

The results are recorded in the following table, where
they are arranged for increasing values of frequency and
of the number of turns of wire in unit of length of the
spiral.

Values of z a

No. of 30 large |

Spiral. |turns per glass
em. Con- | leyden-jars;) Air-con- | 2 air-con-
tinuous} and air- | densers in | densers in | One small
| current. | condensers; parallel. series. | condenser.

in parallel.

Spiral a| 242 | 1 1:02 (eee ei 1:30
» | 3:82 1 117 131 1:34 1:70
ek 622 1 1-48 1-66 1-68 1:89
al Be 1 1-56 172° «| 2-038 2-37

From these results it may be seen that for every spiral
the resistance will always increase with increase of frequency
and also with diminution of distance of the spires.

This phenomenon leads us to suppose that, while in a rec-
tilinear conductor the current will pass through a thin super-
ficial layer only, it becomes localized in a still more reduced
space when the same conductor is wound into a spiral; and
this may be expected, considering the mutual induction
effects between the various portions of the circuit.

This localization is likely to affect the value of the self-
induction coefficient of the circuit, but it ‘may be easily
understood—a fact borne out by the experiments we under-
took for this purpose—that this influence is quite insignificant
in comparison with the effect upon the resistance.

26. From all the facts above mentioned it thus results that
the true value of the resistance of our spirals for a given period
will be obtained by multiplying the value for the resistance
R_, exhibited by the same wire when drawn out to a straight

line, for the same period, by the ratio ea as found experi-
mentally in the above manner. p

We thus have for our experiments the following values
tor RY s—

For the calorimeter No. 2:

Ry! ge7 , 19-6 = 0983 X 1:79 = 1°76.

Oscillatory Discharges. - 29
For the calorimeter No. 1:
ieee 6— 0 do0 <evo— 1-06:
se e19- 0 Oo alo 1-38),
irs aio 0 Golee2 af i65,

For the calorimeter No. 3:
Rr’ _4-7% 19-6 = 0° 440 x 1:84=0°827.

EK. Self-Induction,

27. In the case of the self-induction also the theoretical
treatment with regard to alternating currents has been worked
out only for some special forms of plain circuits, and calcula-
tions relating to circuits wound into a spiral are completely
wanting, as in this case neither Maxwell’s method of the
mean geometrical distance * nor Lord Rayleigh’st method,
nor those derived from the theory of oscillatory discharges
may be made use of, as pointed out by Stefan ¢.

As, however, we wanted to ascertain this element also with
sufficient accuracy, we used the following circuits in our
experiments relative to the period measurements, the theo-
retical value of the self-induction being known in those
cases. 3

(a) Square of copper wire: radius of section of wire
0°04 cm.; length of side 1=398°6 cms.

(L) Circle of copper wire:—

Circle No. 1: radius of section of wire 0:226 cm. ; dia-
meter of circle 201 ems.

Circie No. 2: radius of section of wire 0°226 cm.; dia-
meter of circle 57:2 ems.

The wires these circuits are made up of are stretched out on
suitable wooden frames, and the necessary insulation is obtained
by small ebonite cylinders.

In order to keep the sides of the square as far as possible
from conductive masses during the experiments, the wooden
frame was inclined at 50 degrees to the horizon, and had one
side at the level of the spark-gap. The mean distance between
the sides of the square, the walls of the room, and the ceiling
was 0°85 m.

Now, ‘according to Lord Rayleigh §, the effective self-
induction Lota plane conductor, 7 in length and of an ohmic
* Cfr. Wien, Wied. Ann. liii. p. 928 (1894).

+ Phil. Mag. xxi. p. 381 (1886).
¢t Wied. Ann. xli. pp. 400 & 421 (1890).
§ Phil. Mag. [5] xxi. p. 381 (1886).

30 Prof. A. Battelli and Mr. L. Magri on
resistance equal to R, for currents of high frequency will be
given by

pak
2pl/? 5a
p being =27n and A being a constant. This constant, as
results immedi: ately from for mula (20) of the quoted paper, by

_ putting p=0, is connected to the self-induction for continuous
currents by the relation

Deere:

Hence the preceding formula may be given the form

W=aly— 5(1- = / ae 2

For the various circuits above mentioned the value fer Ly
is given for a square* of the perimeter / by

Ty =2l (loge —1:9103 ),

L=i(A+

for a circle of the radius a by
Sa .
Ly=47ra (log, —_ 1
419

r being the radius of the wire f.

Wien ft controlled the values for Lo, calculated by these
formule and agreeing with each other to 0-1 per cent.,
by those obtained from accurate measurements ; they thus
deserve full credit. By substituting them in the formula (1)
we may calculate the self-induction the above circuits exhibit
for each period of the discharges we have photographed the
spark of.

The following values were thus obtained :—

For the square of copper wire :

T=0:00000425, 0:00000303,
L=27390-emsi, 27329 cms.

For the circle No, 1 |
T =0°00000235, 0°00000167, 0°00000120,
i=7329 ems.; 7824 cms., 7810 cms.

* This formula may be deduced by simple algebraical operations from

the one given in Mascart, Electr. et Magn. vol. i. p. 680, of the second

edition.
+ Mascart, /. c. p. 633.
t+ Wied. Ann. li. p. 928 (1894).

Oscillatory Discharges. 31

For the circle No. 2:
T =0:0000007,

In addition to these plane circuits we also made use of the
two following spirals in our period measurements.

Spiral A.—Vhis spiral is wound on an ebonite tube accu-
rately worked and traversed throughout its length by a glass
rod preventing any deformations of the former. The wire is
placed in a helix cut on the tube by means of the lathe.
The diameter of the copper wire it is made up of is 0:08 cm.,
the mean radius of the cross-section of the spires being
0-713 cm. The number of spires per centimetre is 6°3025.
The whole of the spiral contains 485 spires. Its self-induction,
as measured by Nernst’s method with currents of high fre-
quency (see p. 32), 1s 57,230 cms.

Spiral B.—The support of this spiral is a large marble
cylinder, worked on the lathe with extreme care in the
mechanical workshop of our Institute. Its surface may
be considered as that of a practically perfect cylinder. The
variations of diameter of its cross-section, in fact (this being
23°821 cms. at 23° C.), never reached 071 mm.

The length of this cylinder is 98cms. ‘The spiral occupies
85 ems., the number of spires being 283. The mean thickness
of the wire it is made up of is 1-435 mm. The spiral itself
has been directly wound upon the marble by means of the
lathe. In order to prevent any displacement of the spires
the whole has been coated with a thick varnish layer of
gum-lac. The self-induction of this spiral is 4°546000 cms.

28. To these values there have to be added the values
relative to the portions of the circuit establishing the communi-
cations between the condenser and the spark-gap. In order
to diminish the resistance and to have fer those portions an
easily calculated self-induction, we established the connexions
by means of big brass tubes, their external radius being
p,=1cem., the internal radius p,=0°88cm., and of copper strips
5 ems. in width and 52, mm. in thickness. For these tubes
the self-induction is given by *

‘ uf OPs —p
L=214 log ct praia g Bonsaiett, 7)l

Bae Pia ao Ie pa 2h. pie = Po, s
and for the ie Ie

L=al{ log. — Fe 4st,

/ being the length, a the thickness, and 4 the width.
* Wien, Wied. Ann. lili. p. 928 (1894).

differential exciter sligo

32 Prof. A. Battelli and Mr. L. Magri on

Hence for the three tubes used by us, being 90 ems., 80 ems.,
and 71 ems. in length respectively, we have the values

Jig = 658 0

l3=o00e
and for the strip, 20 ems. in length,

L,=103 cms.

29. With those experiments which served us to determine
the resistance of the spark and whose results we availed
ourselves of in order to compare the energy disposable in the
discharge with the energy exhibited by the various portions
of the circuit, we made use of cirenits wound in spirals, as has
already been stated; and with those experiments also we
photographed the spark.

In order to compare the values for the period of oscillation
as obtained experimentally for those sparks with the corre-
sponding theoretical values, it would be necessary to know
the self-induction of the spir als, whose dimensions are recorded
on page 22.

As theoretical formule to calculate accurately these self-
inductions are wanting, we had to compare them with that of
circuits capable of being theoretically calculated.

Tor these comparisons we availed ourselves of the Nernst*

ghtly modified, as to obtain the equi-
librium we maintained constant the two comparison capacities

and varied one of the two self-inductions. ‘The variable self-

induction was made up of a copper wire spiral, of which any
number of spires could be employed in our experiments
(anean radius of spiral 0°713 em., thickness of wire 0°5 mm.,
number of spires to the unit of length 6°3025).

The arrangement adopted is shown diagrammatically by

fig. 7, where L, denotes the spiral, L, is the comparison circuit,
CG and C, are the two comparison condensers, and R is the

detector, Pas
* Wied. Anz. 1x. p. 600 (1897).

Oscillatory Discharges. 33

After connecting the points C and D with the electrodes
of a spark-gap and with the poles of a Ruhmkorff coil, there
could be sent through the differential exciter currents with a
frequency of the same order of magnitude as those of the
sparks we have photographed.

Then it was tested whether the contact points A and B
between each self-induction and the corresponding condenser
were at the same potential. or this purpose we found most
convenient the detector suggested by Nernst, made up of a
vacuum-tube without electrodes, on whose terminals two
strips of tinfoil connected with A and B respectively had
been wound.

As is known, the luminosity of the tube will be minimum
when the condition

Cy =L,C,
is satisfied.

The accuracy of this method depends upon the precision
with which this minimum is determined, as any one of the four
quantities L,, L,, Cy, Cg undergoes a small variation. This
precision is greatest when the degree of exhaustion in the tube
is the one corresponding to the first appearance of cathode
rays.

Various numbers of spires of the spiral were successively
used until the detector showed a minimum of luminosity.
The self-induction L, of the spiral could be considered as
proportional to the number n, of spires used: denoting by &
the coefficient of proportionality, the above-mentioned con-
dition of minimum was represented by

L 1 Cy = king Cg.

The wire with known self-induction was next replaced
by the spiral whose self-induction « had to be determined,
and the number of spires was again varied, until for some
number » the minimum with the detector was arrived at.

The minimum condition became

aC, = knCo.

Those two determinations gave the self-induction to be
found
n
be ly
No
for high-frequency currents. Our experimental conditions
allowed of such a precision in determining the minimum that
the numbers n and m, ranging as a rule between 70 and 350,
were ascertained to less than a tnit.

Phil. Mag. S. 6. Vol. 5. No. 25. Jan. 1903. D

34 Dr. H. Pender on the Magnetic

We succeeded in reaching this degree of accuracy by using
the following precautions :— |

1, Using two comparison condensers whose capacities C;
and C, differ as little as possible from each other.

2. Covering all the portions of apparatus employed to
produce high- frequency currents (Ruhmkorff-coil, spark-
gap, &c.) w ith a metallic cage, In order to avoid electrostatic
actions between those latter and the various branches of the
Nernst bridge.

3. Covering with a metallic cage also the two comparison
eee

4, Avoiding the use of any conductors in the neighbourhood
of the wires, and especially of the spirals.

By this method the following values for the self-induction
of our circuits have been obtained :—

Circuit. Self-induction.
Spiral No. 1 29470

pA Nor? 74140

alo:-3 17460
Wire No. 4 3669

In these values the self-induction of tubes and copper
strips establishing the connexions are also included.

II. On the Magnetic Eject of Electrical Convection.—Li.
By Haroip Penver, Ph.D).*
INCE the publication of the results of his first experi-
ments on the magnetic effect of a moving charged
body +, the author has continued his investigations, with re-
sults in every way confirmatory of those of the previous
experiments. A brief account of these later experiments
may not be without interest, as they were performed under
entirely new and more favourable conditions, and gave
results which are far more consistent than those previously
obtained.

M. Crémieuf, in criticizing the previous paper of the
author, suggested that the agreement between the observed
and calculated values of the ‘magnetic effect of the moving
charged disks was due to the fact that the speeds and potential
of the disks were of such critical values that a slight leak in
the insulation would produce the observed effect. The first
step then was to test this criticism by varying the speeds and

* Communicated by Prof. J. S. Ames,

+ Phil. Mag. i. p. 169 (1901); Phys. Rev, xiii. p. 203 (1901).
t Journ. de Phys., Dec. 1901,

Lifect of Electrical Convection. 35

potential within as great limits as possible. To do this, the
same method as that previously used by the author, and first
introduced by M. Crémieu, was adopted, namely, to measure
the current induced in a coil when the charge on a rapidly
rotating disk close to it is suddenly reversed.

The great difficulty encountered in the experiments of last
year was the impossibility of shielding the needle of the
sensitive valvanometer employed to detect this current from

o
the disturbing magnetic effects of the electric cireuits in the

vicinity of ae laboratory, although the experiments were
conducted at night after the electric cars had ceased running.
Through the kindness of Prof. Ames, Director of the Physical
Laboratory of the Johns Hopkins University, I was enabled
to move the entire apparatus to the country. The apparatus
was therefore set up at McDonogh School, twelve miles from
the city of Baltimore and two miles from the nearest electric
car-line. Experiment showed that this car-line was too
distant to affect the galvanometer. llectric power for
running the various motors was furnished by the school.

The room first put at my disposal was a large garret. The
apparatus was set up here, and considerable time was spent
in vain attempts to mount the galvanometer so as to be free
from mechanical jarring. This was finally given up as im-
possible, as it was found that the wind caused the whole
building to rock considerably. The apparatus was then
taken down and set up once more in a large basement room
of another building. This room was 14°5 x 19°5 m. in size
and had a cement floor, which was so solid that when the
galvanometer was mounted on a stout table the needle was
entirely free from mechanical jarring

The various parts of the apparatus and their general
arrangement were essentially the same as employed last year.
There were, however, a few changes made which will be
briefly noticed,

The disk apparatus was changed only in a minor point,
which, however, obviated a source of great inconvenience.

o
This change was the mounting of the brushes making contact

with the arlneee of the dieles 7 in such a way that the insula-
tion of the cores could be cleaned without taking the apparatus
apart. Special care was taken to clean this insulation
thoroughly before each set of readings.

A new needle for the galv: Anonaee was made having a
greater sensibility than the old one, and the oround-elass
eeale was placed two metres from ihe ealvanometer. With
the new needle and scale thus arranged it was possible to get
tour times the sensibility previously secured. But it was

36 Dr. H. Pender on the Magnetic

found more advantageous to sacrifice sensibility to steadiness
of the needle, so that the galvanometer was usually adjusted
to have only about one and a half times the sensibility of
Jast year, a current of *7 x 10-1 amperes giving a deflexion
of 1 mm. on a scale 2 metres distant. At this sensibility the
spot of light was ideally steady, the zero position seldom

varying more than 2 mm. during the time required for the
determination of a deflexion (the period of the needle was
about 35 seconds), although there was sometimes a slow drift
of the light to the left. Any error due to this effect was
easily eliminated by taking a reading first on one side of the
zero position and then on the other.

On the shaft of the combined reverser and commutator

which served to reverse the sign of the charge on the disks
and to commutate the galvanometer terminals, a second re-
verser was mounted and connected in series with a Daniell’s
cell, resistance-boxes, and the test-coil T on the disk appa-
ratus. My idea was to adjust the value of the current
through this coil until its effect on the large coil I between
the disks was just equal and opposite to “the effect of the
moving charged disks, thus employing a zero method. It
was found more convenient, however, to note first the de-
flexion produced by passing a known current through the
test-coil with the disks discharged, then to break the circuit
of the conduction current, connect in the Voss machine so as
to charge the disks, and note the deflexion produced by the
convection current, then again note the effect of the con-
duction current, and so on. This was accomplished by means
of a set of switches operated by the observer at the galvano-
meter. The conduction current was adjusted so as to give
about the same deflexion as the convection current. Its.
value was determined from the known resistance of the
circuit and the E.M.F. of the Daniell cell. The zero method
was abandoned on account of the great length of period of
the galvanometer needle, nearly a minute being required to
detect any slight variation from the zero position.

The above method of procedure obviated the necessity of
determining the sensibility of the galvanometer and the
speed of the reverser for each set of readings, and also the
constant ‘“‘A”’ of the former paper. Much ‘trouble was ex-
perienced in getting brushes for the conduction current
reverser which would make a steady contact, but finally this
difticulty was overcome by making ‘the brushes of very soft
copper toil, each brush consisting of ten layers of foil. It
was necessary, in the course of the experiments, to replace
these brushes several times.

Effect of Electrical Convection. 37

As before, a Voss machine and battery of leyden-jars were
used to charge the disks. Instead, however, of connecting
each pole of “the Voss machine to the inside coats of three
jars, one pole of the Voss was earthed and the other con-
nected to the inside coating of all six jars, the outer coats of
which were earthed. The employment of this method
rendered possible the developing of a higher potential, but
the convection current produced by the moving charged disks
was no longer reversed, but simply made and broken by the
reverser. The reverser was run at such a speed that this
make and break occurred about ten times a second.

The potential to which the disks were charged was measured
by a Thomson electrostatic voltmeter having a range of
(—1200 volts. This instrument was carefully calibrated by
comparison with the standard guard-ring electrometer at the
Physical Laboratory of the J ohns Hopkins University.

The following diagram (fig. 1, p. 88) will make clear the
general arr angement of the apparatus.

The letters indicate the following:—D, the disks and
induced coil. M,, motor driving the disks. X, countershatft.
C, commutator and reverser. M;, motor driving the same.
L, leyden-jars. V, Voss machine. M,, motor driving the
same. H, electrometer. ‘'T, resistance-boxes and switch in
test circuit. S, high potential switch. K, key in galvano-
meter circuit. (es galvanometer. S!, scale for same.

Connexions are omitted for the sake of clearness. They
were essentially the same as previously used except that a
separate circuit had to be employed to carry the test-current
through the new reverser.

A number of sets of readings were now taken to determine
the relation between the deflexion d of the galvanometer pro-
duced by rapidly reversing a known current in the test-coil,
and commutating the galvanometer terminals connected with
the induced coil; and the deflexion D, produced by charging
and discharging the disks at the same rate, the galvanometer
terminals being commutated as before. The deflexions
actually measured were 2d and 2D (see preceding paper).
In each set of readings five determinations of both 2d and
21D were made with the disks running in each direction.
2d and 2D were determined alternately. In the first five
sets of readings the potential was kept practically constant,
and the speed of the disks varied from 9°9 to 92-4 revolutions
a second, and in the next six sets the speed was kept prac-
tically constant, and the potential of the disks varied from
905 to 5900 volts. To show how closely the various quan-
tities could be determined the following table, giving all the

38 Dr. H. Pender on the Magnetic

data for one complete set of observations, is appended. A
comparison of this table with Table III. of the previous paper

Biggie

will show how greatly the conditions of the experiment have
been improved. In the latter the greatest deviation from
the mean of 2D is 42 per cent., while in the table below it is

only 4:4 per cent.

Effect of Electrical Convection. 39

The symbols have the following meanings :—E is the elec-
trometer reading, from which is deduced V, the potential of
the disks in volts, by means of the calibration curve of the
electrometer, T, the number of seconds required by the east
disk to make 1990 revolutions, T, the same for the disk on
the west side, N the mean number of revolutions of the two
disks per second deduced therefrom, z the test-current
measured in amperes, d@ and D as described above. The
ratio of the two systems of units is calculated from these data
in the manner described below.

TABLE I.
March 25, 1902. ‘o

Direction of rotation: east disk-+, west disk—.

Be hin op mule at ie pit |e)

poe | 8 59% 878 | 424 |389x10-4
fink. | Bl b GLO!) 2388 429 |
ne | 80 59°5, | 886 42-4
73 len 82 60:5) * | 388 42:0
pe | 3 85 HO ase 41:8
73:0 81-2 603 | 384° 42:2 |:389x10-4|

V=6310 volts. N=49°3. Hence v=3:00 x 10”.
Direction of rotation: east disk —, west disk+.

wee ga | g05 (a6 | 49:2 |-3895<10—4I

72 79 G10: hi e90les| ae." |
73 85 Page aes cr | 428
72 BO 080 wh Be Ont 6 aod
75 81 595 | 384 | 4299
72:8 81:6 598. | 385 | 495 |389x10—4

V =6260 volts. N=49:1. Hence v=2°95x 10". |
Mean value of v: 2°98 x 10".

To compare the observed values of 2D with those which
should be expected on the assumption that the magnetic
effect of a moving charged body is similar to that produced
by a conduction current, the ratio v of the two systems of
electric units was calculated in the same manner as described
in the previous paper. No attempt was made at an accurate
comparison until all the observaticus had been completed.

Referring to my previous paper we have

_ 4VNA B ee (2 ne a
’—{B—=B)D [ute ey OB

where the symbols have the meanings there given. (I take

40 Dr. H. Pender on the Magnetic

this opportunity to call attention to two slips made in the
printer’s copy of my former paper, namely, the symbol 7 for
V in the formula on pp. 199 and 200, and 4 for 8 in the
formula at the hottom of p. 197.) In deducing this formula
the assumption was made that the charge on the disks was
reversed from a positive to an equal negative value and vwice
versa by the reverser. In all the experiments here described
the disks were alternately charged and discharged, sometimes
negatively and sometimes positively. Hence to apply to these
experiments the above formula must be written

2VNA yD Pe Va re,
v= (B—B)D b+ a4 log.(2 COS orl
A is the deflexion produced by reversing unit current in
the test-coil at the same rate as the disks are charged and
discharged. Hence if d is the deflexion produced by the
current 2 under the same conditions,
in ae
a

If the potential is measured in volts and the current in
amperes the above formula then becomes

2VNd Bink: ena
v= 30(B— A) Di [ety log,(2 COS 8) |

yw and v were determined in the manner described in the
former paper. The distance between the condensing plates
was kept constant. While the disks were running at a high
speed one day in the early spring the east disk flew off the
axle and was so badly damaged that it could not be used
again. Instead of waiting to have it repaired, which would
have taken considerable time, I went ahead with the remain-
ing disk, making a virtue of necessity by thus varying the
conditions of the experiment.
The constants in the above formula are as follows :—

Mean value for the two disks. Value for the west disk.

B= 29-432 B= 2-469
B= 356 C= arse
w= 115-0 w=115-0
y= 28°8 y= 28°8

It so happened that the two disks were arranged almost
perfectly symmetrically with respect to the coil, so that w .
and v for the two sides were identical within the limits of

Effect of Electrical Convection. Al
accuracy of measurement. Hence for the two disks
VNd
Ate DEC
and for the single disk
VNd
== 2 (07
v 06 D

Below are given the mean values, determined from a series
of observations similar to that recorded in Table I., of the
variable quantities in the above formule for the various
speeds and potentials employed. Those sets in which the
single disk was used are marked with a *.

Tasie IT:
ee a oy: N. aed 7
a VCE is he 11) OE NEE BA eL es)
103x10-4 205 | 155 9:94 | 5690 | 303x101
299 388 | 368 | 256 6250 3:08
389 | 72-9 815 49-2 6275 | 2:98
‘B17 | 92:6 83:9 630 5960 | 3:00
792 | 113-4 | 1158 92:4 6230 | 2:98
From former paper CFD, |) 10227.) 3il0 3°00
| | |
0813 «=| 205 «| 188 | 59-4 905 301
134 | 260 | 382-7 59-6 2030 | 3-00
* 1005 lalla baie 230, 59-2 2950 | 3:04
* 249 | 835 | 561 57-6 4090 | 2:92
* 249 | 47-1 | 38:1 57-9 5010 | 2-97
O73 | 540 47°] 58-4 5900 | 2-98

Mean... 3°00

Surely no more conclusive refutation of M. Crémieu’s
criticism could be desired than that contained in the above
results. Such close agreement between the observed and
calculated effect under such varying conditions cannot be
ascribed tc the effect of a conduction current caused by any
leak in the insulation, for such a current would certainly,
from its very nature, be independent of the speed. It is to
be noted, however, that the exact coincidence of the value
of v as determined from the above experiments with its known
value must be considered as an accident only, for an error of
at least one per cent. might readily have occurred in the
determination of the constants of the apparatus.

In one of his experiments on the magnetic effect of a
rotating charged disk on a magnetic needle suspended near

42 Dr. H. Pender on the Magnetic

it*, M. Crémieu observed a deflexion of the needle when
between it and the charged disk there was only a single con-
densing plate connected to earth, but when between the
needle and this plate a second metallic plate connected to
earth was introduced no effect could be obtained. It there-
fore seemed worth while to try a similar experiment with
the apparatus above described. In this experiment only one
disk was used. Between the condensing plate next the coil
and the coil itself was introduced a brass plate 1:5 mm. thick
connected to earth. On setting the disk in rotation, but
without charging it, a great unsteadiness of the needle was
noticed. It was discovered that this was due to traces of
iron in the brass plate. By gently tapping the plate when
the disk was at rest the same effect could be produced. To
keep the plate sufficiently steady to make any observations
on its shielding effect it was therefore necessary to run the disk
at a very low speed. With the disk running at such a low
speed, the Voss machine was connected in, and the deflexion
of the galvanometer needle observed. Then, without making
any other change, the brass plate, connected to earth, was
introduced, and the deflexion again noted. This was done
several times. The means of a number of readings with the
plate out and in were respectively 12°8 and 13-0 mm. de-
flexion. From this we can conclude that the introduction of
the plate was without any such effect as noted by M. Crémieu.
It may be of interest to note in this connexion that an attempt
to use a solid aluminium disk in place of the gilded disk in
my first experiments was foiled by the magnetic disturbances
caused by the traces of iron in the aluminium, although the
purest metal obtainable was employed.

The next experiment tried was the application of Crémieu’s
method to the investigation of the magnetic effect of a dielec-
tric moving in a uniform electrostatic field, or, in other words,
the magnetic action of a moving apparent charge. This
question was first investigated by Rontgent in 1888. Réntgen
showed that a moving polarized disk was capable of deflecting
a magnetic needle suspended near it. The maximum de-
flexion observed by Rontgen was 3 mms. One objection
offered to. Réntgen’s experiment was that the effect observed
might have been caused by the disk assuming a real charge
by leakage across from the condensing plates on each side of
it. Crémieuw’s method precludes any such action as this,
inasmuch as the condensing plates are rapidly charged and

* C. R. exxxi. p. 797 (1900).
+ Wied, Ann. xl. p. 93.

Liject of Electrical Convection. 43

discharged, and even though there should be a slight leakage
of a real charge across to the surface of the disk, this charge
could produce no deflexion of the galvanometer, as the charge
would tend to assume a constant value, whereas the deflexion
of the galvanometer is due to a change i in the electrical con-
dition of the disk.

For this experiment two ebonite disks were made, diameter
30°5 ems., thickness °8 em. The gilded micanite disks used
in the first experiment were replaced by these (see fig. 2).
The two condensing plates OC, and Cs Fig. 2.
next to the induced coil I were earthed. ie
The other two condensing plates ©, and
C, were connected through the inter-
rupter to the pole of the Voss machine,
so that they might be rapidly charged
and discharged. Hverything else re-
mained exactly the same as in the first
experiments. When the two outer
plates C, and C, are charged positively,
for example, the two ebonite disks
become polarized, so that the surfaces
next to the outer condensing plates
assume an apparent negative charge,
and the surfaces nearer the inner con-
densing plates C, and C3 assume an
apparent positive charge. Since the
positively charged surfaces are nearer
the induced coil than the surfaces
negatively charged, when the outer
plates are suddenly discharged while
the disks are retating, there will be a
slight current induced in the coil I.
Since the two surfaces oppose each
other in their magnetic action the
resultant effect is very small, being
greater the thicker the disks, for the
same surface-density of the apparent
charge. <A slight deflexion of the
galvanometer was observed with the
disks arranged as just described, but
it was found that a greater effect could
be obtained by mounting the two disks flat up against each
other on the same axle, “thus using only one side of the ap-
paratus. This arrangement amounted to the use of a single
disk 1°60 cm. thick, 7. e. twice the thickness of one of the
disks. Also it was possible to charge to a higher potential

1
a AcTUAL Size

44 Dr. H. Pender on the Magnetic

the single condenser thus formed than the two condensers
above described, for a given speed of the Voss machine and
the interrupter. (It may be here noted that the Voss machine
was always run at the highest possible speed. A machine
of greater capacity would have made possible the procuring
of a greater deflexion.)

To calculate the deflexion which should be expected on the
assumption that a moving apparent charge has a magnetic
action, a method similar to that employed in the previous
calculation. was adopted. Let o be the surface-density of
the apparent charge on the surface of the disk next to the
coil, assumed uniform as a first approximation, N the number
of revolutions of the disk per second, v the ratio of the two
systems of magnetic units, 7 the radius of an imaginary
ring on the surface of the disk with its centre at the centre
of the disk and of width dr, 6 the deflexion of the galvano-
meter-needle produced by a unit current in such a ring on
the surface of the disk next to the induced coil, rapidly made
and broken the same number of times a second as the disk is
polarized and depolarized, 6’ the same for a unit current in
such a ring on the opposite surface of the disk. Then the
deflexion of the galvanometer-needle due to the rapid polar-
izing and depolarizing of the rotating disk will be

5 R
= me aN cis
COO

o is determined from the formula (Webster, Elec. and Mag.
p. 364)

wero (Oy
Aa[ (di +d,) +d]

where wu is the dielectric constant of the disk (for ebonite 2:5),
d, the distance between the outer condensing plate C, and
the surface of the disk, d, the distance between the inner
condensing plate C, and the surface of the disk, d the —
thickness of the disk, and V the potential of the outer plate,
the inner plate being earthed.

“ calibra-

R
The integral | 7(6—0’)dr was determined by a
0
tion of the apparatus” in a manner similar to that employed
in the first experimeuts. A set of coils of known radii was
clamped up against the surface of the disk next to the induced
coil. A known current i was sent through the reverser and
one of these coils. While the current was being thus reversed

in this coil, the frame carrying the disk was drawn back from

Hifect of Electrical Convection, 45

the induced coil a distance equal to the thickness of the disk,
and the resultant change A in the galvanometer-deflexion
noted. The frame was then pushed up into its former position,
and the change in deflexion again noted. A second known
current 7; was then sent through the reverser and the test-
coil on the frame carrying the disk, and the change in galvano-
meter-deflexion B resulting from a known change (2;—7,) in
this current noted. 7, i,, and i, were so chosen that the
deflexion produced by the current #, in the test-coil was equal
to the deflexion produced by the current 2 in the coil on the
surface of the disk, and the change in deflexion A was approxi-
mately equal to the change in deflexion B. In this way the
quantities A and B were measured at the same part of the
galvanometer-scale, thus avoiding any error due to a lack of
proportion between the current and the deflexion, which was
considerable in the galvanometer employed. Let p, be the ratio
of the deflexion produced by unit current flowing through the
reverser and any coil on the surface of the disk next to
the induced coil to the deflexion produced by unit current
flowing through the test-coil, p. the corresponding quantity
when the coil is on the opposite surface of the disk. Then
A (is)

P1— P2= ; B °

From the observations taken as above described p,—p2 was
calculated and plotted for twelve different coils.

Let A be the deflexion produced by a unit current flowing
through the reverser and test-coil. hen

d—6'=5A(p1— pa) ;

(6—6’ is the deflexion due to the making and breaking of a
current, whereas A and B are the deflexions resulting from
a reversal of current, hence the factor 3). The formula for

D therefore becomes
Di

R
The integral | +(p;—p.)dr was calculated graphically trom

R
oe | 1(p1—p2)dr.

0
the plat of p1— po.

A number of observations of the deflexion D were made,
which always agreed in direction and fairly well in amount
with the deflexion as calculated. A close agreement could
not be expected, inasmuch as the assumption that ois uniform
at the edge of the disk is only a rough approximation to the

46 ‘Dr. H. Pender on the Magnetic

truth, and even under the best conditions the deflexion is
necessarily small. The following data, which are the mean
values from one set of readings, will suffice to illustrate the
capabilities of the method.

aw =1°60; ad, =~30, d,= "To:

V=24°9 o.a.s. electrostatic units (=7470 volts).

o =°70 electrostatic units.
2° 51 x 10’ mms. per electromagnetic unit.
JE

i poe

0
2D calculated 4°85.
2D observed 4°5.

2D was the actual deflexion measured, not D.

Considering the importance of the question as to the mag-
netic action of a moving static charge, the following experi-
ment, in which was observed the direct magnetic action of a
moving charged disk on a magnetic needle suspended near it,
may be of interest, though similar results have been obtained
by other experimenters. The uninjured one of the two
micanite disks used in the first experiments was provided
with a row of sixteen brass studs set at equal intervals apart
ina circle of 5 centintetres’ radius around the centre of the disk.
The gilded surface of the disk was then divided into sixteen
sectors on each side, each pair of sectors carrying a stud.
The sectors were separated from one another by a strip of
micanite surface 1 cm.in width. The tinfoil on both the con-
densing-plates, with the exception of a sector on each twice
the width of a sector on the disk, was removed. The tinfoil
sectors were earthed, and the sectors on the disk could be
connected one at a time, through a brush B (fig. 3) set so as

Fig. 3.

aActuar Size

to make contact with the studs 8, with one pole of the Voss
machine, the other pole of which was earthed. The frame
carrying the disk was so arranged that the disk could be set

Effect of Electrical Convection, . AT

in rotation about a vertical axis. A hole about 2 cms. in
diameter was cut through the upper ebonite plate C, dia-
metrically opposite the tinfoil segment, and so that its centre
came 1 em. over the edge of the disk. This hole was covered
on the side next to the disk witha thin sheet of mica. Fi itting
loosely into the hole so as not to touch the sides or the mica
plate at the bottom was a brass tube in which was suspended
a delicate astatic needle N. The two magnets forming the
needle were 5 cm. apart. The needle and attached mirror
weighed about 3 mgs., and was suspended by a fine quartz
fibre. With the control-magnet properly placed the needle
could be given a period of 25 seconds. The case in which
the needle was suspended was fixed to a frame built over the
disk apparatus, having an independent support, so that when
the disk was set in rotation there was no jarring of the
needle. The position of the needle was read by the reflected
image of an electric-light filament ona ground-glass scale
2 metres distant.

When the disk was set in rotation and the brush making
contact with the studs was connected to the Voss machine, a
deflexion of the needle was obtained which was in the proper
direction and of the proper amount to be accounted for on
the assumption of the magnetic action of a moving charge.
The arrangement here adopted precludes any conduction of
charge in the condensing-plates or in the disk itself, two pos-
sibilities which have been suggested to account for the deflexion
observed with solid condensing-plates and a disk of uniform
metallic surface. The results of one set of observations will
suffice to give an idea of the magnitude of the quantities
involved.

Mean distance between the two surfaces of the disk and
needle 1°61 cm.

Distance between the two condensing segments (one on
each ebonite plate C, and C,) 2°18 ems.

Thickness of disk *356 em.

Potential. of the disk 5000 volts.

Speed of disk 69°7 revolutions per second.

Observed deflexion 47:9.

Calculated deflexion 56:0.

The calculation was made in a manner similar to that
employed in the previous experiments, the principle of it
being a calibration of the disk apparatus such as above
described. Only a rough calculation was attempted, as it
would be a matter of some difficulty to calculate the exact
distribution of the charge on the sectors. As a first approxi-
mation this distribution was assumed uniform. The agreement

48 Prof. H. L. Callendar on the Thermodynamical

between the observed and calculated values of the deflexion is
therefore as good as could be expected.

My chief object in setting up the apparatus with the magnetic
needle was to test experimentally certain criticisms made in
my former paper on M. Crémieu’s experiments, especially
his experiments on open electric circuits*. However, in
consequence of unavoidable delays, it was not until the Ist of
June that I was ready to proceed with the work. But now
the damp and sultry weather of the summer had set in and put
an end to all experiments with static electricity for the time.
being.

I wish here to express my thanks to Prof. Ames of the
Johns Hopkins University, to whose kindness I am indebted
for the opportunity of carrying out these experiments, and
whose criticisms and suggestions have proved of great value.

Baltimore, Md., July 1, 1902.

III. On the Thermodynamical Correction of the Gas-Ther-
mometer. By H, L. Catuenpar, If.A., #R.S., Professor
of Physics, Royal College of Science t.

1. Introduction.

FEXHE correction of the gas-thermometer to the absolute
scale is a subject possessing considerable theoretical
interest ; it has also acquired some practical importance at
the present time in view of the increasing accuracy attainable
in thermometric measurements. A number of papers on the
subject have recently appeared in the Philosophical Magazine
and other periodicals. ‘Lhese show some divergence in the
methods proposed and in the results deduced, and little has
yet been done in the direction of calculating tables of cor-
rections for different gases, or in the practical application of
the results to thermometric measurements.
I propose in the present paper to give some account of the
theoretical and experimental work bearing on the subject ;
to explain a method of expression in terms of the ‘‘ Co-agere-
gation Volume” which I have found very convenient in
treating similar problems relating to imperfect gases ; and to
show how to calculate tables of corrections in a simple and
practical manner.

* Comptes Rendus, cxxxii. p. 1108.

+ Communicated by the Physical Society. Read March 26th, 1901.
Publication was delayed to await the results of experiments in progress
at University College. But in consequence of my removal to the Royal
College of Science, it has been found impussible to include this experi-
mental work in the present paper.

Correction of the Gas- Thermometer. 49

The earliest work of any value was that of Reenault
(Mémoires de (Institut, Paris, 1847) (1) on the deviations of
gases from Boyle’s law; (2) on the pressure- and expansion-
coefficients at various pressures; (3) on the comparison of
the thermometric scales of different gases over the range 0°
to 800° C. These experiments established the suitability of
the gas-thermometer as a standard, but the order of accuracy
attained in the comparisons did not suffice to detect any differ-
ence between the scales of the more permanent gases.

The Absolute or Thermodynamic scale of temperature was
invented shortly afterwards by Lord Kelvin, who devised a
very delicate method of detecting the deviations of actual
gases from the ideal state (Trans. Roy. Soc. Edinb. vol. xx.
p- 289, April 1851; Phil. Mag. [4] 1852, p. 481), and
explained how to reduce the indications of the gas-thermo-
meter to the absolute scale. The experimental measurements
were carried out shortly afterwards in conjunction with
Joule (Phil. Trans. 1854, p. 321), and still remain among
the most important data for the determination of the thermo-
dynamical correction. The history of this investigation is
contained in Sir Wm. Thomson’s Mathematical and Physical
Papers, vol. i. pp. 333-455, and need not be considered in
detail ; but it will be necessary to give a brief account of the
method for the elucidation of the notation adopted and the
method of calculation proposed in the present paper.

2. Theory of the Porous-Plug Experiment *.

The notation adopted is as follows :—

H=intrinsic energy of fluid per unit mass.

p =pressure; v=volume of unit mass.

F =H + pv=total heat of fluid per unit mass.

H=heat supplied per unif mass from external sources.

Q = (d@/dp)»=“ Cooling Effect,” or fall of temperature
per unit fall of pressure in adiathermal expansion at
constant F.

S=(dH/dé@)»=specific heat of fluid at constant pressure.

T=(pv/R)=temperature by gas-thermometer.

§ =temperature on the thermodynamic scale.

We have the following relations between the different
quantities :—
By the first law of thermodynamics,
dH=dH—pde. . Slave Sant!)
* For practical details see Preston, ‘Theory of Heat,’ p. 702 (1894) ;
Edser, ‘ Heat for Advanced Students,’ p. 384.

Phal. Mag. 3. 6. Vol. 5. Nox 25. Jan. 1903. 1D)

50 Prof. H. L. Callendar on the Thermedynamical
By the second law of thermodynamics,
(dH/dp)g= —@(dv/de),. ... 2 ee
dF¥=dKh+d(pv)=dH + vdp
= (dH/d@),d@+ (dH /dp)gdp + vdp
=Sd0—(O(du/d0),—v)dp. |. aan

Whence,

When a fluid is flowing steadily along a tube through a
porous plug or throttling aperture without external loss or
gain of heat, as in the experiment of Joule and Thomson, the
function, F= H+ pv, will remain constant provided that the
kinetic energy of flow is the same on either side of the plug.
It is convenient to have a name for this function, which
I have called the Total Heat, employing the expression used
by Regnault for the same quantity in the case of a saturated
vapour. Expansion through a porous plug is frequently
spoken of as ‘* free” or ‘‘unresisted ” expansion, but this
term appears to be inappropriate, since the external work
done is d(pv) and not zero, as in Joule’s original experiment.
It is often said to be “adiabatic” in the sense that no heat
is supplied to the fluid from external sources. But this may
lead to some confusion, as the process is not isentropic.
I have found the term “ Adiathermal” more convenient, as
implying that there is no heat-transmission, and that the
total heat remains constant (dF =0).

Applying the condition dF=0, we have by (3) above the

well known relation,
SQ=S(d¢/dp)y=0(dv/d?),—v. “2 ee

This equation gives the “cooling effect”? in adiathermal
expansion under the condition of constant total heat, which
is the quantity measured in the porous-plug experiment. It
is convenient to employ the single letter Q for the cooling
effect (d0/dp)r, and to measure it in degrees of temperature
centigrade per atmosphere (p=10° c.a.s.=75 cms. Hg. at
0° C. and lat. 45°), in which case 8 should also be measured
in terms of a unit 10° ergs. The sign of Q is positive when
a fall of temperature accompanies a fall of pressure, as in the
case of air and CQ,. It is negative, a heating effect, in the
case of hydrogen at ordinary temperatures.

It is important to observe that the vanishing of the cooling
effect is not in itself a sufficient criterion of the ideal gaseous
state, pv =RO. The condition @(dv/d@),=v would evidently
be satisfied by any fluid possessing the characteristic equation

Correction of the Gas- Thermometer. OL

v/0=f(p), where f(p) is any arbitrary function of p. But
if the fluid satisfies Boyle’s law at all temperatures, we must
have pv=/ (@), and the two conditions together are satisfied
only by the ideal gas. Similarly Joule’s experiment on the
expansion of a gas into a vacuum (dH=0) leads to the
condition 0(dp/d@),=p, if there is no change of temperature,
which is satisfied by any fluid possessing “the characteristic
equation p/O=f (v), where f(v) is any arbitrary function of v.
This condition, in conjunction with Boyle’s law, again suffices
to define the ideal state ; but no one of the three conditions
is sufficient by itself.

3. Application to the Gas-Thermometer.

In the practical application of the gas-thermometer, we
assume an equation of the form pu=RIT, in which T is the
temperature by gas-thermometer, and differs from @ in
proportion as the gas in question deviates from the ideal
-tate. In order to apply the results of the porous-plug
experiment to the correction of the scale of the gas-ther-
mometer, Thomson originally proposed to estimate the
difference 9—T approximately by the following method :—

Suppose the experiment to be performed in a calorimeter
at constant temperature, so that the gas after passing the
plug is restored to its initial temperature. The heat absorbed
in the calorimeter is evidently equal to the amount Sdé
which would have been required to heat the gas up to the
original temperature at constant pressure if the experiment
had been performed adiathermally with a fall of temperature
d@. But the heat absorbed at constant temperature in the
calorimeter is also by the first law equal to the increasé
of intrinsic energy (dH/dv)gdv of the gas, together with the
external work d(pv)g done by the gas. Writing for
(di /dv)¢9 its value Blcip HIG). -p, we have

—S8dd=(0(dp/d0),—p)dv+d(pv), . . (5)

which is evidently equivalent to the equation (4) previously
given, but with v instead of p as independent variable, since
(dp/dd), (dv/dp)g= —(dv/d@) p. Integratin @ this expression
over the range of an experiment from p’ v! to pe" at constant
temperature, vand putting on the left the observed value of
the tall of temperature (6! — 0”), we obtain Thomson’s original
equation,

S(6'— 6") =0(dW/d0),»-W+p"'v’—p'v’, . (6)

in which W is the work represented by the integral of pdv

H 2

Rs Prof. H. L. Callendar on the Thermodynamical

at constant temperature. The integral W and its variation
with temperature cannot be determined for the gas without
an exact knowledge of the form of the isothermals, and of
the coefficient (dp/d@), in terms of the absolute scale.
Thomson therefore proposed to make an approximate esti-
mate by assuming (1) that the gas obeyed Boyle’s law
pul =RT=p’v", (2) that the degrees on the absolute scale
were nearly the same size as on the constant-volume gas-
thermometer at the temperature of experiment, or that we
may write (dp/d0),=(dp/dT),=p/T=R/v. Making this

approximation, we obtain immediately,
dé—T=S(6'—0")/Rlog, (v/v). -..

This approximation is unsatisfactory, because if we knew the
absolute value of the pressure-coefficient and the deviations
from Boyle’s law, the gas-thermometer might be corrected to
the absolute scale without performing the porous-plug ex-
periment. The quantities neglected are evidently of the
same order as the quantity sought. Thomson and Joule
clearly realized this, and devised other methods of correction,
but unfortunately the first approximate solution is still
retained in many text-books *, in a slightly different form,
as the final and correct solution of the problem. The method
of exposition generally adopted is as follows :—

Assuming that the degrees on the scale of the constant-
pressure gas-thermometer are of the same size as those of the
absolute scale at the temperature of the experiment, we may
write dv/d@=dv/dT=R/p in equation (4). Rearranging the
terms and substituting T for pu/R, we then obtain

O—T=Spd0/Rdp. . = (Se

Assuming further that the small difference (@—T) is inde-
pendent of p, the right-hand side is integrated from jp! to p",
substituting for d@ the actual difference of temperature
(@'—@") observed when the gas expands adiathermally from
a pressure p! to a pressure p!. This gives again the ex-
pression

9—T=S8(6'—6")/Rlog p!/p"=8(0'— 6") /Rlog v/v. (9)

When the experiment was tried, it was found that the fall
of temperature (9—6@') was not proportional to log (p/p’), but
simply to (py—p’), so that the second assumption involved
in solution (9) is evidently erroneous. As a matter of fact,

* KH. g. Maxwell’s ‘ Heat,’ p. 214 (1897); Tait’s ‘ Heat,’ p. 340 (1895),

Correction of the Gas- Thermometer. aD

Joule and Thomson did not make any direct use of the
approximate solution in thisform. But owing to its frequent
repetition, it has proved a stumbling-block to many who
have attempted to apply the results of these experiments to
the calculation of the difference between the scales.

In order to calculate the correction for the azr-thermometer
over the whole range, Joule and Thomson proceeded in 1854
by a different method. Combining Regnault’s formula for
the pressure-coefficient at various constant densities, namely,

Pressure-coefficient of Air=*00365343 +°000011575 Vo/v, . (10)

with his experiments on the deviations from Boyle’s law at
4° C., and with their own experiments on the cooling-effect,
they calculated the following formula (the units being feet
and pounds) to satisfy all the available experimental data :—

po=R(O—(:0012811—1:3918/0 + 353°2/62)V,/v). (11)

This is a very simple and direct method provided that the
data employed are accurate and consistent. Calculating
from this formula they obtained the value of the freezing-
point of water on the absolute scale 0° C.=273°72 Abs.,
which is still frequently quoted, and was universally accepted
for many years. They also calculated a table of corrections
for the air-thermometer which has been quoted in many
recent books (e.g. Guillaume’s Thermométrie, Paris, 1839)
as the final result of their work. It is evident, however, that
the value 0° C.=273:-72 Abs. is simply the reciprocal of
Regnault’s limiting coefficient at zero initial pressure, namely,
"00365843, and does not depend at all on the value of the
cooling-effect ; and since Regnault’s formula (7) is well
known at the present time to be erroneous, it is not to
be wondered at that the values of the thermodynamical
correction given in Joule and Thomson’s original table should
be very greatly in excess of the true difference between the
scales.

Other attempts have been made on similar lines to calculate
tables of reduction for the gas-thermometer, notably by Joch-

mann (1860),and by Weinstein (1881),w hose resultsare quoted
in Guillaume’s Vhermométrie, p. 261*. Weinstein quotes
Jochmann’s equation, and endeavours to adapt the method
for calculation of the corrections of the constant-volume
EEO By a somewhat complicated method, taking

* Jochmann, Schlomilchs’ Zeit. Math. Phys. v. pp. 24 & 96; Wein-
stein, Metron. Beitr. n. 3, p. 65.

54 Prof. H. L. Callendar on the Thermodynamical

account of Regnault’s data in addition to those of Joule and
Thomson, he arrives at an empirical equation of the form

6/0,=(1+-003654 2)10, | |, (12)

in which ¢ is the temperature on the centigrade scale. The
values of the corrections calculated by this method are much
smaller than those in the original table of Joule and Thomson,
and are of the right order of magnitude between 0° and 100°,
but it does not appear that an equation of this type correctly
represents the phenomena.

4. Rankine’s Equation for COs.

In the same paper (Phil. Trans. 1854, p. 337) Joule and
Thomson quoted another empirical formula for CO, contained
in a letter from Rankine, namely,

pou=RO—aROy,/0v, -. = & ee

in which the value of the constant a (in degrees of tem-
perature) was given as 1°9, and was deduced solely from
Regnault’s observations of the pressure-coefficient of COs, at
various constant densities. In a previous paper (Trans. Roy.
Soc. Edinb. xx. p. 561) Rankine had given an estimate of
0, the absolute zero, obtained by plotting Regnault’s values
of the pressure-coefficients of air and CQ,, which led to the
value @,=274°'6, but in the formula quoted he employed
O)=274°:0. This formula agreed very well with Regnault’s
coefficients of expansion for CO,, and also with his observa-
tions on the compressibility. Joule and Thomson further
showed that it satisfied their own observations on the
cooling-effect at that time available, employing the expression
Q=3Rad,"/S6?, deduced from Rankine’s formula. Taking
Rankine’s value for a, and putting R=1°89 x 10°,S=8-4 x 10°
c.G.8. we find Q at 0° C.=1°28 per atmo., which is in fair
agreement with the value actually observed.

At a later date (Phil. Trans. 1862) Joule and Thomson
succeeded in obtaining more accurate measurements of the
cooling-effect over a range of temperature extending from 4°
to 96° C., and found that the cooling-effect for air and CO,
varied nearlv as 1/6”, and could therefore be represented by
Rankine’s formula. By adopting the expression Q= A/@ for
the cooling-effect, and integrating equation (4), neglecting
the variations of 8, and assuming that the equation must
approximate indefinitely to v=R@/p at high temperatures,
they obtained the following type of characteristic equation,

v=RO/p—AS/30, . .-. . (14)

Correction of the Gas- Thermometer.

which may also be obtained by substituting pr = R@ in the small
term of Rankine’s. They found, however, that the heating-
effect in the case of hydrogen increased slightly with rise of
temperature, and could not be represented by the formula.
Assuming Rankine’s formula, it would evidently be easy to
ealeulate the value of the absolute zero, and to deduce tables
of corrections for the gas-thermometer. But as the formula
did not represent the case of hydrogen, which was the most
important for thermometric purposes, they did not publish
any turther tables of corrections, and the absolute zero was
still taken at —273°-7 C., as calculated in their previous
paper from Regnault’s limiting value for the pressure-

oO
coefficient in the ease of air.

5. Estimation of the Absolute Zero.

The problem of the thermodynamical correction of the
gas-thermometer is naturally divided into two parts: (1) the
determination of the value of the freezing-point of water on
the absolute scale in terms of the fundamental interval, which
may be called the value of the Absolute Zero; (2) the de-
termination of the correction to be applied at other points of
the scale to reduce an interval of temperature measured on
the scale of the gas-thermometer to the corresponding value
measured on the absolute scale, which may be called the
Scale-Correction. The latter depends essentially on the type
of empirical formula assumed to represent the mode of
variation of () with temperature, whereas the former may be
approximately estimated without any such assumptions.
Moreover, the scale-correction is necessarily small for gases
at or dinary temperatures, whereas the absolute zero correction
may be considerable, and is required for determining the
variations of the pressure- and expansion-coefticients.

A simple and accurate method of determining the value of
the absolute zero from observations of the “cooling-effect
alone, was given by Sir Wm. Thomson in his article “ “Heat ”
in the Ency yclopedia Britannica (vol. xi. p. 554, 1880).
The differential equation (4) may be written in the form

d0/0=dv/(v+S8Q), Se ie PR a)

in which, if we require only to make an approximate estimate
of the absolute zero correction, we may put SQ constant and
equal to its average value between 0° and 100°C. Integrating

this at constant pressure p, between limits 0° and 100°, and
writing Ty for the expression 100% /(v100— to) (the reciprocal of

56 Prof. H. L. Callendar on the Thermodynamical

the fundamental coefficient of expansion, which may be called
the “fundamental zero”), we obtain for the absolute zero
correction the simple result,

6) —Tp=SppQ/ Reese v's)

This expression was applied to calculate the coefticients of
expansion at various constant pressures, and to determine
the value of the absolute zero from Regnault’s coefficients of
expansion of air, hydrogen, and CO, at py=76 ems.

The following table contains the results given in the article
Im question :-—

TABLE 1.—Absolute Zero from Regnault’s
Expansion-Coefiicients.

Gas employed) ae omaeetecn aces see ese Air. ERS. CO,.
Coefficient of Hxpansion, a .............+ 0036706 0086615 = -0037100
Fundamental Zero of Gas, T,=I/a ... 2729-44 273°°13 269°°50
Correction to Absolute Zero, @,—T, ... —+:°70 —'13 Sfoeee
Absolute Zero deduced, 0, ............++- 275714 273°00 273°90

Thomson remarks as the result of these figures that the
correct value is probably within a tenth of a degree of 273°-0,
and that it is satisfactory to find that a gas so imperfect as
CQ,, with so large a value of the correction, should differ so
little when corrected from air and hy drogen. As a matter
of fact, the discrepancy, small as it is, appears to be due to
an error in Regnault’s coefficient of expansion, for if we
adopt instead Chappuis’ value of the expansion-coefficient for
CO, at 100 cms. pressure, namely ‘603742, which gives
T,)=267°:24, we find (increasing the correction in the ratio
106/76) the value of the absolute zero 0)=267°24+5°8=
273°°04, which agrees with hydrogen.

A similar method has been applied by other writers to
estimate the zero correction for the constant-volume ther-
mometer. If we neglect the term d(pv) in equation (5)
(which is not justifiable), and write — (d0/dv)r=Qp/v (which
is a good approximation considering that this term is small),
we obtain

14-SQ/o=(dpid0),t/p= 2 ee =) + ee

Integrating this at constant volume, assuming SQ constant,
we have the solution

log. (0/8) =log. (p/po)/ (1 a SQ/v), at hate (18)

Correction of the Gas- Thermometer. a

from which, since SQ is small, we have the approximate
value of the correction,

Ghd Nese wy os a (19)

This is equivalent in effect to the method adopted by Lehfeldt
(Phil. Mag. April 1898, p. 363), who takes for Q the value
of the “proper mean cooling-effect”? given by Thomson.
Applying the correction to the value of the pressure-coefficient
for CO, found by Chappuis at py=100 cms., namely,
(O03 201.) 1,268" -45, he’ finds) @)=—274°°83, which. is
evidently much too large. The error is chiefly due to the
neglect of the term d(pv). He also applies formula (18)
to evaluate the scale-correction between 0° and 100° for
comparison with Chappuis’ observations. His results for
the scale-difference between the nitrogen and hydrogen
thermometers are given in Table VI. (p. 67), and indicated by
the dotted curve in fig. 1 (p. 69). They appear to be somewhat
in excess of the true values, partly in consequence of the
assumption SQ=constant, which cannot be made in deducing
the scale-correction.

There is a much simpler method of deducing the absolute
zero correction directly from the differential equation, without
integrating on the assumption SQ=constant, which, so far as
I am aware, has not been previously noticed.

For the constant-pressure thermometer, we take the
equation in the form (4), and substitute dv/d@=R/p, and
T'=pv/R, which gives the simple result,

Ce SS pO ae ee C0)

which is accurately true at a point in the neighbourhood of
50° C., where the degrees on the scale of the gas-thermometer
are of the same size as those on the absolute scale. To find
the value of the zero correction 9)—Ty, we have merely to
subtract the value of the scale-correction at this point. But
the latter must be very small compared with the zero cor-
rection, since the whele number of degrees between 0° and
100° C. is the same by definition tor both thermometers.
If, therefore, we substitute the proper mean value of SQ,
which corresponds to the point where the degrees are of
equal size, we shall obtain a very good approximation to the
absolute zero correction, which is in fact seen to be the
same as that given by Thomson for the constant-pressure
thermometer.

To make a similar estimate for the constant-volume ther-

58 Prof. H. L. Callendar on the Thermodynamical

mometer, we take the differential equation in the form (5),
which may be written

—SQ(dp/dv} y= 0(dp/d?),—p +(d(pv)/dp)(dp/dv) 9. (21)

{n the small terms it is justifiable to make the approximations
(dp/dv) p= (dp/dv)g= —p/v. If we also put (ipl eae
which is only true at the point where dT/d@=1, we obtain
O6—T=SpQ/R+ (d(pr)/dp)gp/R. . . (22)
In order to evaluate this for CO, we may take SQ=7°9 c.c.
as the proper mean value. We require in addition the value
of d(pv)/dp at or near 50° C., which may be taken as 2°4 ¢.¢.
from Amagat’s observations on CO. The value of p is the
pressure in the gas-thermometer at the point considered.
Adopting Chappuis’ value of the pressure-coefficient for CO,
at 100 ems. initial pressure, namely, ‘00387251, T)>=268°°45,
we have p=119 ems.=1°58x10° cas. at 50° Taking
R=1°'89 x 108, we find the value of the correction 4° 55,
which gives 6, =273°°0. This neglects the scale-correction
at 50°, which, ioe er, is less than ‘05°. It is clear that the
correction depending on d( pv) cannot be neglected. If we
could replace ( by the cooling-effect in “ free ” expansion

(dE=0), as in Joule’s original ‘experiment, this term would
not be required.

6. The Equations of van der Waals and Clausius.

The above method of deducing the value of the absolute
zero from the cooling-effect may appear at first sight to be
wanting in precision ; but it assumes only that the effect is
small, and dumaanne ee continuously with increase of tem-
perature, and the results to which it leads are really quite as
accurate as the available experimental data. By way of
contrast we may take a method which appears at first sight
to be unimpeachable, but which leads to results which are
obviously wrong.

Van der Waals, in his celebrated essay “On the Con-
tinuity of State ” (Phys. Soc. Translation, Cap. XI. p. 440),
was the first to interpret the cooling-ettect in terms of the
capillary pressure represented by the term a/v? in his well
known equation

(p+a/v?)(v—b)=RO. . . . . (23)

Taking this equation, he showed that, if the capillary pressure
varied inversely as the square of the volume, and the co-
volume 6 was constant, the fall of temperature in the Joule-

Correction of the Gas-Thermometer. D9

Thomson experiment must be to a first approximation
proportional 'to the fall of pressure, or the ratio Q inde-
pendent of p. The expression which he gave for the
cooling effect is equivalent to the following :

SQ=2a/RO—6. TG bebtiie 4.G2e,)

As applied to the constant-volume thermometer, the equation
gives very simple results, since p is accurately a linear
function of 0, so that the scale-correction is identically zero.
The absolute zero correction is given by the formula

OQ —Ty=a/Rv=apy/ RA. Seek arnt (29)

Van der Waals himself observed that the values of a and 6
which he adopted for CO, to represent the experiments of
Regnault and Andrews did not satisfy the results of Joule
and Thomson on the cooling-effect. ‘Rose-Innes, however,
has shown (Phil. Mag. March LSSa ep. 227) that a formula
of the type Q=A/T-— “B (which is the same as that given by
van der Waals) ee the cooling-ettect much _ better
than that of Rankine, including the case’ of hydrogen,
and has calculated the appropriate values of the constants.
Adopting his values of the coefficients A and B, and taking
So x 10°, we find for CO,

Gog Oreo On Hw) cc 2RY a te a(26))

Rose-Innes apphed this formula to calculate the absolute
zero from Regnault’s expansion-coefficients, and obtained
results practically identical with Lord Kelvin’s ; but he did
not apply it to calculate the absolute zero from the pressure-
coefficient. If we take, as before, Chappuis’. pressure-
coefficient for CO, at po=100. cms., namely, *003725,
T)=268°45, the correction is &°°4, which gives 0)=276°9,
a result which is obviously much too large.

This discrepancy is partly due to the fact that the type of
formula assumed to represent the variation of Q with tem-
perature 1s wrong, although it represents the observations
pertectly over the experimental range. It shows very clearly
that the method previously given, which does not assume any
particular type of for mula, but deduces the zero correction
directly from the observations, is much to be preferred,
although it may appear less rigorous at first sight. More-
over, it is evident that the values of a and 6 deduced from
the cooling-effect in this manner would not satisfy the
observations of Regnault or Amagat on the isothermal
compressibility, since they would make d(pv)/dp at 0° C.

60 Prof. H. L. Callendar on the Thermodynamical

(which is approximately given by the expression — (a/R6)—)))
positive and equal to about +0°4 c.c., 7. e. the gas would
appear “ pluperfect,”’ like hydrogen, whereas it is very much
the reverse. If on the other hand we take the values of the
constants given by van der Waals, which would be equi-
valent to the following,

a/RO)= 442 c.e:) *b=110\c:.¢., . - . er

the compressibility at 0° C. is well represented, but the value
of the cooling-etfect is much too small. At higher tem-
peratures the formula gives values of the cooling-effect which
are more nearly correct, but the value of d( pv)/dp at 200° C.
is found to be —1°40 c.c., which is nearly twice as large as
the value given by Amagat’s observations. The formula
would also make the scale-correction of the constant-volume
thermometer vanish at all temperatures, whereas the cbser-
vations of Chappuis (see below) prove that it is quite large
in the case of COs.

On these and similar grounds we are justified in concluding
that the formula of van der Waals does not represent the
behaviour of CO, at moderate pressures with sufficient
accuracy to be of practical value. Clausius, however, has
shown (Phil. Mag. June 1880) that the agreement is greatly
improved if we suppose the coefficient a in the capillary
pressure to vary inversely as 6, which leads to a formula of
the same type as that proposed by Rankine, but with the
addition of the covolume 0. For the purposes of gas-
thermometry, or for calculations at moderate pressures, we
may neglect quantities of the second order, and may write
the equation of Clausius in the form

v= RO/p—a/ RE? +6... ee
Love (Phil. Mag. July 1899) has shown that a formula of this

type represents all the observations on the cooling-effect very
well, but he has not applied it to the calculation of the
absolute zero, or the scale-correction of the gas-thermometer.

(. Expression in Terms of the Co-aggregation- Volume ec.

In the application of this or similar equations to represent
the behaviour of imperfect gases at moderate pressures, |
have found it very convenient to employ the single letter c¢
to represent the term a/R@*. The quantity ¢ represents
a volume, expressible in cubic centimetres, which is to a first
approximation a function of the temperature only, and which
may be called the “ co-aggregation-volume,” as it denotes the
diminution of volume caused by the formation of molecular

Correction of the Gas- Thermometer. 61

ageregates. All the thermodynamical properties of the gas
may be simply expressed (as I have shown, Proc. Roy. Soe.
1900, vol. Ixvii. p. 266) in terms of ie co-ageregation-
volume. This method of expression is more convenient for
practical purposes than expression in terms of the capillary
pressure, since the latter is a function of both volume and
temperature. It is convenient to assume that ¢ varies in-

versely as the nth power of 0, so that we may write
G= Cy Gqieyi ° e ° ° . (29)

where ¢ is the value of ¢ at @). The value of the index n is
apparently 2 for COs, but it may have different values for
other types of molecules. The general expression for the
cooling-effect deduced from (4) on 1 this assumption 1s

SES (ea) eae ee er (250)

and the expression for the slope of the isothermals obtained
by plotting the product pv against p is

d(pv)/dp= —(e—b). ii ae eave. OLD)

For an imperfect gas like CO, or nitrogen, ¢ is greater
than 6. The gas becomes “ pluperfect,” like hydrogen, at
the point where c=}. The isothermals on the pv, p diagram
are straight lines, the inclinations of which to the axis of p
diminish as the temperature rises. This is a much better
approximation than might be supposed at first sight, because
experiment shows the isothermals to be nearly straight for a
considerable range of pressure and temperature.

If we calculate the values of the constants cy) and 6 for each

gas from the experiments of Joule and Thomson on the
cooling- effect, employing the equation (28) above with the
value n=2, so that SQ=3c—l, we obtain the results given
in the following table :—

Taser IIl.—Values of Constants from Observations of
J oule and Thomson.

| | |
| ie Be S. | Qo. ; i Pro oe | ij. | C.
employed. A ah | Hay a iit Nee om (278
‘ x 10°, x 10 . ; Per atmo. (10° C.G.8 s.) c.c. C.C. | CoPo ie Ri
| se seek alt | 3-871’! 10:05 | 0-271 | 0147 | 090 |— -002| -00085
FOOs ae | 1887 | 840 | 1368 | O610 | 456 218 00636

| | | |
REI oh 4 | 415 | 1453 |— 029 |— -048 | 201 | 1023 | -000182

62 Prof. H. L. Callendar on the Thermodynamical

The constant C is employed in calculating the scale-
corrections in Table VI. below. The values are given for
po= 16 cms.=1:0133 x 10° c.a.s.

8. Method of Calculating the Correction.

An incomplete table of corrections, for the air-thermometer
only, was calculated by Rowland (Proc. Amer. Acad.
vol. vii. 1880, p. 114) with the object of correcting the
air-thernrometer which he employed in the reduction of
his observations on the mechanical equivalent of heat. The
method of calculation was not given, but he employed only
Joule and Thomson’s later results (1862) as represented by
Rankine’s equation. His work was probably the first
application of the thermodynamical correction to the actual
results of experiment.

A similarly incomplete table of corrections for the air-
thermometer was given in my own paper “ On the Practical
Measurement of Temperature” (Phil. Trans. A. 1887, p. 162)
for reducing the indications of the platinum-thermometer
to the absolute scale. The method of calculation adopted
was as follows.

For purposes of gas-thermometry the characteristic equa-
tion of the gas employed may be written in the following

form :
6=prv/R+49, ee

in which g is a small quantity of the dimensions of tem-
perature, which represents the deviations of the gas from
the ideal state. In using a gas-thermometer we assume an
equation of the type T=pv/R’, in which T is the temperature
on the scale of the gas-thermometer, and R’ is a constant,
differing slightly from R, and depending to some extent on
the method of thermometry employed. The values of R and
R’ are determined in each case from the observations at the
fixed points 0° and 100° C., which give the following
relations :

R! = (pyv1—Po)/100, R=R (1+ (q1- Go)/100), (33)

in which po, to, go are the values of p, v, g at 0° C., and
py M1, g are the values at 100° C. In deducing these
relations small quantities of the second order involving
squares and products of g are neglected.

To find the value of the absolute zero we have the equation

Oy = poo! R + Go=T0 + Go— (G1—- 90) 0/100. . (34)

Correction of the Gas- Thermometer. 63.

To find the value of the correction dé to be added to the
centigrade temperature ¢ on the scale of the gas-thermometer
to reduce to temperature centigrade on the thermodynamical
scale, since the temperature centigrade on the scale of the

oO
gas-thermometer is given by the formula

— i — ( pu— pov) 100/( pir —Po%). PaO)

we have evidently the simple expression

dt =(8—6@o) — (TT) =(¢—Go) — (Gi — Yo) #/100. (36)
It may be noticed with regard to the separate terms in this
expression that go is the zero-correction, and the second part
(¢,—)t/100 is the correction for the fundamental interval.
The correction at any point of the scale is not simply ¢g—q,
as might appear at first sight, because the values of the
constants R and R’ are dit-rent, and the correction must
vanish at 100° C. as well as at 0° C.

In order to apply formula (36) to the calculation of a table
of corrections, we may select any empirical formula which
represents satisfactorily the properties of the gas under
consideration. The equation is then thrown into the form
(32), and the expression for qg is simplified as far as possible
by rejecting all quantities of the second order, and is ex-
pressed in terms of p, and T or 6. Asa simple example we
may take the equation devised by Clausius to represent the
deviations of CO, from the formula of van der Waals,

(p+a/O(v+@)2)\(v-B)=RO. . . (37)

Neglecting small quantities of the second order, this may be
put in the form

O=pr/R+(a/RO2—b)p/R, . . . (38)
= (a/RO?—b)p/R=(c—b)p/R. . « (39)

Writing p) tor p we have the value of g for the constant-
pressure thermometer. For the constant-volume thermometer
we must substitute y0/@) for ». The values of the constants
may be immediately calculated (as above, Table II.) from
the observations of Joule and Thomson on the cooling-effect,

without reference to any other experimental data. A table
of corrections calculated in this manner may not be the most
accurate possible at the present time, w hen so many more
observations are available, but it is of special interest to
compare the results of an investigation made so long ago
with those of the latest thermometric researches. For this
reason I have calculated the following table of corrections on

whence

64 Prot. H. L. Callendar on the Thermodynamical

the basis of equation (38), assuming only the data already
given for the cooling-effect accor ding to Joule and Thomson.
In the simple case here conedierad it is unnecessary to
caleulate the values of g for each temperature separately,
and then apply formula (36) to find the correction dt. The
expression for dt may with advantage be greatly simplified,
before beginning the calculation, by putting in the numerical
values of Oy and. é,, namely, 273 and 373, and substituting ¢
for 06--0,. We thus obtain the following simple fount
For fits Constant- Volume (Vneminenneiee: —

Absolute Zero-Correction, @)—T)y=646C, . (40)
Scale-Correction, dt = Ct(t—100)/@, . (41)

in which C is used as an abbreviation for the constant factor
Copo/373R, which has the values given in Table II. above
for an initial pressure py=760 mm.

For the Constant-Pressure Thermometer :—

Absolute Zero-Correction, 6)—T)=846C—bdp,/R, . (42)
Seale-Correction, dt=Ct(¢—100)(1°732 + 273/0)/0. (43)

The covolume 6 occurs only in the zero-correction of the
constant-pressure thermometer. The values of the constant
C are the same as for the constant-volume thermometer.
The corrections for the constant-pressure thermometer are
deduced from those for the constant-volume thermometer by
multiplying by the factor (1°7382+273/@), which has values
between 2 and 3 at ordinary temperatures. When the
corrections for any one gas have been calculated, those for
any other follow by simple proportion. The corrections
given in the table are all calculated for an initial pressure
pPo=160 mm. The corrections for any other initial pressure
are simply proportional to the pressure.

If we apply the above formulze to calculate the value of
the absolute zero from Regnault’s pressure-coefficients, we
find considerable discrepancies in the results, as illustrated
by the following table.

TABLE I] ].—Absolute Zero from Reenault’s
Pressure-Coeficients.

A ASPEN OVC. (0055 4k’ e's xn an veel doutnolne sae Air. Hydrogen. CQ;
Pressure-Coefficient (p=76 cms.), @ ... *0036650 -V036673 ~“OU86880
Fundamental Zero of Gas, T)>=1/a ... 272°°85 272°-64 2713
Correction to Absolute Zero, @,—T,... + °56° + ‘09° 44°92

Absolute Zero deduced, 0) ............00+ 273°°41 2°73 219° 4

Correction of the Gas- Thermometer. 65

It appears that these discrepancies are due in the main to
errors of Regnault’s pressure-coefficients, which subsequent
observations have shown to be much less accurate than his
expansion-coefficients, though Regnault himself considered
them more accurate. If we employ Chappuis’ values of
the pressure-coefficients, which are certainly nearer the truth
than Reenault’s, we obtain the following results.

Taste [V.—Absolute Zero from Chappuis’

Pressure-Coefficients.

Reem LO MEC NG. v.gacaise leer snsis ese sone Nitrogen. Hydrogen. CO;

Pressure-Coefticient (p,=100 cms.), @. 0036747 -0036625 °0037251
Fundamental Zero of Gas, Ty=I1/a ... 272°11 273°°03 268°°45
Correction to Absolute Zero, 9,—T, ... +0°:98 +0°11 + 5°55
Absolute Zero deduced, 0, .......se:.e++. 273°-09 «- 273°14 —274°-00

These evidently agree very closely with the results deduced
for the same gases from Regnault’s expansion-coefficients.
The cooling-effect for nitrogen was found by Joule and
Thomson to be larger than for air in the proportion of 103
to 88. I have allowed for this in Table IV. and also in
Table VI. as it gives a better agreement with experiment
on the assumption n=2. But Joule and Thomson did not
regard their experiments on nitrugen with much confidence,
and the true value of n is probably more nearly 1°5 for
diatomic gases (see below, section 20). The value found for
COQ,, namely 274:0, differs from that calculated by the direct
method of formula (22), which is certainly correct. The
explanation of this apparent discrepancy is given below in
section 15.

The values of the scale-correction for the same gases,
calculated by formule (41) and (43) with the values of the
constants given in Table II., deduced from the observations
on the cooling-effect alone on the assumption n=2, are given
in the fellowing table. The table covers a wide range of
temperature, and is intended to illustrate the general eftect
of the correction, but it must be remembered that the
observations on which it rests were confined to the range

0° to 100° C.

Phil. Mag. 8. 6, Vol. 5. No, 25, Jan. 1903. iy

66 Prof. H. L. Callendar on the Thermodynamical

TasBLE V.—Scale-Correction for Air, Hz, and CQg.

Constant-Volume, p,=76 cms. | Constant-Pressure, 76 cms.

| Temp. DEI
Cent. | | :
| Air. heeace: COR iN. Aa cues COs
| etl ane —--- hs ae
| 8900} - ah. 09K Mes as: +586
— 150 |4 258 | +040 | ... |-7-02 +158
— 100 +099 | +015 | -... |+ 328 | +-050
=" .50 |+ -029 | +:00m. | 42 22 5 086) 4-015 eae
— 90 \|+ 0080) +0012 | + -062 j|+ 022 | +0085 |= 2
: — 10 |+ -0036) +-0006 | + -027 |+ 010 | +-0017 |+ -076
| | | |
| | ] |
+ 10|— 0027; —-0004 | = -0207/|— -0073; —0011 |= )-0a6)
+ 20 |— -0046| —-0007 | — -0356|/— -0122} —-0019 |— -095]
+ 30 — 0059 —-0009 | — -0452)— 0155) —-0024 — +119,
+ 40 |— -0065| —-0010 | — -0500||— -0169) —-0096 |— -130]
+ 50 j—.-0066/ —-0010 | — -0504|/— -0170; —-0026 |— -130|
+ 60{|— -0061| —-0009 | — -0470||— -0155| —-0025 |= -190
+ 70 |— 0052) —-0008 | — -0398||— -0132! --0020 |— -101|
+ 80 — 0039) —-0006 — 0295 — 0098 —-0015 |— 074,
| + 90 )— -0021/ —-0003 | — -0162)|— -0052, —-0008 |— -040
}
+ 150 |+ 015 | +002 | + “115 |+ 036 | +006 |— a
+ 200 |4 036 +006 + 275 |+ 083 +4013 + 635
+ 300 14 -089 | +014 | + 6838 4-196 | 4-030) | Saar |
+ 450 |+ -186 | +-029 | 4+:142 ‘+ -392 | 4-061 |4 300%)
+1000 j+ 600 | +098 | + 460 |41-16 | +-I8] 42 )6ae
| +2000 | +1-42 +921 | +109 14962 | 4-407) eeaoe

9. Comparison with Chappuis’ Experiments.

It is interesting to compare the results calculated in this
table with the experiments of Chappuis (Bureau Internat.
Reports, 1888) on the differences between the scales of the
nitrogen, hydrogen, and carbonic acid gas-thermometers.
The most accurate and important of his experiments were
made with the constant-volume thermometer at an initial
pressure of 100 cms. The gas-thermometers were not
directly compared, but the same instrument was employed
successively with the different gases, and the readings at
intervals of 5° up to 50° C., and also at 61° and 78°, were
compared with those of four standard mercury thermometers.

The results of the comparisons of the mercury thermometer
(t) with the nitrogen and hydrogen thermometers (¢, and ¢;)
were represented by the following empirical formulee :—

by —tm = t(100 —t)(—55°541 + 0-48240t—0:0024807#) x 10-8,
ty — ty =t(100—t) (—61°859 + 0-47351t—0-0011577#2) x 10-6

Correction of the Gas- Thermometer. — 67
In order to make a comparison with Joule and Thomson’
it is necessary to take the difference between the nitrogen
and hydrogen scales by subtracting the second formula from
the first, which gives the expression
ta—t,=t(100—t) (+6°318 + 0°00889¢—0-0013230¢07) x 10-% . (44)

This is the formula which is generally quoted for the differ-
ence between the nitrogen and hydrogen scales ; but it must
be remembered that it refers to an initial pressure of 100 cms.
at constant volume, and thatitis obtained as the difference
between two comparisons with the mercury thermometer,
which may have introduced small constant errors, especially at
the higher points of the scale. The ditferences calculated by
formula (44) are compared with those taken from Table V.,
corrected from air to nitrogen by the factor 103/88, and
increased in the proportion 100/76 to reduce to 100 ems.
initial pressure, under the heading n=2, in the following
table, together with later reductions.

TapLE V1.—Difference between Scales of Constant-Volume
Nitrogen and Hydrogen Thermometers t,—t, at 100 cms.
initial pressure.

{
i
; |

| Joule-Thomson. Chappe): | Lehfeldt, | Rose-Innes
a. : ape : Phil. Mag. Phil, Mag.
_ Cent. n=ld.| nao, | Formula | Corrected | jg9g. 1901 |
| i) ile. ahh C4a)> TON SBS: | |
=20 | —-0065 |—-0107 | —-0135 | —0173 | |
—10 | —-0030 | —-0048 | —-0U67 | —-0074 |

+10 | +°0022 +0036 + 0057 +0055 +'006 | +0010
+20 | +0040 +0060} +-0095 +0087 | +011 | +0018
+380 | +°0049 | +0077 +0113 +0105 ,; +014 |— +0023
+40 | +:0055 +:0087 +0110 | +°0110 +4017 +:0025
+50 | +0055 +-0087 +0086 +0103, +019 +0025
+60 | +:0050 | +-0078 +0049 +0090 | +019 + 0024

+70 +°0045 | +-0064 +-001lu | +0069 +°018 | +:0020
| +80 | +0034 | +4-0048, —-0024 | +0045 | 4°015 | +4-0015
+90 | +:0018 +-0028 | —-0032 +0022 +010 | +0008

It will be observed that formula (44) gives negative values
ot the difference t,—t, at 80° and 90° C.; but these are of
the same order as the probable error of observation, which
was *008° or ‘Ol mm. Hg. The only observation actually
taken at this part of the scale, namely, at 78° C. in the vapour

* Chappuis’ latest observations (‘Bureau Internat. Reports,’ 1902)
make the difference tn—th=+:005 at 20°, and +-008 at 40° C., which
agree better with Joule and Thomson.

F 2

68 Prof. H. L. Callendar on the Thermodynamucal

of alcohol, shows a small positive difference of ‘001°. The
negative differences are undoubtedly due in part to the type
of empirical formula chosen. Chappuis himself considered
them to be impossible, because they imply that the mean
coefficient of expansion of nitrogen, after diminishing from
0° to 70° C., begins to increase again ait this point, which
is highly i impr obable. For this reason, in the same paper in
which formula (44) is given, he Eflenlated another formula,
with two terms instead of three, for deducing the mean
coefficient of expansion of nitrogen by reference to hydrogen.
He does not give the values of the scale-difference corre-
sponding to this formula, but I have calculated the values
given in the column headed “Corrected 1888” from the
values which he tabulates of the mean coefficient of expansion
of nitrogen. It is at once evident that the formula of two
terms gives a more probable type of divergence between the
scales than the three-term formula (44) which is always
quoted. It agrees closely with that of Joule and Thomson at
the higher points, but gives rather larger differences at the
lower points, increasing to nearly double at —20° C.

10. Graphic Method of Comparison.

Since the thousandths of a degree in this table are uncertain
to the extent of at least -003°, it is hardly necessary to say
thatthe most that can be expected is a general agreement in
the order of magnitude of the correction. The value of the
experimental evidence is most readily appreciated by the
graphic method. The actual observations are plotted in fig. 1
in which the zero line represents the hydrogen scale, and the
ordinates of the curves the scale-differences. The continuous
curves represent the differences calculated from the obser-
vations of Joule and Thomson, the broken curves the differ-
ences calculated from the formule of Chappuis. The black
dots about the zero line represent the deviations of the ob-
servations with the hydrogen thermometer from the smooth
formula chosen to represent them, and indicate the order of
accuracy of the comparison of the hydrogen and mercury
thermometers. The crosses (x) similarly indicate the diver-
gences of the observations with the nitrogen thermometer
Boa the smooth curve. The crosses Eee. in circles
represent the observations in the second series of comparisons
of the nitrogen thermometer , extending from — 24° to +25°C,
In reducing these Ae See ie it was found that the curve
repr esenting them did not pass through the zero point, as of
course it should. Chappuis assumed that this discrepancy

Correction of the Gas- Thermometer. 69

was due to an error in the zero pressure, which had to be
determined separately under conditions different from those

Fig. 1.—Comparison of Chappuis’ Observations with Results calculated
from Cooling-Effect.

+080

+060

+040

+°020

= DION: © ° °

20 O ZOU AO MEO: SCT 100;
of the thermometric comparisons. A reduction of ‘(025 mm. in
the zero pressure * was required to make the curve pass through
the origin. This correction had the effect of raising all the

e O e e . a

observations by nearly -007°, which is a quantity of the same
order as the difference between the nitrogen and hydrogen
scales. Lf the circled observations in the figure were depressed
by °007°, it is evident that they would be brought into rather
better agreement with the Joule-Thomson curve between O~
and 25° (., but that the discrepancy below 0° ©. would be
increased. The nitrogen observations are seen to be rather
more discordant than the hydrogen, but they were taken first
in point of time, and the error of the temporary rise of zero

* The minuteness of this correction (1 in 40,000 on the zero pressure )
indicates the extreme difficulty of the work, which could not have been
carried out successfully without the highest experimental skill and the
most refined apparatus.

70 Prof. H: L. Callendar on the Thermodynamical

produced in a mercury thermometer by exposure to a low
temperature (corresponding to the temporary depression pro-
duced by exposure to a high temperature), was discovered
for the first time in the course of this series of observations.
Taking these facts into consideration, we may conclude that
the fraeeence of the scales between 0° and 50° is probably
Jess than that given by Chappuis’ formula, and that the
Joule-Thomson curve is more nearly correct, though, as we
shall see, there is other evidence tending to lew that even
the fers is too high.

11. Extrapolation to Higher and Lower Temperatures.

Since the observations of Joule and Thomson were confined
to the range 0° to 100° C., the estimates of the corrections
given in Table V. ( (p. 66) are lable to much greater uncertainty
beyond this range, since they depend on the validity of the
type of equation (39) assumed. According to the table, the
difference between the scales of the constant-volume and the
constant-pressure hydrogen thermometers would be about
half a degree at the ‘temperature of liquid air. This has been
recently contirmed by Travers (B. A. Rep. 1901), and may be
taken as an indication that the diver gence indicated in the
table is at least of the right order of magnitude, even in the
case of hydrogen. Similarly the corrected value of the
boiling-point of sulphur given by Chappuis (Phil. Mag.
1902), namely 444°°7, cbtained with a constant-volume
nitrogen thermometer at 56 cms. initial pressure, when com-
pared with the value 444°°5 obtained with a constant-pressure
air thermometer (Phil. Trans. 1891) agrees in sign and
order of magnitude with the difference of the scales (0°: 2) at
this point indicated in the table. Chappuis has recently
proposed an empirical method of estimating the correction,
which leads toa much smaller result. His or iginal formula
(44) is evidently of a type unsuitable for extrapolation ; but
if we employ it to calculate the true coefficient of expansion
of nitrogen at t, assuming hydrogen to be an ideal gas, we
find that the coefficient diminishes from ‘00367698 at 0° C.
to -003867378 at 80° C., and then increases to *00867393
at 100° C. Chappuis supposes that this increase is illusory,
and that the coefficient really diminishes to a minimum value,
namely °00367378, and then remains constant at all higher
temperatures. This assumption would make the scale-differ-
ence linear above 100° C., increasing by -017° for each 100°,
and amounting to 076° at the boiling-point of sulphur
for a constant-volume thermometer at 100 cms. initial

Correction of the Gas- Thermometer. re:

pressure, or ‘043° for »=56 cms. He finds, as the result
of some experiments between 0° and 100°, that the scale-
difference of the constant-pressure thermometer is about
twice that of the constant-volume instrument. This agrees
very fairly with the result deduced from the Joule-Thomson
equation and exhibited in Table V. Assuming the ratio 2,
the correction for the constant-pressure thermometer at
445° would be about +°115° at 76 cms. initial pressure,
which would give a difference of ‘072° between our instru-
ments at the boiling-point of sulphur. Chree has since
detected a small error in Chappuis’ calculation which would
increase this estimate in the proportion of +023 to ‘O17.
a direct comparison between the constant-volume and con-
stant-pressure scales at this temperature would certainly be
desirable and feasible; but in the meantime the estimate
derived from the Joule-Thomson equation appears to be more
probable than that of Chappuis, and more in accordance with
the known behaviour of gases deduced by other methods of
investigation.

12. Thermodynamical Correction of CO, Thermometer.

The case of CO, is of particular interest because the pro-
perties of this gas have been so widely studied, and because the
deviations from the thermodynamical scale ¢ and the values of the
Joule-Thomson effect are so much larger and more easily
measured. A study of the properties of this gas might be
expected to throw light on the effects to be expected with
other gases more perfect and better suited to thermometry ;
but it must not be forgotten that the type of the molecule is
different, sail does deb thie econ e might be expected to
behave in a different manner to the diatomic or monatomic
gases. The gas actually employed by Joule and Thomson was
not quite pure, but they corrected their results empirically to
the case of pure gas, and their value of the cooling-effect at
17°C. has been independently confirmed by Natanson (Wied.
Ann. xxxi. p- 502, 1887) employing gas from cylinders of
liquid CO,. The values given by Table V. for the difference
from the hy drogen scale in the case of the constant-volume
thermometer at “Po = 160 ems. are compared with the obser-
vations of Chappuis at —10°, + 10°, 20°, 30°, 40°, and 60°C.,
which are represented by the crosses (+) in fig. 1. The full
curve, as before, indicates the differences calculated by the
Joule-Thomson equation, the broken curve indicates the
formula of Chappuis. Three of Chappuis’ observations at
30°, 40°, and 60° were taken with a thermometer filled with

72 ~=- Prof. H. L. Callendar on the Thermodynamical

gas at a slightly lower initial pressure, po>=87 cms. The
observed values for the difference in these cases have been
increased in the ratio 100/87, as required by theory, and the
crosses are distinguished by inclosing them in circles. It
will be observed that the corrected observations agree in the
most remarkable manner with the Joule-[Thomson curve

although their agreement with Chappuis’ formula is slightly
impaired. This would appear to be a striking confirmation
of the validity of the proposed formula in the case of CQ,.
But when we compare the actual values of ¢ and 0 calculated
as above from the observations on the cooling-effect alone,
with those calculated directly from the slope of the isothermals,

we find certain discrepancies which, although they are often
within the limits of experimental error, require examination
as possible indications of some defect in the theory. For
instance, in the case of CO, which agrees so well with
Chappuis’ thermometric comparisons, the value of ¢ according
to Table II. would become equal to that of bat about 120° C.,

and the gas above this temperature should behave like
hydrogen, with an upward slope of the isothermal. The
observations of Amagat show, on the other hand, that CO,
is still notably imperfect at a temperature of 261° C. This
might conceivably be due in part to some effect of surface-
condensation, which would be relatively important in the fine
tubes employed by Amagat; but it is mainly attributable to
the large value of b deduced from the observations on the
cooling-effect. It is evident that the value of 6 cannot be
deduced so accurately as that of ¢ from these observations,
since the expression for SQ is 8-—6. Moreover, no account
has been taken of the variation of S with temperature, which
according to Regnault is considerable in the case of COs.
Both these considerations would be of relatively small im-
portance as affecting the thermometric comparisons between
0° and 100°, since 6 does not enter into the expression for dé,
and we employ the mean value of S at 50°; but they would
materially aifect the extrapolation of the value of c—b. It
would be quite possible to readjust the values of ¢ and 6 in
such a manner as to agree better with Amagat at higher
temperatures, while not ” seriously impairing the aor eement
with Chappuis at 50°. The values of ¢ and 0 for hydrogen
appear to be more nearly of the right order of magnitude,
giving e—b=8-2 c.c. as against Amagat’s value 8:8 cc.
On the other hand, the value of 6 for air is practically zero

according to the observations of Joule and Thomson, 2. e.
air would always remain imperfect. Observation shows,

Correction of the Gas- Thermometer. 73

however, that it becomes “ pluperfect”’ at a temperature
somewhere below 100° C. Here again the value of 0 is
undoubtedly in error. It may also be observed that the
error of the value of the absolute zero deduced in Table IV.
from Chappuis’ pressure-coefficient for CQ,, namely 274°0, is
too large to be attributed to errors of observation in the
coefticient or in the measurement of the cooling-effect. These
discrepancies suggest either that the type of formula is wrong
(t.e., that ¢ does not vary inversely as the square of the
absolute temperature), or else that the variations of the
specific heat are too large to be neglected.

13. Other Types of Formule™*.

Instead of attempting to readjust the values of the constants
in the original formula so as to obtain the best average
agreement with experimental data, we might proceed, as
suggested by Joule and Thomson in 1854 (Phil. Trans. p. 360),
by the more usual method of introducing sufficient arbitrary
constants into the formula to enable it to reconcile all the
apparently discordant data. This method has recently been
applied by Rose-Innes (Phil. Mag. July 1901), who adopts a
formula with three constants, of the same type as that
employed by Joule and Thomson, No. (11) above, in the
calculation of their original table of corrections. But in
place of Regnault’s observations Rose-Innes adopts the later
observations of Joule and Thomson on the cooling-effect, in
conjunction with Amagat’s values of d(pv)/dp. The values of
t,—t, calculated by Ruse-Innes are given in Table VI. (p. 67).
He does not apply his formula to the case of CO,. The
difference between the values of the absolute zero deduced
by Rose-Innes from Chappuis’ pressure-coefficients for H,
and N, is rather larger than that given in Table IV., and
would make the value lie somewhere between 273:15 and
273°36, which appears hardly probable.

To facilitate the comparison of the formule and the caleu-
lation of the corrections, we may employ the notation already
explained in Section 8 above. The formula of Rose-Innes is
equivalent to the assumption

O=pr/R+ ('+c'—b)p/R, . « . « (45)

in which ¢ and é vary inversely as the first and second
powers of the temperature respectively. The corresponding
formule for the corrections are:—

* This section was added subsequently to the reading of the paper.

74 Prof. H. L. Callendar on the Thermodynamical

Constant-yolume, zero correction,
0, —T,=646 C’ +elpo/R, . .. « se
Seale correction,
dt= C(t — 1000) ae) ee
Constant-pressure, zero correction,
0, —T,)= 846 C"+ 646 C'—bp/R, . . . (48)
Scale correction,
di =(O"(1°732 + 273/60) + C’)t(¢—100)/0. . (49)
The formule are the same as before as regards ¢, oe
additional term& are introduced to represent the effect of ¢.

The numerical values of the constants are given in the following
table as deduced from those calculated by Rose-Innes.

TasLe VII.—Values of Constants deduced from Formule
of Rose-Innes.

| |
Gas b. Co. au Co ao |
employed. ¢.c. CC. Cle. les of 373... o Pa
PI Peete 1-62 1:89 0182 | 00179 | 00017 | -
| Nitrogen... . 208 |: 209 | 0378 | 00182 | 005 |
Hydrogen ...| 1073 | 119 1-45 | 000078 | 000095

The values of the scale-correction calculated by these
formule for the constant-volume air-thermometer are about
five times smaller than those given in Table V., but the values
for the constant-pressure thermometer are nearly of the
same magnitude as those in Table V. In general we may

observe that the corrections for the constant-pressure thermo-
meter are nearly independent of the type of formula assumed
within reasonable limits, and are therefore less uncertain than
those of the constant-volume thermometer. The values of ©
and OC” civen above correspond, as before, to an initial pressure
Dj) = 16 cms.

bel: Variation of Specijic Heats.
The pm a followed by Jouie and Thomson, and by the

majority of subsequent writers, has been to assume a formula
for the variation of the cooling-effect (), which is then inte-
grated to find the constants in the characteristic equation,
neglecting the variations of the specific heat 8. This is
perfectly justifiable in the case of the more permanent gases,

Correction of the Gas-T hermometer. @

for which experiment and theory both indicate that the
variations of the specific heat should be small. But in the
ease of vapours like steam or CO, these variations cannot be
neglected ; ; and it is better to employ the reverse method as
in Section 7 above, assuming a convenient type of cha-
racteristic equation and deducing the corresponding expression
for the cooling-etiect for comparison with the results of
observation. In this case it is easy to take account of the
variations of the specific heat by simply inserting the appro-
priate value of the specific heat in equation (30).

We observe by reference to the differential equations (4)
or (5) that the appropriate value of S is that. corresponding
to the final pressure p” in each experiment, and to the mean
temperature (6/+6”)/2. The variation of the specific heat
with temperature can be determined only by experiment.
The variation with pressure must be consistent with the
characteristic equation chosen, and can be calculated in the
following manner.

Referring to equation (3) for the variation of the total heat,
F=E£ + pr, we have the following values of the partial differ-
ential coefficients :—

(dF/d@),=S, (dF /dp)g=v—O(dv/dé),=b—(n+1je, . (50)
which give for the variation of S with p at constant 6,
(dS/dp)g=d.F /dédp= —O6(d.v/d@’),=n(n + l)e/@.. (51)

Integrating this at constant temperature from 0 to p, we
obtain

B= Sot ne Wyepieay +> we ow, ~ 12)

where 8, is the limiting value of 8 at zero pressure and
temperature @.

This equation enables us to find the complete variation of 8,
if we observe the values of S experimentally at any standard
pressure such as 1 atmo, over the required range of
temperature.

Proceeding similarly for the specific heat s at constant
volume, we “obtain by considering the variation of the
Intrinsic energy H,

(dE/d0),= s, (dH/dv) f= O(dp/d@),—p, (ds/dv)g=0 (dy dO”).

whence
S=s-+n(n—1—ne/V)cp/0,. . . s (54)

where sy is the limiting value of s at zero pressure, and
V=R6/p. This formula is of comparatively little use,

(53)

76 Prof. H. L. Callendar on the Thermodynamical

because the direct measurement of s by experiment is gene-
rally impracticable; but it serves to trace the probable
variations of the ratio of the specific heats S/s=g.

In the special case in which n=s)/R the formule may be
somewhat simplified, since R=S,)—so, and may be written as
follows :—

S=8S)(1+7c/V), . .
$ =So(l4+ne/V)1—c/V), . . . SD
whence

g =S/s=o/—dV).. . .- Sag

This appears to be the case for steam (Proc. R.S. vol. Ixvi.
p. 266, 1900), but is not true generally.

In the case of a diatomic gas, if we assume the limiting
ratio of the specific heats to be gy=1'400, as indicated by
theory, we have Sy=3'5R, s9=2°5R, if the limiting values of
the specific heats are constant. The ratio of the specific
heats, if 2 =2°5, would be g=1:400(1+¢/V). If n=2, as in.
Rankine’s equation, we should have g=1:400(1+°92c¢/V)
approximately. Inserting cy=0°90 c¢.c., V=784 c.c. for air
at O° C. and 75 ems. pressure, we should find g=1:4015,
which illustrates the smallness of the variation with pressure
for the permanent gases. Taking the density of air as
1:2930 gm. per litre at 0° C. and 760 mm. in lat. 45°, and
assuming the value of c—b at 0° to be 0°50 c.c. from
Amagat’s observations, we should find R=2°8725 x 10° c.a.s.,
which would give S=3:5R=1:0055 joules per gramme-
degree; or 0°2405 calories at 20° C., if the calorie at 20° ©. is
taken as 4180 joules. This is about 1 per cent. larger than
the value found by Regnault, namely S='2375. The obser-
vations of Joly at constant volume give s=*1721 cals. at
60° C. and v=49 ¢.c., when reduced to the same unit. The
theoretical value at this pressure, assuming c=0°61 c. c. at
60° C., would be 0:1736 calories, which is also nearly
1 per cent. larger than that observed. 1t should be remarked,
however, that even apart from the difficulty of the expe-
riments, there is considerable uncertainty in the units of heat
employed. Joly used Regnault’s value for the latent heat of
steam at 100°, namely 536°7; but his own experiments with
the steam calorimeter give 540°2 in terms of the calorie at 20°.
The difference is nearly sufficient to account for the dis-
crepancy in the observed and calculated values. Considering
the difficulty of experiments on the specific heats of gases, we
are probably justified in the assumption that the limiting
values of the specific heats are constant for the more permanent

Correction of the Gas- Thermometer. (7

diatomic gases, and that the variations with pressure may be
estimated by the formule already given.

15. Constants for CO, corrected for Variation of 8.

In order to correct the values of ey and 6 for CO, calculated
in Table Ii. from the observed values of Q on the assumption
that S was constant and equal to 8°4 x 10° c.G.s., we may take
Regnault’s values of S at 0° and 100° at a pressure of | atmo,
since the final pressure in Joule and Thomson’s experiments
was always approximately atmospheric. The values of §
required may be taken as

i 7°85 x OE C.G.8., and Sp = OS x iGy C.G:S.

but the absolute values, as well as the rate of variation, are
necessarily a little uncertain on account of the defects of
Regnault’s thermometry, and of the error of his formula for
the variation of the specific heat of water.

Adopting the values of Qo and Qj given in Table IT., and
assuming SQ=3c¢—b, we obtain the following values of the
constants,

Gj=9710 Cr C:, b=0°58 c.c.

This would reduce all the values of the corrections for CO,
given in Table V. nearly in the proportion of 5 to 6, since
they depend only on «. The agreement with Chappuis’
observations * plotted in fig. 1 would be slightly impaired,
but the Joule-[homson curve would coincide more nearly
with Chappuis’ empirical formula. The value of the absolute
zero correction for the constant-pressure thermometer is
scarcely altered; so that the value deduced from Chappuis’
expansion coefticient is still correct. But on the other hand
the zero correction for the constant-volume thermometer
(Table IV.) by formula (40) is reduced in the proportion
376/456 from 5°55 to 4°°60, which gives §j=273°05, thus
agreeing with the direct method of calculation given in
Section 5, formula (22).

If we compare the values of the compressibility deduced
from the corrected values of the constants, with the values
observed by Amagat, we find again the agreement much im-
proved, which confirms the importance of the correction for
the variation of the specific heat. It should be remarked,
however, that the values of ¢—b deduced from Amagat’s
observations are a little uncertain, as the observations do

* More recent observations by Chappuis (‘ Int. Bureau Reports,’ 1902)
make the scale-correction for CO, at pyp=100 ems., +:039° both at 20° and
40° C, instead of ‘048° and 059°,

78 Prof. H. L. Callendar on the Thermodynamical

not extend below a pressure of 50 atmos at 100° C. The
following table exhibits the comparison.

Taste VIII.—Comparison with Amagat.

29 39

Temperature centigrade ......... 0°, 100°. 200°.
Values of c—d calculated ......... 3°18 1-44 0:67
observed)... -..sus. 3°30 1:5 O72

There is a small systematic difference which might possibly
be explained by surface condensation, but is har dly beyond
the limits of uncertainty of the data.

It is possible by means of formula (54) to make a rough esti-
mate of the variation of the specific heat of CO, at constant
volume for comparison with the experiments of Joly. Neglect-
ing the small term ne/V, and putting n=2, the formula may
nee written approximately S=sy)+2Re/V, where V=v+e Sep.
Joly’s observations give for v=87 c.c., s='1684; and for
v=27 c.c., s='1734. These values are oh calories, ‘and cor-
respond to a mean temperature of 55° C. The mean —
of ¢c may be taken as 2°61 c.c., so that 2Re=9°3x 10° ces
The values of V are 89 and 29 c.c. respectively, so that he

ecaleulated difference between the values of s comes out
0-228 x 108 c.a.s., or 0°0U54 calorie. The observed difference
is seen to be 0°0050 calorie, which agrees quite as well as
could be expected with the calculated value. It should be
observed, however, that if we extrapolate to zero pressure, we
find the hmiting ‘value of the specific heat s from Joly’s
observations about 0°1655 calorie per gramme-degree. The
Se sas value for S from Regnault’s observations at

5a° C. is 0°2014. The difference of these 7 is only 0:0359 cal.,
or 1°51 x 10° c.g.s., whereas the value of R is 1-887 x 10® c.«. s.
The discrepancy is ‘nearly 5 per cent. of the value of S instead
of only 1 per cent. as in the case of air.

16. Application of the Method to Steam.

The large range of variation of the specific heat of CO,
with temperature shows that the molecule must undergo
some fundamental change of structure within the limits ‘at
temperature considered. It is possible that this may be
associated with the variation of the specific heat of carbon
itself. There is no evidence of a similar variation in the
case ot the diatomic gases. in the case of steam, which is also
triatomic, large nese of the specific heat, fy om S=:387
at 100° C. to S="665 at 160° C., have been found experi-
mentally by Grindley, eropleying the Joule-Thomson method

Correction of the Gas-Thermometer. Oy

(Phil. Trans. A, 1900), and assuming Regnault’s formula for
ane total heat of saturated steam. The following values have
also been deduced by other writers on theoretical grounds :
Zeuner, S='568; Gray, 0°385; Tumlirz, 0°536 to 0°475;
Perry, 0°306 to 0°463. I find, however, by direct expe-
riment, employing the continuous electrical method with a
vacuum-jJacket calorimeter, the value S=0°497 at 1 atmo
and 108° C., which agrees fairly with Regnault’s value 0°475
aed SC. allowing fopiihe wemnionndue fo the coaggregation
by formula (52). I have endeavoured to show (Proc. R. 8.
Ixvil. p, 266, 1900) that all the properties of steam may be
consistently calculated on the assumption that the limiting
value of the specific heat is constant, employing the same
type of equation as for CO,, but leaving the vaiue of n to be
determined from observations of the cooling-effect at various
temperatures. If we adopt this type of formula, it appears
from the observations of Grindley (Phil. Trans. 1900) that
the value of n for steam should be about 3°8 instead of 2.
My own observations on the cooling-effect and the specific
heat of steam would give the values n=3°3, and c=26°3 c.c.
at 100° C. In calculating the properties of steam by this
formula in the paper above referred to, I adopted the mean
value 3°5 for the index, partly to facilitate calculation and
partly in consequence of an hypothesis (doubtfully attributed
to Maxwell) that the number of degrees of freedom of a
molecule containing m atoms is 2m+1. This hypothesis
would make the ratio of the specific heats S/s at constant
pressure and volume, 5/3 for a monatomic gas, 7/5 for a
diatomic gas, 9/7ifor a triatomic gas, and so on; values which
agree very fairly with the ratios of the specific ‘heats actually
observed ‘in many cases. Later and more accurate expe-
riments on the specific heat of steam have shown that the
ratio s/R should be more nearly 3°3, and have so far confirmed
the value of the index given by my experiments on the
cooling-effect.

Adopting the experimental value S=0°497 at 1 atmo and
108° C. we find by applying formula (52) the limiting value
So=0°478 at zero pressure. If we employ this value in place
of the value 4:5R adopted on Maxwell’s hypothesis in the
paper above referred to, we find that the agreement with
experiment in the values of the total heat and “the saturation
pressure is somewhat improved, but the general nature of the
conclusions remains unaltered. Since the value of the inde 2X
n cannot be determined very accurately from the cooling-
effect, it is better in this case to take it equal to s/R for the
sake of simplifying: the equation of the isentropies, which

80 Prof. H. L. Callendar on the Thermodynamical

then takes the form ¢c/V=constant, or p/6"t!=constant, or
p'(vw—b)"*! =constant.

In the case of steam the constancy of the specific heat,
and the accuracy of the value found by experiment, may be
further verified by calculating the values of the total heat and
saturation pressure as follows :—

Adopting the assumption So = constant, it is possible to
express the thermodynamical properties of any imperfect gas
or vapour in terms of ¢ by means of very simple formule :
thus we find

Entropy, $=) log,@—R log. p—nep/9+ A, . (58)
Energy, H=s0—2nep +.B, 1.

in which A and B are indeterminate constants of integration. |
The values of the other thermodynamic fenctions follow
immediately from those of EK and g. Thus we find for the
total heat

FP=H+pv=8,0—(n+lep+bp+B;. . ; (60)

and for the thermodynamic potentials at constant pressure and

volume,

G=F—§¢=8,6(1—log, 0) —R6 log, p—(c—b)p—AO+B, (61)

J=E—6b=s9—S6 loge @—RO log. p—AP+B. . . , (62)
Observing that the difference of the total heats of the liquid

and vapour at any temperature is equal to the latent heat L,

and the difference of the entropies equal to L/@ (or equating

values of G for the liquid and vapour), we obtain the equation

for the saturation-pressure,

Rlog, p= A'— B!/0— (s'—S,) log, 6+ (c—b)p/0, . (63)

in which the specific heat s' of the liquid is assumed to be
constant. <A! is a constant to be determined by the obser-
vation of the boiling-point ; B’ is the difference of the con-
stants B in the expressions for the total heats of the vapour
and liquid, which may be determined by the observation of
the latent heat at the same point.

It should be observed that the equations tor the thermo- |
dynamic potentials and for the yapour-pressure are inde- 7
pendent of the assumption that ¢ varies inyersely as the nth ;

power of the temperature, and are generally true provided
that c—b is a function of the temperature only; but the
assumption c=¢y(A,/8)" satisfies Regnault’s observations of
the saturation-pressure very accurately,

Correction of the Gas-T hermometer. 81

17. Interpretation of the Index un.

Some idea of the meaning of the index n may be obtained
by considering the expression above given for the Hnergy H.
The energy of an imperfect gas is less than that of the gas in
the ideal state at the same temperature by the term ncp,
which represents the loss of energy due to coaggregation of
the molecules, corresponding to the diminution of volume
¢ per unit mass. Considering first the case of a monatomic
gas, in which the whole of the kinetic energy of the molecules
consists of energy of flight (corresponding to three degrees
of freedom), we have the well-known relation pu== R9= 2s6/3.
In a diatomic gas, regarded as consisting of pairs of atoms
rigidly joined together like dumbbells, it appears probable, as
suggested by Boltzmann, that the energy of a molecule may
be equally distributed between each of three degrees of
freedom of translation and two degrees of freedom of rotation,
supposing that the rotation of a molecule about its axis could
not be altered by intermolecular collisions. Such a molecule
would have five equal degrees of freedom, and the specific
heat at constant volume should be 5R/2, which is amply con-
firmed by experiment. Supposing that two monatomic mole-
cules each with three degrees of freedom coaggregate to form
a diatomic molecule possessing five degrees of freedom, there
would be a loss of energy equivalent to one degree of freedom,
or one third of the energy of flight, since the exergy of flight
of the resulting diatomic molecule would be the same as that
of a single monatomic molecule at the same temperature.
If the diminution of volume per unit mass due to coagere-
gation be represented by c, the loss of energy on this
hypothesis would be represented by cp/2, since the product
cp represents two-thirds of the energy of flight in a volume ec.
We onght therefore to have the index n=1/2, in the case of
a monatomic gas, on the simple hypothesis of coaggregation
in pairs, provided that the coaggregation is a purely physical
effect, and that there is nothing in the nature of chemical
combination involving evolution of heat.

In the case of a diatomic gas, a similar line of reasoning
fails to give a definite result, because we have no sure experi-
mental guide or mechanical analogy to enable us to estimate
the number of degrees of freedom of the resulting tetratomic
agoregate. If we supposed with Maxwell that the number of
degrees of freedom could not exceed six, as for a rigid body,
the loss of energy for a pair of diatomic molecules each
possessing five degrees of freedom would be equivalent to four

degrees of freedom on coaggregation, which would make

Phil. Mag. 8. 6. Vol. 5. No. 25. Jan. 1903. G

82 Prof. H. L. Callendar on the Thermodynanucal

the value of the index n=2, as in the Joule-Thomson equa-
tion. There can be no doubt, however, from experimental
evidence, that the energy of flight may be less than half
the total kinetic energy of a polyatomic molecule, otherwise
the ratio S/s of the specific heats could not be less than 4/3.
It is probable that the distribution of energy in the molecule
depends on the type or form of the molecule, and not merely
on the number of atoms it contains, and that the various
degrees of freedom are not all of equal value. The ratio of
the energy of rotation HE” to the energy of flight H’ in the
case of CO, is about 4/3, corresponding to the ratio of specific
heats S/s=9/7T. Whence, if n=2, the ratio Ii”/E! should be
7/3 for a coaggregated pair of molecules. For steam, which
is alsoa fone molecule, the loss of energy on coaggrega-
tion is greater. We have n=3" 3=s/R, so that the whole
energy of a coaggregated pair is no greater than that of a
single molecule. It is further poss ssible that the relative
importance of the different kinds of degrees of freedom in a
complicated molecule would vary with the temperature. We
could not then assume that the limiting value Sp of the
specific heat at zero pressure was constant. The assumption
So=constant is almost certainly true for monatomic or dia-
tomic molecules at ordinary temperatures ; but it could not
be true for unstable molecules, and there is some evidence
that it does not hold for polyatomic molecules of higher
orders.

18. Application to Monatomic Gases.

The only observations so far available to test the hypothesis
n=1/2 in the case of monatomic gases, are those of Ramsay
and Travers (Phil. Trans. A, 1901) on the compressibility of
the inert gases by the capillary-tube method at 11°2 C. from
20 to 80 metres pressure, and at 237°°3C. from 30 to 80
metres. These observations are not very suitable for the
purpose, as they do not extend to low pressures. They also
exhibit, as the authors point out, several anomalies, which
may be due to some hitherto unexplained peculiarities in the
behaviour of monatomic gases, or perhaps merely to experi-
mental errors. The curves representing the variations of pv
with p at the lower temperature are of a perfectly normal
type, the gases helium, neon, argon, krypton, and xenon,
following naturally in the order of their densities. Tt should
be remarked, however, that if we produce the curves for argon
(39°9 gm.) and krypton (81°5 gm.) to zero pressure, they
appear to indicate a limiting value of pv equal to 18, 500

Correction of the Gas-Thermometer. 83

metre cubic centimetres approximately, whereas molecular
weights of the other gases appear to conform to the limit
17,710 m.c.c., which is given as the ideal value for a perfect
gas. At the higher temperature, the order of the gases is
inverted. Helium and neon appear to be more imperfect
than at the lower temperature, and their curves lie below
krypton and argon. It seems to be impossible to offer any
theoretical explanation of these anomalies ; but if we admit
that the limiting values for krypton at zero pressure should
be 18,510 m.c.c. at 11°2C., and 33,240 m.c.c. (the corre-
sponding value for the same mass of gas) at 237°-3 C., the
limiting values of the slope (c—b) may be estimated as 0°84 e.c.
and 0°43 ¢.c. respectively per gramme of gas. In the case
of the other gases the slope is too small, or its initial value
too uncertain, to afford a comparison. If we assume as above
that the coaggregation ¢ should vary inversely as the square
root of the temperature (n=1/2), we find c=1-61 c.c. at
Pet) Abs. and c=1:20 ce at. 510°'3 Abs., whence
b=0°77 c.c. If on the other hand we assumed n=1, we
should find c=0°52 ¢.c. at 510°3 Abs., and 6=0-09 c.c.
A higher value such as n= 2 would make 0 large and negative,
which would be impossible, or at least incapable of rational
interpretation. The volume of liquid krypton at its boiling-
point was found to be 0:46 ¢.c. per gramme, so that the value
of 6 deduced on the assumption n=1/2 is perhaps the most
probable. The fact that helium appears to be less perfect
than hydrogen, and neon nearly as imperfect as nitrogen at
11°-2 C., also supports the hypothesis of a very low value ot
n for monatomic gases.

Adopting provisionally the basis n=1/2, I have calculated
the following tables of corrections for argon and helium in
addition to krypton, since, as 1 have previously explained
(Phil. Mag. Dec. 1899, p. 541), the inert monatomic gases
are peculiarly suitable for thermometric purposes. I have
assumed the values of 6 for helium and argon to be equal
to the volumes of the liquids (which are estimated at 3°3 ¢.c.,
and 0°83 ¢. ¢. respectively) multiplied by the ratio 0:77/0°46
found above in the case of krypton. The values of ¢ are
deduced from the observed compressibilities at 11°2 C. For
helium I have assumed cy=0, since the pv line for helium is
practically horizontal up to a pressure of 50 metres. It
must be admitted that these data are somewhat uncertain,
but they afford at least a reasonable basis for comparison with
experiment.

84 Prof. H. L. Callendar on the Thermodynamical
TABLE IX.

Values of Constants assumed for Monatomic Gases.

| Krypton...) 164 | 0-77 | 0-87 | 1-064) 266 | 1567

| Argon...... 218 | 139 | 079 | 2175 548 | 1016

|
|

1
Helium...) 55 | 55 | 0:00 |208 520 | 0268 , 0352

Assuming the value n=0°5, ¢=¢9(0o/0)"*, co —¢ = 0° 1445 op,
we have the following formule for the zero correction :—
Zero Correction, Constant-Pressure,

6,—T,= (co — 0 + 2°73 X °1445 xX co) po/R,
2 -, Constant- Volume,
6) —T y= 3°73 x (1445 x 6,po/R,

from which we deduce the values of the expansion- and
pressure-coefficients given in the following table, assuming
the value @,=273710 :—

Ali NoesiaRt eee
Expansion- and Pressure-Coefficients for Monatomic Gases.
| | Constant-Pressure, 76 cms. | Constant-Volume, p,>=100cms.
Se |
Teast hte LD, OT, Ty. aa

pau ale 2 ie = il:
| Krypton... ise | 272-65 | -o0s6s12 | tl ee 0036761
| Argon ...... O77 | 27233 0036717 | O72 — 272:38 | -0086710
| Helium ...... 0-10 | 273-00 | 0086628 | 0-19 | 272°91 | :0036640

The value of the pressure-coefficiént observed by Travers
(Proc. R. 8. Ixx. p. 485) for helium at a mean initial
pressure of 60 cms. is from *0036624 to ‘0036631, mean
0036627. The calculated value at this pressure would be
0036632, which is within the limits of possible error, but
may indicate that the value of ¢ assumed is too large.

Correction of the Gas-1 hermometer. 85

The values of the scale-correction for the monatomic gases
given in Table XI. are calculated by the following formule :—

Constant-Pressure, dt = (0°1445 ¢/100 —1 + (85/4) °°) copo/R,
Constant- Volume, dt =(—0°1689 ¢/100 — 1 + (8/05) °°) cop9/R.
Taste XI.

Seale-Correction for Monatomic Gases.

Constant-Pressure,76cms. |Constant-Volume. p,=100 cms.
Temp. |
cent.
Krypton.| Argon. | Helium. ||Krypton.| Argon. | Helium.
fe) | (2)
| —250 0:557 7 |) 1... a "101
_ —200 fas LTS eee —"194 | —:051
_ —150 bee +278 | + 0738 |— -156 | —:101 | —-0265
'—100 |+ -175 | +:114 | + -0298 ||— 072 | —-047 | —-0123 |
|— 90 |+ 053 | +034 | + 0091 ||— 0242) —-0157| —-0041 |
| — 20 |+ -0155} +:°0101 |} + °00265 }— -0070| —-0045|; —-00120
— 10 |+ :0069| +°0045|} + -00118 — -0031) — 0020) —-00053 ©
+ 10 |— 0052; —-0034) — -00089 ||+ -0027) +-0017) +-00045
| + 20 |— 0093; —-:0060) — -00159 |j+ -0045) +-0029| +-00077
+ 380 |— °0116) —-0075| — -00198 |\+ -0058) +-0038, +-00098
'+ 40 |— -0130) —-0084|} — -00222)/+ -0064; +-°0041) +-00109
+ 50 |— :0130| —-0084} — -00222|\4+ -0065) +-0042| +-00113
| + 60 j— 0124) —-0080) — 00212 )|+ :0062|) +-0040) +-00106
| + 70 |— :0105; —-0068} — -00180||+ -0056) +-0036) +:00095 |
| + 80 |— 0078) —-0051) — -00133||+ -@041) +-0027) +:00070 |
/ + 90 |— -0042| —-0027) — -00072|/+ -0021| +-0014) +-00035
| +150 |+ -0815| +-0204| + -0054 || — -0180| —-0116| —-00306 |
| +200 |+ 075 | +°049 | + 0128 || — -045 | —-029 | —:0076
+300 |+ 194 | +°126 | + -0332 | — ‘119 | —-077 | —:0203
| +490 (+ 415 | +°269 | + :071! — 275 | —178 | —°0468
+1000 |+1-42 4-92 + 243 || —1:09 — ‘71 — 187

It will be observed that the correction is negative for the
constant-volume thermometer at temperatures below 0°C.
According to Travers (doc. cit.) the helium thermometer reads
0°-1 above the hydrogen thermometer at the boiling-point of
oxygen, and 0°2 above at the boiling-point of hydrogen.
The hydrogen correction is opposite in sign, and nearly equal
in magnitude. The true values of the boiling- -points, obtained
by interpolating between the hydrogen and helium values,
would be

Oxygen B.-P. 90°13 Abs. Hydrogen B.-P. 20°31 Abs,

86 Prof. H. L. Callendar on the Thermodynamical
19. Variation of the Covolume b.

Van der Waals, in his essay on the Continuity of State
(Phys. Soc. Translation, 1890, p. 372), gives a theoretical
discussion of the effect of the size of the molecules on the
length of the free path, from which on certain simple assump-
tions he deduces that for moderate pressures the effect may
be represented by attributing to the covolume 0 a value equal
to four times the actual volume of the molecules regarded
as spheres. The theory indicates, however, that the value of
b should diminish with increase of pressure somewhat rapidly
when the volume approaches the value 256. He verifies this
by applying his equation to represent the behaviour of CO,
as observed experimentally by Andrews. Adopting for the
constant a in his equation the value -00874 (the unit of
pressure being 760 mm. and the unit of volume the volume
of the gas at 0° C. and 760 mm.) he finds values of 6 ranging
from 0023 to ‘0025 for the vapour, but falling to -0016 and
0018 for the liquid. It appears both on theoretical and ex-
perimental grounds that ) cannot be regarded as constant
for a large range of pressure, and that no weight can be
attached to calculations of the critical temperature based on
the assumption that 6 is the same, as in van der Waals’
equation, for both vapour and liquid. It nevertheless appears
probable that the range of variation of 6 is not large, and
that its value for moderate pressures is nearly constant with
respect to both temperature and pressure. The value of b
cannot be determined theoretically, because the actual volume
of the molecules is unknown, and because the theoretical
assumptions on which the estimate of the ratio 4 is based are
extremely uncertain. Meyer, adopting a slightly different
assumption, finds that 6 should be 4 4/2 times the volume of
the molecules. Jf we assumed, as many writers have
supposed, that the molecules of the liquid at low tempera-
tures are practically in contact, and that the volume of the
liquid in this case may be taken as the volume of the mole-
cules, we should find, if we multiply by the factor 4 or 4/2,
values of / which are much too large to be reconciled with
the observed behaviour of gases at moderate pressures. We
may, however, assume with some degree of confidence that
the volume of the liquid, or the limiting volume of the gas
at very high pressures, is a limit below “which the value of
b at moderate pressures cannot greatly fall: and we may
with propriety reject formule or experiments which lead to
much lower values. The limiting volumes of hydrogen and
CO, at high pressures are given by Amagat as 8°7 c.c. and

Correction of the Gas-Thermometer. 87.

0°86 c. c. respectively, which are evidently quantities of the
same order of magnitude as the volumes of the liquids. The
difficulty in the determination of 6b from experiments at
moderate pressures lies in the fact that it is of the order of
a tenth of one per cent. of the volume of the gas at atmo-
spheric pressure, that it cannot be determined independently
of c, and that the values of both 6 and ¢ depend on small
differences between larger quantities in which the errors of
observation are often of the same order as bitself. Boltzmann
(Gas-Theorie) and van der Waals (Arch. Néer. iv. p. 299,
and vi. p. 47, 1901) have recently given formule for the
variation of 4 with pressure, which might theoretically be
applied to correct the values of 6 obtained from observations
at higher pressures so as to deduce the values at atmospheric
pressure required tor the correction of the gas thermometer
or for the behaviour of gases at moderate pressures. But
the development of these formule rests on assumptions even
more uncertain than the discordant estimates of Meyer and
van der Waals, and the range of variation indicated (Boltz-
mann says it is probably not greater than 1 to 10), would
make the extrapolation of such formule very doubtful. It
seems better to adopt a formula of the type already quoted,
and to determine c¢ and 6 from observations of the com-
pressibility or the cooling-effect on the assumption that 6 is
constant. The application of this method appears to lead to
the conclusion that the value of 6 at moderate pressures
does not differ greatly, if at all, from the volume of the liquid
at or below its boiling-point. In applying the equation to
calculate the properties of steam, in which case 6 is so small
compared with ¢ that it cannot be determined with any
accuracy, I have for this reason simply assumed / equal to
the volume of the liquid, and then calculated the values of
m and c from the observations on the cooling-eftect. The
error involved is necessarily small since the value of (n+1)c
at the boiling-point in this case is more than a hundred times
the assumed value of b.

With regard to the variation of 6 with temperature, we
can learn nothing from theory, and the indications of experi-
ment cannot be interpreted with certainty. From an empirical
point of view the assumption 6=constant is the simplest, and
since it appears to satisfy the observations better than any
other simple assumption, it should be retained unless it is
decisively disproved.

20. Application to Diatomic Gases.

The application of the theory to diatomic gases is of par-
ticular interest and importance on account of the general

88 Prof. H. L. Callendar on the Thermodynamical

employment of hydrogen, nitrogen, and air in gas-ther-
mometers. It also presents peculiar difficulties, as compared
with the case of a less perfect gas like CO,, because the
deviations to be measured and compared are so much smaller,
while the probable error of observation remains the same.
For instance, in the case of the three gases above mentioned,
the deviations from Boyle’s law are ot the order of one part
in a thousand only per atmosphere, and the order of accuracy
of measurements of the compressibility by the capillary-tube
method does not reach 1/1000 except under the best con-
ditions. The advantage of the porous-plug method is that
the cooling-effect represents the whole deviation sought, but
the order of accuracy of the individual observations of Joule
and Thomson did not exceed 5 or 10 per cent. at the higher
temperatures. One of the final series of observations on air
at 40° C. differs from the smoothed curve by more than 5 per
cent., and one of the observations on nitrogen at 92° ©. differs
from the other by about 20 per cent. The nitrogen was pre-
pared by burning phosphorus in air, and the values of the
cooling-effect exceeded those for air by about 20 per cent.,
whereas the compressibility of nitrogen is decidedly less than
that of air. The formula of Rose-Innes, with three constants,
was designed to reconcile this apparent discrepancy, but if
we extrapolate it to lower temperatures we find that it makes
the compressibility of nitrogen much greater than that of air
at —100°C., which is certainly contrary to fact. In Tables
IV. & V., 1 have made a rough allowance for the fact that
the observed cooling-effect for nitrogen was greater than for
air, but little or no weight can be attached to this estimate.
Nor can we overlook the fact that Joule and Thomson con-
sidered their observations on nitrogen much less satisfactory
than those on air.

Air.—In order to obtain a satisfactory measurement of
the constants ¢ and 6 and of their rate of variation with
temperature, it is obviously necessary to. make experiments
over a much wider range of temperature, and especially at
lower temperatures, where the deviations are much larger
and more easily measured. The observations of Witkowski
(Phil. Mag. xli. p. 288, 1896) on Air appear to be the only
ones available for the purpose. His method consisted in
filling two similar bulbs with air at the same pressure but at
different temperatures. The quantities of air in the two bulbs
were then compared by discharging them into eudiometers at
atmospheric pressure and temperature. From these data he
deduced the mean coefficient of expansion at the given
pressure, and all the data required for constructing a diagram
of the variations of pv with p at constant temperature. The

Correction of the Gas- Thermometer. 89

method, though troublesome, is evidently capable of great
accuracy. It avoids or minimizes the effects of surface-
condensation, which are so great an objection to the more
convenient capillary-tube method. Witkowski observes in
fact that his method always gave lower measurements of
compressibility than the capillar y-tube method, amounting to
about 0°5 per cent. at 15° and 90 atmos, which may probably
be explained as due to surface condensation in the capillary-
tube method. For our purpose it will suffice to take one of
Witkowski’s isothermals for air, namely that at —78°°3 C.,

which appears to have been determined with especial care, and
which is so nearly straight up to high pressures that it is
easy to make an estimate of the initial value of dpv|dp,
which gives :—

Aw at —78°3'C., e—b=1-47 e.c.; at 0° C., c—b=0°50 c..

The values of ¢ and 6 for air caleulated from the cooling-
effect alone, assuming n=2, namely, co=0°90, b= —‘002,
give ¢c—b at 0° C.=0°92 c.c., whereas the value should be
0°50 c.¢. to agree with Amagat’ s observations. The value at
—78~3 C. would be 1°79 c. c., which is also greater than that
found by Witkowski. Moreover the negativ e value of 6
cannot be interpreted, and would make the error of the cal-
culated compressibility much greater at higher temperatures.
It is clear that the value of 5 requires emendation. If we
retain the same type of formula with n=2, and calculate the
values of c, and 6 to satisfy the observed values of e—b above
given, we find :-—

pee —— 101 ce. 6=0' 52 1c; 1 O§=07'250, Qi = 0" 110.

The value of / thus found is still too small ; the values of the
cooling-effect deduced are also smaller than the observed
values, namely, 0°271 and 0°-147, and the air would not
become “ pluperfect ”’ till 105° C.

A much better agreement between the cooling-effect and
the compressibility is obtained by taking n=1'5 in the
formula. This is not improbable theoretically, as the number
of degrees of freedom lost by two diatomic molecules (each
possessing five degrees of freedom) in coaggregating should be
less than for triatomic molecules like CO,. It is most un-
likely that the tetratomic aggregate would possess only
six degrees of freedom. The value n=1°5 implies the loss of
three degrees of freedom, which is more likely, if we suppose
for simplicity that the number lost must be an integer. We
then obtain

n=1°5, c= 148, b=0:98, Qo=0°271, Qroo= 0135.

90 Prof. H. L. Callendar on the Thermodynamical

With these values air would become pluperfect at about
90°C., and the value of bis not much smaller than the volume
of the liquid at low temperatures. The agreement with the
observations on the compressibility is very good over a wide
range of temperature. The agreement with the observations
of the cooling-effect is exact at 0° C., and the difference
at 100° C. does not exceed the possible error of the experi-
ments. If we abandon the hypothesis of integral degrees
of freedom for triatomic or tetratomic molecules, we might
of course calculate the value of the index 7 so as to obtain a
better average agreement with observation, but even from a
purely empirical point of view it is a matter of great con-
venience to have a simple value for the index n, provided
that it satisfies the observations within the limits of probable
error. Moreover the hypothesis of Maxwell, which is sup-
ported by the experiments on monatomic and diatomic gases,
is so simple and helpful that it is desirable to retain it as far
as possible.

In applying the formula with the value n=1°5 to deter-
mine the zero-correction and the scale-correction, the simplest
method of proceeding is to find g for each temperature, and
apply formule (34) and (36). The results for the constant-
pressure thermometer do not differ materially from those
previously calculated. The zero-correction for the constant-
volume thermometer may be put in the form

Q—T)= Sle (Cp — Cy) po/ R.

Taking cy=1°48 ¢. c., this gives 0°°72 for the correction at
76 cms., or 0°°95 at 100 ems. If we assume the correction
for nitrogen to be the same as that for air, and employ
Chappuis’ pressure-coefficient, we find @,=273°:06. The
values of the seale-correction for the air-thermometer are as
follows at 50° C. and 450° C. :—
Constant-Pressure, 76 cms.
at 50° C., dt= —°0185° ; at 450° C., dé= +°470°.
Constant-Volume, pp>=76 cms.
at 50° C., dt= —:0044°; at 450° C., dié= +-136°,

Constant-Volume, pg=100 cms.
at 50°-C., di= —-0057° ; at 450" CL di] aie

The constant-pressure correction is nearly one-tenth larger,
the constant-volume correction is nearly one-third smaller
than in Table V., according to the previous method of caleu-
lation with »=2. The constant-volume correction is still
nearly twice as large as that given by the Rose-Innes formula
for nitrogen, and more than three times as large as that given

Correction of the Gas- Thermometer. ot

by his formula for air. For nitrogen, if we simply adopt the
values of the constants given for air, we find that they satisfy
the observations of the compressibility at low temperatures,
and of the pressure-coefficient (0°-—100°C.) rather better
than those given by Rose-Innes, which depend on the very
doubtful observations of the cooling-effect.

Nitrogen—Although we should probably be well within
the limits of experimental error in taking the corrections for
nitrogen to be the same as those for air, [ have thought it
worth while to calculate the values of the constants for
nitrogen from Chappuis’ pressure-coefficient at 100 cms.,
assuming 6,=273°10. This gives ¢,=1:58 c.c.. Whence
if c—b at 0° C.=0°44 c.c., we have b=1:14 ¢.c. Chappuis’
observations of the compressibility at 0° C. give co.—b=0°35
e.c., which would make 6=1°23c.c. The volume of the
liquid at its boiling-point is 1°26 c.c., but this is probably
too large, so I have taken b=1'14. The corrections calcu-
lated with these values are seen to be practically the same as
for air.

Hydrogen —In calculating the values of the constants for
hydrogen on the assumption n=1°5, I have taken Chappuis’
value of the slope of the isothermals at 0° C., namely,

¢;—b=—6'5c. ¢., which is in close agreement with Regnaulit’s
een 55 to 66 c.c. at 4°C. Adopting also Joule and
Thomson’s value of the heating-effect at O°C., namely
G—-0293- per atmo, we have ¢=1°90 ¢.c., b=8:0 c.c.
The value of 6 is slightly smaller than Amagat’s limiting
volume 8°7 c.c. at high pressures, and much smaller than
the volume of the liquid 14 c.¢., but it appears that hydrogen
is much more compressible than other gases or liquids under
these conditions.

Taste XII.

Values of Constants assumed for Diatomic Gases.

|
'

' 76 ems. | 100 ems. |
| |

iat oe 148 | 098 | 0:50 | 2872] 10:05) 0-516 | 0-678
Nitrogen ...| 158 | 1:14 | 044 | 2966) 10:38 0-540 | 0-710
Baie | 1:60 | 800 |-650 | 415 | 1453 | 00367} O-0s82

The oe of a Jae Zero 6,=273° 101 is deduced
from the pressure-coeflicient of hydrogen, and the pressure-

92 Prof. H. L. Callendar on the Thermodynamical

and expansion-coefficients of the other gases are deduced on
the assumption @,=273°10.

Taste XI,

eo and Pressure-Coefficients of Diatomic Gases.

Constant-Pressure. 76 cms. (cca Pp = 100 ems.

Gas |
| employed. | @,-T,.| To. 1/1, pee, saa
isis eect te
jeter 0s Les O71 | 27339 0036709 6:96 27214 00867425
“Nitrogen... 0-70 | 27240 | -0038708 | 0-99 | 27211 | -00367466
| | | |
| Hydrogen ....— 185 | 273235 00365985) + -067 273/084 -00366254

Regnault’s values of the expansion-coefficient for wr.
at 76 cms. range from ‘0036642 to ‘0036586. Chappuis at
100 cms. finds *0036600 for hydrogen at constant pressure,
and :0036726 to :0036735 for nitrogen, the calculated values
being -0036593 and :0036737 respectiv ely.

The values of the thermodynamical corrections for the
diatomic gases are calculated by the following formule :—

Assuming n=1:5, c=¢9(/9)2?, co—¢=0°3738c,.

Zero-Correction ©. P.,

Q—T,)= (co—b + 2 lox wood aX Co) Pol R.

Zero-Correction C. V.,

Gj— oslo x 374 x Copo/ R.

Scale-Correction C. P.,

dt = (0°3738 ¢/100—1 + (8,/@)?*)cg1/R.
Scale-Correction C. V.,
dt =(0°1445 ¢/100—1.+4+ (4)/8)°°)cop,/R-

The densities of oxygen and nitrogen at the boiling-point of
oxygen at a pressure of 760 mm. have been directly deter-
mined by Dewar (Proc. Roy. Soc. lxix. p. 360) by the method
of weighing. The resulting values of the specific volumes
were:—Oxygen, v=225°8 c.c. per gramme, Nitrogen, v=
256°8 c. c. at 90°5 Abs. with a possible error of 0°5 per cent.
The ideal volumes at this temperature and pressure are:—

Oxygen, 231°8 c.c., Nitrogen, 264°9 c.c. The values of c—b
at 90°5 Abs. are: Oxygen, c—b=6:0 c.c.; Nitrogen,

Correction of the Gas- Thermometer. 93.

TABLE XLV.
Scale-Correction for Diatomic Gases.
| Constant-Pressure, 76 cms. |/Constant-Volume, p,>=100 cms.
Temp. | ‘4
cent. : | |
Air. |Nitrogen.| Hydrogen. || Air. |Nitrogen.; Hydrogen,
| |
° ro) | °

=. 250 ne +1:43 Ie ek, Agel +°1005

— 200 uae see + 201 ||+°4388 |+-460 +0311

— 150 |+ ‘901 |+ °945 | + -064 +186 +°195 +:0132
— 100 |+ ‘314 |+ 3828 | + :0225 [+076 '+:080 +0054 >
— 50 |+ ‘086 |+ ‘090 | + 0062 ||4+ 0232 +:0243 | +:00164 |
— 20 |+ °0238)+ -0250! + -00170|+ 0067 +:0070 | + 00048 -

— 10 |+ -0105/+ -0110) + -00075)||+:0030 +-0032 | +:00021

+ 10 — :0078)— °0082| — ‘00055 ||—-0023 |—-0024 | —-00016

+ 20 — -0154)— ‘0141; — :00095 ||—:0041 |—-0043 | —-000238

+ 30 ‘— -0169|/— :0177| — -00120||—-0051 |—-0053 | —-00036
+ 40 — ‘0186)— -0195) — -00182);—-0056 |—-0059 | —:00040 |
+ 50 ‘— -0186|— -0195| — -00132 ||—-0056 |—-:0059 | —-00040 |
==) 60 |— -0172|— -0180| — -00123 ||—-0053 |—-0054 | —00038 |
+ 7 (— :0146|— :0153) — -00104,—-0046 |—-0048 | —-00032 ©

+ 80 |— -0108/— -:01138; — -00077 ||—:0034 |—-00386 | —:00024
+ 90 |— °0058;— ‘0061; — :00041 |;—:0019 |—-0020 | — 00013 |

|
| |

+ 150 |+ :0409/+ 0428 | + -0029 | +-0136 |+-0143 | +-00097

+ 200 '+ 096 |+ ‘101 ; + ‘0068 ||+-0332 |+:°0347 | +:00236

+ 300 + 232 |+ -243 | + -0165 ||+:084 /+-088 +-0059
+ 450 '+ ‘472 {+ 495 | + ‘0886 ||+:180 |+-189 +:°0127 |
+1000 (41-464 |+1:535 | + -1040 \| +616 +646 | 4-'0438 |

e—b=8'1 c.c. Whence the value for air would probably be,
e—b=77¢.c. The calculated values at this temperature, on
the hypothesis n=1-5, would be 6°8 and 7:2 c.c. for air and
nitrogen respectively, which are probably within the limits
of experimental error. If we assumed Dewar’s values of
e—b at 90°°5 Abs., and calculated the values of ¢ at 0° C.
on the assumption n=2, we should find for nitrogen
¢=0°95 c. c., b=0°51 c.c., which do not agree so well with
the values of the cooling-effect or with Chappuis’ values of
the coefficients.

The temperature of inversion of the heating-effect in the
case of hydrogen has been observed by Olzewski to be about
— 80° C., when the gas is supplied at a pressure of 117 atmos
and escapes at atmospheric pressure. The values of the
constants above given on either assumption n=1°5 or n=2,
would give a small heating-effect SQ=—1:'7 c.c. at this

94 Thermodynamical Correction of the Gas-Thermometer.

point. But as the effect amounts to little more than a
hundredth of a degree per atmo it would be easily masked
by any slight impurity in the hydrogen, so that little stress
can be laid on this observation. Assuming that the heating-
effect Q is constant up to a pressure of 117 atmos, the
observations of Olzewski would require cy = 2°0 c.c., b>=8'5 ¢.¢.
if we take n=1'5, and co—b=—6'5 c.c. These values
would make the heating-effect at 0° C. Q=—-024° per atmo,
which is rather smaller than that observed by Joule and
Thomson, but the difference is hardly beyond the possible limits
of error. The absolute zero-correction for the constant-volume
thermometer would be larger in the proportion of 2 to 14,
but that of the constant-pressure thermometer would be
smaller, agreeing slightly better with experiment. The value
of ¢) for hydrogen probably hes between 1 and 2 c. ¢., but we
can hardly expect to be able to determine it more closely with
certainty, since it is of the order of one part in 10,000 only
of the specific volume at 0° C. and 760 mm. pressure.

21. Summary of Conclusions.

(1) The deviations of a gas or vapour from the ideal state
at moderate pressures can be represented by an equation of
the type v—b=R6@/p—c, in which the “covolume” 6 is
constant, and the “ co-aggregation-volume” c is a function
of the temperature only. This conclusion follows from the
observed form of the isothermals combined with the observa-
tion that the “ cooling-effect ”’ is independent of the pressure;
but it could not be deduced from either observation separately.

(2) The value of the Absolute Zero may be approximately
deduced from a knowledge of the cooling-effect Q and the
specific heat S at or near 50° C. without any knowledge of
the mode of variation of S and Q with temperature. But
the determination of the scale-correction of the gas-ther-
mometer essentially requires a knowledge of the mode of
variation with temperature.

(3) The simplest assumption with regard to the mode of
variation of ¢ with temperature is that it varies inversely as
the nth power of @, or that c=co(@/@)". The value of n is
different for different types of co-aggregation or for different
kinds of molecules. The law of Corresponding States must
be restricted to molecules of the same type which coaggregate
in a similar manner.

(4) The index n may be interpreted as half the number
of degrees of freedom lost by a molecule in coaggregation,
the energy of flight of a molecule representing three degrees
of freedom.

On Excited Radioactivity and its Transmission. a

(5) The value of 2 is probably 0°5 for monatomic gases,
and 1:5 for diatomic gases, on the simple hypothesis of
integral degrees of freedom. ‘These values give very fair
agreement with experiment, but there is no @ priort reason
why the number of degrees of freedom should be an integer
for a polyatomic molecule.

(6) The properties of CO, at moderate pressures are well
represented by the assumption n=2, provided that account
is taken of the variation of the specific heat as observed by
Reenault. This reconciles the hitherto discordant results for
the cooling-effect and the compressibility.

(7) The properties of Steam, including the variation of the
latent heat and the saturation-pressure, are well represented
by the value n=3°3, if the limiting value of the specific
heat at zero pressure is assumed to be independent of the
temperature, provided that the variation with pressure is
not neglected.

(8) The value of the Absolute Zero, as deduced from the
pressure-coefficient of hydrogen, is probably within one or
two hundredths of a degree of 273°°10.

IV. EHacted Radioactivity and the Method of tts Transmission.
By HK. Rurserrory, M.A., D.Sc., Macdonald Professor of
Eston: MeGill University, Montreal *.

. Introduction.

. Connexion between the excited activity and the emanations.
. Method of transmission of excited activity.

. Velocity of carriers of thorium-excited activity.
Increase of excited radiation with time.

. Radium-excited activity.

. Distribution of excited activity on the anode.

. Velocity of the carriers.

. Origin of the carriers.

. Nature of the radiations.

. Evidence of chemical changes.

. Summary of results.

CDR EDR DA DADAM COAAUHANUAIU

bo et
eae ey

§ 1.—Introduction.

“Oe of the most interesting properties of the radioactive

substances thorium and radium, is their power of com-
municating or exciting f temporary radioactivity to all bodies
in their neighbourhood. If a wire charged to a high negative

* Communicated by the Author. Preliminary accounts of these
bee were communicated to the American Physical Society, New York,
December 27, 1901. and to Phy ys. Zeit. No. 10, 1902.

+ (Note)— ‘The term “ excited,” has been used throughout these investi-
gations rather than “ induced,” which has found favour with many

96 Prof. Rutherford on Excited Radioactivity and

potential is placed in a closed metal vessel containing a thorium
or radium compound the excited radioactivity is confined
almost entirely to the negative electrode. If the wire is
charged positively, it remains inactive, but the excited radio-
activity is produced on the walls of the vessel.

When no electric field is acting, excited radicactivity is
produced on the surfaces of all bodies in the closed vessel,
independently of their being good conductors or insulators.

In previous papers the author has shown that there is a
direct connexion between the presence of the radioactive
emanation from thorium and radium and the production of
excited radioactivity. It will be shown in this paper that the
production of excited radioactivity is one of the properties of
the emanation from thoriumand radium. This excited radia-
tion is caused by the deposit on the surface of bodies of
radioactive matter, which is transmitted by positively charged
carriers travelling through air in an electric field with about
the same velocity as the positive ion, produced in air by
Rontgen rays.

§ 2.—Connewion between Hacited Radioactivity and
Emanation,

in a previous paper (Phil. Mag. Jan. 1900) I have shown
that thorium compounds continually give off a radioactive
emanation. This emanation loses its radiating power rapidly,
falling to half value in the course of one minute. Dorn
showed later that radium also gave off an emanation, especially
when heated. This emanation decayed much more slowly
than that from thorium. In some experiments where the
radium emanation, mixed with air, was kept ina closed metal
vessel, I have found that the activity of the emanation fell to
half value after standing several days, but was quite appreci-
able after a month’s interval.

These emanations from thorium and radium behave in
all respects like radioactive gases or vapours. They diffuse
rapidly through gases and through porous substances like
paper, but unlike the gaseous ions which they produce in
their path, pass through plugs of cotton wool, and bubble
through solutions with no appreciable absorption. In a more
detailed investigation (Rutherford and Soddy, Phil. Mag.
Sept. 1902) it has been shown that the thorium emanation
behaves like an inactive gas, and that its activity is not

Physicists. JI have avoided using the latter term, as to my mind, it
conveys the idea that the effect is in some way due to an action across
the medium ; while the experiments in this paper show conclusively that
excited radioactivity is transmitted by means of a convection of positively
charged carriers.

the Method of tts Transmission. 97

appreciably influenced by temperature or by the most drastic
chemical treatment.

From the rate of diffusion of these emanations, it appears
that they must possess a considerable molecular weight, An
investigation of the rate of diffusion of the radium etamerion
into air, a preliminary account of which appeared in ‘ Nature,’
1901, p. 157, and Proc. Roy. Soc. Canada 1901, showed that
its molecular weight probably lay between 40 and 100. On
account of the rapid loss of activity of the thorium emanation it
has not so far been found possible to determine with certainty
its rate of diffusion into air or other gases.

The emanations from thorium and radium possess very
similar properties. They both readily diffuse through gases
and porous substances; they both possess the power of
ionizing the gas in their neighbourhood and producing excited
radioactivity on bodies.

The differences between them can be readily accounted for
by supposing them to be radioactive gases or vapours of
different molecular weights. According to the results which
have been given in previous papers, radioactivity is an
accompaniment of chemical change. Taking this view, the
difference in the rates of decay of the radioactivity of the
emanations from thorium and radium merely indicates a
difference in their rate of chemical change, and does not imply
any fundamental difference in nature.

Unlike the radiations from the emanations, the excited
radiation due to thorium decays much more slowly than that
due to radium (see Rutherford and Miss Brooks, Phil. Mag.
July 1902, p. 18). In this case, the chemical change pro-
ceeds more rapidly in the materi al responsible for the ‘excited
radioactivity from radium than in that from thorium.

Hxcited radioactivity is always produced on bodies when
the radioactive emanations from thorium and radium are
present. In order to show the very close connexion existing
between the presence of these emanations and excited radio-
activity, the following experimental facts may be mentioned :

(1) Only the r -adioactive substances which emit emanations,
viz. thorium and radium, have the power of exciting radio-
activity. Uranium and polonium, not giving off any ema-
nation, do not possess the power of exciting ‘radioactivi ity.

(2) The amount of excited radiation obtained from thorium

and radium compounds is directly proportional to the
amount of emanation present. For example, thoria gives
out far more emanation and produces far more excited
activity than thorium nitrate in the solid state. Thoria
and radium chloride, partly deemanated by strong heating,
lose their power of exciting activity in like ratio.

Phil, Maa. 8. 6. Vol. 5. No. 25. Jan. 1903. H.

98 Prof. Rutherford on Excited Radioactivity and

(3) Excited radioactivity can be produced on bodies if the
emanation and not the radioactive substance itself is
present. It can be produced at long distances from the
radioactive compound by blowing the emanation mixed
with air along tubes. In the case of radium, the emana-
tion, which has been introduced into a vessel by blowing
a current of air over the active substance, produces ex-
cited activity after a month’s interval, although the
radioactive substance itself has not been placed in the
neighbourhood. On the other hand, the power that a
thorium or radium compound has of producing excited
activity on a body near it is almost completely lost by
blowing over the compound a current of air which
removes the emanation as rapidly as it is formed.

The amount of emanation or excited activity has no direct
connexion with the radioactivity of the compound in its
neighbourhood, and cannot be ascribed to any action of the
“ straight line ’’ radiation in the gas through which it passes.
For example, deemanated thoria produces only a small
fraction of the amount of excited activity of an equal weight
of ordinary thoria although the amount of the straight line
radiation is not much affected by the process of deemanation.

§ 3. Method of Transmission of Hacited Activity.

The characteristic property of excited radioactivity is that
it can be confined to the cathode in a strong electric field.
It is probable, therefore, that the radioactivity is due to the
transport, in the electric field, of positively charged carriers
of some kind. Experiments were undertaken to test this
and to find the rate at which these carriers moved in an
electric field, in order to obtain a rough estimate of their
dimensions compared with a gaseous ion.

The method employed to determine this velocity is a modi-
fication of one already used in a determination of the velocity
of the negative ion, produced at the surface of a metal by
ultra-violet light*. It depended on the use of an alternating
electric field. By means of a revolving commutator, a direct
P. D. was commuted into an alternating P. D. of known
frequency. If such an alternating field is applied to two
parallel plates, between which a radioactive emanation is kept
uniformly distributed, equal amounts of excited activity are
pr oduced on each electrode. facut

If in series with an alternating P.D. +H) a battery is
placed of H.M.F. HE, less than H,, the positive carrier moves

#* Rutherford, Proc. Camb. Phil. Soc. 1897.

the Method of its Transmission. og

in a stronger electric field in one half alternation than in the
other. A carrier consequently moves over unequal distances
during the two half alternations, since the velocity of the
carrier 1s proportional to the strength of the electric field in
which it moves. It follows from this that the excited radio-
activity will be unequally distributed over the two electrodes.
If the frequency of alternation is sufficiently great, only the
positive carriers within a certain small distance of one plate
can be conveyed to it, and the rest, in the course of several
succeeding alternations, are carried to the other plate.

Suppose A and B (fig. 1) are two parallel plates to be

LMANAT/ONM
A

made radioactive. The emanation is supposed to be uniformly
distributed between them. When B is negatively charged
suppose the P. D. between the plates is E)—H,, when B is
positive the P. D. is Ky +H).
Let d=distance between the plates,
T=time of a half alternation,
p=ratio of the excited radioactivity on the plate B to
the sum of radioactivity on the plates A and B.
K=velocity of the positive carriers for unit-potential-
gradient
On the assumption that the electric field between the plates
is uniform; and that the velocity of the carrier is_pro-
portional to the electric field, the velocity of the positive
carrier towards B is
Ky—H,

t
pL ilatte a @

d
and in the course of the next half alternation
B+ Bh.
a

towards the plate A.
3 H 2

100 Prof. Rutherford on Excited Radioactinity and

The greatest distances * x}, 7. passed over by the positive
carrier during two succeeding half alternations is thus
given by

Hy— Hy ,, Ko+E
A= —— K.. £ anda
d d

Suppose the positive carriers are produced at a uniform
rate of g per second for unit distance between the plates.
The number of positive carriers which reach B during a half
alternation may be divided into two parts :

(1) One half of those carriers which are produced within

the distance x of the plate B. This number is equal to

Kei

sa,qT.

(2) All the carriers which are left within the distance 2,
from B at the end of the previous half alternation. The
number of these can be readily shown to be

Now all the rest of the carriers produced between A and
B during a complete alternation will reach the other plate A
in the course of succeeding alternations, provided no appre-
ciable recombination takes place. This must obviously be
the case, since the positive carriers travel further in a half
alternation towards A than they return towards B during the
next half alternation. The carriers thus move backwards
and forwards in the changing electric field, but on the whole
move towards the plate A.

The total number of positive carriers produced between the
plates during a complete alternation is 2dql. The ratio p of
the number which reach B to the total number produced is
thus given by

vy
1 sae
$491 +32, z gi

fe. Fy _ 12, x42,
a 2dgT Mie Sr ier ea
Substituting the value of xz, and zw, we obtain

go 2g Eye a
iE (iy i ee
In the experiments the values of E,, E,, d, and T were

varied, and the results obtained were in general agreement
with the above equation.

* In the equations that follow it is assumed that x, is less than the
distance between the plates. If 7,>d the equations have to be modified.

the Method of its Transmission. 101
§ 4. Velocity of Carriers of Thorium Eacited Activity.

For experiments on thorium emanation, a thick layer of
thoria was placed in a shallow copper vessel inside an ebonite
box 11 cms. square and 3 cms. deep, which was tightly waxed
down to a metal base. The thoria was completely covered
with two layers of filter-paper, which cut off most of the
direct radiation, but readily allowed the emanation to pass
through. The apparatus was rendered air-tight by a metal
lid, dipping into a mercury trough round the top of the
ebonite box. At the beginning of an experiment a square
sheet of aluminium foil was placed over the paper covering
the thoria, a zine plate on top of the ebonite box, and the lid
placed in position. This was done as quickly as possible,
and the alternating electric field was then applied.

The emanation rapidly diffused through the paper and thin
aluminium foil, and distributed itself between the plates in
the electric field. After an interval, varying in the experi-
ments from 20 to 90 minutes, the aluminium and zine plates
were removed and their radioactivity tested in the usual way
with the Dolezalek electrometer. The ratio of the excited radio-
activity on the two exposed plates was thus determined.
This ratio was found to be independent of the time the plates
were left before testing, as the radioactivity on each plate
decays at the same rate.

The amount of thoria used in these experiments varied
from 25 to 100 grammes. The amount of excited activity
in a given time varied with the amount of thoria, but the
ratio of the activity in the two plates was unaltered. For a
given voltage and time of alternation the value of p was
slightly greater when the lower plate was negative. This is
due to the unequal distribution of the emanation between the
plates ; for on account of the time taken in diffusion, the ema-
nation is more concentrated near the surface of the thoria.
The mean of the values of p with top plate negative and lower
plate negative was taken as the true value.

In the early experiments a two-part commutator driven by
a motor was used. In the later experiments fora more rapid
rate of alternation a four-part commutator was employed.

With this arrangement of apparatus a large number of
experiments were made in order to test the truth of the general
theory. Comparisons of the velocity of the carrier have
been made over a wide range of period of alternation and of
voltage, and for different distances between the plates. The
results obtained were in general agreement with the theory
put forward. When the voltage was kept constant, the value

102. ~—- Prof. Rutherford on Excited Radioactivity and

of p was found to decrease with increase in the number of
alternations per second. With a constant speed of alterna-
tion the value of p increased with the voltage.

When the value of p is small, the velocities of the carriers,
deduced from the equation, were found to be all too high,
and also inconsistent among themselves. There are several
disturbing factors which have a great influence on the value
of p when pis small, These factors are :—

(1) Recombination and diffusion of the carriers. Unless
the electric field is strong, the carriers recombine and diffuse
to the electrodes. With a weak electric field the excited
radioactivity is distributed on both the positive and negative
electrodes.

(2) Inequality of the electric field. In this simple theory we
have assumed that the potential-gradient between the plates
is uniform. This is far from being the case. The experi-
ments of Child and Zeleny have shown that there is always
a sudden drop of potential near the electrodes. The electric
field near the electrodes is consequentiy stronger than the
average. Tor this reason, when the carriers which reach
the plate B are only abstracted from within a short distance
of the plate, the value of p leads to too high a value of the
velocity.

(3) Initial velocity of the carrier. From some considera-
tions which will be developed later (see § 9), it seems probable
that the positive charge on the carrier is due to the expulsion
of a negatively-charged particle of some kind from the
neutral molecule. The positive carrier may thus have
enough initial velocity imparted to it to carry it some
distance against the electric field. This will result in a
distribution of some excited activity on the anode, even with
a strong field. It is difficult to obtain direct experimental
evidence on this point, but there seems little doubt that such
an effect is present.

In order to obtain consistent results, it was found necessary
to have a considerable difference between the strength of the
electric fields during the succeeding half alternations. If
the difference is small, the carriers take so long to reach the
plate A that recombination and diffusion of the ions become
important factors in determining the distribution of excited
activity. For the reasons we have explained above, it was
necessary to use fairly high voltages and correspondingly
rapid speed of alternation in the experiments.

The following tables are examples of some of the results
obtained for different voltages and distances between the
plates. Temperature 18°C. Air fairly dry.

the Method of tts Transmission. 103
Plates 1°30 em. apart.

E,+E,. peso peri: 2 K.

75 30 57 “lif 1°7
2 01 NT OFA 18,
229 t5O 57 "38 ee
300 200 Did, "44. ZA:

The value of K is given in cms. per sec. for a potential-
gradient of 1 volt per em.

For the last example, since the carrier travelled over a dis-
tance greater than 1°30 cm. during each half alternation, a
modified form of the equation was necessary to calculate the

velocity.
The value 1:6 cm. per second for 50 volts is too high for

the reasons explained above.

Plates 2 cms. apart.

E,+E,. pee. ae 0. K.
273 DAWG 44 Oil 1:47
300 200 53 "286 Loss

An average value of the velocity from a large number of
alternations for different distances, voltages, and speed of
alternations was about 7°3 cm. per sec. for atmospheric
pressure and temperature.

This velocity is not very different from the velocity of the
positive ion produced by Réntgen or Becquerel rays. The
most accurate determination of this velocity by Zeleny* gave
a value of 1°37 cm. per sec. for dry air.

§ 5. Increase of EHucited Radiations with Time.

In the course of these experiments a remarkable effect was
observed. It was found that a plate which has been exposed
a short time in the presence of thoria emanation, after being
removed, gradually increased in radioactive power for several
hours. The amount of increase varied with the time of
exposure to the emanation, but in short exposures it increased
to three or four times its initial value. For exposures of
several hours the effect is not so marked, and is difficult to
detect after a day’s exposure.

The following tables illustrate the results obtained.

* Phil. Trans. Roy. Soc. (1900).

104 ~~ Prof. Rutherford on Excited Radioactivity and

(1) Platinum wire, charged —110 volts, exposed 15
minutes ina cylinder containing thoria. First observation
five minutes after removal of wire from emanation

cylinder.
Time Movement of Electrometer in
in Minutes. scale-divs. per sec.
0 39
75 2°8
24 4-()
43 4-6
58 a2
(Ke) a9
99 6°5

In this case the activity had increased over three times in
99 minutes and had not reached its maximum value.

(2) Aluminium foil as cathode in parallel plate apparatus of
fig.1. Time of exposure 41 minutes. First observation
6 minutes after removal.

Time. Radicactivity.
0) 1
21 minutes. 16
ELT yes 13
DA. bs 20
GD) boss, Pan
eee 25
TAO ree maa)
ROO} jee Bw
130) -.55 2-9
22 hours. 1:0
AD 0-21

In this case, for the purpose of comparison, the initial value
of electrometer current is taken as unity. The activity
increases to nearly three times its initial value after an
interval of two hours, and then slowly decreases at the normal
rate, 2. ¢., it falls to half value in about 11 hours.

Similar results were obtained if the plate was made active
without the action of the electric field. The increase of
activity with time is independent of the nature of the elec-
trode, or of the concentration of the radioactive matter upon
it. It was not found possible to influence the rate of increase
of activity with time or the final maximum by heating the
wire to about a red heat.

With increase of time of exposure of the electrode in the
thorium emanation, the ratio of increase of activity after

—S =

the Method of tts Transmission. 105

removal decreases. For a long interval of exposure the activity
begins to decrease at once after removal. This result is to be
expected, for the activity of each portion of the radioactive
matter deposited increases with time for two or three hours,
and then diminishes. Consequently, after the electrode has
been exposed for about ten hours or more, the increase of
activity of the matter deposited in the last few hours does not
compensate for the decrease of activity of the radioactive
matter as a whole. This increase of activity with time
explains an irregularity in the curve of increase of excited
activity from thorium with time of exposure. It was pointed
out ina previous paper (Phil. Mag. February 1900, p. 178)
that, on the hypothesis of a uniform rate of deposit of radio-
active matter, the activity of which decreased in a G. P. with
the time, the curve of rise of excited activity with time of
exposure is the same as the curve of rise of an electric
eurrent in a circuit of constant self-inductance. It was
experimentally observed, however, that the rate of increase
for the tirst few hours was much smaller than would be
expected on this hypothesis. In the light of the present
results, the explanation of this effect is simple. The matter
deposited during the first few hours does not reach its maximum
activity for several hours, and the initial effect is consequently
much smaller than would be expected on the simple theory.
§ 6. Radium Hacited Radioactivity.

Experiments were made to determine the velocity of the
carriers responsible for the excited radioactivity of radium in
the same way as for thorium. The radium in my possession
gave out too little emanation at ordinary temperatures in the
solid state to enable me to use it in the apparatus in place of
thoria. The amount of emanation from radium can, however.
be increased several thousand times by heating the radium
compound below a red heat. A more convenient method of
obtaining a large amount of emanation is to dissolve a small
quantity of radium chloride in water. Radium in solution
gives off several hundred times more emanation than in the
solid state. If the solution is kept in a closed vessel the
emanation continually collects in the upper part of the vessel
It cau be transferred at any time to another vessel by bubbling
a slow current of air through the solution. The procedure
adopted in introducing the emanation into the apparatus was
as follows :—

A large amount of emanation was introduced into a
metal cylinder of about 3 litres capacity. The plates to be
tested were then placed in position in the apparatus of fig. 1,

106 Prof. Rutherford on Excited Radioactivity and

and the alternating E.M.F. applied. By means of side
tubes, the appar atus was put into connexion with the emana-
tion dl and a small fraction of the emanation introduced
into it by sending a slow current of air into the cylinder.
The tubes leading into the apparatus were then closed, and
the alternating E.M.I’. continued for an interval of 15 to 30
minutes. Before stopping the commutator, the emanation
was blown out of the apparatus by a slow current of air. The
plates were then removed, and the amount of activity on them
was compared by means of the electrometer. On account of
the initial rapid decay of the radiations, a difficulty arose in
comparing the amount of radiation on the two plates. As
shown in a previous paper*, the excited radiation from radium,
for short exposures, decr eases rapidly for the first 5 minutes
after removal, but about 15 minutes after removal reaches a
value which is maintained fairly constant for an interval of
about 10 minutes. It then decays to zero, falling to half
value in about 30 minutes. The comparison of the activity
on the two plates was made during this constant interval.
When experiments were made under the same conditions
as those for thorium, somewhat higher values of the velocity
of the carriers were obtained, and the numbers, for different
frequencies and voltages, differed considerably among them-
selves. These discrepancies were found to be due to the
fact that even in a strong electric field from 5 to 10 per
cent. of the total excited activity was distributed on the
anode. In this respect the activity excited by radium differs
from that of thorium. Consequently, the value of p would
be greater for the radium than for the thorium experiment,
under the same conditions, even if the carrier of excited
radioactivity travelled at fhe same rate in both cases.

§ 7. Distribution of Excited Activity on the Anode.

In order to throw more light on the cause of this distribu-
tion of excited activity on the anode, some experiments were
made with the apparatus shown in fig. 2 a.

The emanation vessel A consisted of a brass cylinder 25°5
ems. long and 8:30 cms. diameter. A long central brass rod
BCDH, diameter °518 cm., passed through an ebonite cork
at one end of the tube. The outside cylinder was connected
to one pole of a large battery, the other pole of which was
earthed. The central rod was connected to earth. The
emanation was introduced into the vessel by sending a slow
current of air through a radium chloride solution contained

* E, Rutherford and Miss Brooks, Phil. Mag. July 1902.

the Method of its Transmission. 107

in the Drechsel bottle F. The air passed through a tube
containing cotton-wool, and through a drying- -tube T of
calcium chloride. The central rod was made of three remov-

able parts BC, CD, DE, screwed together. After exposure

for a known time in the presence of the emanation the rod
was removed, and the activity on the portion CD, length 15
ems., determined by the electrometer in the cylindrical testing
vessel L, shown in fig. 26. By this means the excited

Fig 20.

TESTING CYLINOER

activity was determined on that portion of the rod where the
electric field was sensibly uniform.

In most of the experiments the emanation was introduced
into the vessel A a day or two before observations were taken.
This ensured a uniform distribution of the emanation through-
out the cylinder by the process of diffusion. If observations
were required soon after the introduction of the emanation,
the emanation was uniformly mixed with the air by means of
a stirrer not shown in the figure.

Some experiments were made with this apparatus on the
amount of excited activity on the central rod when positively
charged for different voltages. For the purpose of com-
parison, the results are expressed in terms of the percentage
amount on the same electrode exposed for the same time when
negatively charged with 300 volts between the electrodes.
The rod was exposed in the presence of the emanation for
15 minutes, then removed and a fresh rod introduced. In

108 Prof. Rutherford on Excited Radioaciivity and

the course of three or four hours’ work, the amount of excited
activity, obtained for a given time of exposure, diminished
about 20 per cent. This was partly due to the decay of the
radiating power of the emanation during the interval, and
partly to a slight escape of the emanation in removing and
replacing the central rod. By determining the ratio of
excited activity at the beginning and end of the experiments,
a correction was readily made for this diminution.

Table of distribution on anode, diameter 8°3 mms.

Voltage. Percentage.
— 300 100
+ 300 6
+150 6
+ 950 gy
+ 20 10

0 14

It will be seen from the table that the amount on electrode
with + 300 volts P.D.is 6 per cent. of amount on electrode with
—300 volts P.D. The percentage increases with diminution
of voltage, rising to 14 per cent. for zero voltage, when the
distribution is due to diffusion alone of the carriers to the
central electrode. In order to see how much of this amount
on the electrode was due to transmission by the electric field
and how much to diffusion, the experiments were repeated
with the central rod of ‘8 mm. diameter instead of 8°3 mms.

— 300 100
+300 4
+ 90 7

Now, with a central rod of only about 1/10 of the surface
area, it is obvious that the effect due to diffusion must be very
much reduced. We may thus conclude from these experi-
ments that a proportion of the excited radioactivity from
radium (about 5 per cent.) travels to the positive electrode
in an electric field, and the carrier must in consequence have
a negative charge.

A special experiment was made to determine the amount.
of radium excited activity on the anode with an apparatus
consisting of parallel plates. For this purpose the emanation
vessel of fig. 1 was used, with the plates 1°3 cm. apart. With
300 volts between tbe plates about 10 per cent. of the total
activity was confined to the anode. From the previous
experiments we have seen that about 5 per cent. reaches the

the Method of its Transmission. 109

anode in consequence of transmission by the electric field.
The remaining 9 per cent. must thus reach the electrode by
other agencies. With such a strong electric field, the effect
due to pure diffusion must be very small. It fhe seems
likely that some of the radioactive carriers have sufficient
initial velocity to carry them to the electrode against the
electric field.

§ 8. Velocity of the Carrier.
Some experiments were made on the velocity of the carrier
of excited radioactivity, using the concentric cylinders shown
in fig. 2a. If a@ and 6 are the radii of the internal rod and

the cylinder, the electric field X at a distance r from the
centre, for a P. D. of v volts between the cylinders, is given by

eo
b .

r loge
SG

Using the same notations and assumptions asin the case of
parallel plates, it can be shown that the velocity K of the
carrier of excited radioactivity is given by

seats Ob
oe E+E, (b° —a*) log.
~ Ey(Ey)—E,) T Si
The following table shows some of the results obtained for
different voltages and periods of alternation :—

Alternations ' Corrected = |
oe pee per sec. Ir value of p. _
205 308 ei BD “32 1:0 |
205 308 11:2 ‘D4 20 I-23 |
205 308 17-2 19 iS | 1-2
205 308 34 16 ?
385 580 18:3 30 Sh 16S)
385 580 47 16 ?

The values of the velocity of the carrier determined for
the uncorrected values of p in the above table vary much
among themselves. It will be seen, however, that the value
of p increases with the time of alternation and the voltage,
as we should expect from the elementary theory. It was not
found possible to reduce the observed value of p below about
‘16, whether the voltage was diminished or the frequency of
alternation increased. This is to be expected, for we have

10) Prof. Rutherford on Eacited Radioactivity and

previously shown that the amount of excited activity in the
central rod, when diffusion alone is acting, is *14 of the total;
for in cases where the carrier is only able to travel over a
small fraction of the distance between the electrodes during
a half alternation, only a small amount of the excited radio-
activity on the central rod is due to the deposit of positively
charged carriers by the electric field. The greater proportion
is due to the diffusion of carriers to the electrode and to the
carriers which are deposited when the central rod is the
anode. ‘The amount of this latter is, as we have shown,
about five per cent. of the total. It is difficult to make more
than a rough estimate of the amount of excited activity on
the electrode in the various cases. For these reasons the
corrected values of p in the table for the frequencies of 34
and 47 per second are probably not more than about one-
third of the observed value 16. |

In the above table a rough correction is made for some of
the values of p and the resulting velocity calculated.

It will be seen that the values of the velocity of the carrier
lie between 1°0 and 1°5 cm. per sec. for a potential-gradient
of 1 volt per em. ‘This is about the same range of values as
that obtained for the carrier of thorium excited radioctivity.

From the nature of the results itis not possible to definitely
decide whether the carriers of thorium and radium excited
activity travel at exactly the same speed. The results, how-
ever, indicate that the carriers in the two cases are not very
different in speed, and that consequently they do not differ
much in size.

We may conclude from these experiments that the greater
part of the excited radioactivity from both thorium and
radium compounds is due to the deposit of positively charged
carriers, produced from the emanations on the cathode, and
that these carriers travel at about the same rate as the positive
ion produced in the air by Réntgen rays.

When no electric field is acting excited radioactivity is
transferred by the diffusion of these carriers to the surface of
all bodies immersed in the emanation.

§ 9. Origin of the Carriers.

Before discussing the question ot the method of production
of these positive carriers which cause excited activity, a brief
vésumé is necessary of the physical properties of the ema-
nations from thorium and radium. In the first place the
emanations behave in all respects like radioactive gases of
high molecular weight. They do not carry with them any

the Method of its Transmission. pata

charge of electricity, and are consequently unaffected by the
presence of an electric field.

In my first paper on the thorium emanation (loc. c/t.) it
was pointed out that the particles constituting the emanation
certainly did not move with a velocity greater than ‘00001 cm.
per sec. for a gradient of 1 volt. per cm. The conclusion was
drawn that the emanation itself was initially uncharged. A
similar result is true for the emanation from radium ; for the
emanation still persists in a closed vessel after several weeks’
exposure in a strong electric field. For these reasons the
suggestion made by Becquerel*, that the emanations are
composed of positive ions directly emitted from radioactive
bodies, is untenable ; for if such were the case, the ions would
at once be swept to the electrodes by the electric field, and
would very rapidly disappear from the gas.

_ These emanations possess the property of ionizing the gas

and of producing from themselves positively charged carriers
which cause excited activity in bodies on which they are
deposited. This property lasts only a few minutes in the
case of the thorium emanation, and for several weeks for the
radium emanation.

Two hypotheses may be put forward to account for the
origin of these charged carriers :—

(1) The radioactive matter constituting the emanation con-
denses on the positive ions, produced in the gas by the
radiation, and is thus transferred to the cathode.

(2) The particles of the emanation possess the property of
expelling from themselves a negatively charged body of some
kind. ‘he particle would thus be left with a positive charge,
and would be carried to the cathode by the electric field.

It is not easy to decide definitely between these two hypo-
theses, but the evidence as a whole is strongly in favour of the
second.

In regard to (1) if might be supposed that the emanation
condensed more readily on the positive than on the negative
ion; on the principle that water and alcohol-vapour condense
more readily on the negative than on the positive ion. If
this were the case, it would be expected that the emanation
would be removed more rapidly if the number of ions were
increased in the gas through which the emanation was
distributed. There is no evidence that such an effect exists.
Ihave tried the experiment of passing the emanation through
a space strongly ionized by radium rays; but the amount of
excited activity in a given time on the cathode, placed in this

* Comptes Rendus, Dec. 9, 1901,

112 ~~ Prof. Rutherford on Excited Radioactivity and

space, was not appreciably altered. I have also tried expe-
riments to see if the radiation from the emanation was affected
by exposure in a strong electric field, but with negative
results. In order to test this, the thorium was placed in the
bottom of a small lead box, and covered with two layers of
paper to cut off the direct radiation. The top of the box was
tightly covered with a very thin layer of mica. This pre-
vented the escape of the emanation, but allowed the radiation
from the emanation to pass through and ionize the gas above
the vessel. The amount of this ionization outside the vessel
was unchanged if the emanation was exposed to a strong
electric field by charging insulated conductors placed inside
the vessel.

If the emanation is removed to the cathode in an electric
field by condensation on the ion, it is to be expected that it
would continue to radiate at the same rate on the electrode as
in the gas from which it is removed. On this view the
radiation from the cathode should rapidly decrease for the
first few minutes after removal from the emanation. Some
special experiments were tried to settle this point, but no
decrease was observed, although even a minute effect could
have been readily detected.

There is thus considerable indirect evidence against the
condensation hypothesis; and it has consequently been dis-
carded in favour of (2), which offers a satisfactory expla-
nation not only of the production of positive carriers, but
also of the origin of the radiation given out by the emanation
itself. On this view the emanation consists of matter in an un-
stable state, which undergoes further chemical change. The
change consists in the expulsion of a negative particle from
the neutral molecule. The residual portion of the molecule
retains a positive charge, and is carried at once to the cathode
in an electric field. This matter again undergoes chemical
change, giving rise to the phenomena of excited radioactivity.
The exper imental data in tavour of this view are best consi-
dered in the next section ($ 10) on the nature of the radiations.

It has been shown that the carriers of excited activity for
both thorium and radium travel at about the same rate as the
ions produced in the air by Réntgen rays. From data of
the Kinetic Theory of Gases it has been shown that the ion in
air is prooably lar, ge compared with the molecule of oxygen
or hydrogen. This has been explained by supposing that the
ion, immediately after its production, becomes the centre of a

cluster of molecules which move with it. On this view that part
of the emanation molecule which retains a positive charge im-
mediately becomes the nucleus of an aggregation of molecules

the Method of tts Transmission. eke

of the surrounding gas. The size of the cluster is probably
about the same for the positive ion, since the size is mainly
determined by the electric charge which is the same for
both. The velocities in an electric field are thus the same for
the carriers of excited activity and for the gaseous ion. Since
the size of the cluster is large compared with the original
nucleus, the velocities of the carriers of thorium and radium
excited activity would be about the same, even if the original
nuclei were of different masses.

§ 10. Nature of the Radiations.

In considering the question of the size of the body expelled
from the molecule of the emanation, and of the nature of the
radiation from the emanation, it is necessary to take into
account the nature of the emanations emitted from all the
known radioactive bodies; for there is no reason to suppose
that the processes which are taking place in the molecule of
the emanation are essentially different in character from those
occurring in the other radioactive bodies. It is known that
uranium, thorium, and radium emit two types of radiation.
One type is not appreciably deviable by a magnetic or an
electric field, and is very easily absorbed in matter. These will
be called the a rays. The others are deviable and more
penetrating in character, and will be called the @ rays. In
addition I have shown that thorium and radium emit some
rays nondeviable in character, but of very great penetrating
power. All of the radioactive substances including polonium
as well as “excited” bodies and the emanations give out these
a rays. Their power of ionizing the gas is very much greater
than for the other types of rays emitted; and it is probable
that the greater proportion of the energy radiated into the
gas is inthe form of a rays. Thea rays from different radio-
active substances, including the emanations of “ excited’
bodies, do not vary very much in penetrating power. The
“excited” radiations for thorium and radium are the most
penetrating in character and that of uranium the least.

It has been difficult to offer a satisfactory explanation of
the nature of these rays. I have previously shown as untenable
the view that they are secondary rays due to the emission of
Brays. Ihave been recently led, bya mass of indirect evidence,
to the view that the @ rays are in reality charged bodies pro-
jected with great velocity. The ionizing effect of the 1 rays is
due to the collision of the projected body with the molecules
of the gas, in the same way that the cathode 1 rays ionize the
gas in their path. Such a projected particle probably pro-
duces many thousand ions in its path before its velocity is

Phil. Mag. 8. 6. Vol. 5. No. 25. Jan. 1903. I

114 ~~ Prof. Ruthericrd on Excited Radioactivity and

reduced to the point below which it can no longer ionize the
gas. Strutt has put forward the view that the a rays were
positively charged bodies since the 8 rays emitted from the
same body carried a negative charge. This view has also been
advanced in a recent paper by Sir W. Crookes.

The evidence in favour of the projection nature of the
ayrays is so far all indirect in character, and is briefiy
summarized below:—_

(1) The absorption of the a rays in matter (like the 6 rays
which we know are projected particles) is approximately
proportional to the density of the material. It has been
shown that the absorption of uranium, thorium, and radium

rays is roughly proportional to the density for air and for:

aluminium.

(2) The absorption of the a rays by a given thickness of

matter increases rapidly with the thickness traversed.

T have found that this is a general property of the « radiations.

not only for the radioactive elements proper, but for the
radiations from the emanation and excited bodies. This is to

be expected if the rays consist of projected particles, but is.

difficult to explain if the radiations are eether-waves similar to
Rontgen rays.
(3) In the case of the emanations we have direct evidence

that a negatively charged particle * is projected. The radiation.

from the emanation is due to these projected particles which
ionize the gas in their path. This satisfactorily explains the
experimental observation that the amount of excited activity
is directly proportional to the amount of radiation from
the emanation. It also serves to explain the fact especially
noticeable in the experiments on the radium emanation, that
some of the carriers of excited activity have sufficient initial

velocity to move against the electric field. This velocity is.

due to the recoil consequent upon the projection of the charged
body.

it these rays are due to projected charged particles they
should possess the properties of the a rays of deflectability by
a magnetic and electric field.

No deviation of the a rays has so far been detected ina
strong magnetic field, but the experiments have not yet been

* T was at first inclined to suppose that the particle expelled from the

emanation was a negative electron, since it is known that both thorium
and radium compounds and bodies excited by them, emit some deviable.
rays. I have, however, made a close examination of the radiation from
the emanation by the electrical method, but was unable to detect the
presence of any penetrating deviable rays. If such deviable rays are
present, they certainly exist in far less proportion compared with the-
a rays than in the other radioactive substances.

7 =a

the Method of its Transmission 115

pushed to the necessary limit. The results, however, indicate
that if the rays are deflectable, the deviation is minute com-
pared with the 6 rays. This is to be expected if the mass of
the expelled particle is large compared with the electron.
If, for example, the projected body had a mass 10 times that
of the hydrogen atom, it would require a magnetic field about
10,000 times as strong to produce the same deviation as
for the electron moving with the same velocity. There is
evidence that large carriers moving with a high velocity are
produced in vacuum-tubes. W. Wien* has shown that the
“Canal Strahlen” of Goldstein are positively charged par-
ticles moving with high velocity. These rays are deviated
by a magnetic and electric field. When the vacuum-tube is

filled with hydrogen the ratio of the charge to the mass, <,

of these carriers is about 10*, showing that the carriers have
the same mass as the hydrogen atom. In an atmosphere of
oxygen the size of these carriers is considerably greater than
the hydrogen atom.

Itis possible that the electric charge on the expelled particle
may be different for different radioactive bodies under different
conditions. For the emanations of thorium and radium the
expelled particles are for the most part negative. It has
been shown that some of the radium carriers of excited activity
have a negative charge, showing that the expelled body is
positive. In addition, Dorn has shown that in a radium
solution the excited radioactivity is produced on the anode,
and not on the cathode. This shows that the carriers of
excited activity in solution have a negative charge, so that
the expelled body is positive in sign.

§ 11. Evidences of Chemical Change.

In previous papers by Mr. Soddy and myself, the view has
been put forward that radioactivity is an accompaniment of con-
tinuous chemical change. Taking, for example, thorium, which
has been worked out more thoroughly than the other radioactive
bodies, it has been shown that a chemical substance Th.X is
produced at a constant rate by the thorium compound. ‘This
Th.X undergoes further chemical change, one of the products
of which is the emanation. This emanation itself is not
stable, but expels from itself a negatively charged body.
The positively charged portion of the emanation is carried to
the electrodes, and this again undergoes further chemical
change, giving rise to the phenomenon of excited radioactivity.

* Drude’s Arnal. No. 6, p, 244 (1902).
Ea

116 Excited Radioactivity and its Transmission.

There is thus evidence of four distinct changes in each of
which the matter produced has distinct chemical properties.
For example, Th.X is soluble in ammonia, while thorium and
products of the later changes are not. The emanation is not
soluble in hydrochloric or sulphuric acid, unlike the matter
responsible for excited radioactivity. There is strong evidence
also that the chemical changes in the matter responsible for
excited radioactivity are complex in character. It has been
shown that the excited radiation in a body increases after
removal when the body is exposed for a short time in the
presence of the emanation. This effect is analogous to the
increase of radioactivity of Th.X for the first day after sepa-
ration, which has been shown to be due to the excited activity
produced in the matter constituting the Th.X.

“In order to account for the increase in radiating power
after removal, one must suppose that the matter which is
deposited from the thorium emanation gradually undergoes
a chemical change. The transformed matter undergoes a
secondary change, the time-rate of which is slower than the
primary, but which gives rise to greater radioactivity. From
data of § 5 half the matter has undergone change about 1 hour
after deposit, while in the secondary change the corresponding
time is about 11 hours.

Summary of fesults.

(1) Excited radioactivity produced by thorium and radium
compounds is due to the deposit of radioactive matter, which
is derived from the emanation given out by these bodies.

(2) Excited radioactivity is transmitted by positively
charged carriers, produced from the emanation, which travel
in an electric field with about the same velocity as the positive
ions produced in air by Réntgen rays. This velocity (about
1:3 cm. per sec. for 1 volt per cm.) is about the same for the
carriers of thorium and radium excited activity.

_ (3) These positively charged carriers are due to the ex-
pulsion of a negatively charged body from the melecule of
the emanation.

(4) Evidence is adduced for the view that the easily
absorbed and apparently nondeviable rays of radioactive
substance are due to the expulsion of charged bodies at a
high velocity. The rays are thus analogous to the Canal
Strahlen of Goldstein, which Wien has shown to be positively
charged bodies projected at a great speed.

In the case of the emanations the expelled particles are for
the most part negative in sign.

(5) In the case of radium about 5 per cent. of the carriers

On the Hysteresis Loss tn Iron. i bi BY

of excited activity are distributed on the anode in a strong
electric field.

(6) The excited radiations from thorium due to a short
exposure in the presence of the emanation increase in the
course of several hours after removal, to three or four times
their initial value.

(7) The emanations and the matter which gives rise to
excited activity are the result of a succession of chemical
changes occurring in radioactive matter. In thorium there
is evidence of at least four distinct chemical changes.

Macdonald Physics Building,

McGill University, Montreal.
July 29, 1902.

V. Effect of Temperature on the Hysteresis Loss in Iron.
By KR. L. Wits, 6.A.,° A.A.C.Se.1.,, 1851, Lehebition
Scholar, St. John’s College, Cambridge *.

T has been known for some years that for soft iron the
magnetic hysteresis, for a given range of magnetic force,
diminishes considerably as the temperature is raised. Kunz +
found that the curve showing the variation of hysteresis with
temperature for a specimen of soft iron was practically a
straight line, while the corresponding curves obtained by
Morris{ for a specimen of iron show that the fall of
hysteresis is much more rapid as the critical temperature is
approached than during the earlier stages of heating.

The present paper gives the results of experiments under-
taken at the suggestion of Professor J. J. Thomson, on the
effect of temperature upon the hysteresis in iron and a
tungsten alloy for which the effect of temperature on the
magnetic permeability has already been given §.

7 Method.
The method employed is that devised by Mr. G. F. C.

Searle ||, the energy dissipated in hysteresis being readily
determined by observing the “throw” produced in the
movable coil of a sensitive electrodynamometer. Most of the
apparatus used was kindly furnished me by Mr. Searle.

The movable coil of the electrodynamometer is connected
in series with the secondary coil wound round the specimen,

* Communicated by Prof. J. J. Thomson.

+ Electrotechnische Zeitschrift, 1894, p. 196.

t Phil. Mag. vol. xliv. pp. 218-254 (1897).

§ RK. L. Wills, Phil. Mag. vol. 1. pp. 1-21 (1900).

|| G. F. C. Searle, Proc. Camb. Soc. vol. ix. pp. 2-6 (1895).

118 Mr. R. L. Wills on the Effect of

the fixed coil of the electrodynamometer being connected in
series with the magnetizing coil.

The complete theory of the method will be found in the
Trans. Roy. Soc. * and thus it will be sufficient to give here
a brief outline of the theory applicable to the present |
experiments ; for convenience in reference the notation
employed by Searle and Bedford will be used here.

If the primary and secondary coils are wound closely upon
the specimen and if E be the voltage between the ends of
the primary coil, then

B=RO+NAIS, | 9 | ee
where © is the primary current, R the resistance of the
primary coil, A the sectional area and / the mean circum-
ference of the ring, and N the number of turns per unit of
length in the primary coil. 7

If c be the secondary current we may write

dB
0=Set+na—, 48, ee

where 8 is the resistance of the secondary circuit and n is the
total number of turns in the secondary coil.

Now of the work done by E in any time, part is spent in
increasing the magnetic energy of the system, and the rest is
dissipated in hysteresis and eddy-currents in the specimen
and in heating the wires of the primary coil and of the
secondary circuit.

When the specimen is subjected to a complete cycle of
magnetic changes, the magnetic energy on the whole is
unchanged and we have

{ECdt=Al(W +X) +{RC*dt + \Scadt,

where W and X represent the space-averages of the energy
dissipated per cub. cent. per cycle by hysteresis and eddy-
currents respectively. But from equation (1) ‘

i Cat = {Row +nalloD ax,

hence
AlCW +X) =naio® dt — (Sear
NZ nA? 2
= — Ccedt— 2 \(@) dt from (2).

agony F, C. Searle and T. G. Bedford, Phil. Trans. A, vol. 198, pp. 40-52

Temperature on the Hysteresis Loss in Iron. £19

When the whole change is completed in a short time \Cedt is
proportional to the angular momentum gained by the coil of
the dynamometer and this again to the “‘ throw” @.

By means of an earth-inductor placed in the secondary
circuit a known change P in the number of lines of magnetic
force passing through that circuit can be suddenly produced
while a constant current C’ is flowing through the primary.
If —@ be the “throw” of the movable coil and §8’ the
secondary resistance, then

—(Cedt : C'P/S’=0 : ¢.
Hence

Se NCRSve n Ae B
arn) NS “a

When the rate of variation of B is so small that dB/dt may
be taken as uniform over the section we may write
dX 2 Os (ee 2
at ts i)

where Q is a numerical constant depending on the geometrical
form of the section and o the specific resistance of the
material. Searle and Bedford shew that for a circular
section (=1/87=0-03979, and for a square section
We O05512.

Thus, finally we have

ee NOPS (24 S\\(@) ae

nAS! o at
_NOPS@ (Q, dBy: ,
=) eal et gi) tonal Se) ae zac, . (3)

if ¢ be neglected in comparison with C in the integral, then
dB/dH is a function of C but not of dC/dt. Hence for any
given value of C, the contribution to the integral due to the
increment dC is proportional to dC/dt.

Using a suitable reversing key we can, as Searle and
Bedford show, increase dC/dt in any ratio by increasing the
resistance of each of the two parts into which the primary
circuit is divided by the key in the same ratio, the battery
power being at the same time increased in the same ratio so
as to keep the maximum current constant.

Writing U for NC’PS@/nA8'¢, we then have
W=U-—(a+ SR poi cute Ph ea)

where a and 4 are constants.

120 Mr. R. L. Wills on the Effect of

The energy dissipated in hysteresis for any induction can
therefore be determined by making two measurements of U
for different values of R, E being adjusted so as to keep the
primary current constant.

The induction was measured by the ballistic method used
by Professor Ewing and Miss Klaassen *, and the temperature
was measured by a platinum wire as in the previous
experiments.

The general arrangement of the apparatus is shown in
fig. 1. Inthe key F, which causes a gradual reversal of the
current, ab is an arm of insulating material free to turn about
its centre over a circular ring consisting of metal strips e, d,
e, f, g, insulated from each other. Resistances v7 are placed
between the strips 7, g and ¢, d respectively.

The terminals of the battery circuit containing the small
variable resistance R, and the Weston amperemeter C are
connected to the ends of the arm ab which make sliding
contact with the strips. In the figure the arm is shown in
one of its extreme positions; as it is turned to the other
extreme position the current is first diminished by an amount
depending on the value of 7. When the end 6 rests on the
insulated strip ¢, the strips c and g are brought into contact
by means of the contact-piece attached to the end a of the
arm. As the arm is turned further, the current through the
magnetizing coil increases again but is reversed in direction,
and reaches its original maximum value when the end 6 rests
on the stripg. Before the contact-piece attached to the end a
of the arm leaves the strip g, the end 6 rests on the strip /;
it will thus be seen that the primary circuit is never broken
during the reversal of the current. A choking-coil L having
a very large coefficient of self-induction is inserted in the
primary circuit to prevent the current varying too rapidly.
The key M is a modification of an ordinary reversing-key,
and was used for taking cyclic B-H curves when desired.
The terminals e and & are connected together, and an adjust-
able resistance R, is inserted between the terminals / and &.
By suitably adjusting the resistance R, the magnetizing
current can be reversed in direction and reduced to any
value by a single motion of the rocker. |

The reversing-key N is connected to the key M in order
that when the resistance R, is in the circuit the current may
be reversed without altering its value.

The primary current flows through the fixed coils A of the
electrodynamometer and passes through the keys M, N to the

* Ewing ‘Magnetic Induction in Iron and other Metals,’ 8rd ed.
revised pp. 356-370.

Temperature on the Hysteresis Loss in Iron. 121

hha

ull

IQ}

Q
auqgauan
RON ON
PUI

a
ay

ee
iS I
y

T OM

CX eh
primary coil PC wound round the specimen. By means of the
two-way key Kg, either the movable coil B ot the electro-
dynamometer or the ballistic galvanometer G is connected in

if . . e o. N » .

series with the secondary coil SC of the specimen.

122 Mr. R. L. Wills on the Effect of

The ballistic galvanometer is standardized by means of
the solenoid D, the two-way key K, being so arranged that
the current passes through the primary of the solenoid instead
of the coil PC ; the secondary coil, wound on a tube inside the
solenoid, is connected in seriés with the secondary coil SC of the
_ specimen, and is kept continuously in the secondary circuit.

The electrodynamometer is standardized by suddenly turning
over an earth-inductor HI placed in the secondary circuit,
while a known current is passing through the primary
circuit, and observing the “throw” produced in the movable
coil B.

When measuring hysteresis the earth-inductor is replaced
by a coil of the same resistance as the earth-coil but wound
non-inductively.

The movable coil is quickly brought to rest by sending a
very small current through it, in the right direction, while »
the primary current is flowing through the fixed coils. This
is done by connecting one of its terminals to any point in a
closed circuit consisting of a Leclanché cell, a fairly high
resistance, and a piece of german-silver wire, and the other
terminal through a tapping-key to a suitable point in the
german-silver wire. The resistance R; is permanently con-
nected in series in the secondary circuit in order to reduce
the sensitiveness of the ballistic galvanometer or electro-
dynamometer when necessary.

If the maximum current be kept constant, but the resistance
of each of the parts into which the primary circuit is divided
by the key F increased in any ratio by increasing R, and R,
respectively, then dC/dé will be increased in the same ratio.
The main part of the variation in the primary resistance was
made by varying R,, the small resistance R, being used to
adjust the current to any definite value.

The secondary resistance S was varied from about 23 ohms
to 523 ohms, and the throws of the dynamometer coil for each
induction were, as nearly as could be read, inversely propor-
tional to the secondary resistance; the term )R/S in equation
(4) was therefore negligible in comparison with W-+aR.
We thus have

W=UeR 2... See

If, for each value of the maximum magnetizing force, we
measure Uj, Us, Us, the values of U when the voltages of
the battery in the primary circuit are H, 2H, and 3E
respectively, and the resistances of the primary circuit are

R, 2R, and 3R respectively, then
W = 7 OF Sal U; = ae STL ZU

Temperature on the Hysteresis Loss in Lron. 123

By this means we can ascertain how nearly equation (5) holds
for any particular experiment.

The results obtained for a specimen of wrought iron,
sectional area 1:56 sq. cm., for E=8, 16, and 24 volts
respectively are given in Table I., and are shown also in
fig. 2, the curve giving the values of the hysteresis loss being
marked A.

The resistance of the portion of the primary circuit between
a, b (fig. 1) containing the battery and ammeter was very small
compared with that of the rest of the circuit, so that no
appreciable error was introduced by not varying R, in any
definite manner. The values of W obtained by this means
were found to agree within 5 per cent. with the values
obtained by calculating from the areas of the cyclic B-H

curves.
JUN sien JU

a id 2 : aie xX
0.34| 194 | Bag) Teo | 88 4:5 43 — 4:4 4°4
/0°68 = 540 | 5 ae) 38°2 44°] 26°4 26°4 26-4 EY,
| 1-02, 1205 154 169 ee to15) | 139 NEY 138 47-0
Pon 2ear | .58) . §55°4 724 | 5146 524 519°3 201°8
1°70) 4629 | 1528 | 1640 1736 1416 | 1448 1432 | 304
2°04; 6107 | 2471 2702 2919 2240 2268 2254 | 665
| 2°38) 7139-38396 3714 4017 _ 3078 3108 3093 | 924
2-72! 8077 | 4242 4683 6124 | 8801 3801 3801 | 1323
3:06 8749 5159 5702 «| 6211 «| 4616 | 4684 © | 4650 1561
3-40; 9332 | 5940 6551 lia eh 161 5329 5331 5330 1831
01 10148 | 7297 8145 _ 8960 — 6449 6515 6482 2478

We have seen (equation 5) that in these experiments
U—W measures the eddy-current loss ; in this specimen the
eddy-current loss when H=24 volts amounts to more than
30 per cent. of the hysteresis loss. The values of the eddy-
current loss for different inductions for H = 24 volts are given
in the last column of Table [., and are shown graphically in
fig. 2 (Curve X.) (p. 124).

The values of U, W, and X are given in ergs per cub.
cent. per cycle, X being the space-average of the eddy-
current loss.

Keperiments on a Wrought-iron Ring.
Mr. W. M. Mordey* has shown that the increase in the
magnetic hysteresis which had been noticed in the iron cores
* Proc. Roy. Soc. vol. lvii. Jan. 1895, pp. 224-242.

124 Mr. R. L. Wills on the Hysteresis Loss in Iron.

of transformers is due to prolonged heating at comparatively
low temperatures. The experiments of Parshall* and Rogett+
show that this increase of hysteresis in iron does not always
take place, and that in specimens of inferior magnetic quality
the rise in hysteresis is much less than in the best specimens
of transformer iron.

Fig, 2.

LAGS PER CO. PER CYCLE

ae |
2000 4000 6000 8060 19000
B

In order to render the vaiues of the hysteresis at different
temperatures comparable, the specimen, which when annealed
was of inferior magnetic quality, was first heated to about
800° C. and allowed to cool rapidly. In this condition the
values of the hysteresis did not sensibly increase by prolonged
exposure to any temperature.

he specimen having been demagnetized by reversals
values of U, for various ‘inductions were first obtained, using
a battery of 8 volts, and afterwards a corresponding series of
readings for U, was taken for the same magnetic forces
using a battery of 16 volts. From these two sets of readings
the hyster esis losses for different values of the maximum in-
duction were found from the formula W=2U,—U, as
described above. The results for different temperatures are
recorded in Table II., and are shown graphically in fig. 3
(p. 126).

Morris{ has investigated the effect of temperature on the
hysteresis loss of specimens of soft iron for a range of in-

eo
duction of +4550; his curves giving the values of the

* Minutes Proc. Inst. C. E. vol. exxvi. p. 244 (1896).
+ Proc. Roy. Soe. vol. lxiii. pp. 258-267 (1898).
{¢ Phil: Mag. vol. xliy. pp. 213-254 (1897).

ot. Ga

TABLE II...

| Temp. 620° C.

Temp. 15° C. Temp. 202° C. Temp. 331° C.
erway ace a
Hi. B. Wie =| GEL: B. We ee iB: WwW
0-34 | 194) 44 | 034 | 266 | 43 | 0:34 | 368] 65
0638 | 540 26-4 068 803 | 504 | 0-68 | 1186 | 763
1-02 | 1205 | 188 | 1-02 | 2085 | 282 | 0-88 | 2072 | 22:0
| 1:36 | 2657 | 519 | 1:36 | 4058 | 836 | 1-09 | 3391 | 522
“Ter 4629 1432 1-70 | 5664 | 1484 | 1:22 | 4383 |. 771
2:04 | 6107 | 2254 | 2:04 | 6895 | 2165 | 1:36 | 5072 | 1044
2-38 | 7139 | 3093 | 2:38 | 7929 | 2703 | 1-70 | 6648 | 1648
2-72 | 8077 | 3801 | 2°72 | 8668 | 3141 | 2-04 | 7683 | 2151
3:06 | 8749 4649 | 340 | 9669 | 3923 2-72 | 8869 | 2802
3-40 | 9332 | 5330 Ep | Be tO GONIs | aa00

401 10148 6482 |

Temp. 402°C. | Temp. 460° C. Temp. 550° C,
Ee B. Wo |. 18 We a He kB. | Ww.
0:34 | 451 | 86 | 034 | 610 | 13-0 |.9-27 | @22 | 13-0
0-54 | 1012 | 50-4 | 0-48 | 1239 | 67-7 | 0-41 | 1792 | 102
0-68 | 1730 | . 1384 | O61 | 2379 | 186 | 0-54 | 3818 | 344
0-82 | 2510 ; 298 | 0°75 | 3604 | 407 | 0-68 | 5023 | 601
1:02 | 4088 | 687 | 0°95 | 5073 | 753 | 0-85 |. 6156 | 827
1-19 | 5073 | 873 | 1:16 | 6205 | 1036 | 1-02 | 6895 | 1036
1:36 | 5811 | 1162 | 1:36 | 7092 | 1295 | 1-36 .| 7979 | 1279
1:70 | 741 | 1609 | 1°70 | 8028 | 1530 | 9-04 | 8869 | 1546
2-04 | 8077 | 1924 | 2:04 | 8752 | 1769 | 9-72 | 9919 | 1782
2-72, | 9102 | 2434 | 2°72 | 9569 | 2094 | ~
340 | 9978 | 2787 | 3°40 |10153 | 2335

Temp. 678° C. | Temp. 730° C.

| Ee B. W.

Oi | LIS4 36
0-34 | 2565 | 178
0-41 | 3471 | 252
O51 | 4580 | 391
068 | 5861 | 633
0857) 6747 } 799) |
OZ. | 7240 929
1°36 | 8225 | 1075
204° | 8928 | 1279
2°72 | 9453 | 13889
3°40 | 9803 | 1452

Hi. B. W. H. B. W.
Olt | 4644 43 | 0186) 599 | 13-0
0-20 | 1256 | 446 | 0-204] 1536 60°6
O27 | 2565 | 145. |-0:27 | 2843 | 151
0-34 | 3631 | 243 | 0°34.) 3845 | 241
0-41 | 4285 | 320 | 0-41 | 4539 | 312
O54 | 5565 | 447 | 0:54 | 5565 402
0°68 | 6255 | 527 | 0-68 | 6304 497
1-02 | 7240 | 651 | 1-02 | 7190 | 614
1-36 | 7929 | 730 | 1-70 | 8126 664
204 | 8569 | 785 | 2:72 | 8717 | 755

| Temp. 748° C.

Temp. 768° C.

H. Be W.
0186! 844 ! 17-4
0-204! 2194 | 96-0
0-27 | 3311 | 175
0-34 | 4165 | 245
0°54 | 5713 | 339
1:22 | 6895 | 504
2°04 | 7838 | 529

19658

iio] ae |
|
Ga Z00.) allt |
0:136| 1605) 41 |
0:204| 2243 | 86 |
0°34 | 3685 | 142
068 | 3845 | 169
1:36 | 4058 | 186

126 Mr. R. L. Wills on the Effect of

hysteresis at different temperatures show that as the critical

temperature is approached the hysteresis falls very rapidly.
Fig. 3,

7000

10000

ia’)
oT
or
(=)

Hy sTeResis Loss IN ERGS PER CC FER CYCLE
G
oO
oO

S007 > 00 Ne i ; 800°
TEMPERATURES IN DEGREES CENT:- Criticaé
Lemp -

The corresponding curves which I obtained for maximum
inductions of +6000 and +4000 are given in fig. 4. An
induction of 6000 could not be obtained when the tempera-
ture had risen above about 750° C., but an induction of 4000

Temperature on the Hysteresis Loss in Iron, 127

eould be reached even when the temperature was only a few
degrees below the critical temperature, which in this speci-
men is about 776° C,

It will be noticed that the fall in hysteresis with rise of
temperature decreases as the critical temperature is ap-
proached. This is more noticeable in the case of the
tungsten alloy, the corresponding curves for which are given
in. fig. 9,

Searle and Bedford* have studied the effect of strain on
the hysteresis loss of iron, and have drawn curves showing
the variation of hysteresis with induction for constant ranges
of magnetic force. Their curves for any value of H show
that through a considerable range of straining the hysteresis
is a linear function of the induction. In the case of torsion
the hysteresis for this part of the curve is given by
W=caHB—1, where a and } are constants; for a specimen
of soft iron they found that a=0°35, b=600, and for a steel
rod 6=0.

Corresponding curves can be obtained from the data given
in Wable I)., the hysteresis and induction being varied by
heating. Fig. 5 gives three such curves for values of H.

Fig. 5.

N
oa
oO

MWYSTERE SIS IN ERGS PER CC. PER CYCLE.

4000 6000 8000 —
B

of 0°68, 1:02, and 1°36 c.4.s. respectively. It will be seen
that for values of B between 1800 and 5000 the points for
each curve lie on a straight line, and that these lines, when

* Phil, Trans. A. vol. excvili. pp. 89-90 (1902).

128 Mr. R. L. Wills on the Hifect of

produced, pass through the same point )=—100 on the
vertical axis. Within this range of induction, therefore, we
have W=/(H)B—6b. <As near as can be determined
W =0'182H#B—100.

For values of B below about 1800 the values of W are
larger than those given by the equation. As the induction
is increased beyond 5000 the hysteresis rises less rapidly to a
maximum value and then decreases. This is in complete
accordance with the experiments of Searle and Bedford, in
which the induction is varied by straining. In their experi-
ments, however, it was impracticable to continue the curve
much beyond the point of maximum hysteresis. When the
induction is varied by heating the curve may be traced until ©
the critical temperature is reached. Tor low fields we thus
get a closed curve, as shown in fig. 5, Curve I.

From the following table, which is obtained from Table II.
by drawing curves showing the variation in hysteresis with
temperature for constant fields, we see that the smaller the
magnetic force the higher the temperature at which the point
of maximum hysteresis occurs.

| H
He (ie Memperature for 4) || gk. Temperature for
| maximum hysteresis. | maximum hysteresis. |
0°34 705° C. 1°36 | 480° C.
| 0°68 10° Be 1-70 309 ,,
| 1:02 565 ,, ‘| 1°90 290) 75;
|

Experiments on the relation between temperature and
magnetizing force in the magnetization of iron have been
described in a previous paper*, where a curve is given
showing the magnetizing force corresponding to the maximum
permeability for different temperatures. A curve very similar
to this is obtained by plotting magnetic force as ordinate,
and the temperature at which the maximum hysteresis is
reached as abscissa, the temperature giving the maximum
hysteresis for any magnetic force being, as near as can be
determined, the same as that at which the maximum per-
meability occurs for the corresponding magnetizing force.

“ Ageing ”’ of Iron.
The “ageing” of iron by continued heating has been
already referred to. Mordeyt has examined the effect for

* R.L. Wills, Phil. Mag. vol. 1. pp. 11-14, July 1900.
+ Proc. Roy. Soe. vol. lvii. pp. 224-244, Jan. 1895.

Temperature on the FLysteresis Loss in Iron. 129

ordinary temperatures, but the later experiments of Roget*
deal with temperatures ranging from 50° C. to 700° C. In
these experiments the specimens were, however, removed
from the oven, and the tests then made at ordinary atmo-
spheric temperature. It appeared desirable to examine the
effects produced by prolonged heating when the temperature
is maintained constant and the specimen is not cooled for the
hysteresis measurement.

Roget continued the heating at the lower temperatures for
about a month and found that below 135° C. the hysteresis,
for an induction of 4000, during this time increased, at first
rapidly, but more and more slowly as time went on. For
higher temperatures the hysteresis for the given induction
reached a maximum value after a time depending on the
temperatures. Then, as the heating was continued, the
hysteresis fell, the rate of fall being greater for high than
for low temperatures.

In the present series of experiments the specimen was first
annealed and then the hysteresis for different ranges of in-
duction measured at intervals, while the temperature was

kept as nearly constant as was practicable.
The curves II. III. IV. (fig. 6) show the results of tests

Fig. 6.

PIVSTERESIS (N ERGS PEP CC. PER CYCLE

2000 4000 6000 8000 10090
8
made at a temperature of 165° C., after continued heating
for 16, 41, and 84 hours respectively ; the curve I. gives the
initial values of the hysteresis at the same temperature. For
longer periods of heating at this temperature the hysteresis
remained practically constant. After this constant condition
was reached by prolonged exposure to any temperature, the
hysteresis measured at that temperature was practically the
same as its value after the specimen had been cooled to

* Thid. vol. Ixiii. pp. 258-267 (1898), and vol. lxiv. pp. 150-156 (1898).
Phil. Mag. 8. 6. Vol. 5. No. 25. Jan. 1903. K

130 Mr. R. L. Wills on the Eqgfect of

the ordinary temperature of the atmosphere. Reannealing
completely restores the iron to its original condition.
Fig. 7 shows the variation of the hysteresis with time by

Higa.

Oo
(=)
o>}
oO

! e RS) 4 5 6 7.

TIME (N OAYS.

prolonged heating at 165° ©. for an induction of 5000. It
will be noticed that the hysteresis increases rapidly at first,
reaching a maximum value after about four days. Then it
decreases slightly to a constant value.

2000

1000

HWysTeREsIS IN ERGS PER CC PEP CYCLE

Haperiments on a Tungsten Alloy.

The rate of change in the permeability of iron as the
temperature approaches very near to the critical temperature
is so great that, throughout a range of several degrees in
this region, only approximate values of the hysteresis could
be obtained. Moreover, at such high temperatures the iron
is in sucha critical state that it was found that the process of
demagnetizing by reversals does not entirely wipe out all the
effects of previous magnetism, although the residual effect is
only noticeable in extremely weak fields.

In the case of a specimen containing 4° per cent. tungsten
the passage from the magnetic to the non-magnetic condition
is much more gradual, and the demagnetizing process, even
at the highest temperatures, removed all trace of residual
magnetism. The variation of hysteresis loss with temperature
in the neighbourhood of the critical temperature can there-
fore be much more satisfactorily examined with this —
than with iron.

The results obtained at different temperatures are given in
Table III., and hysteresis-induction curves plotted in fig. 8
(p. 182). From these curves the hysteresis-temperature curves
shown in fig. 9 have been obtained ; the scale of ordinates given
applies to the curve for B= 6000, the curve for B=2000 is
drawn to a scale five times as large. It will be seen that as

Temperature on the Hysteresis Loss in Iron. 131

TABLE ITI.

Temp. 15°C. | Temp. 200°C. | Temp. 256°C.

| |

ee Gens We) H. | ). Bae Wee ete te Ba |W.

797 | 1152; 293 | 6388 | 1176 | 436 | 5°58 | 13842 | 500
10°35 3521 5008 | 877 | 3854 | 5490 | 7-97 | 4826 | 6373
11:96 5524 10594 | 10°36 | 6137 |10939 | 10°36 | 7868 |13495
14:35 8602 |21021 | 15°15 | 9651 [22391 | 15:15 (10018 20900
16:74 10333 30033 |

|
| |

|
|
|
|

Temp. 315° C. Temp. 364°C. | Temp. 412°C.

Pee Wk oe Be em | Bs | Ww:

4-78 | 1433 | 639 | 3:98 | 13875 | 376 | 3:19 | 1408 | 300
677 4674 | S077 | 5°58 | 4431 | 3998 | 4°78 | 4674 | 3585
8-77 | 7343 |10806 | 678 | 6661 | 7485 | 6:38 | 7291 | 7233
13-55 | 9965 16991 | 9°57 | 9021 |12078 | 11:16 | 9913 |12411

| Temp. 472°C. | Temp. 543°C. | Temp. 604°C.

mm | 8. eae | Ei yuilaniare OPE Bi || WV
| | | —— _ -— | —— | _ —

2-47 | 1276 | 181 | 1:99 | 1500} 178 | 1-196) 1458 92
3°98 | 4917 | 2917 | 2°79 | 4992 | 2179 | 1-99 | 4219 | 1029
5:18 | 7081 | 53872 | 3:59 | 6556 | 3464 | 3:19 | 6923 | 2795
7-97 | 9179 | 8676 | 7-17-| 9126 | 6830 | 5-98 | 8235 | 3761

Temp. 648° C. Temp. 670° C.

Eee eB eiel aNVcwebh—he B eNie

| 1-036 1425 | 69) 318 | 1359 | 103 |
Pleo) 4128 | 866 | 7-97 | 1873 | 129")

| 6°38 | 5927 | 1730 |

the temperature is raised the rate of fall of hysteresis in-
creases , reaching a maximum at about 350°C. ‘Then, as the
temperature is increased, the hysteresis decreases less rapidly.
The curve for B=2000 shows that the rate of fall of
hysteresis continues to decrease even when a temperature of
670° C. is reached, which is only about 10° C. below the
critical temperature.

Hysteresis-induction curves for constant magnetic forces
corresponding to those given in fig. 10 (p. 133 ) for iron, can be
obtained from the results given in Table ITI. For each
magnetic force the values of B at the different temperatures

K 2

132 Mr. R. L. Wills on the Lifect of

were obtained from the B—H curves and the corresponding
values of the hysteresis found from fig. 8.

Fig. 8.
30000

I5C
| i
25000

= as)

o1 (as)

oS oO

Oo Oo

oO ie)

inst es)
Sal (SI

° (oy oO
io)

IY STERESIS 1 LAGS PEP CC. PEP CYCLE

“2000 + 4000 3 6000-8000 10000

12500

10000

1500

FYvSTERES/S (WN ERGS PEP CC PER CYCLE

2500

0c ° 200 300° 400° 500° 600° 700°
TEMPERATURE .1N DEGREES CENTIGRADE.
Two of these curves for H=5-98 and 7:97 c.G.s. respec-
tively are shown in fig. 10. It will be seen that throughout
a considerable range of induction the hysteresis is a linear

PO gh a i

Temperature on the Hysteresis Loss in Iron. 133

function of the induction. As in the case of iron, the
hysteresis losses, for very small inductions, are larger than
those given by ane equation, and as the induction increases
beyond about 6000 the hysteresis increases less rapidly to a

Fig. 10.

10000

8000

6000

4000

HYSTERESIS IN ERGS PER CC PER CYCLE

%
(e)
o
°

v7 2000 4000 6000 8000 10000!

maximum value. Then, as the temperature is raised, the
hysteresis falls while the induction is still increasing.
Finally, the hysteresis and induction both decrease very
rapidly. For the straight part of the curve the equation
giving the hysteresis as near as can be determined is
WW = SAH SB — 1000. The smaller the magnetic force the
higher the temperature at which the maximum hysteresis
occurs ; and, as in the case of iron, this temperature for any
magnetic force is practically the same as that giving the
maximum permeability w ith the corresponding magnetic

force.

In conclusion I wish to express my thanks to Professor
J. J. Thomson for useful suggestions and kindly interest
during the progress of the work, and to Mr. G. F. C. Searle
for help j in the preliminary experiments.

Cavendish Laboratory, Cambridge.

A | me

VI. On the Conditions necessary for Equipartition of Energy.
(Note on Mr. Jeans’s Paper, Phil. Mag. November 1902.)
Bye EH, BURBURY,, f.isSeo

R. JEANS’S conclusions are in substantial agreement

with mine, as explained in this Magazine for December

1900, so far as regards the nature of the required conditions.

On the question whether these conditions exist in any natural
system, there is perhaps difference of opinion.

Mr. Jeans deals, as.I also dealt, with two supposed proofs
of the law:—(1) that given by Lord Rayleigh interpreting
Maxwell in this Magazine for January 1900; (2) the proof
given by Boltzmann in the Vorlesungen iiber Gas Theorie.
As both profess to prove the truth of the law, the personal
authority in favour of it is at first sight overwhelming. H,
however, we find on examination that the two proofs are
inconsistent with each other, the authority for the law is
not the sum, but the difference of two very great magnitudes.

Rayleigh supposes a natural system defined by coordinates
and momenta 91-.- Qn, P1+++ Pn, Which is supposed to move
under its own internal forces unaffected by any other body,
and therefore to have constant total energy E. With that
constant energy it passes in cycle through the phases ¢ .. . d;-
Mr. Jeans prefers to conceive the system as a “point” ina
space of 6n dimensions. Next we suppose a great number of
systems similar in constitution to the first, and each passing
in cycle through the same phases ¢,... d, unaffected by any
body external to itself. In that ensemble of systems, all
having the same energy H, and passing in cycle through the
same series of phases, the number of systems in any one of
the phases ¢,...¢, at any instant is equal to the number at
the same instant in any other of the phases ¢,...¢,. This
is what Willard Gibbs proves in ‘ Principles of Statistical
Mechanics,’ Chapter I.

If ¢,...¢, include all possible phases in which the system
can be with energy E, the law of equipartition follows.
But there are two objections to this result, one namely
that according to Mr. Jeans, with whom I agree, no such
system ‘exists or can exist in nature, and the other that the
motion assumed is cyclic and reversible ; whereas Boltzmann
appears to me to prove (if only his fundamental assumption be
admitted) that the motion in which energy is equally par-
titioned is irreversible. The two great authorities are thus
inconsistent with each other. Ifthe phases ¢,...¢, through

* Communicated by the Author.

Conditions necessary for Hquipartition of Energy. 135

which each system passes do not include all phases consistent
with energy EH, the law of equipartition is not proved by this
method at all.

We come then to Boltzmann’s proof. Here Mr. Jeans
begins by saying “‘we must make Boltzmann’s assumption
that the gas is in a ‘ molekular-ungeordnet’ state.”” I do not
see the use of making it unless we can reason from it, and
that we cannot do till we know what it means. It is possible
to believe what we do not understand. It is not possible to
reason about what we do not understand. Now Boltzmann
gives us no adequate explanation of ‘‘ molekular-ungeordnet.”
Nor does Mr. Jeans. Boltzmann makes no use of the assump-
tion in argument. Nor does Mr. Jeans. Unless, indeed,
the very definite assumption which they both (as I think)
make, and which is stated below, is to be taken as the inter-
pretation of “ molekular-ungeordnet.” Boltzmann assumes,
namely, the independence of the molecular motions. If
FdUdVdW be the chance that molecule M shall have velo-
cities U...U+dU &e., and fdudvdw the chance that molecule
m shall have velocities u...u+du &e.; then he assumes that
the chance of the two events happening is F/dU...dw. In
other words, the chances are independent at every instant,
and however near M and m be to each other. It is assumed,
indeed, only when they are very near to each other, namely,
at the point of an encounter. It is right to say that the
assumption may be qualified as relating only to molecules
approaching encounter. The condition thus assumed I call
Condition A.

I understand Mr. Jeans to make precisely the same assump-
tion in his equation (18), using pp! as Boltzmann uses F'/.

If that assumption be made, the law of equipartition follows
from it without any use, or any further use, of “ molekular
ungeordnet.”

If that assumption be, as I maintain, untrue, the product F,
cannot be used as Boltzmann uses it, and the reasoning fails

ro)
notwithstanding the. ‘* molekular-ungeordnet ”’ hypothesis.

I think therefore that the one sufticient and necessary
condition for equipartition of energy is that Condition A shall
exist at every instant ; neither more nor less than this, nor any
different thing.

I have said that Mr. Jeans’s proof rests on the same
assumption as Boltzmann’s; and must therefore, like Boltz-
mann’s, stand or fall with the truth of that assumption. It
may nevertheless be that a new proof founded on the same
assumption is valuable.

[so

VII. Note on the Theory of the Fortniahtly Tide.
By Lord RayueieH, O.1., FRS*

me adequate calculation & priori of the tide of fortnightly
period—that which depends upon the moon’s. motion
in declination— would be of great interest as affording the
means, by comparison with observation, of determining the
extent to which the solid earth yields to the tide. -generating
force. On the assumption that the fortnightly tide over an
absolutely rigid earth would be sensibly equal to its ‘‘ equi-
librium value,’ Prof. G. Darwin T has estimated that the
actual rigidity must be at least as great as that of steel, in
accordance with the earlier surmises of Lord Kelvin.

But is an “equilibrium theory’ adequate? The known
properties of a system vibrating about a configuration of
thoroughly stable equilibrium would certainly suggest an
affirmative answer, when it is considered that a fortnight is
a long period in comparison with those of the more obvious
free oscillations. It is to be remembered, however, that a
tidally undisturbed sea is not in equilibrium, and that in
virtue of the rotation of the earth the tides are really oscil-
lations about a condition of steady motion. In Laplace’s
theory the rotation of the earth is taken fully into account,
but the sea must be supposed to cover the entire globe, or at
any rate to be bounded only by coasts running all round the
globe along parallels of latitude. The resulting differential
equation was not solved by Laplace, who contented himself
with remarking that in virtue of friction the solution for the
case of fortnightly and (still more) semi-annual tides could
not differ much from the “ equilibrium values.”

The sufficiency of Laplace’s argument has been questioned,
and apparently with reason, by Darwin ay ho accordingly
resumed Laplace’s differential equation in which frictional
forces are neglected. Taking the case of an ocean of uni-
form depth completely covering the globe and following the
indications of ae Kelvin §, he arrives at a complete ev valu-
ation of Laplace’s “Oscillation of the First Species.” A
summary of hee in’s work has been given by Lamb || from
which the following extracts are taken. The equilibrium

* Communicated by the Author.

+ Thomson & Tait’s ‘ Natural Philosophy,’ 2nd ed. vol. 3. pt. ix. p. 460
(1883).

t Proceedings of the Royal Society, vol. xli. p. 357 (1886).

§ Phil. Mag. vol. 1. p. 280 (1875).

| Hydrodynamics, $210, Cambridge, 1895.

On the Theory of the Fortnightly Tide. 137
value of the fortnightly tide being
FaH/a—
the actual tide for a depth of 7260 feet is found to be
¢/H' =:1515 — 1:0000 p? +1°5153 w* —1:2120 p®
—*2076 w +°0516 w?—:0097 w+ 0018 u1®—-0002 pS,
whence at the poles (u= +1)
¢=— 2H’x 154,
and at the equator (w=0)
¢=FH'x -455.
Again, for a depth of 29040 feet, we get
€/H'=:2359—1:000 w? + °5898 put
—+1623 w® +0258 w®—-0026 wu +-0002 pn,
making at the poles
C= —#H’x 470,

and at the equator
G— nee iO oe

It appears that with such oceans as we have to deal with
the tide thus calculated is less than half its equilibrium
amount.

The large discrepancy here exhibited leads Darwin to
doubt whether “it will ever be possible to evaluate the
effective rigidity of the earth’s mass by means of tidal
observations.”

From the point of view of general mechanical theory, the
question at once arises as to what is the meaning of this con-
siderable deviation of a long-period oscillation from its
equilibrium value? A satisfactory answer has been provided
by Lamb*; and I propose to consider the question further
from this point of view in order to estimate if possible how
far an equilibrium theory may apply to the fortnightly tides
ef the actual ocean.

The tidal oscillations are included in the general equations
of small vibrations, provided that we retain in the latter the
so-called gyrostatic terms. By a suitable choice of coordi-
nates, as in the usual theory of normal coordinates, these

* Hydrodynamics, §§ 196, 198, 207.

138 Lord Rayleigh on the

equations may be reduced to the form

HAN + By 9ot+Bisgst- - -=Q:, ]
Ae Gat C2 Jot Ba 1 + Bos q3+. - OF L (1)
3 73+ C3 93+ Ba G1 + B32 G2 =P ie Leas :

in which

From these we may fall back upon the case of small oscil-
lations about stable equilibrium by omitting the terms in P ;
but in general tidal theory these terms are to be retained.
If the oscillations are free, the quantities Q, representing
impressed forces, are to be omitted.

If the coefficients 8 are small, an approximate theory of
the free vibrations may be developed on the lines of ‘ Theory
of Sound,’ § 102, where there are supposed to be small dissi-
pative (but no rotatory) terms. For example, the frequencies
are unaltered if we neglect the squares of the @’s. Further,
the next approximation shows that the frequency of the
slowest vibration is diminished by the operation of the (’s ;
or more generally that the effect of the 6’s is to cause the
values of the various frequencies to repel one another.

To investigate forced vibrations of given period we are to
assume that all the variables are proportional to ¢’*, where o
is real. If the period is very long, o is correspondingly
small, and the terms in g and g diminish generally in impor-
tance relatively to the terms in g. In the limit the latter
terms alone survive, and we get

m= Qs/a, g2=Qo/ce, &0.)) 5) sae (3)

which are the “equilibrium values.” But, as Prof. Lamb
has shown, exceptions may arise when one or more of the
cs vanish. This state of things implies the possibility of
steady motions of disturbance in the absence of impressed
forces. For example, if c.==0, we have as a solution,
g2= constant, with

= — Piz ¥2/¢1, I3= — B32 J2/¢35 &e.

In illustration Prof. Lamb considers the case of two
degrees of freedom, for which the general equations are

a 1+%%1+B2=Q:, ; (4)
Az G2 + C2 92—Bqi=Qe;

Theory of the Fortnightly Tide. 139

supposing that ¢,=0 and also that Q,=0, while Q, remain-
ing finite is proportional to e’7*, as usual. We find

ye ae , By eC A A
2 Ge(¢,— a0") + B” 42 G9(C, — a0") Ts i (4)

so that in the case of a disturbance of very long period when
o approaches zero,

Since ag is positive, g, 1s less than its equilibrium value ; and
it is accompanied by a motion of type qs, although there is
no extraneous force of the latter type.

It is clear then that in cases where a steady motion of
disturbance is possible the outcome of an extraneous force
of long period may differ greatly from what the equilibrium
theory would suggest. It may, however, be remarked that
the particular problem above investigated i is rather special in
character. In illustration of this let us suppose that there
are three degrees of freedom, and that cy, ¢;, Q:, Q; are
evanescent. The equations then become

(¢— 9741) 91 + 1083292 + 10 Bi 393 = Qi,
— S292 +78q, +1839; =0,
—d393 +2839, +1B32g. =0;

whence, regard being paid to (2),
nf (4—o%a) +” + I (asBi9 F O25") = Oman)

a "903 — Bos"

When o=0, the value of gy, reduces to Q,/c,, unless 6.;=0,
so that in oeneral the equilibrium value applies. But this
is only so far as regards q;. The corresponding values of

Jay 73 are

g2= — 1 1/P32, Y3= — 1 B2i/Bo3 5 ore “(8)

‘and thus the equilibrium solution, considered as a whole, is
finitely departed from. And a consideration of the general
equations (1) shows that it is only in very special cases that
there can be any other outcome w then the possibility of steady
motion of disturbance is admitted.

It thus becomes of great importance in tidal theory to
pore what steady motions are possible, and this question
also has been treated by Lamb (§ 207). It may be con-
venient to repeat his statement. In terms of the usual

149 On the Theory of the Fortnightly Tide.

polar coordinates La ah equations are

du gd >.
i b) Ss ———— —
Fe Pres = — Tv, . . - 2 @
we yp tom cos O= — 8 :

embda cs oh 8.
Lee 1 4 d(husin @) 4 Uhe) Y
di) scisme), 2gP do $2. ae (11)

where uw, v are the velocities along and perpendicular to the

meridian, € is the elevation at any point, ¢ the equilibrium
value of &, a denotes the earth’s radius, n the angular velocity
of rotation, and 4 the depth of the ocean at any point. To

determine the free steady motions, we are to put €=0 as
well as du/dt, dv/dt, d€/dt. Thus

g dg Ae g dg
“u=— tae : = —___
2nasin 6 cos 06 da’ 2na cos 6d6

and
d(hsec@)d& _ d(hsec @) dg __ .
dé d@ da dé Te a (18)

If hsec 6 be constant, (13) is satisfied identically. In any
other case a restriction is imposed upon ¢. If h be constant
or a function of the latitude only, ¢ must be independent
of w; in other words the elevation must be symmetrical
about the polar axis. In correspondence therewith u must
be zero and v constant along each parallel of latitude.

In the application to an ocean completely covering the
earth, such as is considered in Darwin’s solution, the above
conditions are easily satisfied, and the free steady motions,
thus shown to be possible, explain the large deviation of the
calculated fortnightly tide from the equilibri ium value. Whe
does not appear to have been sufficiently recognized is the
extent to which this state of things must be disturbed by
the limitations of the actual ocean. Since v must be con-
stant along every parallel of latitude, it follows that a single
barrier extending from pole to pole would suffice to render
impossible all steady motion; and when this condition is
secured a tide of sufficiently long period cannot deviate from
its equilibrium value. Now the actual state of things corre-
sponds more nearly to the latter than to the former ideal.
From the north pole to Cape Horn the barriers exist ; and
thus it is only in the region south of Cape Horn that
the circulating steady motion can establish itself, It would
seem that this restricted and not wholly unobstructed area

= SS Cl

Thermomagnetic Properties of Crystalline Bismuth. 141

would fail to disturb greatly the state of things that would
prevail, were every parallel of latitude barred. If this con-
clusion be admitted, the theoretical fortnightly tide will not
differ materially feonn its equilibrium value, and Darwin’s
former calculation as to the earth’s rigidity will regain its
significance.

“Some caution is required in estimating the weight of the
argument above adduced. Though there were no free dis-
turbance possible of infinitely long period, it would come to
the same, or to a worse, thing if free periods existed com-
parable with that of the forces, which is itself by hypothesis
a long period. On this account a blocking of every parallel
of latitude by small ‘detached islands would not sufiice,
although meeting the theoretical requirement of the limiting
case,

It would serve as a check and be otherwise interesting if
it were possible to calculate the fortnightly tide for an ocean
of uniform depth bounded by two meridians. The solution
must differ widely from that appropriate to an unlimited
ocean ; but, although the conditions are apparently simple,
it Hoes not seem to “he attainable by Laplace’s methods. A
similar solution for the semi-diurnal tide would be interesting
for other reascns.

In any case [ think that observations and reductions of
the fortnightly tide should be pursued. Observation is com--
petent to determine not merely the general magnitude of
the tide but the law as dependent upon latitude and longi-
tude. Should the observed law conform to that of the
equilibrium theory, it would go a long way to verify
a posteriori the applicability of this theory to the circum-.
stances of the case.

VIII. The Vhermomagnetic and Related Properties of Crystal-
line Bismuth. By Louis Lownops, B.Sc. (Lond.), Ph.D
(Berlin), 1851 Ewhibition Research Scholar, Univ. Coll.,

Nottingham”.

§L FORMER paper, published in the Philosophical

Magazine for October 1901, gave an account of
the Longitudinal and Transversal Thermomagnetie Effects
and the Thermoelectric Properties of a Plate of Bismuth
cut from a crystal of the metal in the possession of Prof.
Groth of Miinchen. The present contains an account
of the investigation of the change of electrical resistance

* Communicated by the Author.

142 Dr. L. Lownds on the Thermomagnetic and

in the magnetic field, the Hall effect, and the conductivity
for heat in and out of the magnetic field for the same
crystal specimen.

The change of electrical resistance and Hall effect were
determined along and at right angles to the chief crystallo-
graphic axis andat three different temperatures, viz. (1) at
room temperature; (2) at —79°C.; (8) at —186°C. The ratio
of the conductivities for heat along and at right angles to
the chief crystallographic axis was determined in zero field
and in a field of 4980 c.@.s. units.

§ 2. The Change of Electrical Resistance in the

Magnetic Freld.

The crystalline plate abed (fig. 1) was mounted in a small
wooden frame ABCD, 43 cms. long, 24 ems. wide, and 1 cm.

Fig, 1,
A =)

TESA OCS

‘is

NLL ON

BES ee

thick. A rectangular piece was cut out at abed, so that the
plate fitted exactly, the front surface of the crystal being flush
with the surface of the wood. ‘Two such frames were used,
according as the effect was to be measured along or at right
angles to the chief crystallographic axis. A current was led
through the plate by means of wires soldered to the copper
strips at ab, cd. These strips were firmly screwed down on to
the crystal, narrow strips of tinfoil bemg placed between
them and the plate in order to ensure good contact and to
avoid fracture. Two brass spring-contacts, e and /, served as
electrodes for measuring the difference of electric potential

ahd
b hea
Bey
Uf

Related Properties of Crystalline Bismuth. 143

between any two points on the plate. These contacts were
adjusted so as to touch two points lying on a line at right
angles to the copper strips. A current of known value was
then passed through the plate, and the difference of potential
between these two points was measured. The field was then
excited and the determination repeated, the current through
the plate being adjusted to the same value as before. Ife,
is the difference of potential without the field, wo the resist-
ance between the points, and I the current strength, e and w
the corresponding values with the field, then

T= =f
Wy Ww
We
Wo €0
.. Percentage Increase W—= Wy e—e&
of Resistance in Field ¢ = 129 - Wo = 100- Ps

The current was only made momentarily, so that heating
effects were avoided. The electromotive force was measured
by the compensation method, a D’Arsonval galvanometer
being used of resistance 1000 ohms. Induction effects from
the current used to produce the fall of potential were avoided
by using a key which first made this current, and afterwards
closed the galvanometer circuit. The magnetic field being
completed the whole time, while observations were being
made with field, had no inductive influence. The current I,
which was of the order 1 to 2 amperes, was measured by an
amperemeter reading to 4 per cent. The electromotive forces
were of the order 300 to 600 microvolts and could be deter-
mined to at least 1 per cent.

The observations were made :—

(1) At ordinary temperature, the whole plate being
immersed in a petroleum bath.
(2) At —79° C.in a mixture of solid carbon dioxide and
ether, contained in a silvered Dewar vessel.
(3) At —186° C. in liquid air.
The absolute resistance between the two electrodes e and 7,

5 €0 -
ViZ- Wo = enables us to calculate approximately the

specific resistance p of the plate.

We have Dt eon sia
=e
where a is the cross-section of the plate in square centimetres,
and 7 the distance in centimetres between the electrodes.
Since 7 was of the order 5 mms. and slight irregularities
existed on the edges of the crystal, this result can only be

regarded as approximate. The determination of p for any

144 Dr. L. Lownds on the Thermomagnetic and

one of the two directions in the plate was made at the three
temperatures without altering the positions of the contacts.
The results for the percentage change of resistance are given
in Table I., and represented graphically in fig. 2. The full-

TaBLe I.—-Change of Resistance.

Parallel to Crystallographic | Perpendicular to Crystallographic
Axis. Axis.
| | |
Wempsc.| 22°5ea) (ng? ei leg: 14°. =79°.4 aie
| wiela, | 100% | 100”=%o | 19090%="0 | 1002=e | 19002 = 20) oe
We, | Wy | 5 2 | 9 Wo Wo
2120 50 22-5 33:5 39 96. aaa
3120 9-2 877 449) 78 14-2"), eae
| 3500 121 4871 47-4 8-6 15-7)
4980 198 62:1 565 0 | 143 PAM yh
|
Fig. 2

Related Preperties of Crystalline Bismuth, 145

line curves refer to the case parallel to the chief crystallo-
graphic axis, the dotted curves to the case at right angles to
this axis

Fig. 3 is drawn from the values in fig. 2, and coordinates

Fig. 3,

temperature with percentage change of resistance for four
different field-strengths. The specific resistances for the two
directions and in zero field for the several temperatures are
given in Table II., together with values obtained by van
Hverdingen* at ordinary temperature.

According to Everdingen’s observations the ratio of the
specific resistances for the two directions at 15° C. is as 1: 1°68,
whereas for the crystal plate used by me it is as 1: 1°78. The
ratio of the thermoelectric forces with respect to copper for
the two directions parallel and perpendicular to the erystallo-
graphic axis was found to be 1:1:91 (between 10° C. and
g07.C.) T.

* E. van Everdingen, Comm. Phys. Lab. Univ. Leyden, lxi. (1900).

+ L. Lownds, Phil. Mag. October 1901.

Phil. Mag. 8. 6. Vol. 5, No. 25. Jan. 1903. L

146 Dr, L. Lownds on the Thermomagnetic and

Parallel to Axis.

TABLE II.

Perpendicular to Axis.

Temperature. p- Temperature. p.
13 269000 c.6.s. is 151000 c.4.s.
_ 79 379000 Eset aS 135000
2186 234000 | —186 86000 |
15° 348000 | 15° 204000 7 |
| / * 229000
| | * 232000
|

* Hverdingen.

§ 3. The Hall Effect.
The Hall constant C is defined by the equation
<p gual
Ce

d ?

where Ef is the difference of potential between points a and 6

in fig. 4 when a current of strength $ flows from A to B, the
Fig, 4.

lines of force being at right angles to the plane of the plate.
In the above, d is the thickness of the plate. Before the
magnetic field is excited a and b are supposed to lie upon an
equipotential line. If the current J is from A to B, and the
field H in the direction indicated by the arrow, then, when
the Hall current is from a through the galvanometer G to 3,
the effect is positive. At ordinary temperatures the sign is
negative for Bismuth. Two different cases were possible for
the measurement of the Hall effect with this crystal plate.

Related Properties of Crystalline Bismuth. 147

The magnetic field was always at right angles to the plane
of the plate, and therefore perpendicular to the crystallo-
graphic axis, while the current 3 was either parallel or
perpendicular to this axis. This current was led through
the plate by means of wires soldered to the copper strips
ab and cd. Two small brass screws g and fA (fig. 1), which
pressed firmly on to the sides of the crystal, were used as
electrodes for measuring the Hall electromotive force EH. g
could be moved in the direction of the length of the crystal,
and was adjusted so that when the current $ passed the
electromotive force between g and A was as small as _ possible.
It was found impossible to adjust the contacts so that they
lay exactly on an equipotential line, but the error due to this
imperfect adjustment makes no perceptible difference in the
mean value of the constant. The electromotive force was
measured by the compensation method. By this method one is
independent of the change of resistance in the plate due to the
magnetic field. Before exciting the field a current of known
strength was sent through the plate, and the electromotive force
between the points g and 4 measured. The field was then
excited, the current 3 adjusted to the same value, and the
electromotive force between g and fh again measured. The
difference between these two readings gave the Hall electro-
motive force EB. ‘The measurements were repeated with the
current reversed, and again, for both directions of current
with the magnetic field in the opposite direction. The mean
of the four values was taken as the measure of the effect.
In order to avoid heating of the plate due to the passage of
the current 9%, the circuit was only closed momentarily. A
special key served to close this primary circuit, and im-
mediately afterwards the secondary circuit connecting the
Hall electrodes; if the Hall electromotive force was not
exactly compensated then a deflexion of the galvanometer
was noted. By repeated trials two adjustments could be
found. for one of which a deflexion could be obtained in one
direction, and for the other in the opposite direction. These
adjustments differed from one another by not more than 1 per
cent., and the mean was taken as the balance-point. By
closing the primary circuit first, induction effects of the
rimary on the secondary circuit were avoided.

Tables I{I. and LV. contain the results for the two directions
and at the three temperatures, and the curves (fig. 5, p. 150) give
a graphic representation. The full-line curves correspond to
the case when the current 9 is parallel to the chief erystallo-
graphic axis, and the broken-line curves to ‘the case when 3

is at right angles to this axis.

L 2

Dr. L. Lownds on the Thermomagnetic and

148

Gol
6.64

191

G8-8+

(5981 — oanyesoduiay,

66:9 —

LTT

*o6L— otnjeieduroy,

PIL-

IGG

‘SOT oanyesoduay,

op)

TL] @tav 5

‘sixy orydeadorpeysday ony 07 JS yuomingy Aavunag— yal [PH

OG16 —
OG1Z —
OGIG+
OZ16+

0ZTE—
OGIE —
O@IS+
OGIS+

oose—
o0¢cs—
oogs+
ouge+

OS6h —
O86 —
O86h+
O86P+

149

Related Properties of Crystalline Bismuth.

69-L+

1¢-L+

"(98ST — oangeaoduoy,

90T

SFI

g3-L—

12S

18-4—-

8E-6—

“ATH

6@ +
Og =
Gci+
Z9I—
AN

Na
TT®H

“GL — eanqeaod way,

r0Il-

T-01—

166 ~

Gol

SLI

+61

“AW

“a

————— |

“(OT eangetodumoay,

0GIG—
OG1G—
0GIZ+
OZIe+

OGIE —
OGIE—
OG1E +
OGLE +

00ge—
o0ge—
oogg+
ooce+

O86> —
O86h —
O86F+
086h+

‘sIxy orydersoypeysday oxy 07 T quota Areunig—pad7 1°

‘AI aT TY,

150 Dr. L. Lownds on the Thermomagnetic and

The direction of the current 3 with respect to the crystallo-
graphic axis appears to have very small influence on the
constant C, This has also been observed by van Everdingen *
at ordinary temperature. He found at a temperature of
15°C. and for a field of 4600 c.c.s. units C= —8-0, and for
a field of 2600 c.a.s. units C= —10°2, when the current was
parallel to the chief axis. In the other case, using three
different plates, he found for 4600 c.¢.s. field-strength

= —10°6, —8°8, and —8*2, and for the field 2600 c.c.s.
C=—12°6, —11:1, and —10°6. These values are of the
same order as those found by me. Fig. 6 is obtained from
fig. 5 by taking the mean of the values for the two directions
OE oy

Fig. 5.

It is to be noted that at ordinary temperature there is very
little dissymmetry in the effect for opposite directions of the
field. At low temperatures this dissymmetry is more marked.
It appears to vary somewhat with the setting up of the
erystal, as will be seen from Table V., which contains readings
for two different settings up of the crystal.

* E, van Everdingen, Joc, cit.

Related Properties of Crystalline Bismuth 151

2)
Z
>
eo
ag
=

Hall Hifect.

Fig. 6,

TABLE V.

Temperature —186°.

2nd setting up.

| Ist setting up,
IEE, S% (amp.)
E.M.F E
MP econ hl abs Mv.
+4980 +2 — 53 +100
0 +2 —153
0 —2 +153
+4980 —2 + 54 — 99
0 —2 +153
0 +2 —153
— 4980 +2 — 430 —271
0 +2 —166
0 —2 +166
— 4980 —2 +430 +264
0 —2 +160
Mean = 183

—141 | Mv.

— 34 | +107
—142 |

+142

+ aoe Bi be 1OF
+144 |

—147 |

—409 —258
— 156

+156 |

+409 | +256
+151 |

152 Thermomagnetic Properties of Crystalline Bismuth.

Table VI. shows that the mean Hall electromotive force is
not appreciably influenced ‘by the Hall electrodes g and h
not lying exactly upon an equipotential line.

TasLe VI.
Hall Effect. Temperature 16°.

§ 4. The Conductivity for Heat.

The other properties of the crystal, such as change of
resistance, Hall effect, &c., have been determined for the two
directions and for different field-strengths, and at several
different temperatures. The determination of the conduc-
tivity for heat, for the two directions, and its variation with
temperature, both in and out of the magnetic field, was not
possible, since the general methods for the determination of
heat-conductivity are not applicable to so small a specimen
as we have to deal with in the present. I have sought, how-
ever, by the method due to de Senarmont* to get approximate
values of the ratio of the conductivities for the two directions
in and out of the magnetic field. The crystal was well cleaned
and coated with a thin layer of elaidic acid. This has been
recommended by Voigtt in preference to the mixture of
wax and turpentine used by de Senarmont. On the centre of
the crystal plate was pressed the pointed end of a stout copper
wire, 1 metre long, which was heated in the middle by means
of a Bunsen burner. The isothermal curves on the plate are

* De Senarmont, C. &. xxv. pp. 459, 707 (1847).
+ W. Voigt, Gottingen Nachricht. 1896, Heft iii.

Prof. Trowbridge on the Spectra of Hydrogen. 153

in the form of ellipses, the squares of whose axes are pro-
portional to the conductivity in that direction. In the
magnetic field the lines of force were at right angles to the plane
of the plate. The axes of the ellipses were measured by means
of the microscope. The major axis of the ellipse was, both in
and out of the magnetic field, at right angles to the chief
crystallographic axis of the cr Fides The ratio of these axes,

without magnetic field, was jj FHL 19, and in a magnetic field
of 4980 c.¢.s. units 4 i=l 34. If we take the squares of these

guantities we have the ratios of the heat-conductivities for
the two directions. The results are :—

Leroriieldnaisa T 1°42,
4980 c.4.8. ... 4 180.

The corresponding values for the electric conductivity are :
Zero field ...... aos:

4980 0.G.8...... 4 1:87.
My thanks are due to Prof. E. Saale for his suggestions
throughout the progress of the work.

Physical Institute, Berlin University,
Sept. Ath, 1902.

IX. The Spectra of Hydrogen, and Reversed Lines in the
Spectra of Gases. By JoHN TROWBRIDGE *.
fy a previous paper (Phil. Mag. July 1902) I described
the spectra produced by powerful condenser-discharges
through Geissler tubes filled with hydrogen. A fairly con-
tinuous spectrum was obtained between the HH lines and
the red end of the spectrum. This spectrum, however, was
traversed by reversed lines. In that paper I expressed the
hope of being able to obtain quartz tubes. This hope has
been realized. Through the kindness of manufacturers f,
working under the direction and accor ding to the method of
Professor Shenstone ft, I have obtained suitable tubes: and
the results given by such tubes are so remarkable that they
seem worthy of a preliminary paper.

The tubes are 8 centimetres in length, with a capillary
4 centimetres in length and about 2 millimetres in diameter.
On account of the difficulty of inserting platinum terminals

* Communicated by the Author.

+ Baird and Tatlock, London.
¢ Clifton College,

154 = Prof. Trowbridge on the Spectra of Hydrogen.

in quartz, I had the ends of the tubes ground smooth, and
the glass-blower of the laboratory prepared glass bulbs in
which suitable electrodes were inserted. These bulbs were
luted to the ends of the quartz tubes. In certain cases metal
plates were luted directly to the ends of the quartz tubes. I
employed silicate of soda asa luting agent; and after this
had hardened I applied on the outside of the joint a hard
preparation of pitch and shellac.

The glass bulbs were covered with other bulbs which
allowed a current of water to circulate from the upper end
of the tube to the lower; great heat, however, was ex-
cited in the capillary of the tube. Quartz prepared by the
method of Professor Shenstone possesses the property of
resisting changes of temperature in a remarkable manner.
One of these quartz tubes can be heated to a white heat and
plunged into water without cracking. Such tubes, therefore,
are very valuable for the experiments I have been conducting
on gases at high temperature.

They also possess the great advantage over end-on tubes of
glass provided with quartz windows, that the capillary can be
placed close to the slit of the spectroscope, thus giving a
very intense light and a broad spectrum; moreover, the
quartz is not melted by the intense heat. A photograph of
gaseous spectra can be obtained with a single discharge and
a very narrow slit ; with tubes filled with ‘hydrogen excited
by a difference of potential of twenty thousand volts, con-
denser *3 microfarads, an extremely intense light is obtained.
This light is dazzling white with a bluish cast: it has more
than three times the actinic effect of the same quantity of
electricity discharged between magnesium terminals. Viewed
with a straight-vision spectroscope the spectrum appears
continuous; and even photography fails to reveal bright
lines between the HH lines and the red end of the spectrum.
In the region, however, beyond the limit set by the absorption
of the olass Geissler tubes there are both bright lines and
dark lines. The principal reversed lines are at wave-lengths—

2889°70
2549-89
2528-60
2524°29
2519°3

2516°21

These lines correspond with the lines of silicon volatilized
by the spark in air. Itseems that we have in this phenomenon

Discharge through a Coil of Variable Inductance. 155

another instance of selective polarization mentioned in my
previous paper. The strongest metallic lines or gaseous lines
are not those which show the strongest reversal. For instance,
my previous photographs show the calcium line at approxi-
mately 4227 to be strongly reversed, while the stronger 3963,
3933 do not show a reversal except with much stronger and
longer continued discharges.

A careful inspection of the negatives shows that the reversals
of the metallic lines occur when they fall on bright gaseous
lines or bands. In the same waya bright gaseous line falling
on a continuous spectrum can show a similar reversal. We
can express this in symbolic language as follows. Let A
represent the intensity of the line and B the amount of the
previous action of light on the photographic plate ; then the
reversal appears to be proportional to AB.

It seems probable that there are similar reversed lines
running through the solar spectrum. I hope to detect them.

This investigation shows that the presence of dark lines in
the spectra of stars dues not imply, necessarily, the presence
of reversing layers of a colder state of the gases; for such
reversal may arise from photographic action on the plates
which are used. Moreover, a gas may show a continuous
spectrum to the eye, or even when photography is employed
with glass tubes and glass lenses, while with quartz tubes such
as [ have employed a large region in the ultra-violet is shown
to be traversed by both dark and bright lines and bands.

Jefferson Physical Laboratory,
Harvard University,
Cambridge, U.S.

X. A Graphical Method of Determining the Nature of the
Oscillatory Discharge from a Condenser through a Coil of
Variable Inductance. By E. W. Marcuant, D.Sc., late
Granville Scholar of the University of London, Lecturer in
Hlectrotechnies,. University College, Liverpool*.

HE method which is described below is an extension of
the one originated by Dr. Sumpner (Phil. Mag. June
1887).

In this paper he describes a graphical construction for
determining the rate of increase of current in a coil having
an iron core. The problem is stated generally as the deter-
mination of the increase of current through a coil with a

* Communicated by the Author.

156 Dr. Marchant on the Oscillatory Discharge

variable self-induction when an H.M.F. is suddenly applied
to it. The results obtained by him were of very great
interest, as he clearly demonstrated both by experiment and
calculation the fact that with an iron core coil, such as that of
a large electromagnet, the current first increases very slowly
until the knee of the magnetization curve is reached, and
that it then increases with much greater rapidity. It ap-
peared that this method might be applicable to the case of
the oscillatory discharge from a‘condenser. We have as the
fundamental equation

d (Lz)

., Q
ai + Ri+ 0;

C
with the condition that just before the discharge takes place
there isa P.D.=E volts between the plates of the condenser.
Liz denotes the number of lines of force linked by the coil
when a current 2 is flowing through it. (With iron in the
circuit L (of course) is a function of 7. With an “air core”
self-induction L will represent the self-induction of the coil
as ordinarily understood.)
R denotes the resistance of the circuit in ohms.
C the capacity of the condenser in farads.
() denotes the quantity of electricity on the plates of the
condenser at any instant.
2 denotes the instantaneous value of the current.
The first term may be written
d( Lz) ae. dlide a lie ye
he ee = ne va )=u dt’

We have therefore

= = ——————————— nr

It now remains to show how the value of Lt may be obtained
from this equation. ae

It will be well first to take the simplest case where L is a.
constant quantity. The equation then reduces to

through a Coil of Variable Inductance, Log

Let OX (fig. 1) be the axis of time, OY the axis of current.
Just before the discharge there is quantity Q,=H,C on
the plates of the condenser.

Fig. 1.

Zz K 77, X, 772,X 5 Pye x

The quantity at any instant T after the discharge has

T
occurred is therefore = ~—Q, + idt, where 2 is considered
0

positive when it tends to diminish the quantity of electricity

on the plates of the condenser, and Q) must therefore be
considered negative.

0
Fan C eC

Qo (1 i ne Qy (: fs Jie) oe

OR Nae
= = SS ip a ge a
R rp
Plot along OZ a length proportional to R? and on OX to
the same scale, time in seconds. x

TOK is in seconds draw KM parallel to OY.
Along OY take a length ON= Qo

RG in amperes to the
proper scale. }

158 Dr. Marchant on the Oscillatory Discharye

At time 0, 7=0, and consequently

a fui (NKO)
R

From © therefore draw a short line OL, parallel to KN,

this will be the beginning of the current-curve since
tan (L/OX) =tan (NKO) = S
ad

It will be convenient to take a time-interval such that dé
is numerically some simple multiple of CR. Thus dt=kCR.
The exact time-interval is unimportant, provided it be
sufficiently small. Since

idt=area of OL, Xy = mym, x OX,= mm, x dt,
he = mm X a and a being =h, ne
ot downwards from theretore, a length &X mm, to
Plot d ds f N, therefore, a length kx mm,
N,, and from L, draw L,Nj’ parallel to OX to meet ON in Nj.

ab. ie
Then N= 2 —k(mym,)—-i= ale a easy
Producing L,N,’ to meet KM in M, and joining M,N,,

‘ NIV = EN tat
tan N,M,N,’= MN = di

Draw from L, therefore a line L,L, parallel to M,N.
This represents the increase of current during the second

=k x mm.

therefore, from the equation above.

time-interval X,X,. To determine the value of S at the

time corresponding to L, draw the mean ordinate mgm, of
the trapezium L,X, L,X,; the area=X,X_ X mgmg, and is as

dt ante
pee for this in-
RE 4
terval=k x mgm. as before. And plotting this length down-
Vide
ee RC
from the beginning of the discharge. Continaing the con- —
struction as before and joining M,N, the slope of this line
di ; =
a at the instant X,.

Curves have been plotted for discharges through a circuit
having a capacity=1 m.f. and a self-induction=1 henry

before =\ ide from X, to X,; the value of

wards from N, to N. the length NN,=the value of

represents the value of

through a Coil of Variable Inductance, Tao

with three different values of the resistance, and these agree
to within 1 per cent. with calculation.

Exactly the same method of procedure is adopted when
plotting the discharge through a coil of variable inductance,
the straight line KM being replaced by a curve drawn to

Fie. 2.—Curve showing the Discharge of a Condenser of 1°25 mf.
Capacity through a Coil having a Core of Soft Iron Wire.
P.D. before Discharge =9400 volts.

Time for Half-Oscillation=2°9 x 10-5 secs,
Experimental value =3'2 xX 10--5 secs.

[2)
in AMPS

CURREN

40 3020 10 0 5 10 15 20 BS 30
+ in 10-*secs TIME iw 10 °sEcE

Fig. 3.—Curve showing the Discharge of a Condenser of 1:25 m.f.
Capacity through a Coil having a Core of Soft Iron Wire.
P.D. before Discharge = 2350 volts.
Time for Half-Oscillation=51 x 10—5 secs.

pemriae sO Ny cueonibi(Onmy Ol, 5) LON Sie 20h y25y FO) |,55 940
+ in lo S&S TIME 1 10~“ 5065

Fig. 4.—Curve showing the Discharge of a Condenser of 1:25 m.f.
Capacity through a Coil having a Core of Soft Iron Wire.
P.D. before Discharge = 450 volts.
Time for Half-Oscillation=15:2 x 10—> secs.

en a
2 er be
Zl

400 320 240 160 80 0 e0 40 60 80 100 - 0 140

0
Ly 1075 SECS Time IN10°°SECS

aa
a
=

sce

4D)
RRENT IN

WR Ics Cd Sie
represent the variation in the value of r with current.
DD

Such curves are shown at A A in figs. 2, 3, and 4.

160 Lischarge through a Coil of Variable Inductance.

The chief difficulty that arises is in the drawing of the
earlier part of the curve, when the current is just starting,
and to do this accurately a supplementary curve is first drawn,
a very much larger scale of current being employed.

A curve of the same character may be drawn for the end
of the first half wave when the current has fallen to 20
amperes. The shape of the curve is, however, not exactly
similar on account of hysteresis. The actual case taken was
that of a coil on which a certain number of experiments had
been made. The coil was in the shape of a square with
about 90 turns of No. 18 g.p. wire on each limb. The seif-
induction of this coil was measured without the core, and
found to be 4°1x10-* henry. A core of soft-iron wire was
used in the experiment, and from the known permeability of
the soft iron for different magnetizing forces the curves shown
at A A were calculated.

A series of curves has been drawn showing the shape of
the current-wave through the coil when-the discharge from a
condenser of 1:25 micro-farads capacity flows, the condenser
being charged with (1) 8400 P.D. (2) 2350 P.D. (8) 450
volts P.D. It is interesting to notice the complete difference
in shape of the discharge curves. In the first case, that in
which the P.D. is 9400 volts, the current increases very slowly
until saturation is attained, that is, when the magnetizing
force 1s about 300, after which the discharge curve becomes
nearly sinusoidal. For the smallest voltage saturation is
hardly reached, so that the curve becomes peaked; the effects
ot hysteresis in this curve are clearly shown. The method is
of course adaptable to any kind of discharge, the curves in
question having been plotted to illustrate its working, and
because experimental values of the actual time occupied by
the discharge have been obtained. It will be noticed that
the agreement between graphical and experimental results is
fairly good. Hxact agreement would hardly be expected on
account of the disturbing effects due to eddy-currents, which
are very powerful (at this frequency) with the finest
laminations.

It is instructive to notice the increase in the time for a
half-oscillation when the P.D. before discharge is decreased.
The table below is taken for the voltages considered. |

P.D. before Discharge. Time for 1st Half-Oscillation. |

9400 29> MOR?:
2350 dys els Oe
450 UR Gl Cee

It is clear, therefore, that with a discharge such as we are

On a Sensitive-strip Spectropolariscope. 161

considering, which is rapidly damped, the time for a half-
oscillation would increase as the discharge died away, a result
experimentally obtained and published in a letter written to
‘Nature’ by the author in August 1900.

An interesting application of the method is the determination
of the deflexion that would be attained by a ballistic galvano-
meter when a discharge passes through it which cannot be
assumed to have ceased flowing before the needle has moved.
In this case the value of would be variable, and the sub-
traction would have to be repeatedly performed from a
variable point.

In conclusion I wish to express my indebtedness to Mr. G.
W. Worrall, B.Sc., for working out some of the values of
the self-induction under varying currents which have been
used in plotting the curves given above.

University College, Liverpool.

XI. A Sensitive-strip Spectropolariscope.|
By Professor D. B. Bracr*.

HE conditions for maximum sensibility of the eye in
making comparisons with the polariscope are the same
as those of a photometer. The entire displacement, except in
technical work, of photometric comparisons with ordinary
light by spectral photometric observations, which the growing
demands in photometry for exact data on specific colours
have produced, illustrates the corresponding condition in
polariscopic work. The importance, both theoretical and
practical, of determining, on the one hand, the relative
distribution of intensities subjectively and objectively in any
radiant and, on the other, the relative transmission of any
absorbent for different periodicities, has necessitated the
highest instrumental refinements.

Tt is now possible to obtain settings for the mean spectral
colours with a probable error of less than one-fifth per cent. F
and on some occasions with a carefully trained eye as low as
one-tenth per cent. This has been brought about by
improving the viewing screen so that the bounding lines
between the comparison fields should be perfectly sharp and
vanish with equal illumination of the fields, the colour of
course becoming the same over the entire field of view. In

* Communicated by the Author. Read before the American Physical

Society at its Pittsburg meeting, July 1902.
+ Phil. Mag, [5] xl viii. p. 420 (1899).

Phil, Mag. 8. 6. Vol. 5. No. 25. Jan. 1903. M

162 Prof. D. B. Brace on a

the spectrophotometer the best results have been obtained by

means of a silver strip. The photometer is subject to the
further restriction in its use of measuring the quantities of
hight. This element, asa difficulty, is really negligible in

the polariscope, but the former difficulty does not seem yet to.

have been overcome.

In a polariscope it is necessary to vary the so-called
sensibility as the amount of light varies. This condition
should obtain too for all colours. For the greatest efficiency,
the polarizing and analysing elements should not displace the

ray when placed in its path, as this would generally affect the:

position of the image for any one wave-length. The bounding
lines between the fields should also vanish for any colour and
sensibility and that too whether a broad or a narrow radiant
is the source of light. Some of these conditions have been
realized in the types already devised, but no one embodies
them all.

In the biquartz of Soleil a vanishing line is partially

realizable, but as the tint of passage is used white light is.

required ; and further the sensibility cannot be varied. In
a double rotary element, such as that of Poynting rotating

differentially in the same direction, a vanishing line is also.

partially realizable; but its use over a finite portion of the.
spectrum of sufficient breadth to give a proper intensity will

make initial settings of different tints in the different parts of

the field, owing to the differential rotation. The neutral

position of the analyser will also vary in different parts of

the spectrum for similar reasons. This form and the modified
form of the biquartz with a small angle of rotation which is
used for monochromatic light do not admit of a practical
variation in the sensibility. Furthermore, the added rotation
of any medium under examination increases the differential
rotation of one portion of the field over the other, thus
intensifying the difference of tint in the two fields, which
diminishes the sensibility in setting. In the polariscopes
of Savart, Babinet, Nodot and others a vanishing and a
displacement of interference-bands take place. The settings
which can be made with these forms are far less accurate
than those already mentioned and in some of them very
fatiguing to the eye. In the system of Laurent, with a half-
wave plate, much used in saccharimetry at the present time,
a vanishing line is attainable and the sensibility can be varied,
but light of only one colour can be used. In the half-shade
polarizer of Jellet any colour may be used, but it is impossible
to vary the sensibility and also to eliminate the dark line
between the two halves of the field. In the half-shade

Sensitive-strip Spectropolariscope. 163

polariscope of Lippich, in which the field is either bisected or
trisected, we have the most adaptable and sensitive instrument
which has been devised. This form embodies the very
essential feature ofa variable sensibility, and, with a sufficiently
broad source, a nearly vanishing line is possible. However,
in most forms of nicols, since it is the extraordinary ray
which is used, there is a displacement of its path. This of
course can be avoided if the ray enters normally a nicol with
the optic axis in the intersection of its face with its diagonal
plane. Most nicols are also found to be slightly prismatic.
The ray will usually receive a further displacement on its
passage through the second nicol which covers a part of the field
of the first one. The two ray systems thus give separate images,

which, in spectral work, is a serious ditticulty i in obtaining a
perfect match over the field. In setting for any one colour
a rotation of either polarizer or analyser should not displace
the image. To avoid this, care must be exercised to eliminate
the errors due to displacement mentioned above. It does
not seem possible to produce a vanishing line between the
different parts of the field except with a source of sufficient
breadth. With such a radiant at a focus conjugate to the
image at the analyser, when the lens is just before the
polarizing nicol, there is a great number of bundles of rays
which thus produce uniform illumination over the entire field.
When, however, the source is very narrow and we have
approximately a single bundle of rays, the case is different and
we generally observe a decided dark or bright line between
the fields, which greatly reduces the delicacy of perception
of the eye. ‘This is evidently an irremedial effect since the
polished side of the second nicol, usually several centimetres
long, will reflect internally or externally any rays striking it,
and it is thus impossible to obtain a continuous system of rays
across this bounding face, particularly if the rays within it
are displaced as described above. In several of the most
sensitive half-shade combinations obtainable this defect
existed to a greater or less extent. In spectral work, except
with bright-line radiants or with absorption cells which never
give sufficient homogeneity, a narrow source or slit is essential.
Hence the Lippich form of instrument does not seem to be
available for general colour observations over successive
portions of the spectrum. The amount of light obtainable
from a bright-line radiant, e.g. an Aron’s lamp, was found to
be far below that obtained from the direct rays of the same
colour from the sun after passing through a spectral system as is
usually desirable, e.g. absorbing media which have anomalous

164 Prof. D. B. Brace on a

rotary effects. Other defects usually found are imperfect
polishing and figuring of the nicols themselves. These are
usually only observed in work with spectral colours from a
narrow source giving approximately a single bundle of rays.
{ The scratches and ridges here become at once evident and
any variation in the curvature of the face manifests itself in
a variation of intensity of the field, producing a shaded or
mottled appearance. This is a well-known appearance ™ in
spectrophotometry when the ray system is not coaxial with
‘othe lenses or when their curvature is not uniform.

In the nicol prism a total reflexion of the ordinary ray
takes place at the internal diagonal faces which are cemented
with balsam or with evaporated turpentine-oil or linseed-oil,
whose indices are less than that for the ordinary ray. This
allows a part when balsam, or practically all when these oils are
used, of the extraordinary ray to pass through. The reflected
ray is absorbed by the sides of the nicol but not completely.
When an intense source like the sun is used the diffused light
is so large as to produce a decided effect on the hue when

_ecolours of very low intensity reach the eye. This of course
' is a difficulty which the optician can eliminate by proper
casing and diaphragming.
_——_ It is not a difficult matter mechanically and optically to
reverse the conditions of reflexion with the optical media now
available. For example, we have as the index of the ordinary
ray of spar for the D-line 1:6584, while for the same line the
value for a-monobromonaphthaline is 1°6582. Schott and
Co., of Jena, also cast a glass the value of which is n,=1°6527.
The dispersion of each of these is of course different, but for
» the mean colours of the spectrum the indices are almost the
same. It has seemed heretofore impossible to obtain glass so
free from strain as to produce no observable depolarization.
The use of liquids, however, has been found perfectly practi-
cable and efficient. Solutions of carbon disulphide may be
.¢ used giving almost any convenient index from a low value
with balsam to an index greater than 1°7p with phosphorus.

The well-known optical fluid a-monobromonaphthaline is,
however, much superior, as it remains nearly colourless if
sealed up and not subjected to actinic action by continuous

) exposure to light. Its index is the same as that of spar for
the mean portions of the spectrum. If now the cementing
film and the prisms of spar are interchanged, we should have
an interchange of the extraordinary and ordinary rays. Thus
a plate of spar placed diagonally at the proper angle within a

* Tuckerman, Astrophys. Journ. xvi. p. 145,

Sensitive-strip Spectropolariscope. 165

eylinder of glass or of this fluid would totally reflect the
extraordinary ray and transmit almost completely, and without
any displacement as is usually the case in nicols, the ordinary
ray. A second cylinder containing a narrow thin strip of the

¢spar would give us a bisected or trisected field with a
vanishing line.

In cutting * the spar for both the first polarizer and for
the sensitive strip, two directions in the crystal have been
tried. In the first system the longest axis of the plate lies

(o ina principal plane through the optic axis, making an angle
of 70° with it. The first plate was cut about 2 mm. thick
and in the form of an ellipse with its edges ground away so
as to fit within the cylindrical cell containing the liquid.
The dimensions of this ellipse were 44 mm. by 15 mm. over

-one face, thus giving a clear circular aperture of 15 mm.
with an angle of incidence of 70°. The sensitive strip was
eut in the same plane but only 5 mm. by 44 mm., and rect-
angular in shape. The thickness was 0°15 mm. and its lateral
edges perfectly sharp and square with its faces. Experience
» with plates of these dimensions and thicknesses show that
they may be safely reduced to 0°l mm. or less in thickness.
In the second system the plates were all cut rectangular and
to the same dimensions as those of the first. Their direction
within the crystal, however, is different, their faces being

2. principal planes through the optic axis which is perpendicular
to the longest edge or length of the plate. More difficulty
was experienced in grinding these as they fractured more
readily and a thickness of 0°5 mm. was found practicable.
More material was also required for this system.

3- In order to obtain total reflexion of the extreme red rays,

an angle of incidence of 65° is necessary. To provide for
total reflexion of a cone of rays, 68° to 70° is required. The
angle of incidence adopted is 70°. This gives a length of
40 mm. for a cell of 15 mm. clear aperture. The cost of a
plate itself is about one-third that of a nicol of the same
aperture. The ellipse or first plate is mounted within a cell
of about twice the diameter of the aperture in order to
provide for sufficient fluid and effective diaphragming. There
are five of these diaphragms fixed to a concentric tube and
> they are slightly slotted along a diagonal so as to admit and
retain the polarizing plate. This latter is cemented slightly
at its ends to the blackened tube with fish-glue (Le Page’s),
mixed in four parts with two of glycerine and five of water.
Care is exercised in avoiding any strain as depolarization will

* The plates were cut and polished by Bernhard Halle, Steglitz-Berlin,

166 Prof. D. B. Brace on a

be present under the slightest effect induced by the cement

or otherwise. Thin cover-glasses are carefully selected and

cemented on the brass caps or end-pieces which screw into
the tube. No moisture or acid used on the metal must be

¢ allowed to reach the plate. The liquid itself shows no action

on.spar. As it is quite volatile the cell is closed tight, with a
bubble of air remaining in to compensate for expansion. The
sensitive strip may be mounted in the same cell, but in order
to vary the sensibility one of the plates must be capable of a
slight displacement. The mechanical difficulties are greater
in such a system ; but higher efficiency is possible. On the
other hand, greater simplicity is obtained by mounting the strip
in a separate cell and then placing the two cells in a common
tube and rotating the first, as is usually done in the mounting of
the Lippich system. With such thin strips of spar, of course
care must be exercised in mounting them so that they will not
fracture or suffer strain. This was done bycutting away a slight
portion in the inner circumference of the caps of the tube and
cementing the ends of the strip to these with the cement
mentioned. ‘Thin cover-glasses were then cemented over the
ends of the blackened brass cell and the liquid inserted through
a small opening which was later sealed up. However, such a
strip might at the outset show no trace of depolarization, and
later not give perfect blackness owing, manifestly, to the
setting of the cement and the induced strain in the strip.
This was obviated by cementing one end only and leaving
the other slightly free within retaining contacts. When these
precautions are taken and the system examined in the ordinary
way with analyser and telescope, the surprising sharpness

> between the fields is at once observed and, with a neutral

setting, as perfect a vanishing line is obtained as with the
most delicately adjusted strip in the best spectrophotometer.
This system, properly mounted with parallel end-plates, when
placed in any ray system will give a single image and

44cause no deviation of the axis of the ray system. The

sensibility of the system can be varied easily and a
vanishing line obtained. It may also be used for any
colour and the neutral setting will not vary for different
parts of the spectrum. When the liquid is freed from

.» suspended particles by filtration no diffused light emanates

from the polarizer and a perfectly black field is obtainable
even with direct sunlight. These conditions are not so

quickly obtained as with the system of Lippich, but when

they are, a greater sensibility is possible. For a single bundle
of rays or such as would emanate from a narrow source or

slit, it is evident that, on account of the narrow edge of the

Sensitive-strip Spectropolariscope. 167
strip as compared with the long polished side of the second
nicol in the Lippich form, a much more continuous system of
rays is possible and hence a far sharper bounding or a
vanishing line between the fields.

Various systems have been tried for obtaining different
monochromatic light of sufficient intensity. As mentioned
above, the intense system of Aron gives only definite wave-
lengths and hence cannot be used for all purposes. Any one
of the mercury lines was also found to be much less intense
than a corresponding portion of the spectrum sufficiently nar-
row to give, within the limits of observation, the same rotation
of all its components in the experiments tried. Absorption
cells are not sufficiently monochromatic for many observations
and are of course restricted in the colours available. Except
in the sensitive-strip system here described, a broad diffusing
source is necessary. Here too sunlight gives the best results;
but in order to use it as such, a diffusing plate, e.g. a ground-
glass or milk-elass plate, must be inserted. This is found to
reduce the available light by 95 per cent. to 98 per cent. Owing
to the sensibility of the system any arbitrary spectral arrange-
ment will not suffice. No light should be allowed to enter
the polarizing system which is not used in the immediate
observations. The spectral system adopted must fulfil these
conditions. The most obvious arrangement and one used
largely is to place a slit at a focus conjugate to the analyser
and with the lens immediately at the polarizer, a dispersing
prism being placed immediately before or after the lens. A
spectrum is thus formed in the plane of the analyser and by
4 proper diaphragm or slit in this plane, the eye, aided by a
telescope or not, will see the field illuminated with a uniform
tint. This is owing to the fact that the retina is a conjugate
focus to the field aperture, which is a colour radiant, and its
Jens converges all rays of different colours radiating from one
point of the field (dispersing prism) to a common focus on
the retina. If, however, a cell of absorbing substance, say for
the green, is placed in the path of this beam, the very small
amount of green which is transmitted may be largely
neutralized by extraneous light or by the smallest fraction of
red and blue which is diffused from the faces of the prisms
or from internal reflexions of the system, which thus becomes
a radiant. This has been found to give apparent rotations
following some regular law predicted on entirely ditterent
grounds. ‘To avoid these spurious results, the entire
dispersion and separation of the colour should take place
outside and beyond the polarizer. This of course may be
attained in many ways, several of which have been tried,

168 Prof. D. B. Brace on a

e.g.the dispersion may be obtained by a single optical system

and the resulting spectrum formed in the plane of the slit above
referred to as conjugate to the analyser. A suitable mirror
before the prismatic system may be made to rotate any colour
into this slit and maintain the system of rays used homocentric
to any axis in the system. It is not easy, however, with such

a system to obtain a uniform intensity over the entire field of
view. The difficulty from diffusion referred to, however, is-
eliminated.

The system which has given thus far the best results is a
modification of one devised by the writer for colour mixtures.
and used by Doubt* in his determination of the colour
equations for different radiants. This is a reversing colour-
system consisting in reality of a double dispersing system.
A concave mirror whose radius of curvature is the focal
distance of the cone of rays emerging from the prism and lens
is placed in the focal plane. The rays of different wave-lengths.
strike it at the same angle and hence are reflected back and
recombined in the prismatic.system and brought to a focus at
the slit source. Evidently any portion of the spectrum would
be recombined here. All screens with such a narrow slit
were found to diffuse more cr less the remaining colours of
the spectrum, so that a single narrow mirror was used to
reflect a corresponding portion of the spectrum, the remainin
portion being allowed to pass cn to the darkened walls of the
room. After returning through the prismatic system where
all rays were recombined, a mirror reflected the cone of rays
through the polarizing system which come to a focus at the
analyser. In this way fields of perfectly uniform tint with
vanishing lines for a neutral setting were obtained, and, using
the sun’s rays, a sensivility for the mean colours greater than
that which had previously been possible with the Lippich
form using white light. The accompanying table (p. 169) gives.
a series of successive settings taken at random by Mr. Bates,
Fellow in Physics, to whom is due much credit for the
perfection of this arrangement and the elimination of the
spurious effects in anomalous dispersive substances observed
by the other experimenters.

These give the deviation of a single setting from the mean of
from one two-hundred-and-fiftieth to approximately one two=
hundreth of a degree for these three wave-lengths.

In natural rotative substances this system needs no special
mounting, but in the study of magnetic rotation it must be
free from the action of the field. his has been accomplished,

* Phil. Mag. [5] xlvi. p. 216 (1898).

Sensitive-strip Spectropolariscope. 169

C-line. D-line. E-line.
OFS? "(95° "1575
"O75 "095 LOUD
“O775 "100 *1600
SUS 025 50
OFS “O95 "1550
‘O75 ‘0975 Gao)
‘070 “0975 oO
“075 "0975 OTD
‘O75 Oot "1525
‘O75 “1000 "1550
“O75 "O95 VSD)

"095

50D

20815)

when it is near the system, by housing it in a thick iron
cylinder of suitable length which becomes at once the
containing tube for the cells. Attention should also be
ealled to the further fact that when the rotation is measured.
immediately by the analyser the different elements of the
field sometimes show a slight difference in tint if the rotation
is considerable. This is due to the fact that the light is
not strictly homogeneous, and the different components are
rotated by different amounts. This could be wholly or
partially avoided by using a rotary compensator, e. g. quartz
wedges.

For perfect adaptability to any wave-length there is no
doubt that systems giving channeled spectra are preferable,
but on this account only, as their sensibility is far less than
the half-shade or sensitive-strip instruments. A rotation
equal to the amount observable in the system described and
referred to in the table above means a displacement of only
one forty-thousandth of the distance between two black bands
in a channeled spectrum. It is very doubtful indeed whether
a setting in channeled spectra closer than one degree can be
made with the same certainty as one two-hundredth of a
degree with this system. This means one two-hundredth of
a band, which ordinarily is very high indeed. However, some
observers have claimed settings as accurate as from ten to
three one-hundredths of a degree or one six-thousandth of a
band. Experienced observers in repeating such observations
with similar apparatus have never been able to set, with
certainty, closer than one or two degrees. Such a realizable
sensibility would truly be an immense step in advance, as a

170 Geological Society :—

channeled spectrum is really the only true representation of
dispersive gradation. Until this can be unquestionably
demonstrated, the use of the sun with the sensitive-strip
system must be relied upon on account of its greater sensi-
bility and adaptability for any spectral study.
Physical Laboratory,
University of Nebraska, Lincoln.

Naturlehre. Von Dr. Atoris Lanner. Mit 377 Figuren, einer
Spectraltafel und 4 meteorologischen Karten in Farbendruck.
Wien: Verlag der Jos. Roth’schen Verlagsbuchhandlung. 1902.
Pp. 37. |

nine task of writing an elementary text-book of reasonable size

which should contain a brief account of all the branches of physics

(including the elements of astronomy) and chemistry is a somewhat

formidable one, and we must congratulate the author on its suc-

cessful accomplishment. Wisely abstaining from trying to confront
his reader with an unmanageable mass of facts, the author makes

a careful selection of such phenomena as serve to illustrate and

bring home to the mind of the student the leading principles of

modern science.

[7 spite of its elementary nature, the book is thoroughly up to
date, wnd the interest of the reader is maintained by frequent
references. to the numercus practical applications of the principles
dealt with in the book.

There is a peculiar interest attaching to this work. It has been
written along the lines laid down by the Austrian Ministry of
Education for the guidance of teachers in the State secondary
schools or ‘‘ gymnasia.” A boy who has mastered the contents of
this book has certainly obtained a good insight into physical science,
and is splendidly equipped for the subsequent training in a tech-
nical college or university. One cannot help thinking how much
easier the work of higher technical education would become in
England, if only every secondary school were to put its pupils
through some such course as that contained in the book under
review.

XIII. Proceedings of Learned Societies.

GEOLOGICAL SOCIETY.
[Continued from vol. iv. p. 520. ]
May 28th, 1902.—Prof. Charles Lapworth, LL.D., F.R.S.,
President, in the Chair.
HE following communications were read :—

1. ‘The Red Sandstone-Rocks of Peel (Isle of Man).’ By
William Boyd Dawkins, M.A., D.Sc., F.R.S., F.G.S., Professor of
Geology in Owens College (Victoria University), Manchester.

The Red Sandstone Series, ranging along the coast from Peel to
Will’s Strand, is faulted into the Ordovician massif of the Isle of

Red Sandstone-Rocks of L. of Man. a7)

Man. It has been referred to the Old Red Sandstone, the Calci-
ferous Sandstone, the basement Carboniferous, and to the Permian.
The series consists of red sandstones containing irregular conglo-
merates and breccias, more or less chemically altered, known in the
Lake District as ‘ Brockram.’ Sections at Ballagnane, Creg Malin,
and at the Gob and Traie Fogog, are described in detail; the
rocks are classified, and their range to the north-east and inland
is described. It is pointed out that the rocks are ditferent in many
respects from the basement Carboniferous rocks of Langness and
elsewhere, and a list of the materials contained in the ‘ Brockrams ’
is given. All these materials have been derived from rocks similar
to those which form the Lower Carboniferous Series in the Lake
District, with the exception of one or two types which might belong
to any other pebble-beach. The fossiliferous pebbles in the rocks
in question are described, and their fossil contents determined. The
whole group of fossils is Lower Carboniferous and Ordovician, and
centres mainly in the Carboniferous Limestone. A comparison is
instituted with the Permian rocks of Barrowmouth, the Vale of
Eden, and elsewhere. The rocks are much sheared and faulted ;
the planes of shearing intersect the bedding-planes, and divide the
rock into lenticular and diamond-shaped masses, which are scored
and slickensided. The earth-movement to which this is due took
place in the interval between the latest Paleozoic and earliest
Mesozoic deposits. The iron in the rocks was probably derived
from the destruction of the Carboniferous shales.

2. ‘The Carboniferous, Permian, and Triassic Rocks under the
Glacial Drift in the North of the Isle of Man.’ By Wilham Boyd
Dawkins, M.A., D.Sc., F.R.S., F.G.S8., Professor of Geology in Owens
College (Victoria University), Manchester.

The whole of the Isle of Man, north of a line drawn due west from
Ramsey, is covered with a thick mantle of Glacial Drift. South of
this line rises the ice-worn Ordovician massif. Six borings carried
out under the advice of the author have elucidated the geological
structure of the Drift-covered area. The borings at Lhen Moar,
Ballawhane, Knock-e-Doony, Ballaghenny, and two at the Point of
Ayre are described in detail, and the rocks classified. The first
shows Carboniferous Limestone under Drift; the second and third,
Trias, Permian, Yoredale, and Carboniferous Limestone ; the fourth,
Trias, Permian (thin), and Yoredale: the fifth and sixth, Trias, with
gypsum and 76 feet of rock-salt. The rocks all dipin natural order
towards the north, and constitute a plateau of marine erosion sloping
to the north and east covered with Drift, which is in places not less
than 450 feet thick.

3. ‘ Note on a Preliminary Examination of the Ash that fell on
Barbados, after the Eruption at St. Vincent (West Indies).’ By
John Smith Flett, M.A., D.Sc., F.R.S.E., F.G.8. With an Analysis
of the Dust by William Pollard, M.A., D.Se., F.G.S.

Two samples of the material were sent by Dr. ). Morris, of the
Imperial Agricultural Department for the West Indies, to Prot. J.
W. Judd, who forwarded them to the Director of the Museum of

172 Geological Society :—

Practical Geology. The fine grey powder is gritty to the touch,
and it all passed through a sieve with 30 meshes to the inch. It
contains plagioclase-felspar (generally idiomorphic labradorite) coated
with a thin film of glass, hypersthene and monoclinic brownish
augite, both frequently in perfect crystals, magnetite, apatite,
possibly zircon, and fragments of a brown glass. Among the finest
débris there is much felspar in the form of minute chips. The
perfect crystalline form of many of the constituents of the dust and
the small amount of glass adherent to them, indicate that at the
time of projection the glassy magma must have been very fluid, and
it must have been to a large extent wiped off the crystals by friction.
From Dr. Morris’s account, the minerals of high specific gravity
appear to have fallen first ; the order being magnetite and pyroxenes.
first, next the felspars. and finally the glass threads and minute
felspar- débris. Dr. Pollard’s analysis is as follows :—Si0,=52°81,

filo ae — 1879, Ke O.=3 28, BeO—458, Mn0= 28.
(CoNi)O= Ue Ca0=9: 58, Me0 = 5:19, K,0O="60, Na O—a2e

£0 aoe — as, Cl" 14, He O=-37; Total 100°35.

June 11th.—Prof. Charles Lapworth, LL.D., F.RS.,
President, in the Chair.

The following communications were read :—

1. ‘A Descriptive Outline of the Plutonic Complex of Central
Anglesey.’ By Charles Callaway, D.Sc., M.A., F.G,S.

The central complex of Anglesey was originally composed of
diorite, felsite, and granite. The gneiss and granitoid rock of the
area, formerly regarded as sedimentary in origin, are now known to.
be plutonic masses. ‘The diorite undergoes numerous modifications,
into hornblende-gneiss, chlorite-gneiss, micaceo-chloritic gneiss,
and kersantite and biotite-gneiss. The felsite has not been found
in its original state, but is converted into ‘hiilleflinta,’ quartz-
schist, mica-schist, and mica-gneiss; granite and quartz-felsite
are intrusive into the diorite and felsite, and the two former are
regarded as derived from the same magma. ‘They are not foli-
ated, and were intruded subsequently to the modification of the
diorite and felsite into gneisses and schists. The diorite, ori-
ginally a xenolith surrounded and injected by granite, has been
modified into an elliptical dome of dark gneiss: into simple gneisses
by pressure. and into complex gneisses by pressure plus granitic
intrusion. This intrusion has often produced fusion at the contact,
sometimes with the generation of biotite in the diorite. In addi-
tion to this, the diorite possesses an imperfect fluxion-structure.

2. ‘Alpine Valleys in Relation to Glaciers. By Prof. T. G.
Bonney, D.Sc., LL.D., F.B.S., F.G.8.

The author discusses some hypotheses about the formation of
Alpine valleys which have been advanced by Prof. W. M. Davis,
but has left the Ticino Valley, on which the latter lays much stress,
to Prof. Garwood, who has very lately visited it. Prof. Davis
maintains that the upper and wider parts of Alpine valleys were
excavated in pre-Glacial times, the lower and narrower portions

De
vo

Alpine Valleys in relation to Glaciers. 1

during the Great Ice-Age. The author tests this hypothesis by
applying it first to the valley of the Visp, of the eastern arm of
which, and of the ‘ hanging valley’ like a gigantic corrie, where
Saas Fee is situated, he gives a description, pointing out that all
parts are so connected that any separate explanation of their form
is impossible,

To obtain an idea of the condition of the Alps in Middle and Later
Tertiary times, we may consider the effect of alterations of tempe-
rature, on the assumption (which, as he shows, is not likely to be
seriously incorrect) that the altitude of the Alps during the greater
part of their existence has remained unchanged. A rise of tempe-
rature of from 6° to 7° Fahr. would have the same effect as
lowering the district by 2000 feet ; a rise of 10° would correspond
with 3000 feet. In the latter case the Pennine chain about the
headwaters of the Visp would be comparable with the range from
Monte Leone to the Ofenhorn. With a rise of 14° glaciers would
almost vanish from the Alps, for the snow-line would then be at
12,000 feet above sea-level. Thus giacial action in the Oligocene and
Miocene ages would be a negligible quantity, and it would gradually
become sensible during the Phocene; but glaciers would not invade
valleys now free from them until the temperature was some degrees
lower than itis at present—in other words, can have occupied these
during oniy a small portion of their existence.

The author passes in review a number of other Alpine valleys,
which lead to the same conclusion. He calls attention once more
to the connexion of cirques with valleys, to the impossibility of
referring the former to glacial action, and to the unity exhibited by
all parts of the Alpine valleys, touching upon some structural difh-
culties which Prof. Davis has been content to meet with hypotheses.
Alpine valleys in all parts, as the author shows, indicate by their
forms meteoric agencies other than glaciers, which can only have
acted for a comparatively short time and have produced little more
‘than superficial effects.

3. ‘The Origin of some ‘‘ Hanging Valleys” in the Alps and
Himalaya.’ By Prof. Edmund Johnstone Garwood, M.A., F.G.S.

Lateral valleys which enter the main valley marked by discordant
grades in the Jongri district of the Sikhim Himalaya have deen
attributed by the author to Pleistocene elevation and super-erosion
-of the main valley by water. Similar valleys in the Val Ticino
have recently been attributed to overdeepening of the main valley
by ice. The author shows that there is no real proof of this
in fact the evidence seems strongly to point to fluviatile, and not
glacial erosion of the main valley. This is shown by the overlapping
profiles and river-gorges situated both above and below some of
these ‘hanging valleys,’ and by the fact that a greater relative
amount of orosion has taken place towards the upper end of the
main valley than at the lower, where the mouths of the ‘ hanging
valleys’ are less elevated. ‘The overdeepening of the main valley
is attributed to an epeirogenic uplift in Pleistocene times, con-
sequent on the melting-away of the ice-cap, the lateral valleys
being merely tilted sideways, This effect is intensified by the

174 | Geological Socrety :-—

protection accorded to the high lateral valleys by ice, which even
nowadays still lingers there. Examples from the Maloja district of
the Engadine are cited as confirmatory of this. The best-preserved
of these ‘hanging valleys’ in three districts examined by the
author all face north-eastward, and show protection by ice; others.
not so protected have begun to cut back their gorges to an accordant
grade with the main valley. Examples of other types of ‘ hanging
valleys ’ not due to the overdeepening of the main valley are given,
and proofs of the greater power of water to excavate over ice are
assigned.

June 18th.—Prof. Charles Lapworth, LL.D., F.R.S.,
President, in the Chair.

The following communications were read :—

1. ‘The Great Saint-Lawrence-Champlain-Appalachian Fault of
America, and some of the Geological Problems connected with it.”
By Henry M. Ami, M.A., D.Sc., F.G.S.

The extent, earth-movements, and striking characteristics of this.
fault-line and of the geological formations which occur along this.
line of weakness in the earth’s crust, with special reference to the
formations in British North America, were discussed.

Recent investigations in the succession of faunas and geological
formations in Eastern Canada have emphasized the fact that those
formations which occur to the south and south-east of this great
dislocation are strikingly like the geological formations referable to.
the same geological systems in Great Britain and Western Europe.
The fault, as it is traced to-day, appears to divide the geological
formations of the Maritime Provinces and Canada into two distinet
geological provinces—one, east of the fault, in which the several
formations resemble both lithologically and paleontologically the
British succession; the other, to the west of this great fault,.
where there occurs the typical American or epicontinental type of
succession.

2. ‘The Point-de-Galle Group (Ceylon): Wollastonite-Scapolite-
Gneisses.. By Ananda K. Coomaraswamy, Esq., B.Sc., F.LS.,

The chief rock-types vary from basic pyroxene-sphene-scapolite--
rock, through intermediate rocks composed of pyroxene, scapolite,.
and wollastonite, with felspar and quartz subordinate or abundant,
to acid types made up of orthoclase-microperthite or coarse-grained
quartzo-felspathic rocks. They differ from the normal types be-
longing to the Charnockite Series in their somewhat coarser grain,
in the presence of wollastonite, scapolite, and sphene, the existence
of definite dykes and segregation-veins crossing the foliation, and in
the absence of garnet, hypersthene, original mica, and hornblende ;.
but they resemble the series in the variability of chemical and
mineralogical composition, in the conspicuous foliation, the common
strike, the petrological character of the acid types, and in the local
tendency to graphic structures. The foliation, dykes, weathering,
and relationship to the Charnockite Series are described; and an

Jurassic Strata between Filton and Wootton Bassett. 175

account is given of the more important of the minerals. The rocks
must be classed as orthogneisses, and the wollastonite and
scapolite are original minerals. Possibly the richness in lime is
due to the absorption of a mass of limestone by a portion of the
Charnockite Series. If this be the case, the lime-silicates must be
regarded as endomorphic contact-minerals. On the other hand,
the local richness in lime might be due to an original variation
in the constitution of the magma. The rocks show a progressive
differentiation from basic to acid types, the coarse segregation-
veins being the last product of the process. That the rocks have
not suffered from earth-movement since their complete consolidation
is evidenced by their microscopic characters, while the interlocking
of the minerals at the junction of the segregation-veins with the
matrix shows that the veins are of contemporaneous character.

3. ‘On the Jurassic Strata cut through by the South Wales
Direct Line between Filton and Wootton Bassett.’ By Prof. Sidney
Hugh Reynolds, M.A., F.G.8., and Arthur Vaughan, Hsq., B.A.,
ise. 1 .G.S.

In this section a thin bed of typical Cotham Marble is followed
by the ‘ White Lias, and that by the Lower Lias, which in this
district attains a thickness of about 200 feet. The following
zones are represented:—(1) the Planorbis-beds, containing the
Ostrea-beds and the Cidaris-shales; (2) the Angulatus-beds, in-
cluding the Conybearz sub-zone ; (3) probably the Bucklandi-bed ;
(4) the Turneri-shales ; (5) the Oxynotus-beds ; (6) the Armatus
and Jamesoni-beds; and (7) the Capricornus-zone. The strata are
remarkably shaly, limestone being predominant only at the base.
The typical ironshot Marlstone is only a few feet thick, and the
Upper Lias is reduced to a thickness of about 10 feet. The latter
consists of a compact, cream-coloured marl with Ammonites falcifer,
a compact marly limestone with Amm. communis, and a pyritic bed
-containing Amm. befrons. The Cotteswold Sands are 185 feet thick,
and contain, at several horizons, hard marly beds with Amm.
striatulus. They are capped by the Cephalopod-Bed, in which
Mr. S. 8. Buckman has recognized four ammonite-zones.

The Inferior Oolite has at its base a rock on the horizon of the
‘ Pea-Grit’’ followed by oolitic limestones and ‘ Z’rgonia-Grit.’ It
is succeeded by an oolitic limestone of considerable thickness
containing fossils of the Fullers’ Earth type, and forming a passage
between the Inferior Oolite and the Fullers’ Earth, which comes
next in succession. Above this are sandy limestones, passage-beds,
with Amm. gracilis, a form found in the Stonesfield ‘Slate.’ The
Great Oolite consists of white oolitic limestones with a Pholadomya-
bed below, and an upper series of wedge-bedded oolitic limestones
containing lenticular patches of clay and sand with a Bradford-
Clay faura. The Forest Marble, which is of great thickness and
monotonous character, consists chiefly of shales, with bands of
sandy, shelly, and oolitic limestones. It is followed by the Corn-
brash. The Oxford Clay with the usual zones, and the Corallian
clays and pisolite close the sections. Fossil lists and paleontological
notes on each subdivision are given.

fi neee oy

XIV. Intelligence and Miscellaneous Articles.

ANOTHER HODGKINS GOLD MEDAL AWARDED.

i March last, Secretary Langley of the Smithsonian Institution

appointed a Committee to consider whether any discovery had
been made since the award of the first Hodgkins Gold Medal in
1895, under the general terms of the gift, ‘‘The increase and
diffusion of more exact knowledge in regard to the nature and pro-
perties of atmospheric air in connection with the welfare of man,”
which would render it proper that such a medal should be again
awarded. This Committee consisted of the following distinguished
men of science:—Mr. Richard Rathbun, Assistant Secretary of
the Smithsonian Institution, Chairman ; Doctor A. Graham Bell, for
Electricity ; Doctor Ira Remsen, for Chemistry ; Doctor Charles
D. Walcott, for Geology ; Prefessor E. C. Pickering, for Astronomy;
Doctor Theodore N. Gill, for Biology ; Professor Cleveland Abbe,
for Meteorology; Mr. William H. Holmes, for Anthropology ; and
Mr. 8S. W. Stratton, for Physics.

Owing to the absence of Mr. Rathbun, Doctor Remsen served as
Chairman at a meeting of the Committee held at the Smithsonian
Institution in Washington, April 15th, 1902. At this meeting
the following resolution was unanimously adopted :—

“That the Committee recommend to the Secretary of the
Smithsonian Institution that it is desirable that one of the
Hodgkins Gold Medals be struck, and that it be awarded to
J.J. Thomson, of Cambridge, England, for his investigations
on the conductivity of gases, especially on the gases that
compose the atmospheric air.”

The finding of the Committee being approved by the Secretary,
steps were at once taken to have the second Hodgkins gold medal
struck, under the personal supervision of its designer, Monsieur J.
C. Chaplain, of Paris. The medal (shown in the accompanying
photographic illustration*) has recently been received by the
Institution, and has been despatched to Professor Thomson through
the Department of State.

* [We regret that want of space prevents our reproducing the beautiful
photograph sent. |

OCU

LANDOLT-BORNSTEIN, PHYSIKALISCH-CHEMISCHEN TABELLEN.

WE are requested by Professor Bornstein to inform our readers
that he and Prof. Meyerhoffer are preparing a new edition of the
Phystkalisch-chemischen Tabellen (edited by Landolt and Bérustein,
1883 and 1894), and would like to receive from English physicists
and chemists any corrections, emendations, or additions, in order to
render the new edition more perfect.

Professor Bornstein’s address is: Wilmersdorf b. Berlin. Land-
hausstrs. 10.

Professor Meyerhoffer’s address is: Berlin W. Uhlandsirs. 162.

THE

LONDON, EDINBURGH, AND DUBLIN :
PHILOSOPHICAL MAGAZINE
1) YANB/ Haat

1] pT Os “as }
JOURNAL OF SCIENCE.

[SIXTH SHRIENS.| & 4

‘ rik

FEBRUARY 100 s

pe
oi WE

XV. The Magnetic and Klectric ie ree

absorbed Rays from Radium. By WH. Rurnerrorp, W.A,,
D.Sc.; Macdonald Professor of Physics, MeGill University,
Montreal*.

ADIUM gives out three distinct types of radiation:—
(1) The rays, which are very easily absorbed by thin
layers of matter, and which give rise to the greater portion
uf the ionization of the gas observed under the usual
experimental conditions.

(2) The 8 rays, which consist of negatively charged par-
ticles projected with high velocity, and which are similar in
all respects to cathode rays produced in a vacuum-tube.

(3) The y rays, which are non-deviable by a magnetic field,
and which are of a very penetrating character.

These rays differ very widely in their power of penetrating
matter. The following approximate numbers, which show
the thickness of aluminium traversed before the intensity is
reduced to one-half, illustrate this difference.

Radiation. _ Thickness of Aluminium,
RCS STDS ‘O005 em,
(5: TREN le Teg eae a ‘O5 em.
SYMON) Sens). ') ss ii OR Ree So ems.

In this paper an account will be given of some experiments
which show that the a rays are deviable by a strong magnetic
and electric field. The deviation is in the opposite sense to

—* Communicated by the Author.

Phil. Mag. 8. 6. Vol. 5. No. 26. Feb, 1903. N

178 Prof. E. Rutherford on the Magnetic and

that of the cathode rays, so that the radiations must consist of
positively charged bodies projected with great velocity. Ina
previous paper * I have given an account of the indirect experi-
mental evidence in support of the view that the « rays vonsist
of projected charged particles. Preliminary experiments
undertaken to settle this question during the past two years
gave negative results. The magnetic deviation, even in a
strong magnetic field, is so small that very special methods
are necessary to detect and measure it. The smallness of the
magnetic deviation of the a rays, compared with that of
the cathode rays in a vacuum-tube, may be judged from the
fact that the a rays, projected at right angles to a magnetic
field of strength 10,000 c.Gc.s. units, describe the are of a
circle of radius about 39 ems., while under the same conditions
the cathode rays would describe a eircle of radius about ‘01 em.

In the early experiments radium of activity 1000 was used,
but this did not give out strong enough rays to push the expe-
riment to the necessary limit. The general method employed
was to pass the rays through narrow slits and to observe
whether the rate of discharge, due to the issuing rays, was
altered by the application of a magnetic field. When, however,
the rays were sent through sufficiently narrow slits to detect a
smal] deviation of the rays, the rate of discharge of the issuing
rays became too small to measure, even with a sensitive
electrometer.

I have recently obtained a sample of radiumf of activity
19,000, and using an electroscope instead of an electrometer,
I have been able to extend the experiments, and to show that
the a rays are all deviated by a strong magnetic field.

Magnetic Deviation of the Rays.

Fig. 1 A shows the general arrangement of the experiment.
The rays froma thin layer of radium passed upwards through
a number of narrow slits, G, in parallel, and then through a
thin layer of aluminium foil ‘00034 em. thick into the
testing vessel V. The ionization produced by the rays in
the testing vessel was measured by the rate of movement of
the leaves of a gold-leaf electroscope B. This was arranged
after the manner of C. T. R. Wilson in his experiments on

* Phil. Mag. Jan. 1903, p. 113. It was long ago suggested by Strutt
(Phil. Trans. Roy. Soc. 1900) that the » rays consist of positively charged
particles projected from the active substance. The same idea has lately
been advanced by Sir Wm. Crookes (Proc. Roy. Soc. 1900).

+ The sample of radium of greater activity than that usually sold was
obtained from the Société Centrale de Produits Chimigues, through the
kindness of M. P. Curie.

Electric Deviation of Rays from Radium. 179

the spontaneous ionization of air. The gold-leaf system was
insulated inside the vessel by a sulphur bead ©, and could be

Bion EA.

Earth <

Yi?) J | Inflow of Hydrogen

St Fl sua ala
oo bE i dm

charged by means of a movable wire D, which was afterwards
earthed. The rate of movement of the gold-leaf was observed
by means of a microscope through small mica windows in the
testing vessel,

In order to increase the ionization in the testing vessel,
the rays passed through 20 to 25 slits of equal width, placed
side by side. This was arranged by cutting grooves at regular
intervals in side-plates into which brass plates were slipped.
A cross section of the system of metal plates and air-spaces
is shown in fig. 1 B.

The width of the slit varied in different experiments between
‘042 and ‘1 cm.

The magnetic field was applied perpendicular to the plane
of the paper and parallel to the plane of the slits. _

The testin g vessel and system of plates were waxed to a lead

N 2

180 Prof. E. Rutherford on the Magnetic and

plate P so that the rays entered the vessel V only through
the aluminium foil. ye

It is necessary in these experiments to have a steady
stream of gas passing downwards between the plates in order
to prevent the diffusion of the emanation from the radium
upwards into the testing vessel. The presence in the testing
vessel of a small amount of this emanation, which is always
given out by radium, would produce large ionization effects
and completely mask the effect to be observed.

For this purpose a steady current of dry electrolytic
hydrogen of 2 ¢.c. per second was passed into the testing
vessel, streamed through the porous aluminium foil, and
passed between the plates, carrying with it the emanation
from the apparatus.

The use of a stream of hydrogen instead of air greatly
simplities the experiment, for it increases at once the ioni-
zation current due to the « rays in the testing vessel, and (at
the same time) greatly dinunishes that due to the 8 and
y rays.

This follows at once from the fact that the a rays are much
more readily absorbed in air than in hydrogen, while the rate
of production of ions due to the 6 and y rays is much less in
hydrogen than in air. The intensity of the « rays after
passing between the plates is consequently greater when
hydrogen is used; and since the rays pass through a sufficient
distance of hydrogen in the testing vessel to be Jargely
absorbed, the total amount of ionization produced by them
in hydrogen is greater than in air.

With the largest electromagnet in the laboratory I was only
able to deviate about 30 per cent. of thea rays. Through the
kindness of Professor Owens, of the Electrical Engineering
Department, I was, however, enabled to make use of the
upper part of the field-magnet of a 30 kilowatt Evlison
dynamo. Suitable pole-pieces are at present being made for
the purpose of obtaining a strong magnetic field over a con-
siderable area; but with rough pole-pieces I have been enabled
to obtain a sufficiently strong field to completely deviate the
a rays.

The following is an example of an observation on the
magnetic deviation : — 3 7

Pole-pieces 1°90 x 2°50 cms.

Strength of field between pole-pieces 8370 units.

Apparatus of 25 parallel plates of length 3°70 ems., width
‘70 cm., with an average air-space between plates of ‘042 em.

Distance of radium below plates 1:4 cm.

Electric Deviation of Rays from Radium. 181

Rate of Discharge of
Hlectroscope in
volts per minute.
(1), Without maenetic field ....0./2...2.. 8°33
(2) Wathemaemetiosneld). 3). aes 72
(3) Radium covered with thin layer
of mica to absorb all @ rays .
(4) Radium covered with mica ae 0:92
magnetic field applied .........

The mica plate, ‘Ol cm. thick, was of sufficient thickness to
completely absorb all the a rays, but allowed the Gand y rays
to pass through without appreciable absorption. The differ-
ence between (1) and (3), 7:40 volts per minute, gives the
rate of discharge due to the @ rays alone; the difference
between (2) and (3), 0°79 volt per minute, that due to the
a rays not deviated by the magnetic feld employed.

The amount of a rays not deviated by the field is thus
about 11 per cent. of the total. The small difference between
(2) and (4) includes the small ionization due to the 6 rays,
for they would have been completely deviated by the magnetic
field. Itis probable that the ionization due to the @ rays
without a magnetic field was actually stronger than this ;
but the residual magnetic field, when the current was broken,
was large enough to deviate them completely before reaching
the testing vessel. (4) comprises the effect of the y rays

together with the natural leak of the electroscope in hydrogen.

‘In this experiment there was a good deal of stray magnetic
field acting on the rays before reaching the pole-pieces. The
distribution of this field at different portions of the apparatus
is shown graphically in fig. 2.

Fig. 2.

H = 8370 (CGS)

The Paneer table alngkae: the rate of dischar ge due to the
a rays. for different strengths of the magnetic field. The

182 Prof. E. Rutherford on the Magnetic and

maximum value with no magnetic field is taken as 100.
These results are shown graphically in fig. 3.

Magnetic field Rate of discharge
between pole-pieces. due to a rays.

0 100
3720 C.G.S. units 66
4840 _,, <s D0
6500, _ do
F360. ic) eae 23
Dome) oss = 11

The curve (fig. 3) shows that the amount deviated is
approximately proportional to the magnetic field.

60 B
50

40 |

Percent. of Rays deviated.

20 §

0 1090 2000 3000 4000 5C00 6000 7000 8000 9000
Strength of Fieid, C.G.S. units.

With another apparatus, with a mean air space of ‘055 cm.,
the rays were completely deviated by a uniform magnetic field
of strength 8400 units extending over the length of the
plates, a distance of 4°5 cms.

Electric Deviation of Rays from Radium. 183

Direction of the Deviation of the Rays.

- In order to determine the direction of the deviation, the
rays were passed through slits of 1 mm. width. Lach slit
was about half covered by a brass plate in which air-spaces
were cut to correspond accurately with the system of parallel
plates. Fig. 4 represents an enlarged section of three of the

Fig, 4.

plates, with the metal plate C half covering the sit AB. If
a magnetic field is applied, not sufficiently great to deviate
all the rays, the rate of discharge in the testing vessel when
the rays are deviated in the direction from A to B should
be much greater than when the magnetic field is reversed,
2.e. when the rays are deviated from B to A. This was
found to be the case, for while the rate of discharge was not
much diminished by the application of the field in one
direction, it was reduced to about one quarter of its value by
reversal uf the field.

In this way it was found that the direction of deviation in
a magnetic field was opposite in sense to the cathode rays,
1.e., the rays consisted of positively charged particles.

Electrostatic Deviation of the Rays.

The apparatus was similar to that employed for the mag-
netic deviation of the rays with the exception that the brass
sides, which held the plates in position, were replaced by
ebonite.

Twenty-five plates were used of length 4°50 ems., width
1°35 cm., and average air-space of (055 cm. The radium was
°85 cm. below the plates. Alternate plates were connected
together and charged by means of a battery of small accumu-
lators to a potential-ditference of 600 volts. A current of
hydrogen was used asin the case of the magnetic experiment.

184 Prof. E. Rutherford on the Magnetic and

With a P.D. of 600 volts, a consistent difference * of 7 per
cent. was observed in the rate of discharge due to the a rays
with the electric field off and on. A larger potential-
difference could not be used as a spark passed between the
plates in the presence of radium.

The amount of deviation in this experiment was too small
to determine the direction of deviation by the electric field.

Determination of the Velocity of the Rays.

It is difficult to determine with certainty the value of the
curvature of the path of the rays in a given magnetic field
from the percentage amount of rays deviated, on account of
the fact that some of the rays which strike the sides of the
parallel plates are deviated so as to pass into the testing
vessel,

From data obtained, however, by observing the value of
the magnetic field for complete deviation of the rays, it was
deduced that

Hp =390,000,

where H=value of magnetic field,
p=radius of curvature of path of the rays.
This gives the higher Jimit of the value Hp.

By using the usual equations of the deviation of a moving
charged body it was deduced that the velocity V of the rays
was given by

V=2°'5 x 10° cms. per sec.,

and that the value = the ratio of the charge of the carrier

to its mass, was given by

“ =6 x 103.

te
These results are only rough approximations and merely
indicate the order of the values of these quantities, as the
electric deviations observed were too small for accurate
observations. The experiments are being continued with
special apparatus, and it is hoped that much larger electro-
static deviations will be obtained, and in consequence a more
accurate determination of the constants + of the rays.

* In later experiments, which are not yet completed, I have been
able to deviate about 45 per cent. of the a rays in a strong electric field-
+ The a rays are complex, and probably consist of particles projected
with velocities lying between certain limits; for the radiations include
ihe a radiations from the emanation and excited activity which are dis-
tributed throughout the radium compound, - os

Electiie Deviation of Rays from Radium. 185

The @ rays from radium are thus very similar to the Canal
Strahlen observed by Goldstein, which have been shown by
Wien to be positively charged bodies moving with a high
velocity. The velocity of the a rays is, however, considerably
greater than that observed for the Carta’ Sirillen:

General Considerations.

The radiations from uranium, thorium, and radium, and
also the radiations from the emanations and excited bodies, all
include a large proportion of a rays. These rays do not
differ much in penetrating power, and it is probable that in
all causes the « radiations from them are charged particles
projected with great velocities.

In a previous paper* it has been shown that the total
energy radiated in the form of a rays by the permanent
radioactive bodies is zbout 1000 times greater than the energy
radiated in the form of 8 rays. This result was obtained on
the assumption that the total number of ions produced by
the two types of rays when completely absorbed in air, is a
measure of the energy radiated. The @ rays are thus the
most important factor in the radiation of energy from active
bodies, and, in consequence, any estimate of the energy
radiated based on the 8 rays alone leads to much too small
a value.

Hixperiments are in progress to determine the charge
carried by the a rays, and from these it is hoped to deduce
the rate of emission of energy in the form of @ rays from the
active substances.

The projection character of the a rays very readily
explains some of their characteristic properties. On this
view the ionization of the gas by the « rays is due to
collisions of the projected masses with the gas molecules.
The variation of the rate of production of the ions -with the
pressure of the gas and the variation of absorption of the
rays in solids and gases with the density at once follows. It
also offers a simple explanation of the remarkable fact that
the absorption of the z rays in a given thickness of matter,
when determined by the electrical method, increases with the
thickness of matter previously traversed. It is only necessary
to suppose that as the velocity of the projected particles
decreases in consequence of collision with the molecules of
the absorbing medium, the ionizing power of the rays de-
creases rapidly, This is most probably the case, for there
seems to be no doubt that the positive carrier cannot ionize

* Rutherford and.Grier, Phil, Mag. Sept: 1902,

186 Magnetic and Electric Deviation of Radium Rays.

the gas below a certain velocity, which is very great com-
pared with the velocity of translation of the molecules.

It is of interest to consider the probable part that the a
rays play in the radioactive bodies on the general view of
radioactivity that has been put forward by Mr. Soddy and
myself in the Phil. Mag. Sept. and Nov. 1902. It is there
shown that radioactivity is due to a succession of chemical
changes in which new types of radioactive matter are being
continuously formed, and that the constant radioactivity of
the well known active bodies is an equilibrium process, where
the rate of production of fresh active matter is balanced by
the decay of activity of that already produced. Some very
interesting points arose in the course of these investigations.
It was found that the residual activity of uranium and thorium
when freed from UrX and ThX by chemical processes con-
sisted entirely of arays. On the other hand, the radiation of
UrX* consisted almost entirely of 8 rays, while that of ThX f
consisted of both a and @ rays. Similar results probably hold
also for radium, for the Curies have shown that radium
dissolved in water and then evaporated to dryness temporarily
loses to a large extent its power of emitting @ rays.

It thus appears probable that the emission of « rays goes
on quite independently of the emission of 8 rays. There
seems to be no doubt that the emission of 6 rays by active
substances is a secondary phenomenon, and that the @ rays
play the most prominent part in the changes occurring in
radioactive matter. The results obtained so far point to the
conclusion that the beginning of the succession of chemical
changes taking place in radioactive bodies is due to the
emission of the @ rays, z.e. the projection of a heavy charged
mass from the atom. The portion left behind is unstable,
undergoing further chemical changes which are again accom-
panied by the emission of a rays, and in some cases also of
6 rays.

The power possessed by the radioactive bodies of apparently
spontaneously projecting large masses with enormous yveloci-
ties supports the view that the atoms of these substances are
made up, in part at least, of rapidly rotating or oscillating
systems of heavy charged bodies large compared with the
electron. The sudden escape of these masses from their —
orbit may be due either to the action of internal forces or
external forces of which we have at present no knowledge.

lt also follows from the projection nature of the a rays
that the radioactive bodies, when inclos.d in sealed vessels

* Soddy, Proc. Chem. Soc. 1902.
+ Rutherford and Grier, Phil. Mag. Sept. 1902,

On Vector Differentials. 187

sufficiently thin to allow the a rays to escape, must decrease
an weiyht. Such a decrease has been recently observed by
Heydweiler* for radium, but apparently under such con-
ditions that the « rays would be largely absorbed in the glass
tube containing the active matter.

In this connexion it is very important to decide whether
the loss of weight observed by Heydweiler is due to a decrease
of weight of the radium itself or to a decrease of weight of
the glass envelope; for it is well known that radium rays
produce rapid colourations throughout a glass tube, and it is
possible that there may be a chemical change reaching to the
surface of the glass which may account for the effects
observed. ve

McGill University,

Montreal, Nov. 10, 1902. IE

XVI. On Vector Differentials. By FRANK LAUREN
Hrtcucock.—Second Paper f.
3 HE calculus of Quaternions enables us to represent a

vector, or directed quantity, by a single symbol,
and to work with it easily and compactly. We are not
obliged to resolve into components, nor do we arbitrarily
introduce any lines or planes of reference.

One of the simplest vectors is that of a point in space, re-
presented by the symbol p. If we have a vector function of
p continuously distributed throughout a portion of space, we
may differentiate it: the result is a linear and vector function
of dp, closely analogous, in a mathematical sense, to a homo-
geneous strain. Any such strain is fully determined if we
know the roots of the strain-cubic, and the three directions
which correspond to them.

In an introductory paper on this subject (Phil. Mag. June
1902, p. 576) it was shown that if v be a vector of unit-
length normal to any family of surfaces, and if its differential
be ydp, then one of the roots of the cubic in yx is always
zero.

The other two roots give directions tangent to the lines of
curvature. For a line of curvature may be defined as ene
such that normals at contiguous points intersect, that is, such
that the three vectors v, v+dv, and dp are coplanar; but
because v is a unit-vector dy is at right angles to v, and
therefore parallel to dp. Accordingly (y—g)de=0, g being
a root of the strain-cubic.

* Phys. Zeit. 1902.
+ Communicated by the Author.

188 Mr. F. L. Hitcheock on ~

If we take e¢ a unit-vector along this direction, and »:
another unit-vector such that ey =v, it is legitimate to write

Vv=vyv + eve + yn 3

the vector part of \7v is equal to the term vyyv, a result of the
paper referred to above; Veye=0 by the last paragraph ;
whence Vny7 also vanishes and 7 gives the other root of the
strain-cubic.

2. To illustrate further these fundamental facts, take Dupin’s
theorem that ‘‘each member of one of three families of
orthogonal surfaces cuts each member of each of the other
families along its lines of curvature.”

Let the unit-normals be vy v,, and v,. Then

Vv, = V (vv) = Vg. ¥ — V2V V — 2YXV 9.
Operate by Sv,, remembering that
SvVv=S87,Vv,=S%Vv,=0;

we thus have at once

Six%V2=0,

that is, yvp is at rightangles to 4. But yv2 isalready known
to be at right angles to vy, and is therefore parallel to rp.
This proves the proposition.

3. In order to study certain quantities related to the
second differential of the vector v we may adopt the nota-
tion

dV\/v= dp,
and remembering that yv and V\/v have the same tensor
we may put
yV=(K; VVv=cp.

Thus A, », and vy forma rectangular unit system. Differen-
tiation with regard to these three directions may be repre-

sented by os = and A respectively. Here X and yp are
not the same as the e and y of Art. 1, except in certain
cases, of which families of cylinders are among the simplest.

The constituents of yy may be arranged according to the
following skeleton :—

Yr=PrA+ ryt qv

hemo + atm,
Wr=git+p'et Ry

Vector Differentials. 189

in which if we interchange p and p’,g and q', 7 and 7’, we
shall change into w’. 7

To build up this function notice first that the quantity c
is tne absolute curvature of the orthogonal trajectories of the
given surfaces. If c, be the tortuosity of these curves then

ae cue ° 5 5 ° ° ° e (L)

of. Tait’s ‘ Quaternions,’ §§ 299, 300. Hence

: me ty eee te
ee (2)

which gives definite values for q and p’, and shows that R
vanishes. Again

de=adaTVVv
= —NSyprrdp, by Tait, § 140 (1)
= —Sdpw'u,
so that
Ve= iu

na de ade de

Dee ene ct, aoa are Ger)

giving values for Q andr. Next take
vdp=aVV vy
=d(vxv)
= —Vyvxdp + Vuddp, say ;
then by taking conjugates,
Widp=x'Vxvdp— 4! V vdp,
whence by putting v for dp and remembering that xyu=y'u,
pv — ey
=c\Sr yu SHG IEV IRs ke eee (4D

giving values for p and y.

190 Mr. F. L. Hitchcock on

Furthermore, because \/?v is a vector,

SV VVv=0

=SOWA + epy + ry)

= —(P+Q+R)
le

ate oa +0}, by | (2) and ta)e

whence we have for the value of P,
de ‘

Pes: (4 a

{t remains to get an expression for 7’. Identically we have
VVVv=(p—p )A+(G—q))u+(r—r')v3 . . (6)

operate by Sv and put for rv its value from (3),

<a
, D/C) —n Wi?
but by the ordinary expansion
S .vV (cu) =cSvVe— = ;

whence by equating values

r=(SyVp. . » + sn

To sum up results,

dc
wbr= — 14 O6 wt co Shoe |

= de ‘
bu =cdsvVe.A+ Tint’ + CYS EXH bs. tae

de
Lys Lo
ary COA + a

or more eompactly
ae. s
vdp= ASdpl = A—cSvV ye. pb ce) — pSdp\/c+ cvSdpypu.
The quantity *’ may be expanded thus
=cSvV wu
=¢SvV (—Ay)

—cSv(VA. v—AVv—2yr)
(SV A—).. "ga se is

Vector Differentials. 191

4, Quantities such as SVA involve operating on v by both
VY and d. These operators are not always commutative. In
fact if P be any scalar, and o and 7 any vectors, whose dif-
ferentials we may call ¢@dp and Odp, we shall have

VSrVP=S8rV.VP—@VP, by (5) of the first paper,
=SrV .VP+iSAVP+75SAVP + kSOLVP,
and this extended to a vector by the usual method gives
VOt=—StV .Vaotiptit+jp0j) +kppk. . (10)

This equation may be obtained in a quite different way.
Write

dp7t=db.t+ ddr,

where df .t indicates the result of differentiating Or as if +
were a constant vector. With this understanding

d¢t=SdpV .81V.¢+¢@dp
=S7V . SdpV -o+ bbdp,

provided we do not substitute for dp any but constant
vectors. If now we call the two terms on the right },dp and
d2dp, we shall obtain from each a part of Vr. The first
term gives

H=STV SV .¢+j81V.S/V .¢+kS7V .SkV oo
=S8rV .USiV .c +98j)V .o + kSkV . oc)
anil:

and the second term gives
q2=1p0i + jh0) + kbOk,
leading to the same result as before.
5. From (10), by putting vy for + and x for 4,
Vx Er taytrtuxtetoyy, 2. (1)

: : Ym.
Here the first term on the right is the same as wv — ae

3 and
because for any direction at right angles to y an

xX” — max +m, =0, a) eee Se}

192 Mr. I’. L. Hitcheock on

it follows that

| AVA + LY" w=A(MyX =) A+ ps (M1gX — M2, )
= 2m, +m,(AxA + HX)
= 2in, + mS(AKXA + UXH + vyv)
= 2in,— mz? ;

the last term of (11) may be written cvyA ; therefore

VV yv= Wy tcvynr
SV x = 2m,—m,? — ——

(lla)

SV xv may also be expanded thus
SV xv=SV (cA)
de

BSC
Be ale
which by comparison gives
seem UA? NU ER ON
SVN= Paes (Dos ter prleas Fee” (13)
and so from (9)

7! =2m,—me2——— + = —c.. «. «. (14)

6. Because d(cw)=de.u+cdu and pu is a unit-vector, it is
clear we may write the value of du by inspection of (8),
dropping the component along mw and dividing the rest by c.
This gives |

ae 1 de ; =
dUY Vv=rSdof - Tae SUV p—cw) +vSdpxypm. (15)
C Qi

The differentials of yv and Uvyy, that is of cd and XQ, are

easily expressed in terms of y and y. For

dyv=d(VVv.v)=cVuydp— Vurdp ;

the first term on the right is the same as cySAydp and the
last term is the same as —ASdp + pSdpw’A : therefore

dyv= —dASdpVc+ wSdpW’/rA+ cvSrxdp. . (16):

For dUxv we have only to drop the component of dyv along
A, and divide the rest by c. This gives

dUxy= ~ wSdpw!h + Sdpy’d.. ee

Vector Differentials. 193

7. As an application of some of these expressions, let us
examine the criterion that the state of affairs contemplated
in Dupin’s theorem may exist: in other words, find the
differential equation which must be satisfied by the unit-
normal to a family of surfaces in order that there may be
two other orthogonal families.

One form of the condition is that SeVe and SyV7 shall
both vanish, e and 9 having the same meaning as in Art. 1.
Furthermore,

Ve= V (nv)
= Vn .v—9\V/v—2yn,

and by operating with Se we obtain for all families of
surfaces

De Ve OV AMEE ede ee CS)
Hence, if the condition just mentioned is fulfilled,
SeVe+SnVn=0. yp ee AS TEC a)

It is here not essential that e and 7 shall be of constant
length. We may, therefore, put for them any other vectors
to which they are respectively parallel. If g and g’ be the
roots of the quadratic equation

XK — mx +iy=0,

so that (y—g)e=0 and (y—g’)n=0, and if we operate on
any vector at right angles to v with x—y' and with y—g,
the two results will be parallel, in order, to € and to 7.
Choosing as a convenient operand the unit-vector yw, that is
UVV¥, we shall have

SXF )HVX—NE TEX eV —g)H=9, - (190)
and by expanding and rearranging
S(2y— mm.) MV XL AS (1292 — 2m, — oy eV ee — SHYeV mg =O. (19)
From (10), by writing y for @ and mw tor 7 and du=@,dp,

dl
VX Mss Tin 4b AXA» au KM XO be + vyOny.
The form of (19¢) shows that we are concerned only with
that part of VV ym lying in the tangent plane. The vector
aed

part of + Vy is wr; the terms AXO,A and “xO,m have no

Phil. Mages. 6. ol. 9. No. 26. feb. 1903. O

194 Mr. F. L. Hitchcock on

tangential component ; the term vx@uv equals cyvxr, by (1)
or by (15). Thus the first term of (19c) becomes

S (2X — mom) (We + €vxA) ;
multiplying, and noticing that ¢v=X while SvyAyue = —my,
S (2 — mz) uv — 2m, —CmM25AXA
is the product. We next obtain from (15)

Vea Sap +(e —SAxpe) —¥— . ee

and here again we are not concerned with the normal com-
ponent. Thus the second term of (19¢) equals

S [ (2209? — 2271) w— max] ASpypt p(a—-Sryp)]
= — cm? + my"SrAK + 2e;m, — 2M Sry —EGm.Spxp.
ding
dn
results and noticing that S(AyA+ wyp) = — m2, we find that
all the terms containing ¢ cancel out, and the result is

dm
1 =O (194)

The third term of (19c) is the same as SAxu. Collecting

S (2x —mo)uypn-+ Sd m2 —2m +
which by (11a) may be written
S(Qy— me) ube—SrAxpSVxv=0. . . (19e)
Again, because of the identity
(p—v') w= V(VVV9) ou
we shall have the following expansions :—
S (2x = me) ppp=S2yp— mp) (y'u—-KV VV")
=8 (24 — ng) wrt 28uypV VVv
=S(2x — my) wr’ + 2BayySvV VV v
=S(2x— my) urp'w + 2ryw(SV xv + V? Vv),
and by using this result in (19e),
S (2x — ms) prp!w+ SrAyw(SVxv t+ 2V?Vv)=0. . (19f)—
Finally, by adding (19e) and (19/)
Seb +h’) (2x — my) wt 2rypV2Vv=0, . (199)

where the only operation involving the second differential

Vector Differentials. 195

of the unit-normal is the pure strain ~+wW’. Thus the
equation is of the first order with regard to VVv.

8. In the paper referred to in Art. 1 it was proved that if
P be a scalar such that V?P=0 the unit-normal to the equi-
potential surfaces satisfies the equation

VVC ON ee: (21)

of which various expansions were given. If vy be given
satisfying this condition P is determined by the equation

lon IVE Va (Vues, (22)

of which the solution is very direct and obvious. We may
thus write, as a set of equations defining orthogonal isothermal
surfaces

SvVv=0

Suly +!) (2x12) p+ 2S xwWVI=00 93)

VV (Vv.v)=0 oF

loa DP == (Vv. v)

where the first two equations are to be satisfied by one unit-
vector in order that there may be three orthogonal families
of surfaces, the third equation must be satisfied by each of
the three unit-normals in order that these surfaces may all
be isotherms, and the last equation serves to determine the
three potentials. Cf. § 336 of Tait’s ‘ Quaternions.’

9. In studying special cases we have evidently at our
disposal a great variety of methods. Hquations like (19)
appear to be chiefly useful in general investigations. In
testing whether any given family of surfaces satisfies the
condition discussed in Art. 7 it will usually be easier to find
a vector corresponding to one of the non-vanishing roots of
the strain-cubic, say parallel to 7», and operate on it with
S.7\/,—though indeed the nature of the surfaces may be such
that (19g) takes a very simple form. As a brief example,
let a family of rings be denoted by the sealar function

P=T"7S“'pdp,
where g=ia+jyt+thke+a and dp=—(wwt+jy). Then
ve dIq= —T“q Spdp,
so that by differentiating the given function,
dP=—4T?q S—'pdp Spdp — 2T4q 8~ *pdp Sdpdp,
and because dP= —SdpV/P,
VP=4pT?¢ 8~*pdp + 26pl'g S~“pgp.
O 2

196 Mr. F. L. Hitchcock on
Then by taking a unit along VP, |
v= UVP= (2pSpgp + bpT?y) (T'y Spdp —4a°S*pgp) —*,

T2hp being here the same as Spgo. In differentiating again
it will be well to put, for brevity, T?¢=¢* and Spdp=s?, so
that we have T?0=7?—a?. The result is

dv=ydp= fdp(2t's' —8a*s") +4s't’pSpdp + dpSdpdp(sa'st —t’)
+ ddp(s*t° —4a’s't?) + 2s*t*pSdpdp + 8a°s*hpSpdp} {st — 4st 3,
This linear and vector function contains six vector terms, ot

which all but the last two are self-conjugate, and therefore
contribute nothing toward VVy. The last two terms give

VV v= (2st! —8a°s') Veobp (st! — 4a°s') —?
= 2V ppp(s°t'--4a’s*)~*.
If this last expression be substituted for dp in ydp above, all

the terms vanish except the first and the fourth, giving

xy VV v=(48Vpdp + 2F6V pdp)(st' —4a°s')—}.
But bv an elementary transformation (Kelland and Tait’s
‘Introduction to Quaternions,’ p. 190, 7), since @ is self-
conjugate, we have
$V ppp = —2V pdp— Vp¢"p,

and also ¢?p9= —dp, whence

yV Vv =2Vpdp(2s—f)(st'—40°s*)",
which is a scalar multiple of VVv. Thus Vpd¢p is a vector
parallel to 7 and

SnV Vode =S(iy —jx)V (iy — ja) = 28k (ty —jz) =0.

It is clear also that (199) reduces to

dm ?

a general property of surfaces of revolution, provided the
axis is the same for all members of the family.

The following may be taken as further illustrations :-—

1. If Sov=0, yo differs from y/o by a normal vector.

2. When applied to a vector in the tangent plane the

operator y[ex{v( )}] or (yx Vv)? is equivalent to a scalar.

Vector Differentials. 197

3. If two vectors at right angles to each other and to the
normal be operated on with 2y—m, they will still be at
right angles.

A. lf ye=ge and yn=o'n, then g=—SyVe and
J =-+ SeV 7.

5. With the notation of Art. 4, it may be proved that

—S7,V . 67;= —87,V . 672+ 60,7.— 6057}.

6. Putting a for Swyu and b for Sry, while dyA=¢ydp,
we may establish these six results :

(a) bv= —xX/YA=A (my — mq”) — mavyYp —CV (a+ Mz) ;
EE ee *) de
” ok woe Nt i ee my AX:

(2) SVyA= («— se (tae ie b de

(e) VVXA=pra— “(a5 “4 bel 1+ 02) exe — eu;

BY ead d\
G60 == 6 = 6 See eons:
(f) dim dl) 214 — (a+ my

from which may be deduced the eighteen constituents of
dyn and dy.

7. If v,¥,, and y, are unit-normals to ee orthogonal
families af surfaces, so that XM=9"1 and vv, ='v2, with Saeles
expressions for g,,g,' and gp», go’, dv may be expressed in
terms of the three normals and the six gs ‘(see Ex. 4).

8. If Sp(¢+P)—p=-—1, where ¢ is self-conjugate with
constant constituents, UVP satisfies (21). Thence may be
found the distribution of electricity on an ellipsoid by means
of (22). (In differentiating we may treat @ + P like a scalar,
that is

UL ($+ P)1p]= (+P) “dp — (6 + P)"pdP).
9. Of ddp and ‘dp only one can be integrable.

cr 198 J

XVII. Animal Thermostat. By Lord KELviy *
THERMOSTAT is an apparatus, or instrument, for

automatically maintaining a constant temperature in
a space, or in a piece of solid or fluid matter with varying
temperatures in the surrounding matter.

Where and of what Eenngzeo is the thermostat by which
the temperature of the human body is kept at about 98°-4
Fahrenheit? It has long been known that the source of
heat drawn upon by this thermostat is the combination of
food with oxygen, when the surrounding temperature is below
that of the body. The discovery worked out by Lavoisier,
Laplace, and Magnus still holds good, that the place of the
combination is chiefly in tissues surrounding minute tubes
through which blood circulates through all parts of the body,
and not mainly in the place where the furnace is stoked by
the introduction of food, in the shape of chyle, into the circu-
lation, nor in the lungs where oxygen is absorbed into the
blood. It is possible, however, that the controlling mechanism
by which the temperature is kept to 98°:4 may be in the
central parts, about, or in, the pumping station (the heart) ;
but it may seem more probable that it is directly effective in
the tissues or small blood-vessels in which the combination of
oxygen with food takes place.

But how does the thermostat act when the surrounding
temperature is anything above 98°-4 and the atmosphere

saturated with moisture so that perspiration could not evaporate
trom the surface? If the breath goes out at the temperature
of the body and contains Bepoiree. acid, what becomes of the
heat of combustion of the carbon thus taken from the food ?
Tt seems asif a large surplus of heat must somehow be carried
out by the breath: because heat is being conducted in from
without across the skin all over the body; and the food and
drink we may suppose to be at the surrounding temperature
when taken into the body.

Much is wanted in the way of experiment and observation
to test the average temperature of healthy persons living in a
thoroughly moist atmosphere at temperatures considerably
above 98°-4; andto find how much, if at all, it is above 98°4. |
Experiments might also, safely I helene be tried on healthy
persons by keeping them for considerable times in baths at
106° Fahr. with surrounding atmosphere at the same tempe-
rature and thoroughly saturated with vapour of water. ‘The

* Communicated by the Author; having been read before Section A
ot the British Association at Belfast.

Lord Kelvin: Animal Thermostat. 199

temperature of the mouth (as ordinarily taken in medical
practice) should be tested every two minutes or so. ‘The tem-
perature and quantity and moisture and carbonic acid of the
breath should also be measured as accurately as possible.

P.S., December 5, 1902.—Since the communication of this
note my attention has been called to a most interesting paper
by Dr. Adair Crawford in the ‘ Philosophical Transactions?
for 1781 (Hutton’s ‘Abridgments,’ vol. xv. p. 147), “ Expe-
riments on the Power that Animals, when placed in certain
Circumstances, possess of producing Cold.” Dr. Crawford’s
title expresses perfectly the question to which I desired to call
the attention of the British Association ; and, as contributions
towards answering it, he describes some very important dis-
coveries by experiment in the Hello g passage, which I
quote from his paper :—

“The following experiments were made with a view to
determine with greater certainty the causes of the refrige-
ration in the above instances*. To discover whether the
cold produced by a living animal, placed in air hotter than its
body, be not greater than what would be produced by an equal
mass of inanimate matter, Dr Crawford took a living and a
dead frog, equally moist, and of nearly the same bulk, the
former of which was at 67°, the latter at 68°, and laid them
on flannel in air which had been raised to 106°. In the
course of twenty-five minutes the order of heating was as
annexed f.

Min. Air. Dead Frog. | Living Frog.
o) [o) fe)

JD, A Oe Re aaa 705 | 673

aie 102 72 68

me 100 (2s 693

Bias 100 | 73 70

39 20 95 | 813 78}

“The Hiceiomotar ait iediaceet: into ai Matacls thie
internal heat of the animals was found to be the same with
that at the surface. Hence it appears that the living frog
acquired heat more slowly than the dead one. Its vital

owers must therefore have been active in the generation

of cold.

* Observations by Governor Ellis in 1758; teachings of Dr. Cullen
prior to 1765; very daring and important experiments by Dr. Fordyce on
himself in heated rooms, communicated to the Royal Society of London
in 1774. .

+ In the two following experiments the thermometers were placed in
contact with the skin of the animals under the axilles.—Ori ig.

200 Lord Kelvin: Animal Thermostat.

“To determine whether the cold produced in this instance
depended solely on the evaporation from the surface, increased
by the energy of the vital principle, a living and dead frog
were taken at 75°, and were immersed in water at 93°, the
living frog being placed in such a situation as not to interrupt
respiration *.

Min. Dead Frog. | Living Frog. |
oo) Sade pM heh! tied Meds iF |
9 | ° |
In 1 85 81 |
ee 8&3 | 85 |
3 903 87 |
at 913 89 |
6 O12 89 |
ane 913 : 89 |
|

“These experiments prove, that living frogs have the
faculty of resisting heat, or producing cold, when immersed
in warm water: and the experiments of Dr. Fordyce proye,
that the human body has the same power in a moist as well
as In a dry air: it is therefore highly probable, that this
power does not depend solely on evaporation.

“Tt may not be improper here to observe, that healthy
frogs, in an atmosphere above 70°, keep themselves at a lower
temperature than the external air, but are warmer internally
than at the surface of their bodies ; for when the air was 77°,
a frog was found to be 68°, the thermometer being placed in
eontact with the skin ; but when the thermometer was intro-
duced into the stomach, it rose to 703°. It may also be
proper to mention, that an animal of the same species placed
in water at 61°, was found to be nearly 612° at the surface,
and internally it was 663°. These observations are meant to
extend only to frogs living in air or water at the common
temperature of the atmosphere in summer. They do not
hold with respect to those animals, when plunged suddenly
into a warm medium, as in the preceding experiments.

“To determine whether other animals also have the power,
of producing cold, when surrounded with water above the
standard of their natural heat, a dog at 102° was immersed
in water at 114°, the thermometer being closely applied to
the skin under the axilla, and so much of his head being
uncovered as to allow him a free respiration.

* In the above experiment the water, by the cold frogs and by the

agitation which it suffered during their immersion, was reduced’ nearly
to 913°.— Orag.

Lord Kelvin: Animal Thermostat. 201

oO O°
In 5 minutes the dog was 108, water 112

ae as Fe “3 WO
eg] - ss 108, ,, 112, the respiration having become very
rapid.
13 Z 4 108, ,, 112,the respiration being still more
rapid.
woe :. ie 109, ,, 112, the animal then in a very languid
state.

‘Small quantities of blood being drawn from the
femoral artery, and from a contiguous vein, the temperature
did not seem to be much increased above the natural standard,
and the sensible heat of the former appeared to be nearly
the same with that of the latter.

“In this experiment a remarkable change was produced in
the appearance of the venous blood ; for it is well known,
that in the natural state, the colour of the venous blood is a
dark red, that of the arterial being hight and florid ; but after
the animal, in the experiment in question, had been immersed
in warm water for half an hour, the venous blood assumed
very nearly the hue of the arterial, and resembled it so much
in appearance, that it was difficult to distinguish between
them. It is proper to observe, that the animal which was the
subject of this experiment, had been previously weakened by
losing a considerable quantity of blood a few days before.
When the experiment was repeated with dogs which had not
suffered a similar evacuation, the change in the colour of the
venous blood was more gradual; but in every instance in
which the trial was made, and it was repeated six times, the
alteration was so remarkable, that the blood which was taken
in the warm bath could readily be distinguished from that
which had been taken from the same vein before immersion,
by those who were unacquainted with the motives or circum-
stances of the experiment.

‘To discover whether a similar change would be produced
in the colour of the venous blood in hot air, a dog at 102°
was placed in air at Ast. In ten minutes the temperature
of the dog was 1043°, that of the air being 130°. In fifteen
minutes the dog w as 106°, the air 130°." A small quantity
of blood was then taken from the jugular vein, the colour of
which was sensibly altered, being much lighter than in the
natural state. The effect produced by oer nal heat on the
colour of the venous blood, seems to confirm the following
opinion, which was first suggested by my worthy and ingenious
friend Mr. Wilson, of Glasgow. Admitting that the sensible
heat of animals depends on the separation of absolute heat
from the blood by means of its union with the phlogistic
principle in the minute vessels, may there not be a certain

202 Lord Kelvin: Animal Thermostat.

temperature at which that fluid is no longer capable of com-
bining with phlogiston, and at which it must of course cease
to give off heat? It was partly with a view to investigate
the truth of this opinion that Dr. Crawford was led to make
the experiments recited above.”

These views of Dr. Crawford and “ his worthy and ingeni-
ous friend Mr. Wilson*, of Glasgow,” express, about as well
as it was possible to express before the chemical discoveries
of carbonic acid and oxygen, the now well-known truth that
oxygen carried along with, but not chemically combined with,
food in the arteries, combines with the carried food in the
capillaries or surrounding tissues in the outlying regions,
aud yields carbonic acid to the returning venous blood : this
carbonic acid giving the venous blood its darker colour, and
being ultimately rejected from the blood and from the body
through the langs, and carried away in the breath. Craw-
ford’s very important discovery that the venous blood of a
dog which had been kept for some time in a hot-water bath
at 112° Fahr. was almost undistinguishable from its arterial
blood proves thai it contained much less than the normal
amount of carbonic acid, and that it may even have contained
no carbonic acid at all. Chemical analysis of the breath in
the circumstances would be most interesting ; and it is to be
hoped that this chemical experiment will be tried on men.
It seems indeed, with our present want of experimental
knowledge of animal thermodynamics, and with such know-
ledge as we have of physical thermodynamics, that the breath
of an animal kept for a considerable time in a hot-water
bath above the natural temperature of its body may be found
to contain no carbonic acid at all. But even this would not
explain the generation of cold which Dr. Crawford so clearly
and pertinaciously pointed out. Very careful experimenting
ought to be performed to ascertain whether or not there is a
surplus of oxygen in the breath ; more oxygen breathed out
than taken in. If this is found to be the case, the animal
cold would be explained by deoxidation (unburning) of
matter within the body. If this matter is wholly or partly
water, free hydrogen might be found in the breath ; or the
hydrogen of. water left “by oxygen might be disposed of in
the body, in less highly oxygenated compounds than those
existing when animal heat is wanted for keeping up the
temperature of the body, or when the body is dynamically
doing work.

* Who, no doubt, was Dr. Alex. Wilson, first Professor of Astronomy

in ‘the University of Glasgow (1760-1784); best known now for his
ingenious views regarding sun-spots.

XVIII. On the Existence of a Relationship between the Spectra
of some Elements and the Squares of their Atomic Weights.
by We MARSHAL WATTS, D.Sc, PoC

T’ is well known that the spectra of some allied elements
exhibit certain resemblances ; so that in the spectrum of
one element we have, as it were, the spectrum of another
shifted through a certain distance. This has been made
clearer by the resolution of the lines of certain spectra into
groups by Kayser and Runge, who have shown that in many
cases the wave-lengths of the lines of a spectrum can be
ealeulated with considerable accuracy by means of a formula
based upon that applied with such striking success by Balmer to
the spectrum of hydrogen. Ina general way it may be said
that an increase in atomic weight produces a shift towards
the red end of the spectrum, and the amount of the shift
seems 1n many cases to admit of simple expression in terms
of the squares of the atomic weights.

There appear to be two distinet kinds of connexion between
the spectra of allied elements. In one class of cases, of which
the family of zinc, cadmium, mercury, and that of gallium
and indium furnish the best examples, the differences between
the oscillation-frequencies of certain lines of the one element
are to the differences between the oscillation-frequencies of
the corresponding lines of the other element as the squares
of their atomic weights ; so that, if it be admitted that the
lmes do correspond, it is possible to calculate the atomic
weight of the one element from that of the other by means
of the spectra.

_ In the other class of cases, of which the families potassium,
rubidium, and cesium, and calcium, strontium, and barium
offer the best examples, the element of greater atomic weight
has the smaller oscillation-frequency, and three elements are
so related that the ditferences of oscillation-frequency between
the elements, in comparing corresponding lines in their spectra,
are proportional to the ditferences between the squares of the
atomic weights; so that we can calculate the atomic weight
of one element from the atoinic weights of two other elements
of the same family by means of their spectra.

In the spectra of lithium, sodium, potassium, rubidium, and
ceesium Kayser and Runge distinguish a principal series and

to)
two secondary series, the lines of each series being connected

* Communicated by the Physical Society : read October 31, 1902.

204 Dr. Marshall Watts on a Relationship
together by a formula of the form
: = A[1—Bn-?—Cn““*],

where A, B, C are constants, and receives the values
12, 42 we.

The lines in each series, therefore, approach closer and
closer together towards the violet, coming to a limit at the
oscillation-frequency given by the value of A, which is termed
the convergence-frequency. The values of the constants
for the principal series of the elements named are :—

|
|

| A. | B. C. |
Lithium ..............| 4858473 | 306688 | 2524012
Fisvcielinetee glee 4153681 3:12939 1933950 |
| Potassium ............ 35086°55 361914 | 17-82216 |
Rubidium ............ 3376211 | 371781 | 1665348 |
Cxesiwm .......eeccee 3150156 | 397050 1555107
| i |

Here the differences of convergence-frequency of potassium,
rubidium, and cesium are nearly proportional to the differ-
ences in the squares of the atomic weights; but the same
does not hold between lithium, sodium, and potassium. The
convergence-frequency of sodium, calculated from those of
lithium and potassium on this hypothesis, would be about
40810.

The two rules stated above are probably only approxi-
mations to the truth—the results of the calculations made
would agree more closely with the known values if the actual
law were not more complicated than that assumed.

The numbers given below will show what amount of accuracy
may be expected.

Example 1. From the atomic weight of cadmium, 111°33,
to calculate that of zine (64:9).

The following are the oscillation-frequencies of the lines
assumed to correspond :— :

Cadmium. Zine.
(a) 306544 107 32500'°0 ar
(b) 3073849 86 32540°1. 102
(ec) 319055 = 8b 329287 100
(d) 32446°8 66 331186 386
(e) 36023°7 - 66 34310°8 4
Ch) 3/384:5. 8 34791°3 - 6
(9) Sssol-1 4 B028071G), 87
(4) 392805 Qn 394089 6
(2) 43690°5 107 3693847 =O
(J) 44086:7. 47 31059°2 2b
(k) 44630:0 6r oA? 2) 86

(2) 455506 1 A7548:1 8

between Spectra and Atomic Weights. 205

From these numbers we vet for the atomic weight of zinc
by combinine—
(a) & (c)” 65-44
(a) & (d) 65°69
(a) & (f) 65-48
iC) Se aay
on) twann(/0) ne OAs Oey
(aay Senn) 65:28
(a) & (7) Gard
(a) & (k) 6512
(ain en (L) F GolG
(2) & le) G6L69
(c) & fe) G477 and so on.

Cadmium. Zine.

(72) 19655°8 107 211700 107
(2) 20826:'7 107 215916. 86
(0) 28840:2 107 243714 2
(p) 303019 ~ 4 QISGon 4

um) & {n) 67-08

(x) & (0) 65°38

(np) & (GQ) Car76

(m) & (p) 65:98

Cadmium. Zine.

(q) 276691 8r 29885:1 107
(7) 29370'4 107 304560 8r

(q) & (7) give 64:78 for the atomic weight of zine.

Heanple 2. From the atomic weight of mercury, 119°7i,
to calculate the atomic weights of cadmium and FANG ye
The following are the lines assumed to correspond :—

Mercury. Cadmium. Zine.
(a) 16250 NOMI My crane Ries. 21559'°5 10r
(6) 183664 107 20826:°7 107 215916 86
(c) 201563 26 21368°7 107
(2d) 20354°0 66 214404 86

(a) & (6) give 66:15 for zine.
(b) & (d) give 111°45 for cadmium.
(6) & (¢) give 109°59 for cadmium.

(e) 203540 60 276691 8 r 29885'1 10r
(f) 240574 406 288402 107 302659 8
50269°2 8r

(Wa) PAE) NTO 29570-4107 304560 8
(hk) 298281 46 306544 10r
(2) 302459 106 307349 8b

(ec) & (2) give 111-06 for cadmium.

(e ae » 118:7 for cadmium and 65:9 for zine.

206 Dr. Marshall Watts on.a Relationship

Example 3. From the atomic weight of indium, 118°7, to
calculate that of gallium (69°9).
The following lines are assumed to correspond :—

Indium. Gallium.

(a) 22159°3. AiO 23961:1 207
(6) 243718 87 24787'3 107
(a) & (b) give 69-47.

(ns0 701 ae. 10s: 339541 1a
(d) 328905 107 34780°8 2

Example 4. From the atomic weight of barium, 136-76,
and that of calcium, 39°99, to calculate the atomic weight of
strontium (87°37). |

The lines assumed to correspond are :—

Barium. Strontium. Calcium.

(a) 15387 6 r 19388 10 21617 1h
(0) 17873) An 22061 6 24390 46
(c) 21951 107 2E€976 6x 29736 86
(d) Die OF 23 far Gon 30991 46
(e) 24201 =8r 29399 ln 32229 In
From (a) we get 87°85 for the atomic weight of strontium.

(b) 87-82

(d) 87-22

(é) 8754

H«ample 5. From the atomic weight of czesium, 132-7, aud
that of potassium to calculate the atomic weight of rubidinm
(85°2).

The following lines are assumed to correspond :—

Cesium. Rubidium. Potassium,

(a) 12469 6 {aya et 14465 7
(d) 21764 67 Zola Gr 24700 67
(ce) 21945 8r 23/91 — Sr 24719 8)
(d) 25707 «Ar 27833 4r 28998 6r
(e) 25787 = Gr 27868 6r 29006 8
Ca) 27638 2r 29832. 27 31068 47
(9) 27678 4r 29852 47 31073 ~6r

(a) gives 86°87

(d) 83°24

(d) 84°51

(e) 84:95

(f) 85°52

(9) 85:51

Letween Spectra and Atomic Weights. 207

And the convergence-frequencies 31502, 83762, and 35086
give 86°02.

Mitscherlich, so long ago as 1864, pointed out the similarity
in the spectra of the Piionde. br omide, and iodide of barium.
and endeavoured to trace a connexion with the atomic w eights
of these compounds.

Lecog de Boisbaudran in 1869 called attention to the
spectra of the metals of the alkalies and alkaline earths, re-
marking that the spectrum of czesium is like that of potassium
shifted bodily towards the red. Hartley in 1890 showed that
three triplets in zine corresponded with three triplets in
cadmium, and that in each of these spectra the triplets had
their lines similarly spaced if mapped on the scale of oscil-
lation-frequency. Kayser and Runge in 1891 confirmed this
statement, and point out many more triplets similarly related,
for which they found a connecting o formula of the form

: = A(1—Bn-?—Cn-*).
r

They further call attention to the fact that the differences in
oscillation-frequency in the triplets increase with increase of
atomic weight; and that they are nearly as the squares of the
atomic w eights, They ala remark that in the spectra of
potassium, rubidium, and czesium the mean differences of the
close pairs are nearly proportional to the squares of the atomic ~
weights.

Ramage (Proc. Roy. Soc. 1901) has discussed many of
these relationships, and gives two diagrams with oscillation-
frequencies as abscissee, one with atomic weights as ordinates.
the other with the squares of atomic weights as ordinates.
He points out that in the second of these two diagrams, the
lines connecting corresponding points are nearly straight i in
the case of potassium, rubidium, and cesium; and in the
ease of calcium, strontium, and ‘Bani He remarks also
that “curious results were obtained by observing the points
in which the converging lines, drawn through corresponding
members of doublets and triplets, intersected. It was ditheult
to determine these points accurately, and the results have
since been regarded more as coincidences.”’

In a more recent paper (June 5th, 1902) on the spectra of
potassium, rubidium, and cesium Ramage confirms his
previous results, andes says that the lines connecting corre-
sponding members of homolog ous doublets do actually intersect
on the line of zero atomic weight,

[ 208 J

NIX. Theory of the Connexion between the Energy of Llec-
trical Waves or of Light introduced into a System and
Chemical Energy, Heat Energy, Mechanical Ener ‘Ji, ena
the same. By Meyer WitpErMan, Ph.D., B.Sc. (Oxon.)*.

|e the Philosophical Transactions of the Royal Society,

October 1902, the author published a paper “ On Chemical
Dynamics and Statics under the Influence of Light,” in the
appendix of which he indicated that the laws found experi-
mentally and communicated there find their rational basis and
explanation in ther ‘mody namics. Here the author would like
to consider the subject in a more general and detailed manner,
not limiting himself to the seanllee communicated there.

A. General condition of Equilibrium of a System exposed
to Light or to Electrical Waves.

The following considerations, the author believes, apply
to electrical waves and light simultaneously, for the reason
that both are ether waves with a great number of properties
in common. White light, as ion consists of light of
different wave-lengths, a though the action of light of dif-
ferent wave- lengths upon a chemical system is different j in
2 quantitative sense, the rays of different wave-lengths do not
differ from one another from the qualitative aspect. We do
not strictly speaking subdivide the different waves of the
spectrum according to their lengths into “ chemical”? and
heat?’ rays. They all act. “ chemically,” and all produce
heat effects, and as far as the “ chemical ”’ effect is concerned
the maximum and minimum “chemical ” effect will fall into
different places of the spectrum, depending not only upon the
wave-lengths of the light, but also upon the nature of the
chemical system itself. Sir William Abney showed that even
the red and ultra-red parts of the spectrum also possess the
property of producing chemical decomposition Tf. In the
same way, from the standpoint of the electromagnetic theory
of light, electrical waves are not to be separated into
a special category different from the lght-waves— both
being sether-waves of the same fundamental nature. We
may safely expect that electric waves when introduced into
a chemical system are, as well as light-waves, capable
of producing phenomena connected with a variation of the
chemical potential, even if phenomena of chemical disso-
ciation or association, &c., may not be directly observed, and
that it will only be a matter of the proper choosing of the

* Communicated by the Author.
+ Phil. Trans. Roy. Soc. 1880, ii. p. 653.

Connexion between Light and Chemical Energy. 209

region of the phenomena and of proper methods to illustrate
this successfully.

In this communication the author will chiefly give his
consideration to the phenomena he dealt with in the above
experimental research, leaving the consideration of other
regions to be dealt with by subsequent investigations.

The condition of equilibrium of a homogeneous system (in
the dark) is the following :
dH =tdyn—pdv + mdm... +pndm, 2.0 (Gibbs’ equation 12).

Let us now assume that the above homogeneous system with
independent variables (¢.e., in which the substances do not
act one upon another chemically) is in equilibrium in the dark.
Let this svstem be now exposed to some constant source of
light, say to the light emitted by a perfectly black body when
it] is heated up to the temperature necessary for its beginning
to emit light, or to the light from any other source, “having
the same ‘intensity and the same composition, or fo, a cone
stant source of the ether vibration of electric waves. Let
us also assume that the system is always removed from the
source of light by the same distance, which may be chosen
ad libitum, so that the intensity of the lght falling on the
system always remains the same. Let us further assume
that the layer of the homogeneous system is only taken very
thin, or that the absor ption of the light by the given system
is so small that the intensity of the light falling upon the
system in the different planes which are in a vertical position
to the propagated rays of light, practically remains the same.

When the system with independent variables is exposed to
light, in the first instance it always absorbs more or less light
energy. Since no energy can be lost in nature the light ab-
sorbed must of necessity transform inthe system into some other
form of energy. As the light absorbed does not transform into
heat (molecular action) alone, even when no visible chemical
reaction takes place, it must of necessity transform into some
form of kinetic energy of the atoms in the molecules as well.
From a molecular mechanical point of view this will mean that
under the influence of light the amount of work present in the
molecules in the form of ener gy of the atoms wiil increase.

Since every system, including those in which light produces
no chemical change, continues to absorb light as ‘long as it Is
exposed to it; since the absorption- -coefiicient of a substance
is independent of the time of its exposure to the light, and
since no energy can be lost in nature, we further arrive at
the following conclusion: Hither the sy stem is able to store
an infinite amount of energy coming from any source of light,
if it is only infinitely long ei gepone to it, which is an impossi-

Phul. Mug. Deo Volo NOreo. Leb. 19035: ig

210 Dr. Mever Wilderman: Connevion between the

bility—or, when light transforms into heat and into the new
kinetic energy of the atoms, the ratio of the amount of light
transformed into heat to that transformed inte atomic motion
is not constant. This further leads us to the conclusion
that having a system with independent components, 2. e.,
which do not act one upon another chemically, the new energy
of vibrations of the atoms in the molecules, as caused by the
light, will for the given conditions gradually arrive at a
mazimum, after which the light will exert no further addi-
tional strain upon the atoms, and the total amount of light
which is further absorbed by the system will completely
transform into heat.

This maximum value of the new kinetic energy, stored in
the system at given conditions of equilibrium, is thus for each
substance a perfectly definite one. It is for each substance of
the system directly proportional to its quantity or mass in
the system, and each of the substances gets its own peculiar
new properties of motion, a new additional potential.

The above conception being most general and fundamental,
it requires experimental evidence of an immediate kind: it
ought not to depend upon results obtained in a more remote
manner only—such as velocity of chemical combination, &e.
The author succeeded in procuring such evidence ; two plates
of the same metal (fig. 1) connected with the galvanometer
and immersed in a conducting liquid, are specially prepared
and treated so that the electromotive :

i : - Fig. 1.

force in the dark is almost zero. One 2

of the plates is then exposed to the hght,
while the other is kept in the dark. A
deflexion of the galvanometer is obtained
(Becquerel, Minchin, Bose, and my own
experiments). ‘These phenomena seemed
to be of a very complicated nature, more
in the nature of an electrical distur-
bance, because as many ditterent curves in shape and form
were obtained as experiments were made; but after much
trouble the author succeeded by more careful arrangement
of the experiments, and especially owing to the fortunate
possession of a constant source of light, in reducing the
apparently numerous forms of the curves to two forms only,
which in reality constitute one, and thus in arriving at
the much needed general law, giving their meaning and
content. These confirm the above conceptions formed first
in order to explain the laws of chemical statics and dynamics
in light in all their details, namely :—(1) There is not only
un electrical disturbance created by the light which shows
itself in all sorts of ways and then, apparently, often dis-

Energy of Light and Chemical nergy. Zt

appears, but the plate in the light always gradually assumes
(passing thr ough an induction per tod) constant new pr operties ;
a constant new electromotive force ts created, which is to be
seen on the photographed curve, from a line parallel to the line
in the dark. Dozens of photographed curves obtained with
different metals establish this generalization. (2) The electro-
motive force ts directly proportional to the intensity of light
and is a function of its composition.

Thus in the above equation (12) new terms X,dm, Agdmg...

Anim, Will be added to indicate the new kinetic energy stored
by light in the different components of the system.

Further reflection leads to the conclusion that this variation
in the energy of the system under the action of light cannot
remain without effect upon the entropy of the system. In
the general equation (12) td is the thermal energy of the
system, and since the same consists not only of molecular but
also of atomic motion, it cannot, therefore, remain the same
when the atomic motion in the different molecules of the
system changes under the influence of light. We are also
able to give evidence for this &@ priori conception ; we shall
carry out for this a cyclic process at a constant temperature,
making use of the following system: Ag, (or Ag,Cl)+ Cl,
=2AcCl. It is known that Agy (or Ag, Cl) and Cl, com-
bine in the dark completely to Ag oC. It is also Inno that
AgCl decomposes under the action of light either into Ag,
and Cl, or into Ag,Cl and Cl, (this point is undecided yet) 3
and consequently if AgCl is exposed to light in a Closed
vessel, this decomposition of AgCl will go on for so long
until just as much AgCl is formed in the unit of time
trom Ag, (or A g0C1) and Cl,, as AgCl decomposes under the
action of light into Ag, (or Ag»Cl) and Cl,; the system will
then be in a state of y akka rare aes

Let us now assume we have
at the temperature ¢t the system Fig. 2.
Ag, (or ClAg,) +Cl,=2AgCl, 5
exposed to light, in equilibrium.
The same is in a cylinder with a
piston, which moves without |
friction, and exerts a pressure
upon the gas Cl, contained in
the same of one atmosphere, the
Ag, or AgCl’ or Ag,Cl and
AgeCl being solid. Let the quan-
tity of Cl, be aad er. molec.; it
will occupy the space of 22 litres,

Ag. CI+AgCl
or

Ags+ AcCl.

AV Dr.. Meyer Wilderman: Connexion between the

» Now we carry out the following isothermal process :— —

1. We remove the light from the same : the Cl, will com-

bine’ with the Ag, (or Ag,Cl) giving 2 gr. mol. AgCl.
During this process of combination the work done by the
piston against the system will be puv= RT; Apuv= very nearly
2 cal., which will be given to the system ; the heat of the
reaction of the combination in the dark will be W,, and this
will be taken from the system.

_. 2. Now we expose the system to light. It will take up
energy from the light, and the light-kinetic energy used up
during the reaction will be H;; if LL be the light-kinetic
equivalent of heat, LH; is given to the system during the
reaction in light. During this reaction 1 gr. mol. Cl, is
formed, which keeps Cl,, AgCl, Ag, (or A gCl) in equilibrium;
the work done by the system is —pu= —RT; — Apv= —2eal.,
and the heat of reaction of dissociation in light is W; and
this is given to the system. The system is thus again in the same
state from which we started, therefore —W,+ W,+LE,=0,
2. €., the heat of the same reaction is at the same teinperature in
light not the same as in the dark. Tf Wa is negative, W, is
< Wa; if Wais positive, W;is>W,. Now in the equation
dHi=tdyn—pdv, tdy is the heat taken up by the system
(positive or negative) when it is passing from one state to
another. Therefore at the same temperature ¢ in the light td7’
or W, is different from tdy or Wy in the dark.

Further, the exposure of the system to light cannot very
often remain without a change in the mechanical energy pdv
of the system, namely, when chemical transformations take
place in the same. It is, however, not impossible that this
is also the case even when no chemical transformation takes
place in the system, however small this change in the value
of pdv may be, considering that the pressure of a gas at a
constant volume ought to change with the variation of the
kinetic energy of the atoms and molecules. Thus our previous
equation for equilibrium of a system with independent vari-
ables assumes when it is exposed to the light or to the action
of electric waves, and when the heat produced by the absorbed
light is removed from the system (say by the surrounding
bath of a constant temperature ¢), the following form :—

dB + dE, =dE’

=t'dn! —p'de' + { (wy dm!) + { (we/dm’)... + pn'dm,’) ii
+ | (Ay/diny') +) (A,/ding')... +2,/dmy!) = (A)

{

where KH’ is the total energy of the system in light, 7! its
entropy, v’ the volume, ¢'n! the thermal energy, p'v' the
mechanical energy in light, (sy/my’), (w2!my!)...(un’ma!) is its
chemical energy, and (Aj/712'), (Agims!) ...(Av/ my’) the new

Energy of Light and Chemical Energy. 213

kinetic energy stored in the components of the system under
the action of light. The connexion between the terms
(Avdmy,’)...(Ax’dma!) and (f1y/dm')...(ua'din,') now requires
special dat ie

What is to be understood by “the energy stored in the
atoms of the molecules, when the same are exposed to light” ?
Itisa thermodynamic necessity that the light absorbed by
the system (which in this case we assume to represent a thin
layer) should transform into some other form of kinetic energy
of the atoms, and that at the same time this new energy should
directly proportional to the total mass of each component,

e., that the new energy ereated in the sys‘em should be of the
forin (A,/dmy’) ...(An’dm,'). This, however, does not disclose
the nature of this kinetic energy itself. A glance at the
above equation (A) shows that more than one interpretation
of the terms (Ay'dm,’}...(An'dinz’) is possible, and_ these
interpretations entirely depend upon how the ultimate nature
of the energy stored in the atoms of the molecules under the
action of light is conceived.

One conception is that the light-kinetic potentials eo),
(A,')...(An') are identical in nature ‘with the chemical potentials
(-1'), (1u3!).. = (Mn! ). In this case it will mean that the kinetic
a. stored in the atoms under the influence of light
(Mdimy’)...(An’dm,’) is nothing else than chemical energy ; it
will mean that under the influence of light the chemical
potentials of all and the sume substances aiways increase
(simply from one value to another). In the light of this
conception, when ligit-energy i is absorbed by any system SO
far as it does not transform into heat it always transforms
into chemical energy.

This.conception would have the advantage of enabling us,
in the consideration of the systems in which the variables are
‘dependent one upon another, at once to see that the laws
which must govern the two important regions of chemical
statics and dynamics under the action of light, must be those
found experimentally by the author and “communicated in
the Philosophical Transactions. It carries, however, little
conviction for systems with independent variables where
no chémical transformation is to be PONE There are
important regions of phenomen: as phenomena of
absorption, dispersion, refraction, fluorescence, GC. * LOR
which the assumption that the energy stored in the iioles
cules and atoms under the action of: “light cannot transform
‘into chemical energy alone, but must also generate an
energy sui generis, becomes almost imperative. In the
mechanical kinetic explanation of the above ‘phenomena,
Stokes, Helmholtz, Lommel, and ot'.ers, have to assume that

214 Dr. Meyer Wilderman: Connewion between the

when light is passing through a system it creates new periodi-
cally oscillating movements of the atoms or molecules which
are similar to those of the ether waves of the light themselves
(this kind of new energy can well be called ‘ light-kinetic
energy of the atoms or molecules”). Since the theoretical
investigations of the above regions of phenomena on the
basis of the above mechanical conceptions met no doubt with
great success, having found in the quintessence extensive
confirmation in the numerous experimental investigations
undertaken for their test, it is only expedient that in the con-
sideration of the subject ‘from a thermodynamic or energetic
point of view the formed conceptions should be brought | into
concord, if possible, with the conceptions of Stokes, ~ Helm-
holtz, pad ethers. The author has been trying to find a more
direct experimental decision upon this very fundamental
point, and he believes he has succeeded in the following
manner :—Z/f the action of light consisted in the tnerease
in the chemical potential only, then the current generated under
ihe action of light should according to Gibbs’ equations, p- 903,
vl — 9! S04 (Ma — pa’) and wv! —v'’=a,( py’ —p,’) always go IN
ONE direction. The author finds that the same metallic plates
give in different mediums, at one time a current from the plate
in the light to that in the dark, at another time in the opposite
direction, and also that different metallic plates give in the
same medium currents in opposite directions.

Thus the author conceives that the new kinetic energy of
the atoms, stored in them under the influence of light, does
not transform into chemical energy alone, but into chemical
energy and into a lght-kinetic energy sui generis at the
same time. In other words, the terms (A;/dit’)...(An ‘dimn’)
must be decomposed into two ea y,dm,’, vodmg’.. aie
(chemical energy), and Aj/dm,’, A,'dm,’ (kinetic energy s
generis for which we may conveniently retain the term “ eae
kinetic energy,” jy’, do’ ..An’ being the light-kinetie poten-
tials), which like gravitation is bound on the same components,
but is not identical with chemical energy.

The equation for the system in the dark being

dK =tdy—pdv+pydm;...+p,dm,20, . . (12)
it thus transforms in light into another
aH! =t'dn! — p'dv’ + py/dmy/ +r,/dm,’... + wn’dm,! + Andina (A’)

where (1y’) +0, = py’... (Un’) +im=wn’, &e., the values of
pz’, ’ being a Aeon of the intensity of light and its com-
position, ot the nature of the components of the surrounding
medium, «ce.

—

Energy of Light and Chemical Energy. 21a

B. The Effect of Light upon the Induction and Deduction
Periods and upon other Properties of Matter*

Since now it is the light pussing through the system which
is producing the new light-kinetic energy of the atoms and
the new additional chemical energy of the molecules of the
system, and this is a tame process, it follows that it is a thermo-
dynamic necessity that all the systems without exception
(since all systems absorb light), those with independent as
well as those with dependent variables of composition, should
arrive at their new state of maximum kinetic energy, passing
first through a period of gradual approximation to the same.
This period is cailed the “induction ” period.

Experimental evidence :—

1. Such an induction period we find when light is acting
upon one of the two plates of the same metal, while the
other plate is kept in the dark, in the arrangement before
mentioned. Here we have a system with independent
variables of composition, where no chemical reaction takes
place in the same under the action of light, though a gradual
increase in the chemical and a crea Aen aril increase of the
light-kinetic energy, no doubt, take place, because if the
chemical potential remained the sume at the two surfaces of
the plates, no electromotive force could be generated. We
may call it the induction period of energy.

2. Such a period of induction we find for the system with
dependent variables of composition, 2.e., where a chemical
reaction takes place. It was found by the author* that the
velocity-constant of chemical combination of GU and Cl,
gradually increases till it reaches its constant value. Bunsen
and Roscoe first observed the phenomenon of “chemical
induction” in their investigation of the combination of
chlorine and hydrogen under constant conditions. The
phenomenon, however, is of a more complicated nature than
conceived by Bunsen and Roscoe. Here we have to deal
with two periods: one of induction of energy, the other of
chemical induction already found by Bunsen and Roscoe.
Indeed chemical combination does not usually start at once on
exposure to light, but the system first passes through a latent
period during which no chemical reaction can be perceived by
the most delicate means, but a gradual increase of the stored
energy in form of chemical energy and in form of a kinetic
energy sw generis undoubtedly takes place in the same manner
as in the case of the metallic plates mentioned above. When

* See the author’s paper “On Chemical Statics and Dynamics under

the Influence of Light,” Philosophical Transactions of the Roy al Society,
October 1902, pp. 378-891,

216 Dr. Mever Wilderman: Connex on between the

the stored energy is great enough to shatter the bonds
between the atoms in the molecules, a new chemical Te-
arrangement between the atoms takes place—the chemical
induction period starts. As the light-energy is further
absorbed by the system, the chemical and light-kinetic
potentials further increase, the velocity-constant of the
reaction increases (period of chemical induction), until as
mentioned before no more strain is exerted by light on the
atoms in the molecules, and the impulses of the ether-waves
prevent the atoms and molecules from losing their state of
maximum energy, keeping them up in the same state of max1-
mum kinetic energy. It is well possible to conceive that the
ratio of the amount of light-energy transformed into chemical
energy to the amount transformed into light-kinetic energy
‘sui generis is not always the same, and this may account for
the fact that it takes a time before chemical induction starts.
But during both periods—the induction period of energy and
the chemical induction period—both the chemical and the
light-kinetic potentials must change at the same time, as 1s
to be seen from the fact that with metallic plates an electro-
motive force is instantaneously obtained on exposure of one
plate to light.

Besides the period of induction, a period of chemical
“deduction” must equally be considered. This, as well as
the induction period, is a thermodynamic necessity. When
light is removed from the system, and the maximum kinetic
energy of the atoms is no longer kept up by the impulses of
the zther-waves, the new kinetic energy of the atoms which
has been acquired in light will use itself up, ¢@.¢., the atoms
and the molecules will sooner or later return to their old
state which they had in the dark. In what manner will the
kinetic energy of the atoms—previously created by light—
use itself up in the dark? If the system consists of inde-
pendent components it will evidently transform into heat.
This we find with metallic plates mentioned before ; and this
period. during which the chemical potential of the plate
previously exposed to light gradually assumes its former
value, while its light-kinetic potential gradually disappears,
may appropriately be called “the deduction period” of energy.
It again under the influence of light a reaction was going
on in the system which was not going on previously in the
dark, then the above-acquired kinetic energy will partly be
used up during the reaction as long as it will still continue
to go on in the dark, and partly transform into heat. This
period of deduction is naturally also a time process, as the
process of induction is; it represents to some extent the

Energy of Light and Chemical Energy. vad

‘reverse phenomenon to the last, 7. e., during this period the
‘kineiic energy acquired under the influence of light gradually
falls from its maximum to zero. Experimental evidence
‘for the deduction period is given in the experimental in-
vestigation of the velocity of combination of CQ and Cl, *
As in the case of the induction period, here we must also
distinguish between the two periods—the ‘“‘chemical’’ de-
duction period at the beginning when light is removed, usually
lasting only a short time (the reaction “stops), and the much
longer “deduction period of energy.” Though chemical
reaction very soon stops in the system, it is still in another
state of energy, and it only gradually returns to its previous
-state of energy in the dark before the illumination. This
-was shown by the author on the length of the induction
periods on fresh exposures of the sy stem CO+ Cl, to light.
As in the case of the induction period, both the acquired
‘new chemical and the light-kinetic energy decrease simul-
‘taneously during the nt: periods of deduction. It may be,
however, that the ratio of the newly-acquired chemical
energy to that of the newly-acquired light-kinetic energy
still remaining in the system on removal of light, is not
always the same during the period of deduction. The
induction and the deduction period evidently equally -ccncern
systems in which chemical reaction goes on both in the light
and in the dark, but with different speeds (H,O,), or systems
in which a reaction goes on in light only (CO+Cl, or
H,+Cl,). It further follows that if after the deduction
period is completed the system should again be exposed to
the light, the system will evidently have to pass again through
a period of induction; and if the light should be again
removed from the system, a new deduction period will have
to follow. Also, that during the induction period, 7 ae
before the ooinswemd maximum of kinetic energy Is scat
the longer the system was previously exposed to the induc-
tion, the longer will be the deduction period through which
the system passes to the old state, and that, after the
induction period has passed and the maximum reached, the
deduction period will always last the same time, sass
long the system may have been exposed to th e light ;
also the less the sy stem reached the old state, i. e., the Ee
the deduction pericd i Is completed, the shorter is os induction
period when it is again exposed to the light: it is also
evident that both the induction and deduction periods must
naturally depend upon the chemical composition of the
system at the different times, and upon the intensity and

* Phil, Trans. 199 A, p. 337

218 Dr. Meyer Wilderman: Connewion between the

wave-length of the sether-vibrations. All these detailed
conclusions, which here follow as a necessity from purely
thermodynamic considerations, find their experimental verl-
fication in the above-mentioned research, published in the
Philosophical Transactions of the Royal Society, Oct. 1902,

and will be further given in the author’s research with.

metallic plates, which ‘will be communicated in due course.

Since the introduction of light into the system with
independent variables of composition changes in any case
their chemical potentials, and with it their chemical energy,
it is evident that all those physical and chemical phenomena
which in one way or another are dependent upon the chemical
potentials of the components of a system, such as the electro-
motive force, the surface-tension, dc., will also undergo a
variation when the system is exposed to light. As all these
phenomena are either changed or created by the variation of
the chemical potentials of the components, they will change
under the influence of light in the same manner as the
chemical potentials do, 7. e., they will all have under the
action of light their induction and deduction periods, with all
the properties of the same which were mentioned above, and
after the induction period has passed they will all reach
a constant value corresponding to the maximum variation of
the kinetic energy absorbed by the system under the action
of ae

. Chemical Statics and Dynamics under the

Influence of Light*.

It remains to be seen what are the results obtained for
equilibrium and for velocity of reaction when each of the
components of the system has not only a (new) chemical
potential, but also a light- kinetic potential.

If we integrate the equation

dK + dy =dH'=tdy! —plde! + wldm! +r!diy'...url'dm! +rXWldmna,

under the supposition that the quantity of the mass of the
given layer or system (under conditions mentioned on p. 209)
with independent variables of composition increases from zero

to a finite value, while the nature and state of the system
remain the same, we get

E+E, =H =0l'y — p'e' + (my + Ay)... + (a F Ag’) mn’. (i.)
Differentiating the same in the most general way :
dE’ =tdy +n dt'—p'de'—v'dp' + (ty! + Ay’) dmy/
“+ gity'A( fey’ + Ay)... (pen’ # An’) dm, + md (py! +n’),

* See author's paper under the same heading in the Phil. Trans. of
the Royal Society, October 1902, pp. 376-895,

Energy of Light and Chemical Hneryy. 219
and subtracting from this equation (i.) we get
9 dt’ —v'dp' +m dp, +m'dry'... +m, dp,’ +m,'dr,'=0. — (iii-)

Here we have a connexion between 2n+2 variables

Pee th: Man's Ay. a If this connexion is known, the equa-
ae concerning 7’, v’, m,’...mx’, which are functions of the
same variables, will be known as well, and we shall have in
the total n+2 such independent equations. Here, however,
du is not independent of dA. General considerations of the
conditions of equilibrium of a chemical system in Jight Jead
to the conclusion that for this the temperature, the pressure,
and the sum of the chemical and of the light-kinetic potentials
of each of the components must be constant through the
whole system. Therefore

fy, +A(=O), ee e ° 5 (y)

Thus we have in the total 2n-+ 2 equations for the 2n+2
variables ¢', p’, ,',%, ..-Ma’, An, and these with (11.) give in total
2n+3 known equations s, while the total number of variables
Be 7, 2", py, v ie N45 A, Race Isom oO. ohn he
system consists of one substance only, then equation (iu1.)
becomes

nidt! —v'dp! + mydyy! + m,'dr/ =0.

Equations (ili.) and (y) give the variation of temperature,
or of pressure, or of chemical, or of the light-kinetic potential,
or of several of them with ‘Ths <aifake von of one or some of
the variables when all the rest of the variables remain

~ constant.

In case of a gas-mixture there is every reason to assume
: mi

that the energy, pressure, density (i. Gg 1", oo) paid © ;)
: v!

temperature, entropy, potentials of each of the gases separ-
ately are the same when they are together as they would be
if they were alone, provided that the gases do not act one
upon another chemically. This is an extension of Dalton’s
law applied not only to pressures but to all other thermo-
dynamic factors of the same. Thus the variation of tem-
perature or of the chemical potentials and of the light-kinetic
potentials of each of the gases in dependence upon the
variation of all the rest will be the same as if the system
consisted of the given gas alone.

Making use of functions ve’, x’, &, introduced by Gibbs
in his treatment of heterogeneous systems when no light-
energy is stored in the same, we ultimately get, putting

B+ E,—t'dy'=w’,

—t'dn! —v'dp! + mg/d! + my dry’... + mtn’ dpe’ + win dan’ =O... (iY)

220 Dr. Meyer Wilderman : Conneaion between the
Putting E+ E,+p’r’=y’, we get

dt! + p'dv! +mjdu,' +m, ‘dry’... +14! dun’ +: mn'dd,/ =0. (v.)
Putting H+ h,—t'n/—p'v’=C’, we get

—t'dn! +p'dv! +my/dpy! +my/drj/... + my/dpn! + m,/dr,'=0 (vi)

Equations ii1., iv., v., vi. are Gibbs’ modified fundamental
equations of condition, when each of the conponents contains
two potentials.

Tfrom equation (1.) we further get

OES > Seen /
ie Uy, My.

pa! += ( My, +» (1)
.e., if we assume that to a given homogeneous mass an
infinitely small quantity of 2,/ is added, while the mass remains
homogeneous s, and its ‘entropy in light, volume, and the rest
ot the substances remain constant then the sum of the
chemical and of the light-kinetic po: tentials of the introduced
substance is equal to the ratio of the increase in the energy
E and in the energy E, (stored by hght in the system),
saused by this introduction of the substance m,’,to the intro-
duced quantity of dm’ *.

It is further evident that if an equation of chemical
reaction exists between the units of the substance of the
system

din,’

mA, + nzA,...=m,A,+m,Bo..., = 72

where Aj, Ag,...B,, B,... are the units of a different sub-
stances, and 7, m2...7,, My... numbers, then if the reasoning
given by Gibbs in the case of one potential be further

applied to our case with two potentials, we have also

n; (wa, +a,’ + my (wa, +Aa,")... =m; (up +Az_’) ae My (wp,’ + Np, )--+

Let us now return to the consideration of the equation (iii ),
first when the system consists of one gaseous substance
only. It assumes in the first instance the fora

n' dt! —v' dp! + myduy! +1ny'dry/ = 0.

Here 9/dt’, v'dp’, m,/duy', m,dr,’, are the variations in the

* In the same manner we have

dy’
yor = aa Soe Sli,
dm,

! a if ' Ul
i eke (or Pig Ms tase 2a
sous! |

' ' ad f Uy ' 7
BH, TA, = = Nene WS asin WI
dm,

Energy of Light and Chemical Energy. 221

2}
the total mass of the system. ‘We can natur ally express the

mass in any unit we may desire to adopt. Let this unit be
the gram-molecule of the gas, because this will allow a simple
use of the gaseous laws and will also be in conformity with
the form and content of the equations for chemical reaction
which for many reasons were finally adopted by the chemist.
Let the total mass of the gas be im,/ gram- -molecules. Then
we have: the total chemical energy is ~;'m,’, and the above

variation in the same mm, ‘dps! ; the total hght-kinetic energy 1s
mX,', and the variation in the PE (aN chew. boul
mechanical energy of the mass is p'e’=m)'Rt’, or nearly
=m, . 2 cal., since (p;'v;') of 1 gr.-mol.=Re’, vessel the above

m-'Rt

7 2: where v’ is the
(2) L

| Flatt
volume of the gas ; the total 7’ of the mass =m! (7 +K,),

dH! (of ma -mol ) Bee ee

1 gr.-mol.= aoe Ke , where K,' is an integration-constant.

thermal, mechanical, chemical, and light-kinetic energy of

variation in the same is vdp! = vd (

when (dy!) of e or.-mol. =

Thus we o instead of (111.)
my (duy' + dX,') =m, Rad! + Bedi ae vo’ —m'H'dlot’ + K’ dt’

MAO © fe + Ay! = Re + Bu lg™ Hig + K+ By i

where K,” is another integration-constant.

Now we are entitled to assume that in the case of a gaseous
mixture Dalton’s law will hold ao in the idee” SN
Ear not only for H=>(E), p=2(p), 7==(m), P=2W
y= (x), as indicated’ by ena but ie for the Prete
and the light-kinetic potentials of each gas in the gas-
mixture.

Having now a chemigal equation of reaction expressed
eram-molecules,

nm gy.-m. of o,+7 2r.-m. of o,=n; gr.-m. of os,
and ny (poy + A’) + Ny( fy’ = rd’) Nyt + A;’) ;
we thus get

ny | Re le’

+ (R+Ky’‘)e ay Wad |
ace Ig SUR HiRes il syle KS |

{ « r / t / ” Hy
=na| Reg +(R+K,’) é —H; Ig? +K, |
aly

299 Dr. Meyer Wilderman: Connevion between the

eal eae
Ae) IN 5!
Ig -
a | ;
a’

= -- [ (ng Ks! — my Ky! — ng Ky’) t/ — (ng +21 — 13) RE’
+ (n, Hy’ + noH,’—n;H;’) lot’ + (n3K3/’—n Ky” — Ny Ko’) | e (Q)

i. €., the fact that each of the components has two potentials
instead of one does not therefore affect the form of the
equation obtained for chemical equilibrium.

/ / /
Mm Ry Higy WES 12 Wey ;
Here (a ) ( : ) : ( -) “ gives the connexion between
A
/

/
(D) 0

the concentrations of the gaseous substances expressed in
gram-molecules per unit volume acting chemically one upon
another under the action of light, which constitutes the law
of mass-action in homogeneous systems ;

(n,H,/+ nH,’ —n;H;’) lye Fook (ng K3 —n, Ky” —n. 5")

the difference between the thermal energy of n, gram-mol. of
o,+n, gram-mol. of o, and the thermal energy of the
pr oduct of their combination (n3 gr.-mol. of o3) in light of a
given intensity and composition, 1. @., 28 the heat of reaction
(let it be denoted by Q,) 7 light, when mn, gr.-mol. of
a,+n, gr.-mol. ay transform into 23 er.-mol. of o3;
m3K3"—m KK, “—n Ko” = K* is a constant 3; — (72 + ,—n3) Rt’
is the work done by ‘the system or against the same during
the same transformation in light, and ¢/ is the absolute
temperature.

Thus an ordinary consideration of Gibbs’ equations under
the modified conditions (1. e., when each component gets under
the action of light a light-kinetie potential besides its modified
chemical potential) shows that the connexion between the

my'\™ (ms\"2 (ms/\" :
logarithm of Ga : ) : (a) : ( - ) , or the logarithm of the
v

i
constant of chemical equilibrium tn homogeneous systems in
light, the heat of reaction or of transformation of nyoy+ngo3
into n3a3 in light, the external work done by the system or
against the same during the reaction, and the absolute tem-
perature remains the same and follows wn light the same lar
as in the dark,—i. e., a system which is in equilibrium in the
dark, when exposed to light passes under the influence of the
same only to a new point of equilibrium, has a new constant of

Energy of Light and Chemical nergy. 22%

equilibrium, new heat of reaction, §c., but the connexion between
the logarithm of the constant of equilibrium, the heat of reaction,
absolute temperature, will always, nevertheless, be governed by
the same law. Since different intensities and different wave-
lengths differently affect the values of the chemical and
light-kinetic potentials, &e., they will evidently also differently
change the values of the different parts of the equation (2).

=>
Thus, having a reversible system mo, Wie IE and

an equation 1,((;' + Ay") + No([o" +r,’) =n3(p 3" +4) in light
instead of my + Nobo = 3643 IN the dark, it will depend upon
the values of the individual potentials of all components
in which direction the equiltbrium will shift. The same will
be the case when the system is broaght from light of one
intensity or composition into light of another intensity or
composition, the point of equilibrium being for given
conditions always a fixed one.

A short notice in a Jetter from Professor van’t Hoff leads
me to think that a general “ pr inciple of movable equulebrium ”
can be established for light, as it was set up by van't Hoff for
heat. J am not sure that this was what van’t Hoff meant.
In the system CO+Cl,=COUl,, H.+Cl=2HCI, it is the
Cl, which absorbs light most. Having a system CO, Cl,
COC], or H,., Cl, HCi in the dark, they do not act one upon
another, but on exposure to light COCI, or HCl is formed,
4. @., ihe system is shifted from ae left to the right. Again,
in the system AgCl (in light) = Ag+Cl, (in light), it is the
AgCl which absorbs light most, and the light has the effect
of forming Ag and Cl, from “AgCl, and not the opposite.
Since all substances absorb light, this leeds to the conclusion
that “each kind of equilibrium between two states of matter
(system) becomes at a constant volume on exposure to light
shifted in the direction which is accompanied by the greater
absorption of light.’ Van’t Hoft’s principle for heat, para-
phrased, is: “ Hach kind of equilibrium between two ditterent
states of matter (system) becomes at a constant volume on
exposure to a higher temperature (heat) shifted in the
direction which is accompanied by the absorption of heat.”

From the above principle, further conclusions can be drawn
about the influence which the intensity of Light and its composi-
tion must have upon the point of equilibrium. The greater the
intensity of light, the greater the influence of a given wave-
length upon the constituents of the system, the oreater is the
maximum kinetic exergy stored in the atoms and molec ules,
and it is natural to expect that the substance which absorbs
light most has also a greater increase in the values of the

224 Dr. Meyer Wilderman: Connexion between the

potentials, 7. e., the greater the increase of the intensity of
light, &e., the more the equilibrium will be shifted from the
left to the right : more AgCl will be decomposed. In the
ease of H,+Cl,=2HCl and CO+Cl,=COCI,, since the
reaction of decomposition of COC], and of HCl in light is
in any case infinitely small, this will show itself in an
increase of the velocity of pres ar of CO and Cl, or of
fas, Cl, as-18 actually the case. What is the more precise
connexion between the constant of equilibrium and the
intensity of light? This is a problem which will require
long , patient, and most difficult experimental investigation.
The author is now endeav ouring to approach step by step the
solution of this problem. Starting first with the study of
one of the simplest cases of equilibrium, namely, with the
effect of the intensity of light upen metallic plates of the
same kind, mentioned above, the author, being in possession
of a constant powerful source of light, was able to establish
the fact that the electromotive force, which in the same manner
as the constant of equilibrium gives the maximum work, is
directly proportional in this case to the intensity of light. A
more exact investigation of the results obtained and on a
larger experimental basis is, however, needed, may to some
small extent modify this conclusion, and will be communicated
in due time.

Returning to the equation (0), we further get that if
no work is done by or against the system during the reaction,
2. €., at a constant v olume (n+ ny —nz) Re’ ==}. “and the total
ail of the given gas can be put (approximately at
any rate) =C,t’, where C, is the specific heat of the given

eas in light at a constant volume, and we get, after con-
tracting the constants, instead of equation (Q),

lo Si (3) =
ve’

. . . . s ee
which, differentiated with respect to t’, gives
= ay (n 3] 2

as! . c >!

|
=) le
vy’ ) =

PEE STN ies ‘—neW,! ) + (nj, C, + ngCy tn, 2) A + Br’
= Ri? = ae

emp (rey
2 ps he (K+ Ble ewe oy ; (Q")

ee,

Energy of Light and Chemical Enerqy. 225

which is van’t Hoff’s equation, 7. ¢., the variation of the
logarithm of the constant of chemical equilibriam in homo-
geneous (gaseous) systems with the variation of temperature
at follow in the light the same law which it follows in the
dark.

At a constant temperature equation Q or O’ becomes

\ it I Nii . IN Fie
My NL fittg \"2 Mis \"8 F
ie ") ("2) : (3) =| COUR Ee eee men Os)

1. e., the law of mass-action must hold good for equilibrium in
“rere systems, when the equilibrium is shifted under the
action of light to a new point in the same manner us in the dark.
This ts exactly what was found to be the cuse in the experi-
mental part of the paper “On Chemical Dynamics and Statics
under the Influence of Light,’ Phil. Trans. of the Royal
Society, Oct. 1902.

The above equation (Q”) can in homogeneous systems be
decomposed in the usual manner into wo equations of two
opposite velocities of reaction,

GIN ton | HUY" Ree da Pn ibe
(Te) =eCEY CE) ant G2) =e" (2)

which at equilibrium become equal, i. e., the velocity of a
chenucal reaction when caused (vr influenced) by the light-energy
introduced into the system follows in light the same law of
mass-actton as it follows in the dark, when a reaction is brought
about by the intrinsic properiies of matter always existent in
and inseparable from the sume, and which we call chemical
ufinity or chemical potential. This is just the principal
result of the experimental research communicated in the above-
mentioned paper. No law analogous to Faraday’s for electro-
lysis was found to hold good for light introduced into the
system.

The experimental results obtained by the author thus led
him gradually to believe that the light-energy introduced
from an external source into the sy stem does “hot act upon
the same in a manner similar to that of introduced electrical
energy; that the above conceptions as to the mode otf
working of the introduced light upon a system must give the
true state of things, the more so as they also furnish a
rational and detailed explanation of the phenomena obtained
with metallic plates when exposed to light, and of the phe-
nomena of induction and deduction, which otherwise seem to
be of a mysterious and complicated nature.

From this result follows further the conclusion, drawn
already in the above-mentioned paper in connexion with

Phil. Mag. 8. 6. Vol. 5. No. 26. Feb. 1903. Q

a) .

26 Mr. W. Makower on a Determination of the

the chemical induction and chemical deduction periods (see
p. d91):—

Since velocity of reaction follows the law of action of mass,
when the molecules taking part in the reaction have attained,
under the influence of light, a. constant value of their chemical
potentials. the same law of mass-action must also be the
governing principle for the velocity of reaction at any given
moment of the chemical induction and deduction periods,
only the velocity constant in the equation for velocity of
reaction will vary as the chemical potentials of the reacting
substances change.

Davy Faraday Laboratory of the

Royal Institution, November 1902.

XX, On a pe ‘mination of os fatio of the , Spee Heats
at Constant Pressure and at Constant Volume for Air and
Steam. By WATER Magower, B.Sc., University College,
London*.

Plate I.)

1. Introduction and General Method.

HE method employed was similar to that used by

Lummer and Pringsheim (Smithsonian Contributions

to Knowledge, 1898), which consists in allowing the gas

under investigation to expand adiabatically and measuring
the lowering of temperature caused by such expansion.

In these experiments the initial and final pressures of the
gas were measured on a sulphuric acid gauge, and the change
of temperature deduced from the variation of the electrical
resistance of a fine platinum-bolometer strip immersed in the
gas under investigation. The gases experimented upon were
air, oxygen, carbon dioxide, and hydrogen, for which the
values of the ratio of the two specific heats were found to be

14025, 13977, 1°2995, 1-4084 respectively.

The chief modifications introduced in the present investi-

gation consist in the substitution of a platinum-thermometer
with compensating leads, for the bolometer-strip of Lummer
and Pringsheim, who employed a somewhat different device
for eliminating errors due to conduction of heat along the
leads. Also, at the suggestion of Prof. Callendar, the elee-
trical contacts were made by means of a specially constructed
automatic mercury switch, instead of by hand. It was also
hoped that it might be possible to use smaller quantities of
gas than Lummer and Pringsheim had used, and it was

* Communicated by the Physical Society : read November 14, 1902.

Ratio of the Specific Heats for Air and Steam. 227

partly with the object of testing this point that the present
investigation was undertaken.

If 6, and @, be the initial and final temperatures of the
gas, and p, and p, the initial and final pressures respectively,

then according to the well-known relation

loge (pi) po) = loa (Cy 2
If then the gas be allowed to expand in such a manner that
Pi, P2, 9, and @ can be measured, the ratio (y) of the specific
heat at constant pressure to the specific heat at constant
volume can be calculated.

In the case of steam, which could not be considered as a
perfect gas at the temperatures at which the present experi-
ments were made. the characteristic equation proposed by
Callendar (Proc. R. 8. Ixvii. 1900) was employed. On this

assumption the adiabatic relation is still given by equation (1).

Pare IE
2. Hwperiments with Air.

The apparatus employed is shown on Plate i. It consisted
of alarge spherical copper vessel (not shown in the figure)
which we will call the “air-vessel,’ of about 50 litres
capacity, connected to a tube CU for admitting the air to be
experimented with; into the “air-vessel ” passed a platinum
thermometer by means of which the fall of temperature on
expansion of the air at a point near the centre of the vessel
was measured. Into the neck of the vessel was soldered a
side tube of 1°8 em. diameter. By withdrawing a rubber
stopper fitting tightly into this tube the pressure in the
vessel was allowed to fall from a value (p,) previously ad-
justed to the atmospheric pressure (j»). By means of the
tube D the “air-vessel’? was connected to an oil mano-
meter M which could be placed in communication with the
experimental vessel or cut off from it at will by means of
the glass tap H. ‘The usual arrangement for measuring
the resistance of the platinum thermometer is also shown in
the figure. In connexion with the “air-vessel” was a
mercury-gauge N which served as an automatic key for
closing the battery-circuit at a definite instant after releasing
the pressure of the air. The gauge N was connected by
rubber 7 to a T-piece in the tube D, through which passed
a platinum wire w, just dipping into the mercury when the
pressure inside the apparatus was equal to the pressure of
the atmosphere. Dipping into the other arm of the gauge

Q 2

228 Mr. W. Makower on a Determination of the

was a wire x passing out through a loosely fitting cork C,
through which also passed a glass tube with a platinum
wire p sealed through it, electrically connected to w. (This
was employed in the chronograph measurements to be de-
scribed below.) When the pressure in the “air-vessel ” was
equal to the atmospheric pressure, the wire w was in elec-
trical connexion with the wire 2; on raising the pressure
the contact between the wire w and the mercury was broken,
thus breaking the electric circuit from the wire w through
the mercury to the wire 2 If the pressure in the “ atr-
vessel ” was now suddenly released, contact was made between
the mercury and the wire w after a definite time had elapsed.
This time (which we will denote by 7) could be varied at will
by raising or lowering the limb containing the wire «, and
also by means of a screw pinch-cock (not shown in the
figure) which served to constrict, to a greater or less ex-
tent, the rubber tubing joining the two limbs of the gauge.
The two wires « and w were connected respectively to the
two terminals of the key K, thus putting the gauge in
parallel with this key.

3. Measurement of Temperature.

From formula (1) it appears that it is necessary to measure
both the temperature (@,) before opening the vessel and the
temperature (§,) to which the gas has fallen, measured at an
instant as soon as possible after opening the vessel, as the gas
begins to heat up, by conduction from the walls of the vessel,
almost at once after releasing the pressure. In order, there-
fore, to obtain reliable results it is necessary that the ther-
mometer which is used should be able to follow as nearly as
possible the variations of temperature of the gas. On this
accourt a platinum thermometer of a pattern similar to that
employed by Callendar in his steam-engine experiments of
1895 was constructed.

A piece of pure platinum wire (p) (PI. I. fig. 2) of diameter
‘OG1 inch was soldered * on to the platinum leads / sealed
through one end of the glass tubes g: these in turn were
soldered on to the copper leads L, passing out of the glass
tubes through the other ends which were left open. Close
to the thermometer leads were placed compensating leads to
which were soldered a piece of fine platinum wire p’ of the

* Tn the air-experiments ordinary soft solder was used. In the steam
experiments to be described below the fine platinum wires were attached
with silver solder.

Hatio of the Speciic Heats for Air and Steam. 229

same diameter as the thermometer wire, but of shorter length,
sufficiently long, however, to eliminate any end-effect error
due to conduction of heat from the stout platinum leads to
the fine platinum-thermometer wire. The four glass tubes
were placed closely side by side, and introduced into the

‘air-vessel”’ through the stopper B. To measure the
resistance of the thermometer, the thermometer and com-
pensating leads were connected to the two arms of the
Wheatstone-bridge, as shown in figure 1. In order to keep
the heating effect in the thermometer, due to the passage
of the electric curr ent, below :01° C. the current used in the
resistance measurements was made sufficiently small, being
supplied by one Leclanché-cell through 240 ohms in the
battery-arm. The resistances of the two ratio arms were
3 ohms each. To obtain the balance position, a Thomson
galvanometer was used, which, however, was rendered astatic
to avoid unsteadiness caused by magnetic disturbances.

In all resistance measurements the galvanometer circuit
was kept permanently closed, the battery circuit being broken
or made by means of the keys. In this way trouble due to
thermoelectric E.M.F.’s was avoided.

Measurement of §;.—Air was pumped into the “ air-vessel ”’
until the pressure inside exceeded that of the atmosphere by
a definite amount (about 67 ems. of oil), time being allowed
for the air to assume a constant temperature. The resistance
of the thermometer was read off by adjusting the resist-
ance R and the sliding contact s with sufficient accuracy to
give the temperature of the thermometer to ‘01° C. The
hattery circuit was closed by hand by means of the key K.

Measurement of 05.—The resistance R was then diminished
and the sliding-contact adjusted by judgment nearly to the
position where there would be no current through the galva-
nometer at the instant when the battery circuit was “made
by means of the automatic gauge-key N. If the sliding-
contact was adjusted exactly to the right position, the
galvanometer-needle remained at rest for an instant and then
eradually moved off as the thermometer heated up again.
TE, however, the shift was too small the needle gave a ‘kick
in the opposite direction to that corresponding to the heating
up of the thermometer, came to rest, and then changed the
direction of its motion, and gradually moved off as before as
the gas heated up. In making the observations that position
of the slider was sought for which the kick of the galvano-
meter just vanished.

To determine the time which elapsed between the instant
of removing the stopper 6 and that at which the mercury

230 Mr, W. Makower on a Determination of the

in the gauge made contact with the wire w, the contact e
was disconnected from / and connected to g, thus cutting
out the Wheatstone-bridge and placing the gauge-key N
in series with a storage-cell S and a chronograph. The
platinum point p, which was electrically connected to w,
was brought just into contact with the top of the mercury-
column, when the air in the “air-vessel””? was adjusted to the
initial pressure (p,). On releasing the pressure the chrono-
graph circuit was broken at p and made again through the
wire w, after the expiration of a certain time (depending
on the rate at which the mercury fell) which was measured
on the chronograph to about ‘01 second.

This time was varied from *5 second up to about 5 seconds.

A. Pressure Measurements.

The excess pressure (7,;—p.) in the “ air-vessel”’ before
opening to the atmosphere was measured on a manometer M
filled with Fleuss pump-oil. The density and coefficient of
expansion having been carefully determined the excess
pressure could be obtained in centimetres of water by means
of the formula

density = 8826 — -000644 ¢

(where t=temperature centigrade) *.

As the oil used was exceedingly viscous some trouble was
experienced at first, owing to the long time taken by the oil
in running down the sides of the tube when the pressure was
altered. For this reason the position of the oil in the mano-
meter was prevented from shifting more than two or three
centimetres by closing the tap E immediately before opening
the stopper 0.

The pressure (p.) was obtained by reading the barometer.

5. Observations.

The following is a series of observations.

The resistances are given in arbitrary units, of which
100=1-31 ohms approximately.

The kicks of the galvanometer-needle are given in terms
of the micrometer-divisions in the eyepiece of the reading
microscope.

By plotting K against + the change of resistance corre-
sponding to no kick of the galvanometer is found to be 10°47.

* The density and coefficient of expansion of the oil were determined

by Mr. N. Eumorfopoulos, of University College, who very kindly
supplied me with the oil used in these experiments.

Ratio of the Specific Heats for Air and Steam. 231
Pasian:
Resistance | Resistance | ae oF Change of
(R) (R) i crenwitee Resistance
before open-| after open-' divisi 7
| divisions.

ing vessel. | ing vessel.

651:00 640°54 no kick 10°46

651°19 640°84 3 10°35
651:27 641-04 5 10:23
651:38 641-24 10 10°14
651-61 641-44 10 10°17
651-62 651°34 5) 10°28
651-82 641°49 4 10°35
651:97 641-54 2 10°45

Barometric pressure = 767°6 mm. mercury at 0° C.
= 1044 ems. of water at 0° C.

Excess pressure=67'1 cms. oil at 18° C.=58°3 cms. water.
The coefficient of the platinum wire used in the thermometer
was ‘003835 and its resistance at 0° C. was 610°58. Hence
2-34 units of resistance correspond to 1° pt.; therefore a
shift of 10:47 units corresponds to a change of temperature
of 4°48 pt.=4°°48 C.

i OD 5
Malia er a OAL Bh sich
an hee 1102°3 PROS) ae ae
log —log

51044 ° 285-4
For this experiment T=°76 second.

6. Corrections and Results.

To the value of y found above there are two corrections to
be applied :—

(1) The air in the immediate neighbourhood of the ther-
mometer has risen in temperature by conduction and con-
vection during the time (7) which elapses between opening
the stopper 0 and closing the battery circuit.

(2) The final temperature as indicated by the thermometer
will be higher than the temperature of the air surrounding it
on account of direct radiation from the walls of the vessel.

(1) In order to find how much the air had heated up before
the battery-cireuit was closed by the automatic key, a number
of observations were taken similar to those given above, but
with different values of +. <A series of values of y was thus
obtained for different values of 7, from which it was possible
to deduce the value yp which would have been obtained had

232 Mr. W. Makower on a Deterinination of the

no time been allowed for the air round the thermometer to
heat up. For since
log (7) a ehe P), . a
Qs 7 p2
we see, by expanding by the logarithmic series and neglecting
all terms except the first, that

(0,—6,)=0,0 1 lene . (approximately) (8)

P2 y
Vaile a ah ae 1 kee
- is proportional to the fail of temperature. = ———

Hence
as calculated from (2) was plotted against 7, and by extra-
, —1 :
polating back to r=0 the value of ee corresponding to

no heating of the thermometer, due to conduction and con-
vection, was obtained.
In Table II. are given the values obtained :-—

Taste II.
Time of closing a]
circuit in seconds y- ge,
Ga): Y
O76 1396 | "2837
1-12 1396 | 2837
1:90 1-386 | "2785
3°33 1381 | "2759
1:83 ‘386 "2785
| 1-45 | 1392 ‘2816
3°00 | 1:380 "2754
2°30 : 1-386 "2785
5-00 1-280 ‘2754
4-01 | 1380 | ‘2754
G95 | 1-396 "2837
515 | 1380 | “2754
1:90 1-389 ‘2801
165 1-389 | "2801
213 1-391 | "2811
215 1391 "2811

Aoi
%

ire) Ci it gene ae
Assuming the variation of Y—= with 7 to be linear over

the small range considered, the value of yar corresponding
to r=0 is "285. Hence y= 1°399. |

(2) The error due to radiation was allowed for by coating
the thermometer with platinum black. Assuming that the
absorption by a platinum-blacked surface is 15 times as
powerful ‘as that of a bright surface*, the error due to
radiation could be estimated.

* Lummer and Pringsheim, loc. cit.

Ratio of the Specific Heats for Air and Steam. 233

The value of y obtained with a platinum-blacked thermo-
meter was 1360 for r=0°86 second.

Since the value of y corresponding to T=0°86 sec. is 1°394,
the correction to be applied for radiation is

1:394—1:360
14

Hence the corrected value of the ratio of the two specific
heats of air is y=1°401.

== 24

Parr Il.
7. Heperiments with Steam.

It will be readily understood that in order to determine
the ratio of the two specific heats for steam, the use of vessels
of the size employed in the experiments with air just described
would be exceedingly inconvenient; and indeed the large
size of the vessel doce not seem to present the same advantage
as in experiments made by the method of Clement Team:
In the latter method the whole of the gas contained in the
vessel is being experimented with, and consequently any error
due to the heating of the gas close to the walls produces
serious errors in the value of y obtained; it is therefore
desirable to reduce the surface of the vessel compared
with its volume. In the present method, however, it is
merely with the variation of temperature at the point
where the thermometer is situated with which we are con-
cerned, and any heating of gas near the walls of the vessel
is unimportant. It dhenetors seemed likely that results of
equal accuracy to those obtained with a large vessel might
be obtained with a far smaller one.

To test this point experiments were made with air con-
tained in smaller vessels, and the following apparatus was
finally constructed for the steam experiments.

A cylindrical copper vessel with coned ends of about
93 litres capacity (Pl. I. fig. 3) was constructed having a
wide tap A, by opening which the steam could be allowed to
expand adiabatically.

A tube D, provided with a tap. through which the vessel
could be Ailted with steam, passed thr ough the lower ex-
tremity. On either side of ‘the vessel tubes (B and C) were
attached ; through Ba platinum thermometer was inserted :
C cormenamicucedl through a tap and a fine tube E with a
glass tube which was aannected to the oil manometer and
automatic key. The whole was inclosed in a copper jacket
filled with steam maintained at an excess pressure of about

234 Mr. W. Makower on a Determination of the

half an atmosphere, so that the steam in the inner vessel was
superheated about 10° C.

The pressure in the jacket was kept constant by means of
an automatic gas-regulator devised by Callendar, which con-
trolled the supply of coal-gas reaching the burner employed
for heating the boiler which generated the steam. It was
found that | vy this device the pressure could be kept constant
to 1mm. of mercury. To keep the temperature as constant
as possible the whole vessel was packed in cotton-wool.

To prevent the condensation of steam in the tube E a
small meta] tap T was attached close to the vessel; this
tap was not opened until the pressure in the vessel had
become constant. By pumping in air the pressure in the
tube E was raised slightly above that of the steam in the
experimental vessel, so that on opening the tap T a small
quantity of air passed into the vessel preventing steam from
passing into the tube E and condensing there. In order
to roughly determine the pressure of the steam before open-
ing the tap Ta small auxiliary mercury gauge was attached
to © close to the vessel ; when the pressure as registered
by this gauge was constant and had been adjusted to about
the value required for taking an observation, the tap T was
opened, thus putting the oil manometer in connexion with
the vessel. As the tube E was fine very little steam dif-
fused into it, and no trouble was experienced from this cause
when the experiment was carried out as described. To get
rid of any small quantity of moisture which might collect
after the apparatus had been working for several hours a
T-piece F provided with a drain-tap was attached through
which such moisture _ be expelled. To carry out an
experiment the jacket was filled with steam under pressure,
the tap A being open, aa the tap D was then cpened and
steam allowed to enter the vessel, until all the air had
been expelled; the taps D and A were then closed. It
was found that the pressure in the vessel rose for a short
time on account of a small quantity of water carried over by
the steam entering through D. The pressure of the steam
was then adjusted to asuitable value (about 56 cms. of water
above the atmospheric pressure) and allowed to become con-
stant. The tap T was then opened, after which the tap A
was quickly opened and the pressures and temperatures

registered, as in the experiments with air. The initial tem-
perature (9) was always observed just before opening the
tap A, only a few seconds being allowed to elapse between
taking this observation and opening the tap. ‘Temperatures
were read to'02°C.and pressures to the nearest millimetre of oil.

Ratio of the Specific Heats for Air and Steam. 235
Before proceeding to a discussion of the results obtained
for steam, the values of y obtained for air using the same
apparatus are given as an indication of its sensitiveness.

Penal

Time of closing the

circuit in seconds (7). ue
0-58 1397
EZ 1:392
2-00 1-392

The value obtained with a platmum-blacked thermometer
was 1°374; the correction to be apphed for radiation is
therefore ‘017, .

cy == leaeige
The striking agreement of this value with that obtained with
the large vessel demonstrates conclusively that it is possible
by the ‘method here employed to work with quantities of gas
far smaller than has hitherto been supposed.

8. Observations and Results.

The observations were taken in a manner similar to that
adopted in the case of air; it was, however, found incon-
venient to take all observations between exactly the same
pressure limits. The excess pressure was therefore adjusted
approximately to the same value in each experiment, and, as
in the air-experiments, the sliding-contact was ee ‘d by
judgment nearly to the position or here there would be no
current through the galvanometer at the instant when the
battery-circuit was closed; from the initial and final tempe-

ratures and pressures a value of u was calculated, which,

as has been shown above, is proportional to the fall of tem-
perature for a constant excess pressure. The kicks of the
galvanometer-needle were recorded and a correction applied

to the value of obtained, in order to allow for the fact

that the sliding-contact had not been eaactly adjusted to the
correct position.
In the first series of observations a kick of 1 scale-division

236 Mr. W. Makower on a Determination of the

—l1.
corresponded to ‘0012 on rss : in the second series of
y
observations a kick of 1 scale-division corresponded to -0016

on aL

The observations are given m full below.

TasLe 1V.—Series I.

| h |

pit. was Kick of 14 (vaat
| inem. | in cm. galvanometer y ae!
bi: | @,. | water at | water at in seale- uncorrected
POOL" Gia Oa) divisions. | for kick | corrected.
| of galv.
38330 | 37902 | 1081-2 | 10280 | 9 | *2250 "2358
383-30 | 37850 | 10846 1028-0 3 |) ‘2349 | 2a
383:20 | 378°37 | 10840 | 1028-0 no Jack (p41 (239500 —
383'50 | 37886 | 1085-4 | 1030-9 2 | "2025 lepaeeeesee
383°40 | 378-79 | 10945 | 1036-0 10 | *2200 | “2a20
38340 37869 | 10516 1036-0 no kiek * |'-"-2267) 9 =F
383°40 | 37863 | 1093°5 | 1036-0 So0r4 |- 2314 |) 42856
383°30 | 37853 | 1092-7 | 10360 nolkick "|, 23400005 —
Seo a0) (enol y! 10916 | 10360" | ory ie aos ‘2373 ||
383-30 | 378°79 | 1090°9 | 1036-0 3 | = “2284 “Zo20) 7%
38330 37876 | 10884 | 1035-0 | H |. 92872 . a saoea ain
383°30 | 37887 | 1087-9 | 1035-0 | 3 | “2331 $40 -2aien
383'°30 | 37883 | 1090'7 | 1035-0 | 17 | 22243 |) soe
383°30 | 387879 1090-4 = 10350 | 4 ‘2272 ..| "2320
383°20 | 37899 | 1086:0 | 1035-0 | 3 ‘2206: loa
383°20 | 379702 | 10869 | 1035:0 2 "2248 2372
383:20 | 37893 | 10910 | 1035-0 Li, PDT 2361
383:°20 | 37893 | 1087°2 | 10350 | justakick | °2308 "2308
383:40 | 37882 | 1090-77 | 1035-0 7 | 2296 2380
383°40 | 378-72 | 10903 | 1035-0 2 | *2355 "2379
383°30 | 37867 10905 1035-0 Zord | « 2320. eae
Boa 10 "| are'ea.| 4079.8 || 1021-0 10 Ls A 2265
383°00 | 37864 | 10752 | 1021°0 2 | 222 "2236
383:00 | 37846 | 1077-1 | 1021-0 5 | +2230 2290
| 383:00)\| 3878°29 1077-7 _ | LOZ") 1 2290 | -2302
38300 3878:25 | 10730 1017-0 | 2 | °2331 "2395
383°00 | 37821 | 1073-4 | 1017-0 1 2331 | 2e4e
382°90 | 378-21. | 1069-4, | 1015-0 5) | *2367 2403
38270 37789 1066°0 | 1609-0 Sond ||. 2302 (oe
382770 | 377°89 | 1063°8 | 1009-0 | 2 | “2390 9) (Sees
302,90 | 37803. | 1073°8. | 1018:0 |=, nokick | °2401 | —
38310 | 37823 | 10769 | 1021-0 nokick | -2395 | —
383°40 | 37842 | 1091-2 | 1035-0 no kick | “2401 ---
| ‘2441 —

38040 | 37851 | 1090°9 | 10350 | no kick

For these observations tT=0°'67 second.

—1
Mean value of aa == 1292 4AQ

whence y—A5307.-

Ratio of the Specijic Heats for Air and Steam. 237

TABLE V.—Neries II.

P Ps ae
Dem. | CIN. Kick of y parted
0, | @,. | water at| water at g galvanometer. uncorrected Y
OF CS nie OCC: for kick | corrected.
. | of galv.
| 383:10 | 378-49 | 1084-9 | 1029-0 6 2290 | 2386
| 383-20 | 37849 | 1084-2 | 1029-0 no kick 2572 os
| 383°20 | 37872 10825 | 1029-0 TONIC. leas | a
| 83°00 | 378-48 1091-0 | 1035-0 4 i PAZ i 83109)
| 38300 | 87834 10916 | 1033°0 4 02) \ | 2366
| asa 10 | 37831 | 1089-5 | 1085-0 = 1 2349 | 2365
| 38390 | 379-47 1098-2 | 1043-0 ] 224? |. 2364
| 38390 | 379-08 | 1100-4 | 1043:0 no kiek a0o) | —-
38390 | 379°35 1098-7 | 1043-0 m6) ksi Chane OOS = -—
| 883°90 | 379°50 1099'1 10430 3 Reeszc0O! |. 2248
| 88390 | 379°44 | 10989 1043-0 4 geass "2307
38390 | 379:32 | 1093°8 | 10480 no Iaicky ap 2302° - —_
38390 | 379:22 | 1099°7 | 1043-0 1 2320 | -2336
38390 | 379:10 | 11006 | 1043-0 no kick 2343 —
| 38390 | 379-42 | 11006 10450 | 1 ie 220671) 2282
383:90 | 379°38 | 1100-5 | 10450 1 | 2290) ||) 52806
sea0) | 37928) | 11015 | 10450 | . no kick | \-2202, | —

Por these experiments T= 0°50 second.

Mean value of vet ee

?
whence Vo:
The values of y obtained in these two series of experiments

are'given for clearness
7 in seconds.

Y:
SCI lis See 0-67 307
meres wei a... O50 1°303

The agreement of these observations was not sufficiently
close to necessitate the application of the small correction for
radiation applied in the air-experiments (correction (2) above).
An attempt was made to apply a correction for the heating
up of the steam round the thermometer in the time 7 (cor-
rection (1) above). The discrepancies were, however, found
to be too great to render it possible to plot a curve and
extrapolate to the value r=

It is worthy of mention that the movement of the galva-
nometer needle was more rapid in these experiments than in
those with air, indicating a quicker rate of heating up of the
thermometer. This indication was further confirmed by a
third series of experiments which was taken, for which 7 was

Lord Rayleigh on the'

14 seconds; the value of y obtained in this series was
291, showing that the thermometer had heated up -cen-
siderably after 1:14 seconds.

I desire to express my best thanks to Prof. Callendar for
his advice and encouragement throughout the course of the
work; also to Prof. Porter I am indebted for many valuable
suggestions.

ae
ifs

XXI. On the Spectrum of an Irregular Disturbance.
By Lord Rayueten, O. M., F.RS*

N my paper * On the Character of the Complete Radiation
at a given Temperature’, I have traced the conse-
quences of supposing white light to consist of a random
aggregation of impulses of certain specified types, and have
shown how to calculate the distribution of energy in the
resulting spectrum. The argument applies, of course, to all
vibrations capable of propagation along a line, and it is con-
venient to fix the ideas upon the transverse vibrations of a
stretched string. Suppose that this is mitially at rest in its
equilibrium position and that velocities represented by $(«)
are communicated to the various parts. The whole energy is
(ee
proportional to | Sdh(xv) dx; and it is desired to know
is
how this energy is distributed among the various components
into which the disturbance may be analysed. By Fourier’s

theorem,

wT Oe) = | A, (k) cos ka dk +

ee U

ie fo (k)sinka dk, . (A)

AoA

ACh) =

It was shown \that the desired information is contained in
the formula

+o ne
(sia) Pde * | nme tAwrla . @)

vy —a v

== eg)

+a
cosku d(v) dv, —fa(k) = sin kev fv)dv. (2)

As an example, we may take an impulse localized in the
neighbourhood of a point, and represented by

b(x) = 6-8, on

* Communicated by the Author.
+ Phil. Mag. xxvii. p. 460 (1889); Scientific Papers, 11. p. 268.

7, ' 2 Ta

Spectrum of an Irregular Disturbance. 239

Equation (1) becomes

1 D
a Ge Hike? Gosek mae ee Tk (5)
while for the distribution of energy in the spectrum by (3)

A +0 1
| en" da = z| AE es eT (6)
bbe Cc Jo

}

“ Tf an infinite number of impulses, similar (but not neces-
sarily equal) to (4) and of arbitrary sign, be distributed at
random over the whole range from —# to +a, the intensity
of the resultant for an absolutely definite value of & would be
indeterminate. Onlythe probabilities of various resultants could
be assigned. And if the value of & were changed, | vy however
little, the resultant would again be indeterminate. Within
the smallest assignable range of. & there is room for an infinite
number of independent combinations. We are thus con-
cerned only with an average, and the intensity of each
component may be taken to be proportional to the total
number of impulses (if equal) without regard to their phase-
relations. In the aggregate vibration, the law according to
which the energy is distributed is still for all practic: ul
purposes that expr essed by (6).”

The factor e-@” in the impulse was introduced in order to
obyiate discontinuity. The larger ¢ is supposed to be, the
more highly localized is the impulse. If we suppose e¢ to
become infinite, the impulse is infinitely narrow, and the dis-
turbances at neighbouri ing points, however close, become inde-
pendent of one another. It would seem therefore from (6)
that in the spectrum of an absolutely irregular disturbance
(where the ordinates of the representative curve are indepen-
dent at all points) the energy between & and k+dk is pro-
portional to dk simply, or that the energy curve is a straight
line when k is taken as abscissa. If we take the wave-length
X (to which & is reciprocal) as abscissa, the ordinate of the
energy curve would be as \~°.

The simple manner in which d& occurs in Fourier’s theorem
has always led me to favour the choice of 4, rather than of
X, as independent variable. This may be a matter of con-
venience or of individual preference ; but something more
important is involved in the alternative of whether the energy
of absolutely arbitrary disturbance is proportional to dk or
to dX. In Prof. Schuster’s very important application of
optical methods to the problems of meteorology, which seems
to promise a revolution in that and kindred sciences, the latter

240 Lord Rayleigh on the

is the conclusion arrived at. ‘‘ Absolute irregularity would
show itself by an energy-curve which is independent of the
wave-length ; 7. ¢.,a straight line when the energy and wave-
length or period are taken as rectangular coordinates .. .”’*.
It is possible that the discrepancy may depend upon some
ambiguity ; but in any case I have thought that it would
not be amiss to reconsider the question, using a ditferent and
more elementary method.

For this purpose we will regard the string as fixed at the
two points #v=0 and #=/. The possible vibrations are then
confined to the well-known “ harmonies,” and & is limited to
an infinite series of detached values forming an arithmetical
progression. ‘The general value of the displacement y at
time ¢ 1s

y= sin Bee COs “ +B, si in ) - ae
in which « is the velocity of propagation and s is one of the
series 1, 2, 3.... From (7) the constant total energy y(T+V)
is readily caleulated. Thus (‘ Theory of Sound,’ § 128) if M

denote the whole mass, 7s the period of component i.

A 2 2
T+V=s7r?M.> raat) .. ae
mse
an equation which gives the distribution of energy among the
various modes.
The initial values of y and 7 are

- STH : TO ws . STL
y,=>As SD qe ae SsBs sin je &
/ Oe ]
whence
2 STa ? L sme
As=,; y sin —._ da: B=) 4, sin — > dee
ee Ys pie was) Yo i (9)

If we suppose that y,=0 throughout and that # is finite
only in the cn. ae 2 2==&, we have As=0, and
Bs= 1 pau . e . e e (10)
Tas
where Y=\% de. The energy in a various modes being

proportional to Bs*/7;?, or to

. 9 STE
+—s sin? —2
S*T52 l ;
in which s?7s?=7,*, is thus independent of s except for the
factor sin? (s7&/l). And even this limited dependence on s
* “The Periodogram of Magnetic Declination, &c.,” Camb. Phil. Trans.
xviii. p. 108 (1899).

Spectrum of an Irregular Disturbance. 241

disappears if we take the mean with respect to & We may
conclude that in the mean the energy of every mode is the
same; and since the modes are unitor rmly spaced with respect
to their frequency (proportional to s) and not with respect to
their period or wave-length, this result corr esponds with
a constant ordinate of the energy curve when /& is taken as
abscissa,

It is to be noted that the above corresponds to an arbitrary
localized veloety. We shall obtain a higher and perhaps
objectionable degree of discontinuity, if we make a similar
supposition with “respect to the displacement. Setting in (9)
Jo=0 throughout and v)>=0 except in the neighbourhood of
E, we get Bs=0 and

Ag= 7 sinZ2Y,, ese) | oe fd, vast CED)

where Y, =| y,d#. By (8) the mean energy in the various
modes is now proportional to 1/ts? or to s?. When / is made
infinite, so that ts may be treated as continuous, we have an
energy curve in which the ordinate is proportional to s? or 2,
hk being abscissa.

We may sum up by saying that if the velocity curve is
arbitrary at ev ery point the energy between & and k+dk
varies as dk, but if the displacement be arbitrary the energy
over the same range varies as k°dk.

In Schuster’s Periodogram, as applied to meteorology, the
conception of energy does not necessarily enter, and the
definitions may be made at pleasure. But unless some strong
argument should appear to the contrary, it would be well to
follow optical (or rather mechanical) analogy, and_ this,
if I understand him, Schuster professes to do. If the energy
associated with the curve o(2) to be analysed is represented
by \{ (2) v)\* dx, d(@) must be assimilated to the velocity and
not to the Pp laevis of a stretched string.

We have seen that when $(z) is arbitrary at all points the
ordinate of the energy curve is independent of &. In the
curves with which we are concerned in meteorology the values
of (x) at neighbouring points are related, being influenced by
the same accidental causes. But at sufficiently distant points
the values of #(x) will be independent. Equation (6) suggests
that in such cases the ordinate of the energy curve (A ‘bei ing
abscissa) will tend to become constant when /: is small
enough.

Another illustration of the application of Fourier’s theorem
to the analysis of irregular curves may be drawn from the

Phil. Mag. S. 6. Vol. 5. No. 26. eb. 1903. R

242 On the Spectrum of an Lrreqular Disturbance.

optical theory of gratings. For this purpose we imagine the
aperture of a telescope to be reduced to a horizontal stri ip
bounded below by a straight edge and above by the curve to
be analysed, such as might be provided by a self- -registering
tide-gauge. Any per iodicities in the curve will then exhibit
themselves by bright lines in the image of a source of homo-
geneous light, corresponding to the usual diffraction spectra
of the various orders. An: aperture of the kind required may
be obtained by holding the edge of a straight lath against
the teeth of a hand-saw. When the combination is held
square in front of the telescope, we have spectra corresponding
to the number of teeth. When the aperture is inclined, not
only do the. previously existing spectra open out, but new
spectra appear in intermediate positions. These depend upon
the fact that the period now involves a sequence of two teeth
inasmuch as alternate teeth are bent in opposite directions
out of the general plane.

The theory of diffraction* shows that the method is
rigorous when the source of light is a point and when we
consider the illumination at those points of the focal-plane
which lie upon the horizontal axis (parallel to the straight
edge of the aperture).

In order to illustrate the matter further, Mr. Gordon con-
structed an aperture (cut from writing-paper) in which the
curved boundary f had the equation

y=sin 2z2+sin (82+2377).

The complete period was about half an inch and the maximum
ordinate about one inch. The aperture was placed in front
of a 3-inch telescope provided with a high-power eyepiece.
When desired, the plane of the aperture could be considerably
sloped so as to bring more periods into action and increase
the dispersion.

The light employed was from a parathn-lamp ft, and it
was convenient to limit it by slits. Of these the first was
vertical, as in ordinary spectrum work, and it was crossed by
another so that at pleasure a linear or a point source could be
used. In the latter case the spectrum observed agreed with
expectation. Subdued spectra of the first order (corresponding
to the complete period) and traces of the fourth and fifth
orders were indeed present, as well as the second and third
orders alone represented in the aperture-curve. But along

* See, for example, “ Wave cent of Light,” Encyc. Brit. ; ‘ Scientific
Papers,’ iii. pp. 80, 87. Make g

+ Figured in Thomson and Thies Natural Philosophy, § 62.
t Doubtless a more powerful source would be better.

Influence of Radiation on the Transmission of Heat. 243

the horizontal axis of the diffraction pattern these subsidiary
spectra vanished; so that the absence of all components,
except the second and third, from the aperture-curve could
be inferred from the observation.

It will be evident from what has already been said that
confusion arises when the point-source is replaced by a linear
one; and this is what theory would lead us to expect. Ina
diffraction-grating, as usually constructed, where all the lines
are of equal length, the spectra are of the same character
whether the source be elongated, or not, in the vertical
direction ; but it is otherwise here. The inadmissibility of a
linear source and the necessity for limiting the observation to
the axis seriously diminish the prospect of making this method
a practical one for the discovery of unknown periods in curves
registering meteorological or similar phenomena ; but the fact
that the analysis can be made at all in this way, without any
calculation, is at least curious and instructive.

It may be added that a similar method is applicable when
the phenomena to be analysed occur discontinuously. Thus
if the occurrence of earthquakes be recorded by ruling fine
vertical lines of given length with abscissee proportional to
time, so as to constitute a grating, the positions of the bright
places in the resulting spectrum will represent the periodicities
that may be present in the time distribution of the earthquakes.
And in this case the use ofa linear source of light, from which
to form the spectrum, is admissible.

Terling Place, Witham.

XXII. The Influence of Radiation on the Transmission of Heat.
By ArrHur Scauster, /.R.S.*

[Plate II.]

HE laws of conduction of heat have been studied in
detail, and something has been done to trace the
influence of convection on the distribution of temperature ;
but the effects of radiation on the transmission of heat
through partially transparent bodies have been almost entirely
neglected. With the solitary exception of a paper by
Professor R. A. Sampson +, with which I became acquainte d
after the greater portion of the results of the present inves-
tigation had been worked out, I know of no serious attempt
to deal with this problem.

* Communicated by the Author.
+ Memoirs of the Royal Astronomical Society, vol. li.

244 Prof, A. Schuster on the Influence of

2. To treat the question in its simplest form I consider, in
the first place, a solid which is an absolute non-conductor
but capable of radiating and absorbing heat; and I take the
flow of energy to be rectilinear, the isothermal surfaces
being parallel planes.

If F be the total radiation sent out in unit time in all
directions by unit area of the surface of a perfectly black
body, the radiation emitted by unit surface of a sheet of
thickness dx of a partially transparent body is «Fda, where
« 1s a constant depending on the nature of the substance, the
etfects of wave-length on « being for the present neglected.

Let A represent the energy of the stream of radiant heat
traversing unit surface of the sheet in unit time from the
positive to the negative side, while B represents the flow of
energy in the opposite direction. The total absorption of the
sheet will be «(A+B)dz; and as its radiation towards the
two sides is 2«F dz, it follows that if c be the heat capacity
per unit volume, w the temperature, and @ the time,

e(A+B=2F)=c5,.. °. | en

If we were only considering the radiation normal to the
isothermal surfaces as Prof. Sampson has done in the paper
already quoted, the law of Balfour Stewart and Kirchhoff
would give

BANS
dis

c(EF—A). |.) on

If A represents the total flow in all directions, the equation
still holds in the limiting case when the temperature is uniform.
For A is then independent of «, and also equal to F.

1 shall assume equation (2) to hold also in the case
which we are now considering, and shall discuss afterwards
how far this assumption invalidates the results.

The corresponding equation for B is

at =(B—P). .. . :

By combining (2) and (3) we obtain

and

£ (A-B)=«(2F—A-B). ee

Radiation on the Transmission of Heat. 245

Hence, taking account of (1),

d du 3
We (A—B)=—c 7. ° ° ° : 5 ° (5)
From (4) and (5) we may deduce
d? d
ae (A+B)=«—7 (B—A)
Mow seleiie
a

and finally by two differentiations of (1) and elimination of .

A and B,

a? e du oS
ieee Fa ee ny

If the variations of temperature are ci small to

allow Newton’s law to be applied, we may write F= Ru ;
so that

This is in essence the equation which Prof. Sampson has
deduced in a different manner. Though I am not in agree-
ment with Prot. Sampson as regards the deductions he has
made from it, the priority of having established a somewhat
important equation belongs to him,

If we adopt Stefan’s law, we must write F=Sw*, so that we
obtain the more correct equation

d? SN) Gd Vand tanhs
GES =H oT a8 5% =0.

It will be noticed that the equation remains unaltered when
cp, Kp, pda is writen for c, «, dx respectively ; so that we
may take ¢ to denote the specific heat, « the coefficient of
absorption per unit mass of a thin sheet, and dg# the mass
per unit surface of the sheet.

3. To consider more particularly the case of steady tempe-
rature, | imagine a plate of a non-conducting and partially
transparent material placed with its surfaces in contact with
two other surfaces which are kept at constant but different
temperatures. These surfaces will radiate heat; and if they
are black the radiation towards the inside of the plate is known
at both boundaries. The surface conditions are (1) for e=0,

A=, and (2) for s=d, B=F),, where Fy and F, are the

246 Prof. A. Schuster on the Injluence of

radiations corresponding to the temperatures of the bounding
surfaces.
When the steady state is reached, (5) leads to
B—A=2K,
where K is some constant which is to be determined. Putting
this value of B—A into equation (4a), we get
B+A=2Kxvr 25 4G.
where ¢ is a second constant. Hence
B=Ker+K +e,
A=K«a—K +e.
The values of the constants may now be expressed in
terms of the radiations at the surfaces. We find in this way :

Sy ee Bott D+F
eek ae Kt +2
The temperature inside the body is determined from F if

the law of radiation is known. In the case considered (1)
gives

2F=A+B=2Ker+c¢. 2

If the temperature variations are comparatively small,
Newton’s law may be applied, in which case the temperature
will be proportional to F, and will vary uniformly in the
plate. The important point in the solution of the problem
lies in the discontinuities of F, and therefore also of the
temperatures at the boundaries.

To calculate the discontinuities we take the values of F at
the boundaries, as obtained from (8) after substitution of K

and c. We find:
veda for

i amp ==)
F= Bit + 1) + Bo for vt.
Kl +2

But Fis the radiation received from the outside when & =0;
the discontinuity at that surface is therefore

F,— Fo
Kt +2

Bey f=

The same discontinuity occurs at the other surface. Any
radiation I in its passage through the plate is reduced to
Te~**, When «t is large the plate j is practically opaque, and

Radiation on the Transmission of Heat. QAT

the discontinuities are small; but they do not disappear
until the plate is of infinite thickness unless the opacity Is
complete. If, e. g., the opacity of the plate is such that the
light is reduced to e~!° times its original value, and the tem-
peratures of the bounding surfaces differ by 100°, there would
still be a discontinuity of 82° at the surfaces.

According to Melloni’s experiments, the absorption of heat
in rock-salt is independent of the wave-length, a plate of
‘26 em. thick transmitting 92 per cent. of the radiation.
From this I calculate the value of « to be 032. If we had a
plate of rock-salt 1 em. thick and placed it between black
surfaces at temperatures of 100° and 0° respectively, a state
of equilibrium would be reached in which, if conduction were
entirely absent, the rock-salt in contact with the temperature
of boiling water would acquire a temperature of 50°74,
while at the other boundary the temperature would be 49°26;
so that the plate would take up a temperature which nearly
throughout its thickness is equal to the ar jLunietnie mean. of
that of the bounding surfaces.

For the extreme cases the above equations eine to

F=4(F)+F)), THE ke,

F=| PF \¢—2)+ Pye i/t, if xt is very large.
In the latter case the temperature distribution is the same as
that established by conduction.

4, The discontinuities which have been proved to exist
when conduction has been neglected show that conduction,
however small, must always Ihe taken into account. Before
doing so we may extend our calculations to the case that the

bounding surfaces are partly reflecting. The surface con-
ditions are then:

A=(l—o)F,+ceB for c=0,
B=(l—oc)F,+¢eA for «=t,

where o is the reflecting power, which must be taken to be
one for perfect reflectors.

The same reasoning which previously determined K and ¢
now gives the equations :

[ (xt + 2) —o(xi—2) |K=(1—o)F,—
[ (Kt+2)—o(Ki—2) |c =(1l+o)Fo+(1—o)(etF) + F)).
The discontinuities of F at both boundaries are

(F\—F.). +0)/[«t(1—c) +2(1+0)].

248 Prof. A. Schuster on the Influence of
For perfect reflectors c=1, and the discontinuities are
one 0)

and hence the more perfectly the boundaries reflect the more
nearly will the plate assume a uniform temperature, which is
halfway between the temperatures of the bounding surfaces.
5. If conduction be taken into account, equation (1)

becomes

du du

ee) = SS @ 9)
K(A+B 2P)+r 79 ¢ Te (9)

r being thermal conductivity of the body.
Differentiating twice and substituting: equations (4@) and
(40),
12
av D): aia (B—A)

=K
dx? dx

=<OF— A— Bi.

This equation and (9) allow A+B to be eliminated, giving
the differential equation

ea a? du, dazu
reais Rie RAN 7h) Wheater eS peo ae
Md (a : )( Te i) .

When the temperature is steady and its variations across
the plate are sufficiently small to admit of the interchange
of radiation between two bodies to be proportional to the
difference in their temperatures, the equation becomes

dazu dtu :
daz dx*’

(2eR+ xr) r

or, say,
{2 4
gota! a
Ga Vas
The distribution of temperature in the plate is here not a
linear function of the distance. This is a curious result.
Radiation alone or conduction alone would cause the slope
of temperature in the plate to be uniform; but the combi-
nation of both effects destroys the uniformity. The explanation
of the apparent paradox is found in the consideration that
although the distribution of temperature due to radiation
varies uniformly with the distance across the plate, it is
not identical with the distribution of temperature due to
conduction, owing to the tendency of radiation to cause dis-
continuity at the surfaces, as has been explained in § 3.

get ep ale
a. > a ee

a a oa

Radiation on the Transmission of Heat. 249

The solution of (10) may be put into the form:
pe en ida p Meme goes) «oC 12)
P, Q, a, and } are four constants, and «& satisfies the equation
eee Die? Nina Wee cay Bet (me) (13)
The constants are determined from our knowledge of up and
ua at the ends of the plate and the conditions which hold there
as regards radiation.

The heat (H) transmitted in unit time through any
isothermal plane in the negative direction is

ee
da
From the original equations
CCAS ew
a er
and
ait
K(A + B) =2«eF—2A— (14)
dix?’
Banks du
2 Ps SS Oa eas 5 \
«’(B—A) 2K i Do a Me cS bes ike)

Substituting F=Ru, the heat transmitted takes the form

au Bi GN
aoe ES || =
da? da

so that finally for the heat transmitted we have the simple
expressions
Hee = (= +2 )a. Tena Sra,

In this equation R js a constant such that the excess of
heat radiated from unit area of an infinite plane black surface
of temperature uw, over that received from a similar surface
placed parallel to it and of temperature w,is R(w,—w,) 3 « Is
a quantity such that the radiation falling ona plate of thickness
I/« is by absorption within the plate reduced in the ratioe: 1;
r is the thermal conductivity, and a is a quantity which must
be determined from the conditions of the problem.

If U=up—up be the difference in temperature between the

250 Prof. A. Schuster on the Influence of

two sides of the plate at which « is t and 0 respectively,
equation (12) gives

U=P(ett—1) + Q(e-#*—1) +. at. .

Two further equations are required to determine the con-
stants P,Q, and a. These are obtained by considering the
relations which hold between A and B at the two surfaces. The
radiation A leaving the surface «=0 is made up partly by
the reflexion of the incident radiation By which we may put
equal to «B, and partly by the radiation of the surface itself
which is (l—o)Ru. Hence Ao, Bo, wo, the values of A, B, u

ron¢ =,
Ao—agBo= (1l—c) Rup. . 2 “ise

Similarly at the second surface where r=t
Bio Ap= do Rae 2 y . (185;

For surfaces which are black o=0, for surfaces which are
totally reflecting c=1. Substituting the values of F and w
in (14) and (15) we find for g=0 and x=t

K(B) +A,)=2«Ruy—rAa?(P+Q), ]

K(By— Ao) = 2aR— ak, (P—Q), |,

«(Bit Az) = 2«Ru;— da? (Pe + Qe) |
«(Bz—Az) = 2aR—2Kr(Pert*—Qe-**) J

The four last equations determine Aj, Bo, Ar, By in terms of
a, P,Q, and hence by substitution in (18a) and (180) the two
relations which together with (17) allow the three constants
of the equation to be calculated. The calculation of these
constants is simplified when o=o’, so that the two surfaces
have equal reflecting properties. Symmetry shows in that
case that the temperature at the centre of the plate must be
3(u,+u). Applying (12) we obtain the equation

t
$ (ust Up) =$P(1 + e%*) +Q(1 +07”) + 5 +b,

= ald t at at
eet 2 u=Pez +Qe 2 +0.
Equating the two expressions we derive
Pet +-O=0, °°... .
Hence (17) becomes
W=2P(eF—1) +a. <<. 3) ol ee

Only one further equation is necessary, which is obtained

eo Se oe ee

Radiation on the Transmission of Heat. 201

by combining the two first equations of (19) with (18). We
then find
2aR(1+o)=Aa[«(1+o)(P—Q)—a(1—o)(P + Q) ]. . (22)
i will consider the two extreme cases ¢=0 and o=1 in
greater detail, For c=0:
20h——Nale(e— O\— alk Oa). . (22a)
jor ao—1 -
Diy = Nvorre (le = CN) «sei sem eR ce) i, (22)
The values cf P and a, as found from the combination of
(20), (21), and either (22 a) or (226), are as follows :—
For c=0:
Unda «(Ee +1) + a(e*?—1) ]

~ (4R+ at) ( (e’—1) + AaKt (ert + J 1 - +. (234)
P= —Qe-*
Se a
ie (4R + rat )(e%—1) +raxt(et + yy (24 a)
For o=l1:
i ; Undan (e+ IL) ihe
ae 1) eel (23D)
P= — (Je
2
a (24)

~ 4R (e%—1) + rant (e* +41)"

In order to show the characteristics of the temperature
variation indicated by (12) I have plotted curves, taking
for « the value of ‘64 and putting A=1:3x10-*. A body
possessing these constants would have the transparency of
clear rock-salt, and a thermal conductivity equal to that of cork.
I have calculated the appropriate value of R by taking the
radiation of a black body per unit surface to be 10-”x u’,
where u is the absolute temperature. This is in close agree-
ment with the best observations. Two black parallel surfaces
differing in temperature by a small amount dw, exchange
heat therefore at the rate of 4x 10—-Pudu. If uw is equal
to 300° on the absolute scale this will be nearly 10-* x du.
Hence for temperatures nearly equal to 30° C. we may in the
above equations put R=10~*.

Curve I. (PI.I1.) gives the temperature change ina plate of
a substance having the properties described, the plate being
5 ems. thick and “placed between two totally reflecting sur-
faces, the average temperature being about 30° C, Curve II.

252 Prof. A. Schuster on the Influence of

shows the variations in the plate when placed in contact with
two perfectly black surfaces. The effect of increased radia-
tion is shown in Curve IIL, which gives the temperature

variation for totally reflecting surfaces, and with a value of
R=10-% corresponding to a temperature of about 360° C.
The curve for the higher temperature and black surfaces has
not been drawn, as it would confuse the figure, being nearly
coincident with Curve I. The temperature scale is of course
arbitrary. The curves show very clearly that radiation
destroys the uniform temperature slope which is obtained

when conductivity alone is taken into account, and that the
is iations from uniformity are greater when the surfaces are
reflecting than when they are black.

To investigate the effects of radiation on the transmittance
of heat it is best to take the two extreme cases: one in which
the plate is so thin that very little heat is absorbed in it, and
the other in which the plate i is so thick that very little radia-
tion can traverse its whole thickness. For small thicknesses
we may in equations 23a and 230 expand the exponential,
retaining only the terms as far as at in the numerator, and
2°42 in the denominator. After the necessary transformations
we find for the case of black surfaces

See)

Hence for the heat uae according to (16)

lal 7 a sy +RU,

The first term represents the heat calculated according to the
laws of conduction, and the second term gives the effect of
radiation. In the case of a very thin plate we are justified
therefore in taking the two eftec ts separately and adding the
results) JA “pare ealculation shows that for the case of
reflecting boundaries the heat transmitted by a thin plate is
that calculated from the known laws of conductiv ity, viz.. UAE.

A different result is arrived at when absorption within the
plate cannot be neglected. If we transform equations 23,
taking c’ as large compared to one, we find for black
surfaces

and for reflecting surfaces :

Ur a ( Al
Bal Gee ( eee:

Radiation on the Transmission of (Heat. 253

When ¢ is sufficiently large the reflecting property of ths
houndary becomes immater ial, and the transmitted heat is
Un l 2,

t ( a KN )
The ordinary measurements of thermal conductivity neglect
the effects of radiation and would yield incorrect results if
2R/«KX were appreciable. ‘his will only be the case for
transparent bodies possessing very low conductivities. When
the measurements are made at the ordinary temperatures, it
is the transparency for rays of low refrangibility that comes
into play, so that rock-salt and fluorspar are the only bodies
which can come into consideration. According to Melloni’s
experiments the constant « for rock-salt is 32, but this must
be doubled to make it apply to rays traversing the substance
obliquely as well as normally (see § 7). The thermal con-
ductivity of rock-salt according to Lees is‘014. The fraction
4R/«d in this case works out to be ‘002. The measurements
of conductivity are affected by an error of that amount,
which is probably beyond the reach of experiment, but if rock-
salt possessed a thermal conductivity as low as that of cork,
or *00013, the error committed in measurements of thermal
conductivity by neglecting radiation would amount to 20 per
cent. That the effects of radiation may be neglected in pro-
portion as the body absorbs the radiations: may appear
surprising at first sight, but is explained by the fact that in
the case of good absorbers any portion of the body is
affected only by the radiation coming from other portions in
its immediate neighbourhood which possess temperatures
nearly equal to its own.

6. The effects of radiation become conspicuous, and more
important than those due to conduction of heat, in the case
of gases ; but the ordinary method of treatment which con-
siders the two effects separately is, according to § 4, sufficient,
when the thickness of the layer is not too large, so that a
considerable fraction of the heat-radiation may pass through
it. ‘This investigation has been undertaken primarily with a
view of clearing up the influence of radiation on the tem-
perature distribution inside a lar ge gaseous body, such as we
imagine the sun to be. Here we have to deal with a oreat
thickness which ultimately must be opaque. How far very hot
gases may be transparent it is difficult to Judge, but opaque-
ness must ultimately result, if only from the scattering of
light by molecules, assisted probably to a great extent by
internal reflexions taking place at surfaces at which the
density or temperature varies very rapidly. We are all

(Fie St ok i di) 23, (209

254 Prof. A. Schuster on the Influence of

familiar with this kind of opaqueness, due to reflexions
within convection currents set up by the solar heating of a
valley. It is advisable therefore to extend the foregoing
investigation to include the effects of scattering and irregular
reflexions.

If sAdz is the proportion of the incident light A which is
intercepted by the layer dx, 3sAda will pass out of the layer
in either direction. Hence A will be diminished by gsAda,
and B will be increased by the same amount, if B is the
radiation in the opposite direction. Adding the effects of
absorption, already discussed, we have

= cheesy
AW

7, = (BF) +$s(B—A)

from which we obtain an equation corresponding to (4a) viz.:

l
- (A+B)=(«+s)(B=2A), . .) ee
while (40) remains the same.

Proceeding as in § 3, we obtain the differential equation

ak d? Gh d2u
er pa a ee
ae ae + (ae —#+9) ) (C9 Gat =

This equation, which includes (10) for the special case
s==(), is one which can be discussed.in the same manner.

For steady temperatures the solution is of the same form
as (12), the value of @ now satisfying the relation

a h=2KkR+K(K+s5)}.

It is of interest to deal with the special case when there is no
absorption properly speaking. Putting «=0 in (12) we may
write the solution

U=arte,

which shows that in the absence of absorption but the presence
of scattering the temperature gradient is constant.

To determine the effect of radiation on the transmission of
heat we use the fact that for «=0 equations (4 6) become

£ (A—B)=0.
Putting

A—B=e,

Radiation on the Transmission of Heat, re

and hence

ad(A+B) 5am
res =s(B—A)=—s:,

A+B=-—scex+d.

If the boundaries are at a considerable distance, it cannot
matter what their reflecting properties are, and we may take
them to be black radiators of temperatures U, (c=0) and
U; (c=t). Writing therefore A= Ru, for r=0, ‘and B= Ry;
for «=t, the two equations for A and B determine ¢. It is
found that

— 2R(ay— Uz)

PSE QENe
or for a great thickness ¢

_ 2R(u,— us)

a st :
The heat transmitted is

~,@ + A—B=)* m= (1+ —).

Comparing this with (23) it is seen that as regards its
effect on the transmission of heat, scattering has the same
wae as absorption.

It remains to discuss how far the two assumptions made
in "this investigation may affect the results. In the first
place equation (2) is not strictly correct, and the value of «
will not be the same as that obtained by the measurement of
the absorption of radiations passing through the plate. Con-
sider unit area of the surface and let the radiation incident
on the plate be equal in all directions. The radiation enter-
ing unit-area normally will be Ad, and that entering in a
direction forming an angle § with the normal w “ill be
A cos 6 da, where dw is a small solid angle which, in the case
under consideration, will be 27 sin @dé@. If de is a small
thickness of the absorbing plate, the length of path of a ray
through it will be dz/cos@. Hence the total absorption in
the plate will be

27AkK' du * sin 0d0=27rAk'de,
0
the total incident radiation is

27 Adz ‘ 2 sin @ cos 6 d@=TA,

Hence the ratio of absorbed radiation to incident radiation,

256 Influence of Radiation on the Transmission of Heat.

which in the above investigation has been denoted by «, 1s
found to be
K=2x’'.

Here «’ represents the coefficient of absorption of the normal
rays. As long as the radiation at any point of a solid is
equal or nearly equal to the internal radiation of a body at
uniform temperature, the previous results are correct there-
fore, provided we take « to be equal to twice the coefficient
of absorption of the normally incident rays. But the absorp-
tion of the body itself will tend to diminish the intensities of
the oblique radiation, and though this diminution is partly
mad+ up by the radiation of the absorbing layer, the tendency
on the whole will be that the normal radiations will increase
relatively in intensity. The effect will be that « will gradually
diminish from its original value to half its amount. As the
purpose of our calculation was not the exact numerical caleu-
lation of the effects of radiation, but rather the study of its
general influence and the determination of the order of mag-
nitude of the effects, the results looked upon in this light will
not be affected by the assumption made. The same will
apply to the neglect of the dependence of radiation on waye-
length. This simplification will introduce an error the character
of which will be of the same nature as that Just discussed, so
that the apparent coefficient of absorption will gradually
diminish, only those radiations traversing an appreciable
thickness of the plate which are not strongly absorbed by it.

As a matter of experimentit has, however, been found that
by a proper adjustment of the constant «, the total radiation
traversing a thickness ¢ of a plate diminishes as e—*’, with a
near approach to accuracy, which justifies the equation on
which our calculations are based. While it is well to draw
attention to the approximate nature of the results, in so far as
they depend on the assumptions made, the nature of the
influence of radiation in the transmission of heat is sufficiently
well represented by the equations which have been obtained.
It will be the object of a further communication to study
effects of radiation on the temperature distribution in large
masses of gas in a state of convective equilibrium.

Description of Plate 11.

The curves represent the temperature variation within a plate
5 cm. thick, the»surfaces being kept at a difference of 1°, the
ordinates representing temperatures, and the abscissx distances
across the plate. The material of the plate is supposed to have a

On Screens Transparent only.to Ultra-Violet Light. 257

coeflicient of absorption equal to that of rock-salt and a thermal
conductivity equal to that of cork. Curves I. and II. give the
distribution of temperature when the average temperature is about
30° C., Curve I. representing the steady state when the boundaries
are totally reflecting, and Curve IT. when they are black. Curve ITI.
represents the steady state for totally reflecting boundaries when
the average temperature of the plate is abont 360°C. This curve
shows the approach to the steady state, when the transmission of
heat is entirely effected by radiation, thermal conductivity being
neglected. The temperature distribution in the limiting case being
uniform, but discontinuous at the surfaces. The numbers from
which the curves are plotted are given in the following Table, which
includes also under column IV. the case of black surfaces, with an
average temperature of 360°. It is only necessary to give the
temperatures near the colder bounding surface, as the distribution
is symmetrical at both sides and uniform near the centre of the
plate. The columns headed Temperature Differences represent
the difference between the temperature at any point and the tem-
perature of the colder surface ; the complete temperature change
in the plate is supposed to be 1°.

Pe. fr xl Temperature Differences.

| Colder | ; ae

in ems. i Peace, Metered eee (1 |

Pee OPOE, gh 082. Fala MeO Nl aT |
Oatley ac lies wi) FORA. yi Yess | G8 by 7:
‘4 HOG pbc ly 47 peaieee || 5-22
05 7a We) F188 388 | 221
10 Dye ORs harser eb GONE 1 caps

pee 20 335 Oi Tie 2b 315

| |

XXII. On Screens Transparent only to Ultra-Violet Light
and their Use in Spectrum Photography. By R. W. Woop,
Professor of Experimental Physics, Johns Hopkins Uni-
versity”.

[Plates ITI. & IV.}

i es who has repeated Tyndall’s beautiful lecture

experiment of kindling a pine stick in the dark heat

focus of a burning-glass, concentrating light from which the
visible raciations ear leon removed by means of a solution

* Communicated by the Author.

Phil. Mag. 8. 6. Vol. 5. No. 26. Feb. 19038.

(f.,

258 Prof. R. W. Wood on Sereens

of iodine in bisulphide of carbon, must have wished that we
possessed a screen, opaque to visible light and transparent to
the ultra-violet.

I have recently succeeded in making a screen quite trans-
parent to these radiations, though a gas flame cannot be seen
through it. By combining it with a lar ge condensing-lens
and an are-lamp, it is possible to form a dark focus of ultra-
violet light in which a lump of uranium nitrate glows with a
vivid green phosphorescence like a great emerald.

Besides giving us the means of performing a most beautiful
lecture experiment. these screens make it possible to photo-
graph the ultra-violet lines in grating spectra of higher
orders than the first, entirely uncontaminated by the visible

radiations which overlie them. Other applications at once
suggest themselves, such as the complete removal of the
highly actinic blue and violet rays, in certain investigations
of the ultra-violet region where the long exposures necessary
are apt to produce fogging of the plates. It seems quite
possible too, that photographs of the moon, planets, and
nebule taken by means of ultra-violet light may furnish

valuable data, as I shall attempt to show at the end of this
paper.

The substance which has made possible the production of
such a screen is nitroso-dimethyl-aniline, the remarkable
optical properties of which J have already alluded to in a
previous paper. As I have already said, a prism formed of
this substance yields a spectrum about 30 times as long as a
quartz prism of the same angle, the dispersion resembling ¢ some-
what that of selenium. I was of the opinion that the absorp-
tion, which commences at about wave-length :0005, would
increase continuously from this point down to the end of the
spectrum, as was found to be the case with selenium. On
commencing a study of the absorption, however, I was
astonished to find that it ended abruptly a little beyond the
H and K lines, and that from this point on, the substance was
transparent even down to the last cadmium line, of wave-
length :0002.

It at once occurred to me that if some substance or sub-
stances could be found absorbing the red, yellow, and green,
and transparent to the ultra-violet, we could, by combining
them with the nitroso compound, ‘produce the long-sought
screen.

Very dense cobalt glass, coated with a thin film of gelatine
lightly stained with the nitroso, was found to be transparent
only to the extreme red and the ultra-violet, and the red was

Transparent only to Ultra- Violet Light. 259

eventually removed by means of a thin sheet of Chance’s
“sional-oreen ”’ glass, such as is used for one of the reflectors
in the Ives Kromskop.

This combination is wholly opaque to visible light, while
freely transmitting everything between wave- lengths 34 and
38. Of course the employment of glass screens limits the
ultra-violet transmission, and a screen of this description is
useful chiefly for lecture demonstrations. Considerable care
must be used in the adjustment of the strength of the solution
of the nitroso in gelatine, otherwise the intensity of the ultra-
violet light is considerably weakened.

The best strength is such as will be just sufficient to remove
the blue and violet ight transmitted by dense cobalt glass.
Quite a number of trials will be found necessary in adjusting
the densities of the three components of the screen to secure
the maximum effect, but when the balance is just right, it is
possible to form a focus in which a piece of paper is quite
invisible, while a mass of crystals of the nitrate of uranium

which I have found superior to anything else) glows with
sufficient intensity to be seen from the back of the largest
lecture-room.

It is best to exclude carefully all light which does not pass
through the screen.

With the assistance of one of our students, [am at the

resent time investigating the absorption of a large number
of substances, which, so far as I know, have not been pre-
viously studied, and I hope in time to. dispense with glass
entirely, and produce an opaque screen which transmits ultra-
violet down to the end of the spectrum.

A combination of a tube furnished with quartz ends, on one
of which is a thin film stained with nitroso, trans smits all of
the ultra-violet, and only the extreme red, but itis very incon-
venient to work with. For use as a screen in spectrum-
photography there is no especial object in removing the red,
yellow, and green, the nitroso alone blocking out completely
the actinic portions of the visible spectrum, ‘which overlie the
ultra-violet in the second and third order spectra, and [| shall
next consider solutions of the substance in various fluids in
connexion with spectrum-photography.

I have found that the best method of quickly securing a
record of the absorption of a solution is to bring a prismatic
layer of the liquid, contained in a quartz cell, before the slit
of a quartz spectrograph, and photograph the spectrum _ the
cadmium spark. We secure in this way a record of the

absorption of the liquid in various thicknesses, in the for m of
S 2
ie

260 Prof. R. W. Wood on Screens

a curve, quite similar to the curves laboriously constructed
from the readings obtained with the spectrophotometer*.

The curve obtained with asolution of the nitroso in glycerine

s shown in Plate ILI. figs. 4 and 5.

It will be noticed that after a certain thickness has been
passed we begin to get a noticeable absorption in the ultra-
violet, the form of Whe ee on Ue region being well shown
in fis. 3 and 4. The band inthe blue and violet is, however,
so much heavier that, by employing a film of suitable thick-
ness, we can get complete opacity in this region, combined
with almost perfect transparency in the ultra-violet. The
nitroso is soluble in water, glycerine, ether, alcohol, bisulphide
of carbon, and many other Huids, and the region of heaviest
absorption varies somewhat with the nature of the solvent,
the shift of the band not, however, following Kundt’s rule in
every case.

A stained gelatine film on a quartz plate forms a fairly
suitable screen, if we do not wish to photograph below the
group of cadmium lines at wave- length 2314. It is opaque,
however, to waves much shorter than this. The glycerine
solution “oeewns down to the last cadmium line, X=2147,
and some other solvents appear to work equally well,

In photegraphing the spectrum of the cadmium-spark in
the ultra-violet of the second order, with the fourteen-foot
concave grating, I found that the prolonged exposure of the
solution in elycerine to the light of the spark resulted in its
decomposition. Gas- bubbles ‘formed i in the thin quartz cell,
and by bridging across the space b between the two plates
allowed the passage of blue ana violet light.

The same thing occurred with pure glycerine under a
quartz plate, while glycerine under glass was unaffected,
showing that the decomposition was caused by the extreme
ultra-violet.

In addition to the formation of bubbles, a gradual bleaching
of the solution occurred. To obviate this difficulty I constructed

* It is my intention to prepare a monograph on the absorption of a
large number of the aniline dyes, and other organic compounds such as the
nitroso- dimethyl-aniline, which have not been previously investigated.
The spectra w ill be approximately normal, all on the same scale, and will
extend from the C-line down to the end of the spectrum. They will be
photographed in the manner which I have described, and will, I hope,
make it possible for the spectroscopist or physicist to pick out at once the
combination necessary to “produce any desired result. Pr eliminary experi-
ments are now in progress to determine the best form to give the apparatus,
and the most suitable source of light, and I shall be. very glad of any
suggestions pertaining either to the apparatus or to par ticular substances
worthy of investigation. {A similar method of studying absorption
within the range of the visible spectrum was employed many years ago
by the late Dr. Gladstone —Ed. Phil. Mag. |

Transparent only to Ultra-Violet Light. 261

a small cell of quartz, by cementing two plates together,
with a space of about 0°5 millim. between them, the cell thus
formed being cemented to the bottom of a small thistle tube
with a very small bore. By filling the thistle tube with the
glycerine solution a flow took place through the cell at the
rate of about a dr op every two minutes. This device worked
admirably, and gave no trouble at all, the cell being placed
close to the slit of the erating camera, in the path of the
convergent beam from the quartz lens. Another very satis-
factory screen can be made by dissolving celluloid (previously
boiled for some time in water) in amyl acetate, adding a
little nitroso, and flowing the solution on a quartz plate. It
is, however, opaque to the last two cadmium lines.

The use of the screen necessitates considerable increase in
the time of the exposure, the amount varying from two to ten
or even twenty times, according to the density of the screen.

The streneth of the elycerine solution must be adjusted
according to the work required of it: a strong solution
gives a wider band in the blue and violet, but diminishes the
intensity of the ultra-violet as well. In general the best

results are obtained when the blue line of wave-length 4799
in the spark-spectrum of cadmium can be just barely dis-
cerned.

in Plate ILI. fig. 1 the wave-lengths of the principal lines
in the spark-spectrum of cadmium are given for reference.
Sie ocion Of tie nitroso screen is. welll shoamn in fig. 2,
the spectra being photographed with a small quartz spectro-
graph made by Fuess. The first seven spectra were taken
through the glycer ine-nitroso cell which I have just described,
with the followi ing times of exposure: 5, 10, 15, 20, 30, 49,
and 60 seconds. ‘The cell was then remov ed, and the followe
ing six spectra taken. with exposures 24, 5, 10, 15, 20, and
30 seconds. <A study of these spectra enables us to calculate
just what can be done with this screen, and the necessary
increase In the time of exposure resulting from its use.

In fig 6, which is a negative, we have the absorption
spectra of the various components of the screen which |
mentioned in the first part of this paper, taken with exposures
of 20 seconds each.

The spectra were taken through screens as follows :—

1. Nitroso in gelatine on glass (thin film).

ee » _ (thick film).

a ama be on cobalt glass (thin film).

HE ais < » (thick film) strong

99 99
ultra-violet absorption.
5. Dense eobalt olass.
6. Turnbull’s blue in gelatine.

262 Prof. R. W. Wood on Screens

7. Chance’s * Signal-green ”’ glass (two thicknesses).

8. No screen, 3 seconds’ exposure.

9. Cyanine in canada-balsam.

11. Aurantia in collodion.
12. Signal-green glass (one thickness).

These photographs were taken on an orthochromatic plate,
the yellow and yellow-green being compressed into the small
strip which appears alone by itself in No. 11.

The utility of the nitroso screen in photography with the
concave grating is very clearly brought out in the photo-
graphs of the iron spectrum shown in Plate IV. These were
made with a 14-foot grating, with a glycerine nitroso cell
before the slit during one of the exposures. Tigures 1 and 2
are from the same plate. Strip B in each was made through
the screen, and shows the ultra-violet of the third order, un-
contaminated by the blue of the second. In strips A, which
were made without the screen, the two orders are mixed.
Strips C were made through a glass screen, which cut off the
third order ultra-violet, leaving the blue of the second. I
have marked a few of the wave-lengths to aid in the identi-
fication of the lines.

The times of exposure were for strips A and C ten minutes,
for B fifty minutes.

The group of cadmium lines in the neighbourhood of
wave-length 2314 is, in the second order spectrum, mixed up
with a lot of blue air lines of the first order spectrum. The
separation of the two by the nitroso screen is well shown in
fio. 3, in which the two orders are shown superposed in strips
iN and the ultra-violet of the second order in strip B. The
exposures in this case were 15 minutes and 2 hours re-
spectively.

Another screen which I believe may prove useful in astro-
physical work is made by combinin @ nitroso-dimethyl-
aniline with a small amount of the dye uranine, the latter
removing the bluish-green portion of the spectrum which
affects the photographic plate. By a proper adjustment of
the two in gelatine on glass, a screen can be formed which,
when used with an ordinary (i. ¢., not orthochromatic) plate
gives us a photograph ‘ingle exclusiv ely by ultra-violet
light, comprised between wave-lengths 345 and 365, a rather

narrow range.

I have made a few photographs with a screen of this
description, which have brought out some interesting points.
In a photograph of the full moon, taken by ultra-violet light,
the contrast between the bright and dark areas is very strongly
accentuated, while in photographs of landscapes made in the
same way there is almost no contrast at all except between

Transparent only to Ultra- Vi role: Light. 263

white objects and objects not white. I have also photo-
graphed a collection of rocks and minerals with Si: -violet
light and with yellow light. In the negative taken by yellow
light there is a great deal of contrast and detail, especially
in the marbles and conglomerates, while in the negative taken
by ultra-violet light all this is absent, the white specimens
coming out very black, with everything else of a thin and
almost uniform grey. 1 hope in the near future to have an
opportunity of making some lunar photographs on a large
seale, the only instrument at my disposal at the present time
being the nine-inch equatorial of the University. Photo-
eraphing by ultra-violet light appears to diminish the con-
trast between all objects “nok a hite, and to increase the
contrast between white objects and those not white. I do
not wish to be hasty in drawing conclusions, but it appears
to me to be probable that the more luminous portions of the
lunar surface, if not as white as plaster-of-paris, must at least
be much whiter than grey sandstone. In Plate IV. fig. 4 are
reproduced two photographs of the same landscape, taken at
the same time and under similar conditions of illumination,
the one (A) taken on an orthochromatic plate by yellow light
through a screen of dense aurantia, the other (B) taken on
an ordinary plate by ultra-violet light.

The absence of contrast between the chimneys and walls in
Bis especially noticeable in the right-hand part of the picture.
I tried various times of exposure, and the picture reproduced
is the best of the lot. Another curious effect is the almost
complete absence of shadows in the ultra-violet picture (it
was taken in full sunlight like the other), showing that most
of the ultra-violet light comes from the sky, which is what
we should expect, though we should hardly anticipate that
the effect would be so pronounced. This is best seen on the
monument and on the snow in the middle distance. The
increase of “atmosphere ”’ in the ultra-violet picture ix very
marked. It is sostrong that under-exposed plates fog in the
shadows of objects not over one hundred yards from the
camera, a circumstance which shows the great scattering
power of the air for these short waves. The two pictures
are also interesting as showing that our eyes have developed
a maximum sensibility for that region of the spectrum which
shows terrestrial objects in strongest contrast. Nitroso-
dimethyl-aniline is the only substance, other than the ordinary
aniline dyes, that | have examined thus far, and I feel v a y
hopeful of finding, among the large number of allied sub-
stances, absorbing media even more transparent to the ultra-
violet radiations than the one which I have described in this
paper.

[ 264 |

XXIV. How to apply the Resolution of Light into Uniform
Undulations of Flat Wavelets to the Investigation of Optical
Phenomena. By G. JoHNsToNE Stoney, J/.4., Se.D.,
TRS

[The letters «fw are used throughout the present paper as an
abbreviation for undulation of flat wavelets. |

Introduction.

1 IGHT while within a uniform transparent medium, or

any other event which the medium can without
external assistance propagate forward as waves, may be
resolved within that medium in an infinite number of ways,
and among them into undulations of convex or of concave or
of flat wavelets. That a resolution into uniform flat wavelets
is always possible is proved in the October number of the
Philosophical Magazine of 1896, p. 335, where this theorem
is enunciated and deduced from an already known theorem +
in optics ; and a more direct proof of the resolution by the
Principle of Reversal is given in a paper published at p. 570
of the Report of the British Association fer 1901. This
proof is better than that previously given, because it is more
direct and less inelegant, and also because it furnishes addi-
tional information which is useful. <A third and extremely
elegant proof has recently been publisbed by Mr. Edmund
Whittaker, Secretary of the Royal Astronomical Society, at
p. 619 of the ‘ Monthly Notices’ of that Society issued in
September 1902, where he shows that the general solution
of the equation

late
aN oe See eS Pe)! CNS SS ae
ve kt Bite om
may be made to assume the form
Tr 2a
V= BY GaGa = <0 ae (2)
0 0

where F is an arbitrary function of the three arguments
(vsin 6 cost ysin @siny +2cosO+kt), 6, and w;

* Communicated by the Author, haying been read in September 1902
before Section A of the British Association.

+ The theorem here referred to is enunciated at the foot of p. 335
(loc. cit.), and illustrated by the diagram on p. 340. It is the theorem
by which Fraunhofer’s beautiful experiments with crossed gratings,
which were then recent, were explained in the University of Dublin
when the author was a student of Trinity College in the forties of the
last century. There were two proofs of it current—one an analytical
proof by Professor, afterwards Provost, Jellett, based on an extension of
one of Airy’s theorems in his Tract on Light; and the other a proof by
the Principle of Reversal, a new and powerful tool of investigation which
MacCullagh had then recently introduced.

Resolutien of Light into Undulations of Flat Wavelets. 265

in other words, the solution is brought into a form which by
Fourier’s theorem can be expanded i into terms each of which
represents an undulation of flat wavelets and is also a
ua solution of equation (1).

2. Mr. Whittaker’s proof has the advantage of deriving
the resolution directly from the far deren differential
equation (eqn. (1)) of those wave-motions in which the speed
of propagation is constant as regards 2, y, z and t—a con-
dition which, as Clerk Maxwell showed, is ‘fulfilled by electro-
magnetic waves in an isotropic medium whenever we may
assume that the product of the two inductive capacities of the
medium is independent of the intensity of the alternations
of electromagnetic stress, although in dispersing media
it is not independent of their periodic time. (See Clerk
Maxwell’s ‘ Electricity and Magnetism,’ § 786.) This con-
dition is doubtless complied with by those electromagnetic
waves that constitute any light that our eyes can see,
if we may omit from comenlecadian the absorption of part
of the light by the medium, as we legitimately may when
dealing with journeys of any length in the open ether, or with
journeys of moderate length across transparent media.

3. On the other hand, the proof by the Principle of
Reversal has an advantage which is of great value to the
physicist, namely, that it not only proves, like the analytical
method, that a resolution into flat wavelets exists, but further,
Sie: in each individual case details of the Fexoibion an
of the relations in which this resolution stands to other neigh-
bouring resolutions: amongst which the most useful are its
relations to resolutions into concave or convex wavelets that
are nearly flat. It thus furnishes the general solution of
eqn. (1) which is presented in eqn. (2); along with details
that are of practical value ; and further, with what may be
io ae as equivalent to a solution of ahe theorem in the
Calculus of Variations which would investigate the relation to
one another of the various functional forms which the solu-
tion of eqn. (1) can assume: of which functional forms
eqn. (2) is one. This great additional insight, and the adapt-
ability of the method to individual inst: ances, offer such
assistance to the experimental physicist that it is fortunate
that we are in possession of both proofs. We shall be in a
better position to appreciate the advantages here spoken of
when we come to the experimental menidontions: An account
of some of these is in preparation, and the author hopes to
publish it as a sequel to the present paper.

4, The resolution of a given distribution of light into its
component undulations of “Hat wavelets is unzque in the same

266 Dr. G. J. Stoney on the Resolution of Light

sense in which resolutions by Fourier’s theorem, or into
Spherical Harmonics, are unique ; and it has the immense
advantage over every other method of resolution that each of
the flat wavelet components advances unaltered across the
medium. When we aim at the most complete theoretical
resolution from the purely mathematical point of view, we
are to regard each of the component undulations as an
uninterrupted train of waves which are all alike—of the
same wave-frequency, intensity, and state of polarization
throughout—and each occupying the whole of space for all
time. Nevertheless it is quite permissible, and is for most
purposes convenient, to consider separately what happens
within a limited space and definite duration. Moreover, we
shall presently see that it is legitimate, when investigating what
happens within a limited space, to divide the whole body of
undulations of flat wavelets into little groups and to substitute
a single undulation of flat wavelets for each of these groups;
and that, in ike manner, when dealing with a definite time, itis
legitimate to divide the wave-frequencies into little groups
and to substitute a single wave-frequency for each group.
By these familiar devices we substitute large numbers which
can be accepted by the physicist, for the infinite numbers of
the mathematician ; and values estimated at a point which
falls short of the limit for the limiting values of the mathe-
matician. We thus sweep aside the difficulties which would
otherwise result from ponderable matter consisting of mole-
cules, trom electricity consisting of electrons, and from the
consequent necessity when dealing with nature of substituting
the puncta of the physicist for the points of the mathe-
matician.

5. The proof by the Principle of Reversal has another
advantage, not yet referred to, viz. that it can be applied to
doubly refracting as well as to isotropic media. The investi-
gation at p. 570 of the Report of the British Association for
1901, goes with detail only into the resolution of light in
isotropic media, as being the case of most practical impor-
tance. This having been accomplished, it is easy to modify
the investigation so as to embrace both isotropic and doubly-
refracting media. To do this it suffices to substitute
throughout that proof the term wave-surface in the medium
for the term sphere, when treating of light diverging from or
converging towards a punctum. ‘Thus, Theorem I. on p. 573
of the B. A. Report furnishes, when generalized, the following
more comprehensive one :

into Uniform Undulations of flat Wavelets. 267

THEOREM I., extended.

All light traversing a uniform medium whether isotropic or
doubly refracting is susceptible of being resolved into undulations
of unifor m flat wavelets sweeping across that medium with
speeds in the different directions represented by the lengths of
the perpendiculars in those directions from the centre of the
wave-surface upon its tangent-planes.

6. In like manner the primary aim of the present paper is
to develop a convenient way of applying the flat-wavelet
resolution of light to the iny estigation of the optical problems
that arise in isotropic media; but, like the investigation
referred to above, it also can with ease be generalized | sO as
to provide for the optical problems that arise in any uniform
medium, whether isotropic or doubly refracting (see § 8).

The inquiry which we have in view naturally divides
itself into two portions, the first of which deals with what
we may call the dhemler study of optical phenomena, and
the other with their laboratory study—that is, with the
making of actual exper! iments and understanding them. The
present writer has made extensive use of the new method of
analysis in both branches of the study.

Part I.—AHow to employ the resolution of light into flat
wavelets in the chamber study of optical phenomena.

7. If we conceive the light within an isotropic transparent
medium to be resolved into its component undulations of flat
wavelets, the following will be found a convenient way of
dealing with them.

Imagine a straight line in space, which we may call the
optic avis. In most cases the best position for this line is
from the observer to the middle of his field of view. Draw
a plane perpendicular to the optic axis, preferably near to
the object looked at. This we may call the base-plane. With
c (the intersection of the optic axis and base-plane) as centre,
describe a hemisphere with its convex side towards Hie
observer, and with radii of any assumed length, R. This we
may call the reference-hemisphere.

8. In doubly-refracting media we have to use half the
wave-surtace of the medium instead of the simple hemisphere
which suffices for isotropic media. But for the present we
intend to confine our attention to the latter.

Now (see Theorem I. on p. 573 of the B.A. Report for
1901, or in §5 above) the light with which we are dealing,
whatever it is , might be withdraw n, and undulations of flat

268 Dr. G. J. Stoney on the Resolution of Light

wavelets substituted for it, without producing any change in
nature. Hach one of these uf w’s (undulations of flat
wavelets) travels in the direction of some radius of the

a
me
OS
aoe
LQ Bs
KAS

Xeference-hemisphere.

reference-hemisphere, and has its wave-fronts parallel to
the tangent-plane at the outer end of that radius We may
call undulations outward-bound when they travel along the
radius from centre to surface of the hemisphere e, and inward-
bound when they travel in the opposite direction.

9. Practically, in most real problems, we know beforehand
whether we are dealing with outward-bound or inward-bound
undulations, so that no appreciable inconvenience results
irom the circumstance that two undulations—one inward-
bound and the other outward-bound—are represented by the

same radius cP;. We may eall cP, the guide-r adius ot
whichev er of the two we have to deal with. It may equally
well be represented by the point P; on the hemisphere (which
we may call its gwide-point); and still better by I,, the
orthogonal projection of P, on either the base-plane or some
parallel plane (which we may call its ¢ndex-point). For
purposes of mathematical investigation it 1s more convenient

into Uniform Undulations of Flat Wavelets. 269

to project the guide-points into index-points on to the base-
plane, w hereas in experiments the projection is usually
exhibited on some parallel plane. The positions of the index-

points—2. e. of the projections of the guide- points—are the
same in the resulting diagram, whether it is formed on the

co)
base-plane or on any parallel plane.

10. Accordingly, if x, v2, &e. are the uf w’s we have to
deal with, then the directions in which they are advancing
and the orientations of their wave- fronts, are adequately
represented by the index-points h, b, &e. oot by the above
construction ; and whether the projection by which we arrive
at the index-points is a projection on to the base-plane or on
to some parallel plane, they occupy the same positions within
a circle in that plane which is the projection upon it of the
flat side of the reference-hemisphere, and which, therefore,
has R for its radius. This circle and its contents may be
called the Indicator-diagram.

11. By applying simple geometrical considerations to the
foregoing construction, we get the following propositions :—

Fig 2.

Indicator-diagram,

Let uw, and uw, be two inward-bound uf w’s, consisting of
waves similarly polarized and of wave-length X; and let |,
and I, be their index-points upon the indicator- diagram.
Then a simple geometrical proof furnishes the following
elegant theorem.

THEOREM VII.*

The light which these two ufw’s throw on the base-plane,
or on any parallel plane, ts a luminous ruling perpendicular

* The propositions in this paper are numbered in succession to those
in the paper at p. 570 of the L. A. Report for 1901.

270 Dr. G. J. Stoney on the Resolution of Light
to the line d; und the spacing from crest to crest of this ruling

“LS ~ 1 R
ae

The position of this ruling will become fully determined if
we know the position of any one of the points which the two
undulations reach simultaneously in the same phase. We
shall use the letter & to designate such a point.

12. Hitherto we have considered only individual uf w’s
Let us now consider an entire sheaf of them. By a sheaf of
uf w’s is meant a group of them whose guide-radii form a
solid cone. It will be represented either by this cone, which
may be called the guide-cone of these undulations, or by their
guide-patch (in which this cone intersects the surface of the
hemisphere) ; or preferably by the projection of this guide-
patch upon the indicator- diagram, which we may call the

macula of the sheaf of uf w’s.
Thus a point on the indicator-diagram represents a single
ufw, amacula (or patch on the indicator-diagram) represents
a certain sheaf of such undulations.

Let it further be provisionally assumed that the undulations
of this sheaf all reach the point / in identical phases at each
instant of time, that they are polarized alike, and that they
have equal intensities. The point 4, which the undulations
of the sheaf reach in identical phases, may be either on or off
the base-plane. Draw through /a plane parallel to the base-
plane, and call it plene # ; or it may be called the screen Kk,
as we are about to inquire in what way it is Uluminated by
the light with which we are dealing.

13. The macula of the sheaf may have any shape or size.
Let us begin with the simple case where the sheaf of undu-
lations is such that its macula on the indicator-diagram is a
rectangle with sides a and b. — Bisect
this macula, as in the figure, by a line
parallel to one of its sides, and let I,
and [,’ be similarly situated points in
the two halves. The line connecting
them is parallel to 6, and =b/2. Hence,
by Theorem VII., the two uf w’s of
which J, and L/ are the index-points
would, if they alone were present,
produce on plane K a luminous ruling of which one crest
passes through /, of which the crests are perpendicular to
the line 6 of fig. 3, and which are spaced asunder by the
interval aR

o=rA—

A rectangular macula on
the Indicator-diagram.

into Uniform Undulations of Flat Wavelets. 271

We may represent this by fig. 4, or by the upper strip of
fig. G,in which the continuous lines are the crests of the
luminous ruling, and the dotted lines are positions of cipher
illumination. ;

!
I
!
!
1
U
{
1
!
1
1
t
i
!
1
'
'

re me me ee we we ee
wee we ee Ke ew eee eH KH Ke

| I
| t
1 1
{ i
! i
I I
1 {
1 J
t I
1 i
' !
1 [
1 i
1 1
' t
‘ I
( t

Soo Soo oO

Part of plane Kk.

All other points, I,, 1, I,, &c. in the left-hand half of ~
fig. 5, have corresponding points in the right-hand half ; and
each such pair, if acting alone, would produce a ruling on
plane K represented diagrammatically by fig. 4, and ther ot,
with cipher illumination along the dotted lines of fig.
Accordingly when they are all present, there is cipher Sila.
mination along these lines. Moreover, there is maximum
illumination at the situation k, since we have made the
assumption that all the uf w’s reach it in identical phases :
but elsewhere, wherever light is superposed on light, the
resultant illumination will range between cipher and that
maximum.

The next step to be taken is to divide the macula into four

equal parts by lines parallel to a. Then

Fig. 5. all its points may be grouped in pairs

like {and I’, separated by the distance
b/&4 and with the line joiming them
parallel to 6. Hach such pair of index-
points belong to two ufw’s which, it
The same macula acting alone, would produce a luminous
as in fig. 3, ruling on plane K, parallel to the ruling

co)
on fig. 4, with one cae passing through

k, but with its positions of cipher illumination as in strip 8
of fig. 6 (p. 272).

So, again, by dividing the macula into eight parts, we find
that the illumination it produces on plane . K is confined te
positions which are not on the dotted lines of strip y of fig. 6:
and so on.

Finally, by this process, » we learn that there is cipher

272 Dr. G. J. Stoney on the Resolution of Light

illumination on all the dotted lines of fig. 7, 2. e. on all the
lines dotted or undotted of fig. 4, except the central one.

Fig. 6.

Each strip is the same part of plane K as in fig. 4.
Bae. af, Fig. 8.

—— ei oe ee Oe
=xm—— — — ee |e eo
ad

The same part of plane K.

By similarly dividing the rectangular macula into 2, 4, 8,
16, &e. equal parts by lines parallel to 4, we find a second
set of dotted lines along which the illumination is cipher, as
in fig. 8.

The results we thus arrive at may be summarized as
follows :—

Tororem VIII.

Tf the sheaf of wf w’s represented by a rectangular macula
on the indicator-diagram are of the same wave-length, similarly
olarized, and of equal intensity ; and if they all reach the
point k in the same phase ; then, if a flat screen parallel to the
indicator-diagram pass through the point k, the illumenation
produced on it by the uf w’s of this shear 7s such that there is
maximum tliumination at k, where the phases are identical ;
considerable brightness close to it, where the phases do not
differ much ; cipher illumination along all the dotted lines of
fig. 8; and probably glimmers of illumination in the interspaces
between them.

into Uniform Undulations of Flat Wavelets. 273

14. To quite obliterate these glimmers requires, in fact,
more Gane to be thrown upon plane K than is furnished by
the undulations of the sheaf, where these are all alike, as we
have supposed them to be. The requisite additional light,
when resolved into its component uf w’s, would furnish on
the indicator-diagram certain out-lying and on-lying appen-
dages * to the rectangular macula of the sheaf, of the kind
described in a paper ‘‘ On the Cause of Spurious Double Lines
and of Slender Appendages,”’ read at the Oxford Meeting of
the British Association (see B. A. Report for 1894, p. 583).
But usually the light that is indicated by these appendages
in the indicator-diagram is a very small proportion of the
total light, and in many practical cases need not be taken
into account. Whenever it is legitimate to exclude them
from consideration, we may regard the sheaf of undulations
as producing illumination upon plane K, only within the
central patch of fig. 8, which is shut in by dotted lines.

15. When, as more frequently happens, the macula of a
sheaf of undulations is a circular disk or oval instead of a
rectangle, the modification of the above analysis is obvious.
Airy’s investigation of the image of a star in a telescope is a
particular case of the above more general theorem, viz. the
case where the macula is a circular patch situated exactly in
the middle of the indicator-diagram.

16. From Theorem VIII. the following one may with ease
be deduced.

THEOREM IX.

When light reaches the point k in the same phase &c., from
two or more sheafs of uf w’s, represented on the indicator-
diagram by separate macule, then, as before, the illumination
of plane K is chiefly within a central patch surrounding k
such as that represented in fig. 8; but this central bright
patch new consists of a luminous ruling of parallel bands if
there are two sheafs, this ruling being finer the more distant
the two macule are on the indicator-diagram. Similarly, if
there are three macule not in a straight line, the bright patch
of fig. 8 is resolved into rows of bright specks ; and so on.

ey of these effects can be shown experimentally.

When we have occasion to deal with a very small

* The demand made by nature for the presence of these appendages
is a requirement analogous to the mathematical necessity of substituting
a series of sines and cosines of which the arcs are not commensurable
for the ordinary Fourier’s series, when the series is to represent an
isolated event without repetitions: 2.e when beyond that event the
sum of the series is to be everywhere absolutely cipher.

Phil. Mag. 8. 6. Vol. 5. No. 26. Feb. 1903. T

274 Dr. G. J. Stoney on the Resolution of Light

sheaf of uf w’s, it is often convenient to substitute a single
undulation for the whole of the little sheaf. That this is
legitimate when the macula of the sheat is small enough,
may be proved as follows. The guide-cone of the sheaf is

by supposition, a very acute one. Draw a line from its
vertex, within the cone. This we may call its axis. Let J
be the ‘corresponding point in its little macula. Let u be any
one of the undulations of the little sheaf, and let 1, be its
index-point. Along the axis imagine two

undulations v, and v,’ to be sent, with the Fig. 9.

same wave-length, state of polarization, and nore
intensity as 2%, One a which uY reaches k in i
the same phase as uw, and v;’ in the opposite _
e@ ;
phase. Under these circumstances v; and we

vy/ cancel one another, so that their addition The small macula.
to the system makes no change. Now uw, (Part of indicator-
and v,' produce a luminous ruling on plane diagram.)

K of which one of the lines of cipher illu-

mination passes through /, and of which the spacing is

where d is the very short distance from I, to J. If this
distance is short enough the nearest maximum of brightness
on either side will be so far from k, that within a limited
field of view, such as is seen on looking into an optical
instrument, cheer will be no appreciable light from this
ruling. And if so, we may omit w, and v,’, and v, alone
remains. Similar substitutions of vs, vs, &e., all of them
advancing along the axis, may be made for w, 25, &e., the
other undulations of the little sheaf. When this tee been
done, all these v’s may be combined into a single resultant
v travelling along the axis. This establishes Theorem X.,
which is as follows :

THEOREM X.

When dealing with a limited field of view we are at liberty
to substitute the resultant v for any very small sheaf of undu-
lations, and this substitution is legitimate, however unrelated
the phases, states of polarization, and intensities of the undu-
lations in the little sheaf may have been.

This is the first of the two substitutions spoken of above in

§ 4, which are of the kind that must be legitimate to justify
ee applying to nature conclusions obtained by mathematics
from data which are of necessity almost immeasurably
simpler than the complex details that nature everywhere

into Uniform Undulations of Flat Wavelets. 279

reveals to us when we attempt to pry into her operations at
close quarters.

18. The other of the two substitutions spoken of in § 4,
may be effected in almost exactly the same way. When two
uf w’s of wave-frequencies $, and ¢y (or of the corresponding
wave-leneths A, and A.) travel in the same direction, they
may, if similarly polarized and of equal intensity, be repre-
sented by equations which, by a suitable selection of origin
and coordinates, simplify into

yi =A sin [ 27(a#—vt) dy] (3)
yo= Asin [2a(a—vt)d.| I

When both of these undulations are present they produce a
resultant effect represented by

—d;
Yt Yo= 2A sin Ea (oo) OF PA) . GOS | 2m (ae) oa :

which tells us that at each station in space beats occur with a
frequency (@.—¢;)/2, and that the loops between the nodes

consist of waves of which the frequency is (2+ $1)/2, the ~

phases of the corresponding waves in any two consecutive
loops being the reverse of one another.

195A are neat way to deal with them is to imagine the

ae to become stationary and rigid at a given instant of
tame *, and then to imagine the w hole of this rigid system to
be borne forward, in a direction perpendicular | to the wave-
fronts, with the speed v, 2.e. with the speed of light. It will
then sufficiently represent what occurs in nature.

Let us select ¢=0 as the time when the system becomes

rigid. The components will thenceforth be represented by

the equations
yy=A sin (27 vy) (5)
Y= A sin (27 edo)

2 _€03 (2are 95 — ee

which isa rigid undulation + with loops and nodes, the middles

and the resultant by

Y, —Yg= 2A sin (202°:

* Another convenient device is to make x=O in eqn. (4), and in this
way to ascertain what happens at a given station in space as time flows
on. It is quite immaterial which method we employ,: of the two, that
in the text is perhaps the more easily handled.

+ In speaking of the rigid system it is convenient to continue to use
the terms wave, undulation, &c., although there is no motion. They
are used in the same sense as when one ‘speaks of an undulating land-

scape.
2

(+)

276 Dr. G. J. Stoney on the Resolution of Light

of the loops occurring upon the planes where (¢,—$,)@
(which is of cipher dimensions) is one of the series 0, 1, 2, 3,
&e., and with nodes lying upon the planes that are midway
between these positions. This may be represented diagram-
maticatly by fig. 10, in which the axis of Y is supposed to

Fig. 10.

é
aE

z 7
i
1
<

BAe Zero
Pot Pp, f a
2
be perpendicular to the plane of the paper; and in which the
lower figure represents a spectrum ot wave-frequencies.
Draw the planes «a, dg, &c. parallel to the plane YZ and at
the distances furnished by the equations

iL 2 a
C= i Soe = =
om om 6

éG. + Jaa

where 6 is an abbreviation for ¢.—@,. Then the middles of
the loops of the rigid undulation represented by eqn. (6) are
on these planes, and the nodes of that undulation lie on the
dotted planes midway between them. These latter planes,
€1, €2, €3, &e., are accordingly the situations where the trans-
versal of the waves that form the undulation becomes cipher.
The nearest of the dotted planes to plane YZ are the planes
e, and —é, Viz.:

ail 1

&=55, and #= Tos?) = =e (8)

which, therefore, mark the limits of the central loop.
Let us now indicate upon the spectrum the positions that

into Uniform Undulations of Flat Wavelets. DEG

correspond to the wave-frequencies @,—6/2 and b: + 0/2.
Let us suppose that ufw’s of all the wave-frequencies
between these limits are present, and further assume that
they are so related to one another that they are all polarized
alike and of equal intensity, and that they had all reached
the plane YZ in the same phase when the solidification took
place. ‘These would be represented on the spectrum by a
band extending from m ton. Let this band be divided into
equal parts by the line ec. Then the whole of the light can
be divided into pairs of rays, one in the left-hand half of the
band, and the other in the right-hand half, and with 6 as
the difference of wave-frequency between the two components
of each pair. Every such pair, if it alone were present,
would produce the distribution represented in fig. 10, with
loops of waves from —e, to +e, from e, to és, and 20 on,
and with their positions of cipher intensity occurring on
the dotted planes. Accordingly, as each pair if acting
separately would produce cipher intensity on the dotted
planes, they all when simultaneously acting produce cipher
intensity on those planes. We may make use of strip «
of fig. 6 to represent this distribution. And as we are
equally at liberty to divide the band mn on the spectrum
into 4 parts, or 8, or 16, &e., and thus to group the whole of
the light of due (emel tanto pairs of rays with a difference of
wave- -Frequency which we can make either 8/2, or 8/4, or
6/8, Ke. 5 we by this process find that when the whole band
of light is in action there is cipher intensity on the dotted
lines of strip 8, and on those of strip y, &e. of fig. 6, as well
as on those of strip 2 This means that there is cipher
intensity on all the planes, dotted or undotted, that are
represented in fig. 10, except the plane YZ. On this plane
the intensity is a maximum, because by hypothesis all the
uf w’s corresponding to the individual rays of the band
reached it in the same phase when the solidification took
place. Up to the present we have followed the same line of
argument as in § 13, and by continuing it to the end, we

learn that nearly the whole’ intensity of what results from
the coexistence of all the uf w’s is to be found in the central
loop between the planes —e, and +e,, while beyond those
limits there may be intensities that correspond to glimmers
of light, which become fainter the wider the band mz in the
spectrum is, and which, for their total extinction, would
require the cooperation of certain appendage rays other than
the rays of whichwe have yet taken account, which appendages,
however, in many of the practical cases that arise supply so
little light that they may be ignored.

278 Resolution of Light into Undulations of Flat Wavelets.

All that remains to be done is to start the rigid system
forward in the direction OX with the speed of light. It then
represents what occurs in nature, and furnishes the following
theorem :

THEOREM XI.

If ufw’s of ali the wave-frequencies that le within the
band mn in the spectrum travel in the direction OX ; if they
are of equal intensities and polarized alike; and if their
phases are such that their crests coincide at some one instant
of time with any one plane YZ parallel to their wave-fronts -
then this light produces at each station in space an illumination
which lasts for a period 1/8v, where 6 is half the range of
wave-frequencies within the band ; with perhaps glimmers of
ullumination before and after that period.

These glimmers would require for their extinction the
simultaneous presence of certain appendage uf w’s which,
however, in many practical problems represent s0 small a
part of the light that they need not be taken into account.

20. We may also infer the following theorem, which
is the converse partly of Theorem VIII. and partly of
Theorem XI.

THEorREM XII.

Light that at our station extends over a limited space and
lasts for a limited time is theoretically susceptible—i. e. would
be susceptible if the physical conditions prevailing in nature
justified our pursuing a resolution of the kind to its mathe-
matical limit—e7 being resolved into u f w’s injinite in number
and each occupying the whole of space for all time.

In dealing with the actual problems of nature, a resolution
is found to be sufficient which falls short of this extreme, and
which is well within what the physical constitution of matter
tolerates.

21. We are now in a position to effect the second of the
two useful substitutions spoken of in $4. If we have only to
consider what happens at our station within a limited duration
which we may call 7, and which may be a second, a minute,
an hour, a week, or any other: then we may proceed as
follows :—The light with which we are concerned may be of
various wave -frequencies extending over either the whole or.
a part of the spectrum, and the rays of which the spectrum
consists may be of any (either the same or different) inten-
sities and states of polarization. They need not be in any
way related to one another. We may conceive the spectrum
to form a map of wave-frequencies. Then we may divide
the length of this spectrum into equal degrees, each of which
corresponds to a fixed difference of wave-frequency, which
we may call 6, and we may make these degrees large or

The Theory of Electrolytic Dissociation. 279

small as we please. Jet us then make them so small that
the duration 7 shall be but a small part of the duration 1/é:.
Then we are at liberty to substitute a single u fw with one
definite wave-frequency, for the entire of the little group ot
ufw’s of different wave-frequencies that furnish the rays
that fall within any one of the foregoing degrees. ‘To see
this it is only necessary to proceed by successive steps which
are so exactly analogous to those adopted in § 17, that it is
ao to repeat the procedure here. We thereby learn
that

THEOREM XIII.

When we have to consider in any problem what happens
within a limited time, it is permissible to divide the wave-
frequencies (or the corresponding wave-lengths) of the laght
with which we are concerned, into little groups and to substitute
light of a single wave-frequency for each of these.

It is important to bear in mind that this substitution can
be effected whatever be the intensities, phases, and states of
polarization of the individual undulations of the little group,
inasmuch as it depends upon our pairing each member of
the group with a supposed one which we are at liberty to
conceive of as in the opposite phase, in the same state of
polarization, and of the same intensity as that member of the
group with which it is paired; and this can be effected
however unrelated in these respects that member of the group
may be to its colleagues:

22. The foregoing theorems (with perhaps a few additions
such as the theorem which explains how to resolve a beam or
pencil of light into its component uf w’s) would be a suffi-
cient foundation on which to proceed with the chamber study
of optical phenomena by the new analysis. It will, however,
be convenient to continue the study in conjunction with ex-
periments which will afford assistance ; and accordingly we
intend next to inquire how to exhibit in optical instruments
the resolution of light into its component u f w’s, and how to
employ this resolution as our guide in making and in inter-
preting experiments.

[To be continued. |

XXV. The Theory of Electrolytic Dissociation. By W.C.
D. Wuernam, JLA., F.R.S., Fellow of Trinity College,
Cambridge *.

HE theory of the ionic dissociation of electrolytes, chiefly
due to Arrhenius, was successful in explaining the
electrical properties of aqueous solutions, and in co-ordinating

“ Communicated by the Author.

280 Mr. W. C. D. Whetham on the

those properties with the phenomena of osmotic pressure and
chemical activity. Hence there followed a general though
not universal adoption of the theory, despite the opposition
of some chemists. Lately, however, evidence has been offered
to show that the general connexion between the properties
of electrolytes, which seems to exist in the case of solutions
in water, fails when other solvents are used, and that the exact
numerical relations between, for example, conductivity and
osmotic pressure, which were at one time thought to hold,
are inexact at moderate concentrations even for aqueous
solutions. It has hence been argued that the fundamental
conceptions of the dissociation theory are erroneous, and that
it should no longer be accepted as a valid explanation of the
electrolytic phenomena. In the present stage of the dis-
cussion, it may be of interest to examine the foundations on
which the theory rests, and to inquire how far they are
affected by such criticism as we have indicated.

The conception of the complete independence from each
other of certain parts of the dissolved molecules of electro-
lytes is attained by two distinct lines of research: (1) the
examination of the electrolytic conductivity; and (2) the
consideration of the thermodynamic theory of osmotic pressure
and allied phenomena.

The appearance of the products of electrolysis at the elec-
trodes, and at the electrodes only, indicates that the opposite
parts of the solute must travel in opposite directions through
the liquid under the influence of the electric forces, while
Haraday’s experiments show that the separation of a definite
quantity of substance at the electrodes is always associated
with the passage through the solution of a definite quantity
of electricity, which is proportional to the valency of the ion.
We are thus led to conclude that the process of electrolytic
conduction is a kind of convection, in which the opposite
ions are moved electrically through the liquid, and carry
with them definite electric charges. This view of the pheno-
mena was further developed by Kohlrausch, who showed
that a calculation of the velocities with which the ions moved
under a given electric potential gradient could be made from
a knowledge of the conductivity of the solution and of the
transport ratio, which had been investigated by Hittorf.
The numerical values of the mobilities of different ions
obtained by Kohlrausch’s theory were confirmed by Lodge,
Whetham, Orme Masson, and Steele, who have experl-
mentally determined the velocity of certain ions by tracing
their effect on an indicator, or by measuring the rate of
motion of the boundary between two different solutions,

Theory of Electrolytic Dissociation. 28]

It is well known that a finite electromotive force is needed
to effect electrolytic decomposition ; but, when the process is
examined more closely, it is found that the reverse electro-
motive force of polarization exists only at the electrodes. If
this reverse force is eliminated, by the use of alternating

‘arrents or otherwise, the conduction pr oceeds in conformity
with Ohm’s law, that j is, the current is proportional to the
electromotive force, so that any force, however small, causes
a corresponding current. Thus within the liquid there are
no reverse forces of polarization, and consequently no work
is done by the current in causing reversible electrolytic
separations. The freedom of passage indicated by the facts
of electrolysis must therefore exist, whether a current flows
or not; the function of the electric forces is merely directive,
and the only work expended is done against that frictional
resistance to the motion of the ions which is called the ionic
viscosity.

So far our results show that under all conditions the ions
possess the freedom necessary for their passage through the
liquid. That freedom may, however, on the facts enumerated,
be secured by a possibility of interchange between the
oppositely electrified parts of two dissolved molecules at the
instant of collision, or to the successive formation and decom-
position of molecular aggregates. Let us trace the con-
sequences of such suppositions.

In accordance with the elementary principles which hold
good for the chance encounters of a large number of moving
particles, the frequency of collision, or the number of mole-
cular aggregates formed per second, will be proportional
to the square of the number of dissolved molecules. Now,
on the view suggested, the motion of the ions, and therefore
the average lonic mobility, will depend on such chance
collisions, ‘and be pr oportional to the frequency with which
they occur. The velocity of the ions under a given potential
gradient will thus be proportional] , approximately at any rate,
to the square of the concentration of the solution. The
quantity of electricity conveyed per second under a given
electromotive force, that is, the conductivity of the solution,
must depend on the product of the relative velocity of the
ions and the number of ions per unit volume. It follows
that, on any hypothesis of molecular interchanges, the con-
duetivity of a solution will be approximately “proportiona!
to the cube of the concentration. This result is quite contrary
to observed facts. In dilute solutions, the conductivity is
nearly proportional to the first power of the concentration,
and, as the concentration increases, the conductivity usually

282 Mr. W. C. D. Whetham on the

increases at an even slower rate. We are bound to conclude
that no process which requires the conjunction of two mole-
cules is involved, and that the ions move independently of
each other through the liquid. It should be noticed that
migratory independence from each other on the part of the
ions is quite compatible with connexion between the ions and
the solvent, whether such connexion is of the nature of
definite chemical combination or more general physical
influence. The electrolytic dissociation theory is quite inde-
pendent of any particular view we may take of the nature

of solution, which may be produced by actions analogous
either to physical or to chemical processes.

Many other purely electrical phenomena indicate the same
independence of the ions, and receive a ready explanation if
that conclusion be accepted. Thus, Kohlrausch’s specific
coefficients of ionic mobility are definite constants for each
ion in dilute solution, and do not depend on the other ion
present. Again, when a layer of water is placed on the top
of a solution of an electrolyte, owing to the diffusion of the
two ions the water takes with reference to the solution a
positive or negative potential, according as the positive or
negative ion in that solution has the oreater mobility. From
al knowledge of the osmotic pressures and of the specific
coefficients of mobility of the ions, Nernst has shown that it
ix possible to calculate the observed numerical values both for
this difference of potential and for the rate of diffusion of the
salt as a whole.

Let us now turn to the second series of observations which
led to the development of the dissociation theory. The phe-
nomena of osmotic pressure, and the laws to which those
phenomena conform, can be deduced by the application of
thermodynamics, either in the manner of vant Hoff and Lord
Rayleigh, from the observed relations between the solubility
of gases and their pressure, as formulated in Henry’s law,
or from the fundamental ideas of the molecular theory, as
pointed out by Willard Gibbs, von Helmholtz, and Larmor.
Adopting the latter method, it is clear that the osmotic pres-
sure which a solution will exert against a solvent is measured
by the rate of change of the available energy of the system
when solvent is allowed to enter the solution reversibly
through a semi-permeable membrane. On the molecular
theory, we must imagine the solute to be distributed through
the liquid as a number of discrete particles, each of which
may atfect, either by way of chemical combination or physical
influence, a certain minute volume of the solvent lying round
it. The nature of this influence is unknown, but, whatever

Theory of Electrolytic Dissociation. 283

it may be, as soon as the solution becomes so dilute that,
except for an inappreciable fraction of the time, these spheres
of influence do not in general intersect each other, any
further addition of solvent will only increase the separation
of the spheres of action; it cannot change the internal
condition of one of these spheres or affect the interaction
between the solute particles and their surrounding solvent.
The change of available energy produced by the entry of
solvent must then simply be that due to the dilution of the
solute particles, and cannot depend on any interaction between
solute and solvent. The rate of change of available energy
with dilution, that is, the osmotic pressure, must consequently
be independent of the nature of the solve ent, and will there-
fore have the same value if no solvent be present. Thus, in
cases where this is possible, that is, for volatile solutes, 1
follows that the osmotic pressure must be equal to the
gaseous pressure corresponding to the same concentration.
We thus theoretically establish the gaseous laws for the
osmotic pressure of volatile solutes. and, since volatility is
probably only a matter of degree, it seems reasonable to
extend this result to non-volatile bodies. Whether this
extension be regarded as theoretically valid or not, there is
abundant experimental evidence that it is practically justified,
since the osmotic pressure of solutions of such substances as
cane-sugar is well known to have the gaseous value.

When in solutions of electrolytes we examine the osmotic
pressure or the correlated effects such as the depressions of
the freezing-point, abnormally great values are obtained,
and, by the course of reasoning given above, it follows that
a pimebor of solute particles greater than that indicated by
the chemical formula must adel: in the solution ; that is, that
dissociation must have occurred. To connect this result with
the migratory independence of the ions of electrolysis, it is
necessary to show that for solutions so dilute that the solute
particles are beyond each other’s sphere of influence, the
number of ions indicated by the electrical behaviour is the
same as the number of independent particles required to pro-
duce the observed osmotic effects. Thus fora dilute solution
of potassium chloride, which yields two electrical ions, potas-
sium and chlorine, the depression of the freezing-point should
be twice as great as for a solution of cane-sugar of equivalent
molecular concentration. For bodies yielding three ions,
such as sulphuric acid or barium chloride, the freezing-point
depression should similarly be three times the normal value.
When the concentration of the solution is increased, the
spheres of influence of the solute particles will intersect, and

284 Mr. W. C. D. Whetham on the

the thermodynamic deduction of the gaseous value of the
osmotic pressure ceases to be valid. Unless we know at
what concentration this intersection begins to produce appre-
clable effects, and what its result will be both on the
electrical and on the osmotic properties, we cannot infer that
the decrease in equivalent conductivity will proceed in
accordance with the decrease in the abnormal excess of
osmotic pressure.

Tt has commonly been assumed, as a necessary consequence
of the dissociation theory, that the number of ions indicated
by the electrical conductivity must agree with the number of
particles producing osmotic pressure both at extreme dilution,
when the ionization is usually complete, and also when the
concentration is increased to a moderate extent and some of
the ions recombine. While it seems likely that the first of
these relations should hold in cases where the ionization is
known to be complete, it will now be evident that the second
relation can only exist if the connexion between the ions.
which is produced by increasing the concentration, affects
equally both the conductivity and the osmotic properties.
Such might be the case were the only result of increasing
concentration to cause a certain number of ionic re-combi-
nations to form electrically inactive molecules, each molecule
producing the normal osmotic effect; but, if any other appre-
clable influence arises from ion to ion, it may possibly change
the rate of variation of available energy with dilution, that
is, the osmotic pressure, before it decreases the ionic mobility.
The second relation then can only be expected to hold while
the solute particles are beyond each other’s sphere of action,
and the experimental examination of the relation merely
gives a means of estimating at what dilution this condition
tails. The conductivity shows that ionization begins to be
incomplete at very great dilutions. Even for monovalent
salts, such as potassium chloride, the equivalent conductivity
begins to diminish at concentrations of about 10—* gram-
equivalent per litre, while, with salts containing divalent
ions, it is doubtful if complete ionization is more than just
reached at the greatest dilution which can be investigated
experimentally, namely about 10—° gram-equivalent per litre.
Incomplete ionization, however, does not necessarily connote
inter-ionic influences except at the moments of collision and
in the combined molecules, while for non-electrolytes, the
gaseous value of the osmotic pressure is known to extend to
much higher concentrations. It is possible, therefore, that
the second relation suggested by the theory should hold good
for a certain small range of concentration. Nevertheless, as

Theory of Electrolytic Dissociation. 285

Dr. Larmor has pointed out to the writer, there is reason to
believe that the gaseous laws would fail at much smaller
concentrations in solutions of electrolytes than in those of
non-electrolytes. If, as is most likely, the forces between the
dissolved molecules are electrical in nature, the effect of two
non-ionized bipolar molecules on each other ail be analogous
to that between two short magnets: the force will vary
inversely as the fourth power of the distance. On the other
hand, with two isolated charged ions, the force will be that
between two small electrified bodies, and will vary as the
inverse square of the distance. Thus, beyond a certain
minute range, the inter-molecular forces will rapidly become
insensible, and solutions of non-electrolytes will then conform
to the gaseous laws. LHlectrified ions, however, will produce
sensible effects on each other at ranges much ‘beyond these
inter-molecular spheres of action, and, even at gr eat dilution,
will diverge from the ideal outa. Such divergence
will certainly change the quantity of work done on dilution,
and thus affect the osmotic properties. It is not clear, how-
ever, that it will also diminish the migratory freedom neces-
sary for electrolysis: the inter-ionic forces will, on the
average, be equal in all directions, and may not. tndmenee
the mobility of the ions under an electromotive force. Asa
conclusion, then, it follows if we accept the dissociation theory
that, in those somisione which are known to be fully ionized
at oreat dilutions, the limiting values of the osmotic pro-
perties and of the electrical conductivity should indicate the
same number of ions to the molecule ; when the concen-
tration increases and the ionization of such solutions ceases
to be complete, it is possible, but not necessary, that, through-
out a smail range, the two methods should give identical
ralues for the coefficient of ionization; the concentration at
which such identity ceases should pro bably indicate the
point at which inter-ionic forces begin to prevent further
contormity with the gaseous laws; and finally, for the case
of solutions in which complete ionization is not shown by
the equivalent conductivity, we cannot assume that any exact
relation between the two mee of research will be found.

We must now see how far the experimental facts bear out
these theoretical conclusions. The equivalent conductivity
of electrolytes reaches a definite limit at a dilution which ean
only be experimentally examined with accuracy in solutions
of simple salts, such as potassium chloride, which contain
two monovalent ions. In these cases alone, then, can we look

the verification of the ideal relations. At the present
time, the best known of the osmotic properties is the depression

286 Mr. W. C. D. Whetham on the

of the freezing-point, and in Raoult’s book on Cryoscojne
are given the following results obtained by Loomis for the
molecular depressions at a concentration of 0-01 gram-mole-
cule of salt in 1000 grams of water, as in themselves trust-
worthy and in accordance with the best of other results
published before the year 1901.

Group I.

ovarsimm hydrate... 3°71) Nitric acid eee 3°73
Hydrochloric acid ... 3°61 | Potassium nitrate...... 3°46
Potassium chloride ... 3°60 | Sodium nitrate ...... .. Ye,
Sodium chloride ...... 3°67 Ammonium nitrate 3°58
Group II.
Sul plrurre @erd #1...2.. 4-49 | Calcium chloride ...... 5°04
a | = , ~ . .
Sodium sulphate ...... 5°09 | Magnesium chloride... 5°08
Group III.
-Magnesium sulphate... 2°66 | Zine sulphate ........ 2°90

In the first group are substances which are shown by their
electrical properties to yield in solution two monovalent ions.
On the dissociation theory, therefore, the osmotic pressure
effects should, at high dilution, tes double their normal
value. The normal value for the molecular depression of the
freezing-point is 1857, calculated from the osmotic theory,
and confirmed by experiments on dilute aqueous solutions
of non-electrolytes. Twice this value is 3°714, a number to
which ali the observed molecular depressions of substances
in Group LI. clesely approximate. The electrical behaviour
of bodies in the second group similarly indicates dissociation
into three ions, which would produce a molecular depression
of 5°57. The experimental numbers differ from this value
by about 10 per cent., but the error is in the right direction,
since the electrical conductivities at the concentrations used
show that the ionization is still far from complete in salts
with divalent ions. The corresponding error is yet greater
in salts of the third group, which give two ions both divalent;
the molecular depression should be again 3°714, a number
exceeding the observed values by about 30 per cent. All
discrepancies are thus of the kind to be expected from a con-
sideration of the electrical phenomena ; and the salts of the
first group, which are about 95 per cent. ionized at the con-
centration used in the cryoscopic experiments, yield very
concordant results.

Since the date of Raoult’s book, the most important and

Theory of Electrolytic Dissociation. 287

accurate determinations of freezing-points are those under-
taken by Dr. E. H. Griffiths by the methods of platinum
thermometr y. The results as yet obtained were announced
to the British Association in the year 1901... From concen-
trations 0:0005 to 0:02 normal, the molecular lowering of
the freezing- point of water produced by cane-sugar was
found to be ae 858, while that produced by potassium Eilers
slowly increased with the dilution, till, in a solution of
0:0003 gram-equivalent per litre, it reached 3:°720. Thus
the non-electrolyte gave the theoretical result, ne the binary
electrolyte twice the molecular depression of the non- -electro-
lyte, within extraordinarily narrow limits of experimental
error. At this concentration the conductivity indicates that
the ionization 1s about 99°7 per cent. Thus the evidence at
present available goes to support the accuracy of the first
relation of Arrhentns’ theory in the case of aqueous solu-
tions; the observed depressions never appreciably exceed
the theoretical values, and the discrepancies in the other
direction are readily explicable by incomplete ionization.
Passing to solutions in solvents other than water, we
find that suthcient data are not available to decide lnedhes
the same relation between the electrical and the osmotic
phenomena holds good. The difficulties of experiment are
much increased, and no observations on osmotic effects seem
to have been made on solutions in which the dilution was
carried far enough to secure complete ionization. In many
aqueous solutions, such as those of acetic acid and ammonia,
complete ‘onian ee cannot be experimentally attained ; eal
without definite evidence, we cannot assume that it is in
general reached by possible dilution in another solvent.
For reasons already indicated, measurements on stronger
solutions are of little use in this connexion. Moreover, for
non-aqueous solutions we usually have little knowledge of
the general electrolytic behaviour, and of such electrical con-
stants as the transport numbers, so that it is not safe to
conclude that the ions are of the same nature as those of the
corresponding solutions in water. In alcoholic solutions, at
any rate, what little evidence is forthcoming suggests that
complex ions are very numerous, even at moderate dilutions,
and any such complexity will diminish the number of solute
particles and consequently the osmotic effects. Kahlenberg
finds that solutions of diphenylamine in methyl cyanide show
abnormally low molecular weights, and yet are non-conductors
of electricity. Such a result perhaps indicates a dissociation
yielding products which are not electrically charged, or a
non-electrical double decomposition with the solvent. Until

288 Mr. W. C. D. Whetham on the

- further experiments have been made, it is impossible to say
whether or not the first relation suggested by the dissociation
theory holds for non-aqueous solutions. In fact, however
great be the likelihood of the general similarity as all con-
duction in solutions, we have not sufficient knowledge of
electrolysis in non-aqueous media to conclude that the

nature cf the process is the same as in aqueous solution. It
is not yet certain that we can here apply Faraday’s laws,
Ohm’s law, and Kohlrausch’s theory of ionic ‘velocity.
though, for ‘alcoholic solutions, a certain amount of evidence
in favour of this view has been accumulated,

The second relation enunciated by Arrhenius suggests that,
when the dissociation is incomplete, the coefficient of ioniza-
tion measured electrically should agree with the value caleu-
lated from the osmotic effects ; but, as we have seen, such
a relation can only hold for eran cases, and then only
within very narrow limits of concentration. In order to
obtain a valid basis for exact comparison with cryoscopic
determinations, it is necessary to measure the electrolytic
conductivities at the freezing-point. When this is done, it
is found that the two values of the ionization, though they
approach each other with decreasing concentration, only
actually coincide at the most extreme dilution reached in the
eryoscopic experiments. Thus, in a full discussion of the
subject which will be found in a treatise on the ‘ Theory of
Solution ’ lately published by the present writer, it is shown
that the disturbing causes we have indicated become appre-
ciable at concentrations considerably smaller than hitherto
believed ; but it is now evident that the discrepancies that
then arise are not conclusive evidence against the general
truth of the explanations advanced by the dissocuitiass theory.
Such discrepancies merely afford useful information about
the nature of the disturbing influences, and about the value
of the concentration at which these ioeeneee begin to be
appreciable.

Passing as before to solutions in solvents other than water,
we again “find the phenomena more complicated, even if the
general nature of the conduction should prove to be the same
as in aqueous solutions. Complex ions seem to be common,
and other disturbing factors appear to be present. Kahlen-
berg has called attention to cases in which the boiling- or
freezing-points of conducting solutions indicate molecular
weights equal to or greater than the normal, and this suggests
that no dissociation occurs. Until the specific ionic mobilities
in these solvents are known, we have no means of estimating
what percentage ionization is required to give the observed

Theory of Electrolytic Dissociation. 289

conductivity ; if the mobilities are high, it is possible that a
small value would be enough. In any case, such obser-
vations may be explained by association of the non-ionized
solute molecules, or by the existence of complex ions.

Summing up the results of our inquiry as far as we have
gone, we may say that, in those cases for which the theory
indicates exact relations, the experimental evidence is in
favour of their existence, while all discrepancies are either
suggested by the theory itself, or else occur under conditions
where the experimental knowledge is too fragmentary for
valid conclusions to be drawn.

We must now turn to other deductions from the theory,
towards which considerable criticism has lately been directed.
In the first place, the mass law of chemical action, which can
be established thermodynamically for dilute systems, has been
applied to electrolytic dissociation by Ostwald with complete
success in the case of aqueous solutions of weak acids; but
the law fails when applied to strong acids and other highly
ionized electrolytes, and this failure has been regarded
as one of the great objections to the dissociation theory.
It is probable, however, that the explanation is to be
sought in that difference in the law of the variation of the
force with the distance which we have already pointed
out must exist between solutions containing non-ionized
bipolar molecules and those containing dissociated electrified
ions. The thermodynamic basis of the mass law is only
valid for dilute systems, and, as we have seen, even at small
concentration, the forces between dissociated ions may be
quite sensible and produce disturbing effects.

The dissociation theory has also co-ordinated the electrical
ionization of aqueous solutions and the coefficients of chemical
activity. There is no such definite theoretical deduction of
this relation as of that between the conductivity and osmotic
effects ; the connexion of electrical ionization with chemical
activity is a matter of observation, and the conclusion that,
in the rapid chemical actions characteristic of electrolytes,
it is the ions which alone are active, rests on the evidence of
this connexion alone. ‘The numerical relations given by
Arrhenius, and the many deductions from this hypothesis
which have been verified for aqueous solutions, have led to
the idea that a similar explanation of the nature of all rapid
chemical action might be given, whatever the solvent and
whatever the conditions. There seems, however, no valid
theoretical reason which necessitates such an extension, and
it is possible that, in other solvents and for gaseous systems,

Phil. Mag. 8. 6. Vol. 5. No. 26. Feb. 1903. U

290 Notices respecting New Books.

rapid chemical change may be brought about by non-electrical
double decomposition. This idea is supported by an obser-
vation of Kahlenberg on the instantaneous production of a
precipitate of copper chloride when hydrochloric acid is
passed into a non-conducting solution of copper oleate in
benzene. It is evident that such an observation indicates
that, in the particular solvent used, chemical action may
occur which is not correlated with electrolytic conductivity,
but it does not in the least weaken the electrical and osmotic
evidence which we have adduced above in favour of the
theory of the ionic dissociation of the aqueous soluticns of
electrolytes.

Annuaire pour VAn 1903, Pubhié par le Bureau des Longitudes.
Avec des Notices Scientifiques. Paris: Gauthier- Villars (55 quai
des Grands-Augustins). Pp. viii+808. Price 1 fr. 50 ¢.

; pauls important annual contains, besides the usual astronomical,

physical, and chemical tables, a number of specially contributed
articles, the most important of which are :—“ Shooting-Stars and
Comets,” by R. Radau; ‘‘Science and Poetry,” by J. Janssen ;
‘On the Work carried out at the Mont Blane Observatory,” by
J. Janssen ; and the speeches delivered by a number of distinguished
French scientists as a tribute to the memory of the late A. Cornu
and that of H. Faye.

Compte Rendu du deuaiéme Congrés International des Mathématiciens,
tenu a@ Paris de 6 au12 Aowt 1900. Procés-verbaux et Communi-
cations, publiés par EH. Duporcg. Paris: Gauthier-Villars, 1902.

Atmos1 every department of mathematics, pure and applied, is
touched on in this volume ; and a mere glance through its pages
cannot fail to be instructive to mathematicians of all classes.
Cantor contributes a paper on the Historiography of the science ;
Volterra an interesting estimate of the careers and labours of Betti,
Brioschi, and Casorati. Hilbert discusses at considerable length
the future problems of mathematics ; Poincaré the réle of intui-
tion and logic; and Mittag-Letiler reproduces, with comments,
some important letters of Weierstrass to Sophie Kowalewski. Then
follow some thirty papers of various lengths upon the theory of
numbers, analysis, geometry, dynamics, history, and methods of
teaching. At one of the meetings some discussion arose in regard
to the proposed adoption of Zamenhot’s artificial language Esperanto
as a universal language in science and commerce; but although the
growing disadvantages attending the publication of scientific papers
in so many different languages were fully recognized, the motion
earried was that of Vassilief, that Academies and Societies study
the means for remedying the evil at present existing.

Notices respecting New Books. 291

Legons sur la Théorie des Gaz. Par L. BoutzMann, Professeur a
V Université de Leipzig. Traduites par A. GaLLoTrTI. Avec une
Introduction et des Notes de M. Brittovurn, Professeur au
College de France. Premiere Partie. Paris: Gauthier-Villars,
1902. Pp. xix+204.

Tue kinetic theory of gases is a subject possessing a peculiar
fascination for the mathematical physicist: almost every dis-
tinguished member of that body has, at one time or another,
devoted a good deal of attention to it. The fascination seems to
be largely due to the difficulty of the subject, and to the extremely
wary manner in which an investigator must tread on this ground
if he is to avoid falling into countless pitfalls. Then, again, a
subject so full of delicate and debateable points is sure to be fruitful
of controversy; and controversy is always stimulating, and ministers
to that lust of battle which, in some form or another, has always
dominated the human race.

The results arrived at in the kinetic theory of gases are, however,
of much more than purely mathematical interest. As is the case
with all really important theories, the kinetic theory has powerfully
reacted on experimental science, and stimulated research. To the
experimenter, as well as the mathematician, it has yielded a rich
harvest of results.

Those students who have neither the time nor the mathematical
equipment necessary for a full study of this important yet difficult
subject, will probably find the best account of it in a simple form
in Meyer’s ‘Kinetic Theory of Gases,’ recently translated by
Mr. Baynes. To the advanced student, we can heartily commend
the work under review—the first part of a comprehensive treatise
on the subject by Professor L. Boltzmann. Few authors could
speak with greater authority on this subject, and still fewer could
handle it in a manner at once so clear and cautious as that which
characterizes Prof. Boltzmann’s treatment of it.

The three chapters into which the present volume is divided
correspond to three hypotheses regarding the gaseous molecules :—
(1) The molecules are elastic spheres ; there are no external forces,
and no sensible molar movements. (2) The molecules are centres
of force; external forces and sensible molar displacements are
assumed to exist. (3) The molecules repel one another with a force
which varies inversely as the fifth power of the distance.

One cannot help being struck by the evident care which the
author has taken to make the reasoning as clear as the nature of
the subject will permit, and to point out the exact limitations ot
the results arrived at, and their connexion with the fundamental
assumptions on which they are based.

M. Brillouin contributes an interesting introduction dealing
with the historical aspect of the subject, and some valuable
notes at the end which embody the results of the most recent
investigations.

292 Notices respecting New Books.

The Theory of Optics. By Patt Druve, Professor of Physics at the
University of Giessen. Transiated from the German by C. Rispore
Mannand Rosert A. MitiiKkay, Assistant Professors of Physics
at the University of Chicago. London: Longmans, Green,
and Co. 1902. Pp. xxi+546.

Tue English translation of Prof. Drude’s important work on
Optics must be regarded as one of the most welcome additions to
that series of text-books for advanced students which is beginning
to supply a long-felt want. Our scientific literature is overloaded
with text-books of an extremely elementary kind, while the
number of books suitable for the use of the more advanced
student is very limited indeed. The late Professor Preston ren-
dered capital service to the cause of English science by the publi-
cation of his excellent treatises on Light and Heat; indeed, he
may be said to have inaugurated a new era in the history of text-
books on physics: and signs are not wanting that his example is
likely to be followed by others.

The new work by Drude must take its place as one of the
standard treatises on the subject by the side of Preston’s ‘ Theory
of Light’ and the treatises on Geometrical Optics by Heath and
by Herman. It is, in a sense, supplementary to these. Its
leading features are the clear and connected account of the
principles underlying the construction of optical instruments, and
the masterly exposition of modern optical theories, considered
from the electromagnetic standpoint. There is no other book in
which the reader will find so complete an account of the present
state of the electromagnetic theory of light, or in which the
various difficulties connected with that theory are dealt with in so
clear and painstaking a manner.

The work is divided into three Parts—Geometrical Optics,
Physical Optics, and Radiation. The first Part deals with the
fundamental laws of geometrical optics, the geometrical theory of
optical images, the physical conditions for the formation of an
image, apertures and the effects depending on them, and optical
instruments. The subjects comprised under Part II. are the
velocity of light, interference, Huygens’s principle, diffraction,
polarization, the mechanical and electromagnetic theories of light,
propagation of light in transparent isotropic media, optical pro-
perties of transparent crystals, absorbing media, dispersion, optically
and magnetically active substances, effects produced by bodies in
motion. Part III. is devoted to the consideration of the energy
of radiation, the application of the second law of thermodynamics .
to radiation, and the theory of incandescent vapours and gases.

The translation is well done, with only here and there a sug-
gestion of foreign idiom; the English reader would, no doubt,
preter to see some of the Americanisms in the spelling removed ;
but that isa small matter in view of the great service rendered by
the translators to the English-speaking student. The publishers
deserve great credit for the high-class ‘‘get-up ” of the book.

Fig. 1.

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PHILOSOPHICAL MAGAZINE

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JOURNAL OF SQER

[SIXTH SERIES

MARCH £903:

XXVIII. On the Free Vibrations of Systems apicied with
Rotatory Terms. By Lord Rayieiex, O.M., FR.S*

B’ a suitable choice of coordinates the expressions for the
kinetic and potential energies of the system may be
reduced to the forms

enon tae Ce ee Ce)
IN Cy cy Op oe aie yd) usdente ayes Wy VES)
If there be no dissipative forces, the equations of free
vibration are
anh; + edit Biohs + Biss +
dsb, + Cobo + Bandi + Bosbst...=0.7. . - (3)

where 9,s==— 8s; and under the restriction contemplated all

the quantities 8 are small.
If in equations (3) we suppose that the whole motion is
proportional to e’%,

(6, — 0° Gy) $1 + 1g Byphy + ic Bish; +. . pi
Page Pn ey Nasa aS - ..=0 mf aa aha Rare)

and it is known that Ww hatever may be the magnitudes of the
8's, the values of the o’s are real. The frequencies are equal
to oy Qa.

* Communicated by the Author.
Phil, Mag. 8. 6. Vol. 5. No. 27. March 1903. x

294 Lord Rayleigh on the Free Vibrations of

If there were no rotatory terms, the above system of
equations would be satisfied by supposing one coordinate @, to
vary suitably, while the remaining coordinates vanish. In
the actual case there will be in general a corresponding
solution in which the value of any other coordinate @, will
be small relatively to ¢,.

Hence if we omit the terms of the second order in 8, the
rth equation becomes

(¢,—0,70,)0;=0,". 2 2 = ne

from which we see that o, is approximately the same as if
there were no rotatory terms.
From the sth equation we obtain

(¢, Te g,,'d,) , ay 10,8 ee ae 0,

terms of the second order being omitted ; whence

C.— 6,4, a(o,°—o,2)’ . ° ° (6)

where on the right the values of o,, ¢, from the first approxi-
mation (5) may be used. This equation determines the
altered type of vibration; and we see that the coordinates
gs are in the same phase, but that this phase differs by a
quarter period from the phase of ¢,.

We have seen that when the rotatory terms are small, the
value of o, may be calculated approximately without allowance
for the change of type; but by means of (6) we may obtain
a still closer approximation, in which the squares of the #’s
are retained. The rth equation (4) gives

o Hp ee ( 7 )
as (c,’ ae G5) ;

Since the squares of the o’s are positive, as well as a,, a,, ¢,,
we recognize that the effect of B,, 1s to increase o,? if o,2 be
already greater than o,”, and to diminish it if it be already
the smaller. Under the influence of the §’s the o’s may be
considered to repel one another. If the smallest value of a, be
finite, it will be lowered by the action of the rotatory terms ™*.

The vigour of the repulsion increases as the difference
between o, and o, diminishes. If o, and o, are equal, the
formule (6), (7) break down, unless indeed 3,,=0. It is

a,o2=¢ +

* This conclusion was given in Phil. Mag. v. p. 138 (1903), but without
some reservations presently to be discussed. Similar reservations are
called for in ‘Theory of Sound,’ §§ 90, 102.

Systems agected with Small Rotatory Terms. 295

clear that the original assumption that ¢, 1s small relatively
to ¢, fails in this case, and the reason is not far to seek.
When two normal modes have exactly the same frequency,
they may be combined in any proportions without alteration
of frequency, and the combination is as much entitled to be
considered normal as its constituents. But the smallest
alteration in the system will in general render the normal
modes determinate ; and there is no reason why the modes
thus determined should not differ finitely from those originally
chosen.

A simple example is afforded by a circular membrane
vibrating so that one diameter is nodal. When all is sym-
metrical, any diameter may be chosen to be nodal ; but if a
small excentric load be attached, the nodal diameter must
either itself pass through the load or be perpendicular to the
diameter that does so (‘ Theory of Sound,’ § 208). Under the
influence of the load the two originally coincident frequencies
separate.

In considering the modifications required when equal
frequencies occur, it may suffice to limit ourselves to the case
where two normal modes only have originally the same
frequency, and we will suppose that these are the first and
second. Accordingly, the coincidence being supposed to be
exact,

CO i— Op — Oye enc AE a ee)

The relation between ¢, and ¢, and the altered frequencies
are to be obtained from the first two equations of (3), in which
the terms in $3, ¢,, &e. are at first neglected as being of the
second order of small quantities. Thus

Cee a 9)
; Tok Spe On Pape
(2—o ta) 62 — to Bi 26, =9
in which the two admissible values of o? are given by
(¢;— a,0°) (¢) — a7) — 0? 2=0. ° ° e (10)
If one of the factors of the first term, e. g. the second, be
finite, (312° may be neglected and a value of o? is found by
equating the first factor to zero; but in the present case both
factors are small together. On writing oo for o in the small
term, (10) becomes
(0? — 0,7)? = 06° Bi2?/ aya, ° . ° . . (11)
so that
P—o2= +0) P/V (aa), . » « (12)

or
T=) t4Byo/V/ (ayaro) acs ° . (13)

296. Vibrations of Systems affected with Small Rotatory Terms.

The disturbance of the frequency from its original value is
now of the jirst order in By, and one frequency is raised and
the other depressed by the same amount.

As regards the ratios in which ¢;, ¢2 enter into the new
normal modes, we have from (9)

ft = HOES) = iV (ashe ee eu
2 COW Ae

From (14) we see that in the new normal vibrations the
two original coordinates are combined so as to be in quad-
rature with one another, and in such proportion that the
energies of the constituent motions are equal.

5 : ;
The value of any other coordinate 6, accompanying @, and
e 1
dé» in vibration s is obtained from the sth equation (4). Thus,
squares of /3’s being neglected,

(qa Wald, herds ete) ee
in which, if we please, we may substitute for @ in terms of
o, from (14). |

For the second approximation to o we get from (15) and
the two first equations (4) .
g? a P : o sM 59°
{ Cot — = Pi ! Qt | Bs +> - eal de

ee Q
C—O, oA,

7 | a3 ae 7} ° cry OF Ce
| Cy— OAy pee i db. + { ioBy, + Eee | o,=0,
in which the summation extends to all values of s other than
land 2. Inthe coefticients of the second terms it is to be
observed that 31.= —G, and that ,, [Bs2= B25 Ba ; so that
the determinant of the equations becomes

2 PI 2 Pag a2
{q—o%a—3 Shu { e083 EE | —o°B,2=0

¢,—o7a, { | C,— oa, ‘
| (16)
terms of the fourth order in B being omitted. In (16)

C— 07a, €,—o7d, are each of the order 3. Correct to the
third order we obtain with the use of (12)

2 2)2 2Pis’ = 7 P12 a TP 5 Pos + Bu", (17)

(0° —oy)?’—oy

QG2 " (aa)? (a2) C;— Oya
whence
i 2 1 2 D) 2
2 Jes Br2 a SB i5 aE A) ~~ G39, + aQ3,,2
ge ee 7g) 2 : . (8)
Vv (4,42) A142 Aya, C,— 69 a,

Vibrations of a Rectangular Sheet of Rotating Liquid. 297
In (18) Pi is supposed to be of not higher order of

small quantities than Bis, Bos- For example, we are not at
liberty to put B,,=0.

In the above we have considered the modification intro-
duced by the (’s into a vibration which when undisturbed is
one of two with equal frequencies. If the type of vibration
under consideration be one of those whose trequency is not
repeated, the original formule (6), (7) undergo no essential
modification.

In the following paper some of the principles of the present
are applied to a hydrodynamical example.

XXVIII. On the Vibrations of a Rectangular Sheet of
Rotating Liquid. By Lord Rayurics, OWL, FAS.*
ae problem of the free vibrations of a rotating sheet of

gravitating liquid of small uniform depth has been
solved in the case where the boundary is circulart. When
the boundary is rectangular, the difficulty of a complete
solution is much greater ; but I have thought that it would
be of interest to obtain a partial solution, applicable when the
angular velocity of rotation is small.
If € be the elevation, wu, v the component velocities of the
relative motion at any point, the equations of free vibration,
when these quantities are proportional to e’, are

tou—2nv=—q dé/dz,
eae ne i (1)
cov+ 2nu=—g de/dy,
and
2 2 Oe Tee
vt GIGS OG: ue a ON Sema:

dx" dy gh
in which n denotes the angular velocity of rotation, h the
depth of the water (as rotating), and g the acceleration of
gravity. ‘The boundary walls will be supposed to be situated
Tate Tn ate Oye

When n is evanescent, one of the principal vibrations is
represented by
Vea COE wie Ow ee ey ay CS)
and € is proportional to sin a, so that
Gey SG eanaiis i chre MGASY, Bh (A)
This determines the frequency when n=0. And since by
* Communicated by the Author.

+ Kelvin, Phil, Mag. Aug. 1880; Lamb, ‘Hydrodynamics,’ §§ 200,
202, 203.

298 Lord Rayleigh on the Vibrations of

symmetry a positive and a negative n must influence the
frequency alike, we conclude that (4) still holds so long as n*
is neglected. Thus to our order of approximation the fre-
quency is uninfluenced by the rotation, and the problem is
reduced to finding the effect of the rotation upon that mode of
vibration to which (3) is assumed to be a first approximation.
The equation for g is at the same time reduced to

TOME TAG
— =0. 4) .4 re
da? * da? +€ | (9)
Since v is itself of the order n, the first of equations (1)
shows that uw, as well as © satisfies (5).

Taking w and v as given in (3) and the corresponding ¢ as
the first approximation, we add terms w’, v’, ¢’, proportional
to n, whose forms are to be determined from the equations

tou =—g dC fdas). b. 4.0.) 6 rn

iov' = —g dC /dy—2n cose, -. . 2 ene

(ida? +@2/dy +t C,w,c)=0... se

They represent in fact a motion which would be possible in
the absence of rotation under forces parallel to » and pro-
portional to cos z. This consideration shows that u'is an odd

function of both w and vy, and v' an even function. If we
JY;
assume

u =A,sin 27-- A, sin 4¢+...,°-. . 2 (9)

the boundary condition to be satisfied at a= +47 is provided
for, whatever functions of y A», Ay, &. may be. If we
eliminate ¢ from (6), (7), we find

dv _ dw’ Qn <:
Aa — dy Ere Xv
da, sin 2v-+ —_ sin 4a + a ae sin &@;
dy dy o
or, on integration,
2nd dA dA, d
v' = —cos ae Ae, —1 cos 4¢ — — (10)

dA,/dy being the constant of integration. In (10) the A’s’
are to be so chosen that 7 =0 when y=+y; for all values.
of 2 between —47 and +37.
From (8) we see that A,, A,, &c. are to be taken so as to.
aA

satisty
dA, 2 4
ya ae Tema eee a AE

a Rectangular Sheet of Rotating Liquid. 299

or, since the A’s are odd functions of y,
AG be simi 7 3).7), Age simin (x7) 7), akc,
Also Ao= Bog sin y.
In these equations the B’s are absolute constants.
The boundary conditions at y= +y, now take the form

2nt
O= — cos x—Bycosy;
Oo

— ee B, cosh (1/3 . y;) . cos 2a
_ M15
4
which can be satisfied if cosx be expressed between the
limits of # in the series
cos 2=C,+C, cos 2a+C,cos4a+.... . . (12)

By Fourier’s theorem we find that (12) holds between 2 = —4ar
and «= +4m, if

B, cosh (/15.4,).cos 4¢—...... a ae CLE)

4.
Gee
(13)

, Ch = (be

A = 2m siny A.— 2m 2 4 sinh (/3.y)
molt cosy 4 ot WulGun/faamcosmy/onyy):

2nt 2m A(—1)™+! sinh(y 7 4m?—1)

o J (4m?—1) (4m*—1)a cosh(yy /4m?—1)'

Agom —

Hence, finally, for the complete values of wu and v to this
order of approximation

ae _, 2nt (8sin2e2 sinh(V/3.y)
HUGS a 3./3.7 cosh (/3.y;) ee ; 2)
pa Pepe CoS VE oe case OV. - a) Hevap

T Cosy, 31 “cosh (73 «7/1)
: (15)

The limiting values of « have been supposed, for the sake
of brevity, to be +47. If we denote them by +2), we are
to replace x, y, y, in (14), (15) by dr v/a, 40 y/x,, 40 y,/2}.
At the same time (4) becomes
moh

ae
o*= -——~
Aa,

(16)

300 =Vibrations of a Rectangular Sheet of Rotating Liqud.

As was to be expected, the small terms in (14), (15) are in
quadrature with the principal term. The success of the
approximation requires that the frequency of revolution be
small in comparison with that of vibration.

If y, be such that cos (47ry;/2,) vanishes, or even becomes
very small, the solution expressed in (14), (15) fails. This
happens, for example, when the boundary is square, so that
y,=2,. The inference is that the assumed solution (3) does
not, or rather does not continue to, represent the facts of the
case as a first approximation.

From the principles explained in the previous paper, or
independently, it is evident that in the case of the square (3)
must be replaced by

U=COS Uv v= +7c0s2 TE ne ie
? a ?
corresponding to which

f=“? (—isin« + sin y). 02 ie

These values satisfy all the conditions when there is no rota--
tion, and o)>= J (gh), asin (4). For the second approximation
we retain these terms, adding to them w’, v’, ¢’, which are to
be treated as small. So far, the procedure is the same as in
the formation of (6), (7); but now we must be prepared for
an alteration of o from its initial value oy by a quantity of
the first order. Hence, with neglect of n’,

76!
1(a—o) Cosa +iagu’ + 2n2 cos y= =92 « we, wal
|
+ (o— oy) cosy +i0,v' + 2n cos = 0% mens (-21())

These equations are the same as would apply in the absence
of rotation if we suppose impressed forces to act parallel to u
and v proportional to

i(o—ay) cosx+2nicosy, . c. (21)
+(o—o,) cosy+2ncos#, . . . . (22)

respectively.

The complete solution of (19), (20) to the first order of 7
would lead to rather Jong expressions. The point of greatest
interest is the alteration of frequency, and this can perhaps
be most easily treated by a simple mechanical consideration.
The forces given in (21), (22) must be such as not wholly to
disturb the initial motion (17) with which they synchronize.
Accordingly (21) must be free from a component capable of
stimulating a vibration similar to w=cosz, and in like

A Suggested Theory of the Aluminium Anode. 301

manner (22) must be incapable of stimulating a motion similar
to v=cosy. The necessary conditions are

{\ cos x {(o— ) cosa+ 2ncosyjdady=0,
\\ cos y {(o—«o) cosy + 2n cos efdue dy=0,

the integration being taken over the whole area. On account
of the symmetry the two conditions coincide ; and it is
sufficient to integrate for # and y between the limits 0 and 37.
Thus
(o—o,).$7.47=+2n.1.1,
so that
lon
C= OO a + WeEWORS ° e ° ° ° ° (23)
ale Pi
Since n and o are of the same dimensions, this result hoids
good, whatever may be the side of the square.
“It may be of interest, and serve as a confirmation of the
above procedure, to mention that when applied to the principal
vibration in a rotating circular trough it gives
2n

pe 7h al Vi)
Eas)

Onan Oj ae (24)
me z, Is the first root of J,’(z)=0, equal to 1°841, so
that :

25)

2n
Tel fot ae vaso Pra Aba ON oh
An accordant result may be deduced from the analysis given
by Lamb, § 203, by putting s=1, and taking account of the
properties of the function J,;. The corresponding value of
Cis given by

Geo J (er eos asim: 2 2) wk) XO)

XXIX. A Suggested Theory of the Aluminium Anode. By
We. W. Tavnor, WA), DSe, and J) KH." Inetts,
M.A., B.S&c.* |

LTHOUGH aluminium is one of the metals which de-
compose water, it is very slowly acted upon by dilute
sulphuric acid, even at moderately high temperatures. With
dilute hydrochloric acid the action is violent, and it is found
that, if a little hydrochloric acid or soluble chloride (e. ¢.,
potassium chloride) be added to dilute sulphuric acid, the action
is, to all appearance, as violent as with hydrochloric acid of
similar concentration.

* Communicated by the Physical Society: read November 14th, 1902.

302 Dr. Taylor and Mr. Inglis :

The primary object of this investigation was to find an
explanation of this anomalous behaviour of sulphuric acid,
and of the effect produced by the addition of chloride. It
has long been known * that, when an aluminium electrode is
employ ed as anode in a solution of a sulphate or of sulphuric
acid, there is a very great resistance offered to the current,
and that this resistance is due to a film which separates the
electrode from the solution. If the aluminium is the cathode,
or if other acids are substituted for sulphuric acid, this great
resistance does not exist. The film cannot merely act as a
dead resistance, for the resistance is different according to
the direction of the current. It seems probable, then, that
the two phenomena are related, and that the film is also the
cause of the slow action of sulphuric acid on aluminium.
This paper is an attempt to find an explanation which will
satisfactorily account for all these phenomena.

Hlistorical Summary.

The behaviour of aluminium as anode in dilute sulphuric
acid has been the subject of many investigations, but they
have been mainly directed to proving the existence of the
abnormalities, and not to finding the cause of them. The

earliest measurements appear to ‘have been made by Wheat-
stone 7, who tried to ascertain the position of aluminium in
the voltaic series. He found that its position depended on
the electrolyte used. and he noticed especially the slight
action of nitric acid and of sulphuric acid, and the small
current obtained with the latter acid. His experiments were
repeated in greater detail by Butf i, who observed remarkable
peculiarities with dilute sulphnric acid as the electrolyte.
He found on electrolysis of dilute sulphuric acid with an
aluminium anode and an external battery, that the anode
became covered with a dark skin which he supposed to be
silicon. Tait § investigated the polarization of the alu-
minium cell, using a variable polarizing battery. If six
Grove’s cells een the polarizing battery, the reverse E.M.F.
was 3°20 Daniells ; in this case the polarizing E.M.F. was
10°44 D. As his measurements were made with a Thomson
electrometer, they were independent of resistance.

The dark skin first observed by Buff was the subject of
several investigations made by Beetz ||. He at first supposed

= Buff, Liebig’s Annalen, cii. p. 269 (1857).

Phil. Mag. [4] x. p. 143 (1854).
Loe. cit.
Phil. Mag. (4! xxxviii. p. 245 (1869).

Pogg. Annalen, vol. cxxvii. p. 45; vol. clvi. p. 464; 1877, vol. ii.
4.

COS Ort: =f

A Theory of the Aluminium Anode. 303

it to be an aluminium suboxide; but, later, came to the
conclusion that it is merely the ordinary oxide or hydroxide.
More recently Norden * showed that the film is the ordinary
hydroxide, Al (OH);. Lawrie t had previously come to the
conclusion, based on experiments upon the effect of amal-
gamation on the electrochemical behaviour of aluminium,
that the peculiarities are due to a layer of oxide or of sub-
oxide. |

The subject has also been investigated by several physicists
who endeavoured to explain the physical peculiarities. At
first the film of oxide was supposed to act as a layer which
protected the electrode from the action of the electrolyte ;
but Oberbeck } and Streintz § suggested that the film acts
as a non-conductor, and that the electrode, the film, and the
electrolyte form a condenser ; and a condenser consisting of
two aluminium plates with a solution of a sulphate as
electrolyte has been described by Haagn ||. In all these
cases a neutral sulphate or sulphuric acid solution formed the
~ electrolyte, Streintz especially mentioning that in nitric acid
the behaviour of aluminium is quite normal. The question
became one of practical importance when Pollak { and
Gratz ** independently showed that a cell consisting of one
aluminium electrode and one carbon electrode in dilute
sulphuric acid could be used to change an alternating current
into a direct current, since the phase in which aluminium is
the anode is stopped by the cell. Various investigators ft
found that currents of 20 volts or even of 100 volts potential
can be so transformed. Later researches have not brought
to light many new facts, though Wilson {{ showed that the
transformation is not complete if the period of alternation is
less than j!, second. None of the investigators attempt to
explain how this film is produced and maintained. Norden §§.
however, gives the following explanation :—When sulphuric
acid is electrolysed with an aluminium anode the secondary
oxygen produced acts on the anode to form Al (OH);, which

* Zeit. fiir Elektrochemie, vi. pp. 159, 188 (1899-1900).

ft Phil. Mag. [5] xxii. p. 213 (1886).

t{ Wied. Ann. xix. p. 625 (1883).

§ Wied. Ann. xxxil. p. 116 (1887); xxxiv. p. 751 (1888).

|| Zert. fiir Elektrochemie, iii. p. 470 (1896-97).

{| Compt. Rend. cxxiv. p. 1448 (1897).

** Wied. Amn. lxii. p. 323 (1897).

Ai Blerbliitter, xxiii. pp. 108, 502, 564, 650; Elektrotechn. Zetts. xxi.
pe 3.

{{ Electrical Review, 1898, p. 371; Proc. Roy. Soe. vol. Ixiii. p. 329
(1898).

§§ Loe. cit.

304 Dr. Taylor and Mr. Inglis:

is slowly dissolved by the sulphuric acid or by the aluminium
sulphate already in solution, and thus the film is continually
renewed on one side and dissolved on the other. If hydro-
chloric acid be used as electrolyte, the free chlorine acts on
the aluminium and forms a soluble salt AlCl,, and not a
difficultly soluble oxide.—This explanation is hardly sufficient,
for no reasons are given for the formation of secondary
oxygen ; and, further, aluminium sulphate is a fairly soluble

salt. Hence a full explanation is still wanting.

Hepervmental Results.

Experiments were made, in the first instance, to ascertain in
what way the addition of certain salts to the electrolyte affected
the aluminium anode. Tor this purpose the 12 volt storage-
battery of the laboratory was used, and in the circuit were a
3 ohm (approximate) resistance, an ammeter which could be
read to 0‘01 ampere and up to 3:0 amperes, and the electro-
lytic cell, all in series ; a voltmeter reading to 0°05 volt and
up to 15:0 volts was also in parallel circuit with the cell.
The cell consisted of a beaker containing a 1/1 molar solution
of sulphuric acid and the two electrodes, the one of sheet-
aluminium, and the other a spiral of thick platinum wire.
The procedure was as follows :—The circuit was closed, with
the acid alone as electrolyte, and the readings of the volt-
meter and ammeter noted as soon as they became constant.
To the acid were added successive small quantities of a
solution of the salt under investigation ; and, after closing
the circuit, readings were noted every few minutes until they
again became constant. It was found necessary to use a
fresh piece of aluminium each time, as, through the continued
action of the weak current, the film on the anode became-so
thick and resisting that addition of even large quantities of
potassium chloride had no influence on the current, although
a small quantity only was required when a fresh surface was
taken. It was therefore necessary to have the surface in as
uniform a condition as possible in order that the experiments
should be comparable, and this was most easily ensured by
using a fresh surface each time. |

Effect of Chloride and of Bromide.—The results are given
in the following tables. :

In the case of ammonium alum solution (Table I.) the effect
of potassium bromide was also determined, and after addition
of 0°3 ¢c.c. of a 4 molar KBr solution, the current passed
treely, though it did not increase so rapidly as after addition

of chloride.

A Theory of the Aluminium Anode.
TABLE I.

Solution of H,SO,=1 molar.
KCl =3°9 molar (saturated).

|
1

The experiments were then repeated with more dilute

solutions of chloride and bromide.

TaBue IT,

Solution of Hj,SO,=1 molar.
a Cl =0:39 molar:

+2:'0 c.c. KCl...|
(fresh.
surface)...|

39 =9)

11-7 volt.

+1:0 cc. KCL...
+1:2 cc. KCl...
41:4 ¢.c. KCl...
+1°6 ec.c. KCl...

falling to 7:0

falling rapidly.

rising to 0°50)

rising to 0:80.
<0°01

0-025 (rising)

]
|

| 0-02 (rising)

0-02 (rising)
e

In the second of these experiments the currents rose at
once to 1:0 ampere after addition of 1:6 c.c. KCI solution,
but with smaller concentrations of chloride the current was
rather variable, as if the resistance of the film was continually
changing. In the case of bromide the current did not
increase until 5:0 ¢.c. of a O'4 molar KBr solution had been
added. It then rose steadily to 0°5 ampere, but the increase
was not so rapid as with chloride.

306 Dr. Taylor and Mr. Inglis:

Similar experiments were made with other salts, and the
results may be very briefly described.

Nitrate —A 2°6 molar solution of potassium nitrate was
used. After addition of 3:0 c.c. of the solution to 25 c.c. of
acid, the current at once rose steadily ; considerable irregu-
larity was shown after addition of 2°0 c.c. of the nitrate
solution.

Acetate.—Addition of sodium acetate to sulphuric acid had
no ettect. In order to attain a considerable concentration of
acetions, a saturated solution of sodium sulphate was then
used instead of sulphuric acid, but this made no difference.

Thiocyanate-—A 2°V molar solution of potassium thio-
cyanate was used. Addition of 2°0 to 3:0 ¢.c. of the solution
was found necessary to enable the current to pass readily.

Chlorate.—Addition of potassium chlorate was also found
to enable the current to pass readily.

As the presence of aluminium salt might, conceivably,
influence the results, several of the above experiments were
repeated after 1-0 c.c. of 0°5 molar aluminium sulphate solution
had been added to the acid, but no differences were found.

These experiments show that the presence of certain ions,
even in small concentration, enables a large current to pass
through the cell; and it seemed to us probable that the reason
is that the film of aluminium hydroxide with which the anode
is covered is permeable to certain ions, but impermeable to
others*. If this is so, any anion which can readily pass
through the film will enable a current to pass, whilst anions
which cannot readily pass through will not enable it to do
so. The anomalous behaviour in sulphuric acid would then
be due to the impermeability of the film to SO,” ions, and
also to Al:*: ions. This explanation is also in accord with the
fact that reversal of the current immediately causes a current
to pass through the cell, this being due to the permeability
of the film to H ions, for it is dificult to suppose that reversal
of the current immediately removes the film and subsequent
reversal immediately restores it.

We next made a series of experiments to determine the
relative rates of diffusion of these ions through a film of
aluminium hydroxide. The method adopted is one devised
by Walden f and consists in forming a film of gelatine
containing ammonium chromate over one end of a glass tube,
exposing it to daylight, and then washing out all soluble

* Cf Ostwald, Zeit. f. Phys. Chem. vi. p 71 (1890).
ft Zeit. f. Physik Chem. x. p. 699 (1892).

A Theory of the Aluminium Anode. 307

substances. The tube is then placed ina solution of alum-
inium salt, and ammonia solution is put inside the tube. In
this way a film of Al(OH); is formed where the two solutions
meet, i.¢., in the interior of the gelatine. A solution of the
salt under examination is then added to the ammonia solution
in the inner tube, and from time to time the outer solution is
tested for the salt. From the fact that a film of aluminium
hydroxide can be formed in this way, one may conclude that
it is impermeable to Al**: ions, and to OH" ions, as otherwise
diffusion would continue until one or other of the salts was
completely removed. :

Having set up a large number of cells we found that KCl,
KBr, KNO;, KC1O;, and KCNS all diffuse through rapidly,
though not equally so; NaC,H;O, diffuses slowly, and
K.SO, only to a very slight extent. To confirm this result,
‘more cells were set up, and mixtures of KCl and K.SQO,,
KBr and K,S0O,, were added to the ammonia solution, so that
the rates of diffusion through the same film could be observed.
The same results were obtained.

It now seemed very probable that the abnormal behaviour
of the aluminium anode in sulphuric acid was due to this
impermeability. According to Ditte *, the surface of alum-
injum is covered with a thin film of hydroxide which
preserves it from the further action of the air. If, there-
fore, a piece of aluminium be made the anode in dilute
sulphuric acid, the SO," ions are unable to pass from the
solution through the film to the anode, and similarly Al--:
ions are unable to pass from the anode into the solution.
Hence there are no ions to carry the electricity through
the film, and no current can pass. A very slight current
does pass, and this may be due to Al**: ions being formed at
the anode, H- ions of the water passing at the same time
through the film and thus leaving OH! ions which form
Al(OH); with the Al-:* ions just formed. This aluminium
hydroxide replaces that which may be removed by solution in
the acid, and in this way the continuity of the film is main-
tained.

If Cl’, Br’, or NO,! ions are present, they can migrate
through the film, thus carrying electricity to the anode
where they unite with Al--* and form neutral salts ; and
this formation of salt behind the film will break it loose, and
so enable the current to pass easily. In this way the results
obtained admit of an easy and rational explanation.

If this explanation is correct, it should be possible to

* Compt, Rend, cxxvii. p. 919 (1898).

308 Dr. Taylor and Mr. Inglis:

reproduce the peculiarities of the aluminium electrode with a
platinum electrode and a film of aluminium hydroxide, There
are various ways in which this might be done, but for
practical.reasons the jollowing was adopted. The cell con-
sisted of two large pieces of platinum foil as electrodes, an
inner porous cell containing ammonia solution (1 molar) and
an outer glass beaker containing aluminium sulphate solution
(: molar). In this way a film of aluminium hydroxide was
deposited i in the wall of the porous cell.

Tf the aluminium sulphate solution contained the anode,
no current should pass, since Al-*: ions cannot migrate
through the film to the cathode, nor OH’ ions to the anode.
Addition of SO,” , ions to the ammonia should have no effect
on the current, but addition of Cl! ions should cause a current
to pass. Reversal of the poles, also, should cause a current
to pass, for NH ions can readily pass through the film.
With such a cell, and with the 12-volt storage-battery and
the same arrangement of apparatus as already described, the

following results were obtained :-—

(42 ohmsin circuit.)
The small current which passes is due to the low con-
ductivity of ammonia solution ; so a similar experiment was
made with a solution of sodium carbonate in the porous cell,
as sodium hydroxide might act on the film. The only

difference found was fiat. the maximum current was much
greater.

A Theory of the Aluminium Anode. 309

In the next experiment also sodium carbonate solution was
used, and after the current had fallen to 0:07 ampere, part
of the sodium carbonate solution was replaced by a saturated
solution of potassium chloride. The current increased steadily,
after 60 minutes it was 0°35 ampere. On reversal, the
current rose immediately to over 2 amperes.

In a similar experiment, after the current had fallen to
0:08 ampere, half of the sodium carbonate solution was
removed, and a saturated solution of potassium sulphate
added ; even after 60 minutes there was no change in the
current. Ammonia was also used in the inner cell, and half
of it replaced by saturated solution of potassium sulphate
after the current had decreased to 0:04 ampere. After 60
minutes the current was 0:05 ampere, and after 20 hours it
was constant at 0°10 ampere. On reversal it immediately
rose to over 2 amperes.

An experiment was also made with solutions of sodium
carbonate and aluminium chloride. In this case, after the
current had fallen to 0:05 ampere, the poles were reversed
and the current increased rapidly (to 0°6 ampere in 1°5
minute) ; but on again reversing, it quickly diminished to
its former value.

There is still another way in which the explanation might
be tested—by direct measurement of the resistance which
the film offers to the passage of different ions. Suppose that
solutions of the four salts Al,(SO,);, AlCl, K,SO,, KCl, be
prepared se that they have the same conductivity at say
25°C., and that now the two electrodes be separated by a
film of Al(OH),; then the resistances depend upon the rapidity
with which the ions can pass through the film, and the four
solutions will, in this case, have’ different conductivities,
The differences should, moreover, be of quite a high order.

Phil. Mag. 8. 6. Vol. 5. No. 27. March 1903. ¥

310 Dr. Taylor and Mr. Inglis:

For in the case of Al,(SO,)3, neither ion would pass through
the film, and the resistance measured should be high; in the
ease of AICl;, and of K,SQ,, only one ion could pass through,
and the resistances should be of the same order, though
much smaller than in the first case. The presence of the
film should not make much difference to the resistance
of the KCl solution, since both ions can pass through ; this
solution should, therefore, have the smallest resistance.

The apparatus which we used consisted of two glass tubes
with flanges ground to fit one another.
Between the two tubes was placed a Fig. 1.
piece of filter-paper which had been
soaked in a dilute gelatine solution. The
flanges were pressed together while the
gelatine was hot, so that a close and
water-tight junction was made. Dilute
solution of aluminium sulphate was
poured into one tube which was closed
with a rubber stopper provided with
an overflow tube; the apparatus was
then reversed and a dilute solution of
ammonia was poured into the other
tube. In this way a film of Al(OH);
was formed in the gelatinized paper,
and after a few hours the whole was
carefully washed out with distilled
water. One tube was then filled with
the solution to be examined, the corre-
sponding electrode adjusted to a definite
mark —an overflow tube preventing
rupture of the film ; the apparatus was
then reversed and the other tube filled
with the same solution, and the electrode
inserted. The whole was placed in a
thermostat at 25° C. and measurements
of the resistance made. They were as
follows :—

Al,(SO4)3 289 ohms
AICI, 259 ohms
KCl 248 ohms,

These differences are very small, espe-
cially as we found the error of adjust-
‘ment of the electrodes to be considerable.
It is doubtful if it is practicable to determine these differences

re n Reo = i
| —s ers —r 5 eae a Te 1 S a =. Hf
i :
. oH
aedge =< . oo o ast om oer ~~
peer Tl on
ty rin BATH
ie ”
tt te Wy
| ee i
1 ee ee SS SESS = : '
" SLA RD i I i
f oy
{ ure
f
Hi
at

A Theory of the Alununium Anode. ole

with an alternating current. There can be no migration of
the ions (witha high frequency and small current), and there-
fore a very small amount of certain salts in the film is
sufficient to enable a current to pass; and will, in fact, largely
determine the conductivity. Now the formation of the film
by the interaction of the two salts necessarily produces such
a salt in the film; and this, no doubt, is very difficult to
remove completely by mere washing *.

We propose therefore to repeat “the experiments with a
more suitable arrangement of electrodes, and with special
preparation of the film. We also hope to make measurements
of the resistances using continuous currents.

The explanation of the peculiarities of aluminium when
used as an anode in solutions of sulphates, which has thus
been suggested, may be applied to the phenomena observed
in the reaction between aluminium and dilute acids. But it
seemed desirable to determine by experiment whether the
presence of those ions which have so marked an influence on
the anode has a similar influence on the rate of solution of
aluminium in sulphuric acid. Accordingly, the following
rough determinations were made of the rate of evolution of
hydrogen from the acid, both alone, and with addition of
certain ions.

Preliminary trial showed that at temperatures of 80° C. to
85° C., and with a 2-molar solution of sulphuric acid, the
reaction proceeded at a rate which could be conveniently
measured. A thermostat was adjusted to 85°C., and all the
experiments were made at this temperature. Small flasks of
about 80 c.c. capacity, and pieces of sheet aluminium of
uniform size and weight (25 mm. square, 0°45 gm.) were
used. Hach flask contained one piece of the metal and
60 c.c. of a 2-molar sulphuric acid solution, and in addition
a known quantity of a concentrated solution of the salt
under investigation. The gas evolved was collected in a
burette. The salts employed were KCl, KBr, KNO,, and
KCNS. The results are summarized below.

Chloride.—Four experiments were made to determine the
effect of chloride, a 3°9 molar solution of potassium chloride

* With a direct current this salt is removed from the film by the
action of the current. This is probably the reason why, in the series of
experiments last described, the current at first is so lone (20 hours) in
reaching a minimum, although aiterwards it reaches the same minimum
in much less time (about the same time that had e lapsed between the
two previous commutations),

312 AL Suggested Theory of the Aluminium Anode.

being used. The intervals of time required for the evolution
of 50 c.c. of hydrogen were

(1) 60c¢.c. acid. 180 minutes, diminishing to 150 minutes.

(2) 60 c.c. acid+1ec. KCl. | 70 minutes, diminishing to
50 minutes,

3) 60 c.c. acid +2 c.c. KCI. 2 minutes.

4) 60 c.c. acid+4 e.c. KCI, 2°5 minutes, diminishing to
1-7 minute.

These figures show that chloride has a very decided
influence on the velocity of the reaction, but it does not seem
to play the part of a simple catalysator. One noticeable
feature is that when 2 ¢.c. of the solution have been added,
its maximum effect has been almost reached.

The action may be explained as follows—when a piece of
aluminium is put into dilute sulphuric acid, it is covered with
a film of hydroxide; this film, being impermeable to SO,!’
ions, is impermeable to H° ions also, for the one ion cannot
go anywhere without the other. Thus there is no action
between the metal and the acid. The aluminium, however,
acts slowly on the water in the film, forming hydrogen and
aluminium hydroxide, which maintains the continuity of the
film. In this way a slow continuous action takes place. If
potassium chloride be added to the acid, H- ions can permeate
the membrane, for the Cl! ions can go with them, and the
metal thus comes in contact with H: ions. This action
breaks up the film and so admits the sulphuric acid to the
surface of the metal.

If the concentration of Cl’ ions is too small to cause violent
action and so destroy the film, they will still have an accele-
rating influence, but the maximum effect will not be attained.

Bronude.—Addition of bromide appears to have very little
influence on the velocity of reaction. Four experiments
were made, a 4-molar solution of potassium bromide being
used. The times of evolution of 50 c.c. of hydrogen were

(60 cic. acid 150 minutes.
(2) 60 c.c. acid+ 2 c.c. KBr. 160 a
(3) 60 cc. acid+4 c.c. KBr. LD Oe ieee

(4) 60 cc. acid (mo. 1)+1 ¢.c. KBr. 140) Ga

The fourth experiment was made with the aluminium and
acid already used in experiment (1), in order to remove
uncertainty as to the uniformity of the surface. Hence the
influence of bromide is very slight and the experiments are.
not sufficient to show whether it accelerates or retards the.
reaction.

On Loaded Lines in Telephonie Transmission. 313

Nitrate and Thiocyanate.—These salts were found to have
an accelerating effect. With nitrate the reaction was some-
what irregular, and the gas evolved was found to contain
nitric oxide. In the ease of thiocyanate, hydrogen sulphide
was produced in considerable quantity. The results, con-
sequently, are of no value.

Finally, two experiments were made, with acetic acid, and
‘with a mixture of acetic acid and potassium chloride ; for
according to the theory, presence of chloride should have an
accelerating effect. The acetic acid solution was that of
maximum conductivity, and the potassium chloride solution
was 3°9 molar. The action was very slow and the curves
obtained were irregular. In 30 hours 18 ¢.c. of hydrogen
were evolved when acetic acid alone was used, and in the
same time 22 ¢.c. of hydrogen with a mixture of 2 c.c. KCl
and 60 ¢.c. of acetic acid.

These experiments must be regarded as rough prelaminary
observations, and we wish to return to the subject at a later
date.

Summary.

1. The influence of chloride, bromide, nitrate, acetate,
chlorate, and thiocyanate, in varying concentration, on
an aluminium anode in sulphuric acid was investigated.

2. A theory io explain the results was brought forward and
tested experimentally.

3. The essential peculiarities of an aluminium anode were
reproduced by means of a platinum anode and a film of
aluminium hydroxide.

4, Some measurements were made to determine the influence
of chloride and of bromide, on the reaction between
aluminium and sulphurie acid.

Chemical Laboratory,
University of Edinburgh.
October 1902.

XXX. On Loaded Lines in Telephonie Transmission.
By Grorer A, CAMPBELL*.
[Plates V. & VI.]

NHE loaded line discussed in this paper is an eleetrieal
circuit of two long parallel conducting wires having
self-induction coils inserted at regular intervals. An ele-

mentary mathematical treatment adapted to engineering

* Communicated by Prof. Trowbridge.

314 Mr. G. A. Campbell. on Loaded

applications will be given; a second paper will present an
engineering study and an account of experimental methods
and results.

Vaschy *, Heaviside}, and others have either suggested or
unsuccessfully tested the insertion of self-induction coils on
actual lines. Heaviside stated in 1893 that there was “no
direct evidence of the beneficial action of inductance brought
in in this way,” and no progress was made till 1899, when
the subject was investigated independently by Professor M,
I. Pupint and myself. It has been shown that the loaded
line affords a practical method of improving the transmission
efficiency of long lines employed for telephonic, telegraphic,
or other electrical purposes.

An interesting contribution to the general properties of
this structure has been made by Mr. Charles Godfrey § in a
paper on waye propagation along a periodically loaded string
and I am indebted to that article for equation (18) which
furnishes a complete solution of the propagation.

This study has been made with special reference to tele-
phonic applications, and I have limited the mathematical
treatment to the forced harmonic steady state, as that fur-
nishes all the theoretical information which we are in
position to use in telephony, and_ practical applications
generally, provided only a sufficient frequency range is con-
sidered. The range which it is necessary to consider in
telephony might be determined by constructing a network
which would transmit uniformly all frequencies._between
_certain limits, and then experimentally determining the in-
terval which is just sufficient to preserve the full character
of speech. Practical cable transmission sbows that speech
remains intelligible even when the superior limit is compara-
tively low. Cable quality is, however, not desirable, and for
unimpaired articulation it appears from the tests which have
been made that the limit lies well above two thousand cycles
per second. Hfficient, clear transmission requires a low and
constant attenuation, and constant velocity, throughout the
telephonic frequency interval, and constant line impedance
of negligible reactance is desirable. With an open wire line
of heavy copper wire (resistance R, inductance L, capacity
C) this is approximately attained, the attenuation-coefficient,

{

~D * La Lumiére Electrique, January 12, 1889.
_ + Electromagnetic Theory, i. p. 445 (18953).
~ t Trans. Am. Math. Soe. p. 259, July 1900; Trans. Am. Inst. Elec.
Eng. xvii. May 1900.
§ Phil. Mag. xvi. p. 356 (1898).

Lines in Telephonic Transmission. ald

velocity, and line impedance being respectively —

ey a
WP ie
Ii
S83 SS=

SLC’

kan [2
C

For a loaded line these formulee apply approximately and
the problem taken up in this paper is the determination of
the correction factors. This is direct; the approximation of
loaded to uniform line shows only indirectly the performance
of the loaded line.

A summary must be given of the -general transmission
formule upon uniform lines which will be required. An
harmonic electromagnetic steady state is resolvable into a wave
propagation with definite velocity and attenuation, but no dis-
tortion, throughout each uniform interval of the line, the
wave suffering reflexion at points of non-uniformity. This
is mathematically an exact and simple analysis of the steady
state, but it conforms only approximately to the physical
action. It neglects the diffusion or distortion resulting from
dissipation which is, in the steady state, not in evidence,
except indirectly, as a variation with the frequency of the
velocity and attenuation. This variation of the velocity and
attenuation furnishes sufficient measure of the distortion at
the head of an advancing wave for most practical applica-
tions. xcept for this head distortion an harmonic steady
state is established by pure wave propagation—the line
presents a definite line impedance which determines the
initial current at the impressed force; the electromagnetic
wave originating at the impressed force travels with a de-
finite attenuation and a definite velocity along the line and
divides upon reaching a point of non-uniformity into a re-
flected wave and a transmitted wave. Repeated reflexions
establish the steady state.

The equation of a simple current wave upon a uniform
line is |

HR elvt

= iu Tite ie aie ye
a Polo (1)

where the line impedance k, the propagation coefticient y,

316 Mr. G. A. Campbell on Loaded

the attenuation coefficient a, and the velocity of propagation
v, are given by i:
—— / Aad). : - - F ° ° 5 (2)
pe if Jy 3
= 7} —— ae ee A - :

Y a5 z EY (3)
where, if R, L, C, S are the effective loop-line resistance,
inductance, capacity, and leakage conductance at a frequency
p/2a, the series and shunt impedances are

Jj=R+Lp, . . 2. ee
Jo= (Sc Cpy)* 3. 4a. ys
consequently
a= VE7 (B+ Lp) + Cp) +H(RS—LCp) . (6)
= = EU + oR) for large Land smallS. . (7)
“ia 2a P
OR sans ° 4 - ° s 2 5 ( )

For transmission from one construction of impedance k, to
a second of impedance f, the current reflexion and trans-
mission coefficients ure respectively

= at te at re!

hy + ko’ ( )
dating)

i +a2a= aes . : ° . ° (10)

If upon a line of length / with terminal sets of impedances
Js, J,, at the sending and receiving ends, there is an im-
pressed force He’, the current at distance « from the sending
set is
He? = e-¥2 +. a,ev2—-271

bed. Vege" ”

(11)
where the reflexion coefficients are
k—J,. k—dJ,
== = oO = =
iy eats). 7 k+J,

If the line attenuation is large and the sending and re-
ceiving sets are similar, the receiving current is approxi-
mately

wr aft Hert Ak J,

— 2S - aaa? 4 : 4 ‘ (12)

Lines in Telephone Transnussion. 317

If terminal transformers are added and the transformer

impedances are J, for the set side winding, J, for the line

side winding, and Jj, between the two windings, then (12)
becomes

_ Hert) shd. _\/ Jih tds) yer (13)

Pde) aun) ene RAISER

where the four factors are, respectively, the value of the
eurrent for a circuit consisting of the two sets alone, the
effect of terminal reflexion, the effect of transformers, and
the effect of transmission over the line. For transformers of
high inductance, negligible resistance, and negligible magnetic

leakage (13) becomes

dp
_ Ber mf J.

8, (ey Dia

and the transformers are equivalent to a change in the line
impedance from & to kJ,/Jo.

he impedance of a circuit consisting of length J of uniform
line (ky) closed through an impedance Jy at the further end
is by formula (11)

(13a)

1—ae-?v’

De are ar UT iE By Ue RAS
where a=(k—Jy)/(K+d,) is the reflexion coefficient from
line to terminal impedance.

Diagram I. (Pl. V.) shows the value of the reflexion factor
in equation (12). The factor involves the two impedances
symmetrically, is a function of their ratio only, and becomes
unity if they are equal. Let the absolute value and angle of
the impedance ratio be r, 0, and of the reflexion factor be

e—, o, then

=F GIS wh

, 1] ]
b= log ne A Jag cos 0 . - (15)

(16)

318 Mr. G. A. Campbell on Loaded
and (12) may be written
oh ie Dp
i, = oye ee cis —($+4 / ) «| GE Oe ee

where the second and third factors are, respectively, the
effective attenuation and the phase lag due to the line. As
b can be negative, reflexion may augment the receiving
current, but in general the effect is a loss which may be
comparable with the attenuation loss. Thus for k/J,=10,
b=1:11, and the range of ‘easy commercial’ telephonic
transmission, which requires an effective attenuation co-
efficient of 3°2 with present instruments, would be reduced
1°11/3°2, or 35 per cent.

By Diagram I. (Pl. V.) the transformer efficiency in equation
(13a) is a maximum and completely offsets the reflexion loss
when J./J,= | k/J,| =. It follows that, by introducing trans-
formers into a line at every point of non-uniformity “due to
apparatus or a change in line construction, reflexion losses

may be entirely eliminated and the effective attenuation made
as small as or smaller than the real line attenuation.

The effect of loading a line uniformly is shown by Diagram il.
(P1. V.), which gives the attenuation coefticient for lines having
ios, and different values of L. Also the velocity,
for with these values of the constants the velocity and
attenuation coefficient are numerically equal. With no in-
ductance the attenuation curve is a parabola. Any increase
in inductance reduces the attenuation and makes it more >
nearly uniform, and by a sufficient increase in the inductance
the attenuation can be reduced to any desired value, but for
this 1t is essential that the leakage be null.

The effect of leakage is added in Diagram III. (P1. V.), which
is plotted for K=1, L=1, C=1+yp, S=1—u, but gives the
attenuation coefficient and velocity curves for any “uniform
line by a change in scales only.

PE:

An infinite loaded line will be considered first in order to
treat propagation and terminal conditions separately. We
might follow in detail the repeated division of the wave by
reflexion at loads and the interference of the resulting wave-
lets which mutually annul each other, with the exception of
a group suffering reflexion and peneniicciin in a certain ratio.
aaaeh gives rise to a wave of small attenuation and negli-
gible distortion, although the individual wavelets may be

enormously attenuated and distorted by the length of their

Lines in Telephonic Transmission. 319

course back and forth upon the line. The following theorem
will, however, lead directly to the solution and avoid the
infinite summation.

Upon an infinite line of periodic recurrent structure a steady
forced harmonic disturbance falls off exponentially from one
periodic interval to the neat. The theorem is proven by the
consideration that as the line is infinite, there are identical
circuits beyond points separated by a periodic interval, and
the relative effect upon the disturbance of advancing an in-
terval must be the same for all portions of the line.

Consider a uniform line (4, Y) with loading coils A, B, &c..
at the interval d of impedance Hd, or H per unit length of

Fig. 1.

A Energy RB

Y eta Y e Ta

__ a ie

line, and we will designate by (K, I) the impedance of the
loaded line at the middle of a load and the propagation coeffi-
cient of the loaded line. Then if X, Y are the direct and
reflected current waves at the further side of the loading
coil (A), at the next coil (B) the direct and reflected waves
are Xe-7¢, YetY4 on the sending side, and Xe-"4, YetT? on
the further side. At a coil the reflexion coefficient is
k—(Hd+k) _ Hd J 2k
koHd +k ~— 2k+ Hd’ a Qh-+ Hd
is the transmission coefficient ; the equations of condition at
B are therefore

Hd Qk
PY on aay Sp eet ae ~yd UN = Ea
; es aaa.
Fe Hd Qk aa
xX —Td— — SA —jd 3 ne AN gp VE
‘ 2k+ Hd BP CAIUS

Eliminating X and Y, we have

1
cosh (Cd)=cosh yd + 5 sinh Whee el CLO)

which completely determines the propagation coefficient of

320 Mr. G. A. Campbell on Loaded

the loaded line, including the attenuation coeflicient and
velocity of propagation*.

To determine the line impedance (K), observe that the
impedance is periodic and apply formula (14) to the circuit,
beginning at the middle of one coil and extending to the
middle of the next coil :— ;

17 He ot
HES tay He
ror

a i—(S°+K)
Tee ae
Hd
k -- ~+K,

or
K= oh ke + no + Hdk coth yd

yp ae
=ka/ (1 -- “tanh \( 1+ spoons.) - (19)

which completely determines the loaded line impedance at
the middle of a load. The impedance at any other point
might be found by the same method.

Substituting the values of I’ and K given by (18) and
(19) in equation (11) we have the formula for the current at
any load, or substituting in (12), (13), (134), or (17) we
have the value of the receiving current, but the substitution
can best be made after numerical values are obtained.

The method which has been employed in deducing (18)

* For a simpler proof of equation (18), short circuit the loaded line at
che middle of the coil B and consider the ratio of the current at A to
the current at B. As section A-B may then be considered, either, (1)
as a uniform line of constants k, y, aud length d, terminating in an im-
pedance Hd/2, or, (2) as a portion of a uniform line of constants K, I,
and length d, terminating in a short circuit, two values for the ratio of
the current at A to the current at B may be obtained, and the two
equated give a relation between the two sets of line constants. The two
expressions are found on making the proper substitutions in (11) to be |
identically the right and left hand members of equation (18).

In this proof it is to be noticed that the loaded line is short-circuited
at the middle of a load in order that it shall act like a short-circuited
uniform line with the constants K, IT; if the line is not short-circuited
at the middle of a load (or at the middle of a line section) a wave tra-
verses on reflexion a line which is not throughout of uniform periodic
structure. For the suggestion leading to this proof I am indebted to
Dr. A. E. Kennelly. (July 1902.)

Lines in Telephone Transmission. 321

and (19) is quite general and has been applied to a variety
of cases of interest, such as artificial lines with mutual
induction between loads, 8. P. Thompson’s compensated cable,
and periodic lines of two or more different intervals, but
these constructions he outside the scope of this paper.

PL:

To give a precise and comprehensive idea of the per-
formance of the loaded line, formule (18) and (19) must be
reduced to diagrams giving the attenuation coefficient (A),
velocity (V), and line impedance (K). The diagrams can
best be constructed for the correction factors a, 7, «, defined
by the equations :—

Re we Gs
p eee he Bc aed UI GA ete)
Pa f b+? oe
1 a
avd 9 Se ee ly 21 :
“CCC Si
et er al oe Gur doo an

where R, L, C, R’, L’, are the line resistance, inductance,
and capacity, and the load resistance and inductance, all
per unit of length. We can reduce the number of inde-
pendent variables from 7 to 4 by introducing in place of
k, L. C, R’, L’, d, p, the new variables w, 6, p, % defined by

1 SIR BE Ne ee ae
o= gpd /(L+ Le. SENSE <b 1e oegieiti (Oy)

Rea! On
eee = <0
R!

Pes a : . 5 ° : 5 - e e e (25)
Uf

For a discussion of practical applications we may assume
that there is no leakage, no line inductance, and that 6 is
small. While leakage, on a heavily loaded line, seriously
increases the attenuation, the effect of small leakage will be
given with sufficient accuracy by the correction (7) for uni-
form lines. The practical effect of distributing a small
portion of the total inductance along the line must be to make
the line act a trifle more like a uniform line. Its general
effect as shown by Godfrey’s results will be discussed later.

899 Mr. G. A. Camnbell on Loaded

In cable circuits the inductance is quite negligible, and a
moderately loaded open wire circuit would have several times
more load than line inductance. 6 is the attenuation co-
efficient for a periodic interval, and will be small if the line
is to be efficient.

Substituting (20) to (26) in (18) and (19), and expanding

daa |G! )—207/ 46
(Qn +1)A+np9) ae 2) , (21)

LE Coe hoi.

y 0 (2n+1)! 1+p
"S| | 2(2n+1)( Qw?+2 nw me dw’ —inp(4n°— Ly(on—p + 2))( =)
io
x <a : ae Ge iuey ay Si (4n+i ce ! a
aman J 4 Gun \” agen
4 Pata lee faeces
‘ Se (2n+1)! Ge ' (

tor all values of the variables. As the series converge

rapidly these formule may be used for general computation
by noticing that

cosh-(e + yt) =cosh—1_V (@ +1)? Py =e ae

2
ets 24
a6 COS: 0 ————.. (29
V (etl tet Ve-ty Oo
Tn the limiting case 60, the formulse become :-—
POPs 207 aa
| 34) Vine! 7 a
wall ; @ .
= al oT - - ° 2 : ° . (31)
c= isa an,
foe Meee ee
9
eZ], 2 ee re
i LEE.

c= t's/@? 1s) a) Gh ae eee (35)

These simple formule, which furnish the practical information ©
we require, are reduced to curves in diagrams IV., V., VI.
(Pl. V.), which also give a few curves for 6=0-1, to show the
close approximation with which the (a, y, «) curves for 6=0
will apply to any practical loaded line, for 6 would, perhaps,
never approach 0:1 in actual lines, but have a value nearer

0:01.

’

Lines in Telephonie Traasmission. 320

Inspection of the diagram shows that at o=1 the character
of the propagation changes; that at this point reflexion,
per se, introduces attenuation. With Bee conductivity
(6=0) there is no attenuation below »=1, but there is
attenuation above this value, and this is es necessarily, to
reflexion. Below w=1 the attenuation is proportional to the
resistance so long as the resistance remains small, while above
© =1 the attenuation is almost independent. of he resistances
(or may even decrease with an increase in resistance), but
increases rapidly with the value of o. Consequent on this
change in the character of the propagation there is an
accompanying change in the line impedance from pure
resistance below w=1 to pure reactance for higher values
of w. The velocity curve also changes its imecMon end
character abruptly at @=1; there are two coils per actual
wave- -length for o=1, i.e, the disturbance is in opposite
phases at consecutive coils. The critical value o=1 fur-
nishes the first essential condition for an efficient loaded
line, viz. :—

Sta IU OG OY Ps eo (S16)

2.e., there must be more than two coils per actual wave-
length, or approximately, a coils per wave-length with the
load ety distributed. This has long been known for
loaded strings *.

I have made use of these results by employing artificial
loaded lines for cutting out harmonics in generator currents.
The harmonics may all be-cut down as far as desired by the
use of a sufficient number of sections, while the attenuation
of the fundamental can be reduced at pleasure by decreasing
the resistance. The line does not require tuning, and with a
small value of p the action would be quite independent of the
frequency throughout a considerable range. The curves for
_p=a correspond to the case of an artificial line. Combining
condensers and inductances, we may make a system which
will not only cut out higher fr equencies, but also all frequencies
below a certain limit, as suggested at the beginning of this
article. This system will be an inversion of a model of
J. H. Vincent’sf.

The velocity and impedance are approximately independent
of the resistances. The attenuation below @=1 is not only
approximately proportional to the total resistance, but the
curves also show that the attenuation is reduced by trans-

* Routh, Advanced Rigid Loess p. 260, § 411 ; Rayleigh, Theory

of ee 1., § 148, pp. 233, 234.
+. Phil. Mae. ia p- 557 (1898),

324 Mr. G. A. Campbell on Loaded

ferring resistance from the coil to the line, and that the
loaded line attenuation may be less than that®for a uniform
line of the same total resistance, inductance, and capacity.
Inspection of the formulee shows that this applies to any line
of high inductance for which

p<2;
w< v301— 3p) (1+) ;

and that the maximum reduction is for

p=0,
il
Oi Tey =
V2

when it amounts to 5°7 per cent.

Lye
To determine the loading for maximum efficiency, the total
weight of copper in cable and load being given, we may make
use of the following formule for the weights of loading coils
and cable conductors per unit length of line, the formule
applying to coils of similar proportionsiand cables of similar
cross-section :—

I\§
yW=u' (Fa) 5 SU Se PS eS (37)
- , Ww
a-pyWw= 2 (38)

where W is the total weight of copper per unit length ; w, w’
are constants made a minimum by suitable proportions of
coils and cables, respectively ; d is the spacing of the coils ;
and 7 is the proportion of the total copper in the coils. We
will assume that the line is to be of high efficiency so that
formule (30), (31), (32) apply, and suitable terminal
apparatus or terminal transformers will be employed to
practically annul terminal reflexion. The problem reduces:
to securing minimum attenuation at the frequency of trans-
mission. Taking the product of equations indicated by (20),
(23), (30), (37)4, (38)s, and substituting R’=pR, we obtain
for the attenuation

2) ‘ 2 ° fi 5 il
3+ dp— 20° W sWspt

A= ep A= ilar We sath

(39)

Lines in Telephonic Transmission. 325
which takes its minimum value

A=1°639 (wp? WS. «© | (40)

for

== n/3) 7004
and therefore :—

For « given total weight of copper in cable and load the
attenuation of a given frequency 1s made a minimum by placing
2/7 of the copper in coils having a resistance equal to 3/7 of
the line resistance and spacing them 7 V7/3=4'80 per uniform
line wave-length, i.e., m/sin1V3/7=4401 per actual wave-
length on the loaded line. These proportions make

a=12058,
ji 9 ceed ls
f2\W\
qu 2028 ) (41)
Wp
LH SN ae
a aa 696 Soyo t 07 7 5 . ° ° : Y.
R : aaa? (42)
apis w? 1
Se ea oy] (easel S| ae cel cae a
is 1488 ocew eo)

Daps 2ync ple 2
Wi=1-759(—aie- } syne eral a

The last formula, giving the total weight of copper in a
Jine of length / and attenuation e—“’, shows the relative im-
portance of the different factors. The weight increases as
the 2°14 power of the range. Open wire circuits also increase
in weight somewhat faster than the square of the length, but
cable weights vary as the cube of the range. Loading, there-
fore, presents the greatest possibilities upon long cable
circuits. The weight is evidently comparatively independent
of the frequency. ‘The attenuation coefficient comes in
approximately inversely as the first power. Of the two
specific weights w, that for the cable is far more important
than that for the coils w. Thus the total weight W/ will be
doubled by changing w to 2°64 w, or w! to 11:3 w’. This
shows the comparative importance of the coil weight.

In practical engineering, costs must be substituted for
theoretical copper weights, (387) (88) being replaced by the

Phil. Mag. 8. 6. Vol. 5. No, 27. Alarch 1908. Z

326 Mr. G. A. Campbell on Loaded

actual relation between gross costs and effective time con-
stants at telephonic frequencies, and a variety of practical
reguirements are involved which will materially modify the
above results. In special cases it may be necessary to connect a
loaded line of high impedance directly to an unloaded line
or terminal apparatus designed for present lines. Diagram I.
(PI. V.) will give the reflexion loss and reduction in range.
From the formule already deduced, the proportions may be
determined for maximum efficiency with a given total weight
of copper and given terminal conditions.

EXPERIMENTAL WoRK.

In January 1899, I was assigned the problem of investi-
gating the possibilities of improving the efficiency of cables
For telephonic service. After considering some other methods
I concluded that the loaded line presented the greatest pro-
mise, and, as I felt that more progress would be made by
exper imental tests than by mathematical work, I immediately
planned to have made an artificial line with 100 loading coils
on a twenty-mile cable circuit. Before this line was com-
pleted, becoming more confident of the success of loading
an experiment on an actual cable was planned, and for these
tests three reels of 100- -pair telephone cable, commonly known
as ‘ Conference Standard” cable, were brought to the labo-
ratory. Hach reel contained about 600 feet of cable, so that
the entire circuit, when connected back and forth, formed a
metallic cable pair thirty-five miles in length, with a resistance
of about 87 ohms per mile and a mutual capacity of about
‘057 microfarad per mile. For a laboratory test a cireuit
thirty-five miles in length could not be stretched out to its
full length, and we actually used the cable on the reels with
the circuit looped bavk and forth, fifty times through the
first cable, then into the second and third cables. The equi-

valence of a looped circuit of this kind to a straight-away
circuit had been shown, provided the circuit was balanced as
all telephone circuits must be balanced in order to eliminate
eross talk and noise. This point was also carefully tested
during the investigation.

For the loading of this cable 300 coils were manufactured.
A cross-section of this loading coil, known as the T-14
coil, is shown in fig. 2. Ona ~ wooden spool a primary of
578 turns of No. 20 single cotton-covered wire was wound,
and a secondary of 465 turns of No. 20 single cotton-covered
wire. The turns were so chosen as to give the primary and
secondary the same inductance, and they also had approxi-
mately the same resistance. The cable circuit, as has been

Lines in Telephonic Transmission. 327

explained, consisted of 300 lengths connected in series.
Between each length and the succeeding length a T-14 coil
was inserted, the primary in one wire of the pair and the
secondary in the other wire of the pair, the connexions being

Fig. 2.

k c |G YZ ,
Z Yh
—— = ——— = 7 - ~~ SST COS oe, ”,
— SOX OR OSB ORD SOG Xs)
S 3 OY OQ O SS
| BRSSiseenne ie Ee es
M x > 4 P
t XSI E609 Q A
XX KSA XIN b
| SS AKKKSX SL
' ay SS ONS ‘ KORE KLK 2
rr (aes Oo ‘ore! 4 r KOR KAKI
| : esas Sees x xs ARSC
a XS RISK K KS
“ Lx XS.

LK
2K

| s| jj

n |

so made as to put the coil into the cable inductively. Hach
coil added about 11 henry and 12 ohms to the circuit. To
ensure the reliability of the test it was necessary to so place
the loading coils that the mutual induction should be negli-
gible. Accordingly they were spre:d over all the space
available, and texts showed that any effect of mutual induction
between coils was quite negligible.

The experimental line is shown in the photograph on
Plate VI. The three reels of cable are all visible: one is in
plain sight, another is at the extreme left, and the third can be
distinguished at some distance to the right. The reel at the
extreme right had no connexion with this experiment. The
cables were brought out to pot-heads, and each wire termi-
nated in a serew-cup. In this way any combination of con-
nexions could be made. Two of the pot-heads of the middle
reel of cable are in plain sight in the phot graph. The coils
were placed upon shelves—being. placed horizontally and on
edge on alternate shelves. With this arrangement there was
practically no mutual induction except between one coil and
the adjacent coil, or two on either side. The four coil ter-
minals were carried underneath the shelf to a distributing
board between the pot-heads, and this enabled us to connect
in the coils in any desired manner.

An artificial section was also made and loaded with 100
T-14 coils, and this is seen in the right-hand half of the
photograph. The coils upon the shelves are plainly visible.

Z 2

328 Mr. G. A. Campbell on Loaded

The artificial cable, which consisted of mica condensers and
German-silver resistances, does not show conspicuously.

One of the transmitting stations is shown at the left of the
photograph. The receiving station is shown in the second
photograph. At this station there were switches and an
artificial cable, in addition to the telephone set. The artificial
cable, known as the ‘cable standard,” consisted of mica con-
densers and German-silver resistances. The photograph (fig. 3)

. a 2 : et Ne
ae

il | — mul Ta ,
UL ee ee i Ee
I ess AALAUATLL UM | mn
; i Bsa ||
f — io |

shows the thirty boxes, each containing ten condensers, and,
somewhat indistinctly, the German-silver wires. Jt also
shows a jack strip and two cords and plugs, by means of
which any length of cable up to thirty miles, by steps of one
mile, could be put in cireuit. For lengths greater than thirty
miles another artificial cable was added to this.

The manner of making the test was as follows :—The cable
was connected back and forth without the loading coils and
the artificial section was also connected up without the load-
ing coils, and then the whole of this circuit was compared
with the cable standard. It was found that the entire cable
and artificial section were equivalent to forty-six miles of the
cable standard, and shorter lengths were equivalent to cor-
responding lengths of the cable standard. Next, the coils
were introduced into the cable circuit and into the artificial
section, making a cable circuit forty-six miles in length with
four hundred equally spaced loading coils. The transmission
was greatly improved and found equivalent to the trans-
mission over twenty-three miles of cable standard, and in

Lines in Lelephonic Transnussion. 329

addition the articulation was clearer and sharper. In addition
to this the side tone at the transmitting end was reduced so
as to be hardly noticeable, so that the resuit of loading was
to inerease the receiv ing-end eurrent while decreasing the
sending-end current. este were made upon different lengths
of the loaded cable and the results of one set of ee are

shown in the accompanying diagram (fig. +). The results were

Lou enw. oar nae

: Eogoeaeea
= nae eal Sadie a niga PACTIAT
ry 4 —

Ty | ee a ee Feta aco
= { — 2 best! a Si }
fe feta eel

Pee St
0 nea aaagEs
Zz BEeDSCaSas =

SSE
Bie DoCcnea es Soe jet
A BRNEZO ORES eee Tit
EGE Pao oo ee i
DEEBE RSs ORR see
BAG EES R Se we Se a
: pe iesisaetetis ae Leeper et cr a
po es eh

SS eee Sneed eee urement taser ee =

NR eee aaa Pafdif ope seees pag gg PUN ESE
Se SL Le naan one ae
Se er oe a eae Seseeuueucsaenae BesHecSee64ee BER ADRASEoR
Seaeanenneaaeeee ee nm t i
TES Pie RS Sa et Pa SaGeW0 500 a5e050005005neRe
REGS Ree Seraeesesacses SBeana See Seaagdesaseaa
nuns HH saaunes eee eeeeeees eeESeaaas HH] SeSees see eee eee
Se eo on eee ve. “ait es, rae ee a
) Sf 10 5 20° 25 30 35 40 45

represented fairly well by a straight line which corresponds
to the appr oximate formula (17). This line shows that the
initial loss was equivalent to nine miles of standard cable,

but on account of the greatly reduced attenuation, the loaded

330 On Loaded Lines in Telephonic Transmission.

Hine is better than the unloaded line for all distances greater
than fifteen miles. If the line representing the experimental
results is to be parallel to itself, lowered nine miles we have
the curve for a line with terminal transformers, and for this
case the loading is shown by the experiment to nearly treble
the distance over which transmission of a given volume is
obtained, and it actually accomplishes more than that, for
the quality is improved. The tests upon which this diagr am
is based were made with telephonic transmission and ear
estimates at the other end of the line and are, of course, more
or less qualitative, since the difference of quality prevents a
sharp estimate. At the transmitting end a person talks in a
steady, monotonous manner, and it is arranged so that the
person listening at the other end can switch instantly from
the loaded line to the artificial cable standard, and vice versa,
and alter the length of the cable standard to secure an equal
volume of transmission over the two. The comparison gave
the equivalents of the two circuits for commercial service,
which answered the questions which I had before me.

Fora complete scientific investigation it is desirable to
use a sinusoidal current and make qualitative measurements,
and we have made some tests in this way. A great deal of
experimental work has been done, both upon this cable with
the T-14 and other loading coils with different separations
between loads, with iron-cored loading coils and with ter-
minal transformers, also with other cables and with loaded
aerial lines several hundred miles in length, but the results
are incomplete, and I am not prepared to attempt a discussion
of them at present.

Any description of the experimental work must include a
discussion of the actual performance of loading coils under
periodic currents, which is an extended subject. For the
mathematical work it has been assumed that the effective
inductance and resistance of the coil is the same for all
frequencies, which cannot be assumed in experimental
work.

For the extended experimental work which has been
done, which has been laborious and most painstaking, I am
indebted to Mr. BK. H. Colpitts, who has had charge of the
experimental tests described above.

June 7, 1901.

XXXII. The Variation of Potential along a Wire transmitting
Electric Waves. By C. A. CuHant, University of Toronto,

Toronto, Canada*.
[Plate VIL]

I. Introductory.

ERTZ+ was the first to explore a wire along which
electric undulations were passing. His oscillator con-
sisted of two sheet-brass plates 40 cms. square, connected by
a copper wire 60 ems. long, in the Hieriles of which was a
spark-gap. Opposite and parallel to one plate was placed
another of equal size, from which was led otf a copper wire,
the first metre of which was curved and the rest of it straight.
As a detector he used his circular resonator, 70 ems. in
diameter. The nodes were well marked in two wires, the
length of the straight portions of which were 5°35 m. and
8 m. respectively. The half-wave-length was determined
to be 2°8 m.

These experiments were repeated and extended by Sarasin
and de la Rivet, who somewhat increased the effect by using
two wires led off from two plates placed opposite the oscil-
lator plates, the resonator being held between them. These
experiments showed very clearly that the apparent wave-
length measured along the wire was dependent purely on the
size of the resonator, the wave-length being equal to eight
times the diameter of the resonator.

Somewhat similar results were obtained by Waitz§, who
used a circular resonator to which were attached two wires,
one joined near each terminal knob, and led off either
parallel to each other or in opposite directions. In the
former case, by sliding along a bridge laid across the wires,
the sparks between the resonator knobs passed through
maximum and minimum intensities ; in the latter case, by
hanging capacities on the wires and sliding them along, the
sparks aed similarly. He worked with plate oscillators ot
two sizes, as well as cylindrical and spherical ones. He
found that his minima depended entirely on the dimensions
of his circular resonator.

The conclusion naturally drawn by Sarasin and de la Rive
and Waitz from their experiments was that the oscillator

* Communicated by Prof. Trowbridge.

+ H. Hertz, Wied. Ann. xxxiv. p. 551 (1888); ‘ Electric Waves,
p06. ©

{t HE. Sarasin and L. de la Rive, Archives des Sciences Physiques et
Naturelles, Geneve, t. xxiii. p. 113 (1890).

SUK: Waitz, Wied. Ann. xli. p. 435 (1890).

332 Mr. C. A. Chant on the Variation of

emitted waves of various lengths, extending over several
octaves; but this hypothesis has been shown to be impro-
bable, a more satisfactory explanation being based on the
fact that the oscillations of the oscillator are very rapidly
damped, while those of the resonator are very persistent*

In Lecher’s+ experiments the exciter consisted of two
sheet-metal plates, 40 cms. square, joined by a bent wire
2 m. long, with a spark-gap in the middle of it. Opposite
each plate and parallel to it was another of the same size,
from which ran long straight parallel wires. On the farther
ends of these was laid a vacuum-tube, and across the wires
at different points were laid metallic bridges. When these
were properly placed, namely, at the potential nodes, the
tube at the ends lighted up. The wave-lengths he obtained,
however, were not those proper to the exciter, but those of
that part of the wire-system on that side of the first bridge
next the plates which was in resonance with the rest of the
wire-system.

In Cohn and Heerwagen’s{ experiments with Lecher’s
method a condenser was added to the ends of the wires.

Blondlot$ also experimented with parallel wires, but used
an oscillator of quite different construction. In Lecher’s
arrangement the capacity is large compared to the self-
induction ; in Blondlot’s the reverse is the case. The latter
has the advantage that the damping is much diminished.

These “‘ wire-waves”’ have been the subject of numerous
investigations, a notable one being that by Drude||. He
found that the oscillator must be considered as composed of
the Blondlot semicircular primary exciter, together with that
portion of the secondary wire-system as far as the first
bridge ; and that when the bridges are properly placed there
is resonance between this oscillator and the rest of the system.
Very convenient forms of this apparatus are given by Cool-
idge | and Hormell**.

Donle tft, who used chiefly the Blondlot oscillator, joined
the ends of the parallel wires with a glow-lamp. His aim

* See Poincaré, Les Oscillations Electriques, Art 55 & fol.; J. J.
Thomson, ‘ Recent Researches,’ p. 349.

+ E. Lecher, Wied. Ann. xli. p. 850 (1890).

t Cohn and Heerwagen, Wied. Ann. xliii. p. 343 (1891).

§ R. Blondlot, Comptes Rendus, exiii. p. 628 (1891).

|| P. Drude, “Eine bequeme Methode zur Demonstration des elec-
trischen Brechungsexponenten von Flussigkeiten,” Wied. Anz. lv. p. 633
(1895).

q W. D. Coolidge, Wied. Ann. lxvii. p. 578 (1899).

** W.G. Hormell, Am. Journ. Science, xii. p. 483 (1901).

++ W. Donle, Wied. Azn. liti. p. 178 (1894).

Potential along a Wire transmitting Electiie Waves. 333
was to diminish the wave-length, which he reduced to
130 cms. Coolidge’s smallest wave-length was 12 cms.

In Rubens’s experiments the exciter was of the Hertzian
form, with plates 40 ems. square. The two opposing parallel
plates were but 10 cms. square, though the smaller plates are
not quite as etticient as those of equal size*, From these
smaller plates the parallel wires went out—in this instance
to a distance of 570 cms.—and were explored by a_bolo-
metric method. Rubens+ found that the oscillations along
the wires were not the same as those of the oscillator ; in
other words, the oscillations were not forced along the wires,
but were those natural to them.

These experiments were verified by Rutherford {, who
substituted a magnetic detector for the bolometer, and found
it equally sensitive.

In all these experiments it will be observed that the wave-
lengths determined along the wires are not those proper to

the oscillator, but are either due to the detector used! or to
the wires vibrating naturally.

In Birkeland’s§ and Jones’s || researches the reverse seemed
to be the case. The wire-systems were both similar to that
of Sarasin and de la Rive, but the means of exploration were
different. Birkeland examined the potential at various points
of his wire, which was 30 m. long, by measuring the length
of the spark which leaped from it to an earth connexion, the
existence of the spark being indicated by a telephone re-
ceiver held to the ear. He obtained minimum points which
varied as the period of the oscillator was changed, thus indi-
cating that the measured wave-length depended on its period.
‘These minima were unequally spaced, which irregularity was
attributed to the damping of the waves and the loss on re-
flexion at the ends of the wires ; but the explanation does not
seem entirely satisfactory 4.

Jones used a thermal junction inserted at different points
of his wire which was 130 m. in length, the effect being
indicated by a low-resistance galvanometer in circuit with it.
The oscillator was of the usual type, with plates 40 ems.
square, but the length of the connexion between the plates is
not given. Several well-defined maxima and minima were
observed, and the wave-length was determined to be approxi-
mately 43 m. It is interesting to read that ‘* several

* Drude, Physik des Acthers, p. 446.

+ H. Rubens, Wied. Ann. xlii. p. 154 (1890).

{ E. Rutherford, Phil. ‘frans. A, 1897, vol. clxxxix. p. L.
§ Ky, Birkeland, Wied. Ane. xlvii. p. 583 (189: als

el), 18). Jones, Brit. Assoc. Report, 1891, pp. 561—

{ See Poincaré, Les Oscillations Electriques, p. 176,

dd4 Mr. C. A. Chant on the Variation of

curious results were recorded for which no explanations were
forthcoming ”’*

It may be orth while to recall how the wave-length of
Hertz’s plate oscillator was determined. He obtained it with
the aid of his circular resonator, but, as has been already
remarked, the wave-length thus found is always eight times
the diameter of the resonator. If, then, we could know when
the resonator was exactly in unison with the oscillator, the
wave-length could be deduced with considerable accuracy.
But this is not at all possible; the resonance is far from
being sharply defined. Indeed, Hertz says that the same
resonator, of diameter 70 cms., was in resonance with three
‘different oscillators. The first consisted of two spheres of
diameter 30 ems., connected by a wire 70 cms. long, with a
spark-oap in the middle ; the second, of two plates 40 cms.
square, joined by a sive 70 ems. long with a spark-gap as
before ; the third had plates of the same size, but the wire
was 60 cms. long f.

Thus the wave-length emitted by each of these was taken
to be the same ynamely, 560 cms. Now the period and wave-
leneth of the first oscillator have been found theoretically.
Hertzt calculates the period to be 1°26 hundred-millionths
of a second, and the wave-length to he 4°6 m., while Drude §
makes the latter 4°8 m. Both values differ considerably from
that obtained by resonance. Again, the second and third
oscillators differ considerably in. period, though that of the
second was found to be the same as that of the first (see
below). We must conclude that the wave-length 5°6 m. is
not a very close app Ota

In the experiments to be described presently it will be seen
that oscillators of the same type may differ decidedly in their
behaviour; that some seem able to force their vibrations upon
a wire, while others cannot. The wave-length of an oscillator

the same as the third of the three just described was coneluded
to be 5°88 metres.

Il. Experimental Arrangement.

While engaged during the session 1900-1, in the Jefferson
Physical Laboratory of Harvard University, on another |

* “Nature, vol. xliv. p. 454 (1891).

+ Hertz, ‘ Electric Wanen, Art. V. pp. 81-2; Art. VI. pp. 96-7;
Art. VII. pp. 108 & 113.

t Hertz, ibid. pp. 51 & 270 (note 6).

§ Drude, Physik des Aethers, p. 397. See also J. J. Thomson, ‘ Recent
Researches,’ Arts. 289 & fol.

Potential along a Wire transmitting Electric Waves.. 335

investigation * in which the magnetic detector was used, the
fact that an electrical disturbance about a wire parallel to the
wings of the detector exerted a strong action on the detector
was continuously and painfully evident. Indeed, the effect

arising from the connecting wires at first entirely masked the
true radiation from the oscillator.

This suggested the possibility of conveniently exploring
the field along a wire by shortening the wings of the detector
and then placing it close to the wire at various points in its
length. The experiment was tried, but the demagnetization
of the detector was small. However, on removing one wing
and placing the other near the wire the effect was much
oreater and easily measurable.

But the action with one wing is not at all the same as with
two. When the detector with two wings is placed along the
wire, the surging in its helix and the consequent demagneti-

zation 1s greatest at points where the current oscillati. nis
ereatest, 2. e. at a current loop; the ettect is least at a current
node. With a single wing these results are exactly reversed,
the effect is greatest at a current node, which is, of course, a
potential loop. This can be explained in the following way :—
The little wing and the portion of the wire just beside it act
as a miniature condenser, and when there is a maximum
variation of potential in the element of wire there will also
be a maximum variation in the detector wing, which will
cause currents to surge back and forth in the helix, and so to
demagnetize the iron core. At a current loop (or potential
node) the variation in potential is a minimum, and so the
detector when placed there will show minimum demagneti-
zation. Indeed, the indications of the magnetic detector
should be precisely similar to those of the bolometer as used
by Rubens.

An attempt was then made to force standing waves in a
wire, and preliminary experiments seemed to show the possi-
bility of determining the wave-lengths of oscillators in this
way. Some measurements were made then, which, since the
writer’s return to Toronto, have been considerably extended.

c
The oscillators were of four kinds, illustrated in fig. 1.
* C. A. Chant, ‘An Experimental Investigation into the “* Skin”

effect in E lectrical Oscillators, Am. Journ. Sci. xiii. p. 1 (1902) ; Phil.
Mag. [6] vol. iti, p. 425 (1902).

336 Mr. C. A. Chant on the Variation of

The cylinders of (a) were 2°5 cms. in diameter and 12°5 cms.
long, with hemispherical ends; the spheres of (b) were of
two. sizes, namely, with diameters of 10 cms. and 30 ems.
respectively ; the larger spherical ends of (¢) were 19 mm.,
the smaller 6 mm., “and the straight portion 4°2 mm. in
diameter, while the length over all was 12°5 ems.; in (d) is
shown the ordinary Haein plate oscillator.

The sparks were produced by an induction-coil capable of
giving sparks 12°5 em. long, and fed by five accumulators in
series.

The interrupter was similar to that used in the other in-
eee It consisted in a platinum-tipped rod, which,
by means of a motor, was alternately plunged into and Ww ie
drawn from mercury, the surface of which was kept clean by
a stream of water continually flowing over it. In series w ith
this were a pendulum interrupter and a contact-key. This
key was depressed during any desired number of Ba,
vibrations of the pendulum—nsually five swings Hig. 2.
—during which time the coil was interrupted
approximately 60 times. This number, of course,

varied somewhat with the speed of a motor,
but it did not change much during any series
of readings.

The magnetic detector was the same as that
used in the other research. It had twenty pieces
of iron, 0-014 cm. in diameter and 1 em. long,
fold from each other by paraffin, and wound
over with {0 turns of fine insulated wire. It
was mounted in the end of a glass tube, and all |
held on a small sheet of hard rubber by means of |
wax. It is shown one-half of natural size in i

|
|
|

hee 2.

The magnetometer and telescope, as well as the
method of placing the detector behind the mag- .
netometer, were as described in the former paper.

The manner of producing the oscillations along the wires
is shown (for the cylinders) in fig. 3. AB isa long straight

Fig. 3.

COIL

wire (0°7 mm. in diain.) ending at A in a small knob 6 mm.
in diameter, which was separated from an end of one of the
cylinders by a piece of mica, M, usually 0°15 mm. thick.
By this means the surgings on ‘the cylinders were impressed

Potential along a Wire transmitting Electric Waves. 337

upon the wire, which was explored by placing the little
detector near it at different poiits in its length.

Since the magnitude of the effect depends on the distance
the detector wing is held from the long wire it was necessary
to regulate this accurately. To do so a small glass tube
about 4+ ems. long, T, fig. 4, with bore just great enough to
allow it to slide over the wire, was
taken, and to the outside of this was
fastened a bit of finely-drawn tubing,
m, into which the wing fitted snugly.
In all the experiments the wing was
1 cm. long.

The glass tube was attached to a
piece of hard rubber (or mica), M.
which, again, was cemented to the
top, C, of a carriage which moved
along beside the wire.

Thus, to examine any portion of the wire, the carriage was
moved along to the required place, the distance of which
from the end of the wire was measured by a scale on the
ways on which the carriage moved. The detector was mag-
netized, then placed in its pocket beside the glass tube, and
sparks made to pass at the oscillator for a certain length of
time. The detector was then removed and examined by the
magnetometer. This process was systematically carried out,
beginning at the end of the wire and advancing by equal
spaces.

For the linear oscillator, shown in fig. 1, c, the arrange-
ment was precisely the same as for the cylinders. For the
Hertzian oscillators, fig. 1, d,a rounded end was given to
one of the plates by taking a piece of brass rod 6 mm. in
diameter and about 2 ems. long, rounding the ends, and then
making a slit in one end, which allowed it to be slipped over
the plate. This is shown in fig. 5.

The arrangement for the spherical doublet is shown in
fig. 6. When the coil was in action sparks passed between

338 Mr. ©. A. Chant on the Variation of

A and B and B and G, and the oscillations on the sphere C
were transmitted to the wire across the mica plate, m.

The wires used were quite short, ranging from 1 metre to
8°6 metres in length. ;

Ill. Results of Experiments.

It will be convenient to divide the results into two parts :—
A, those obtained with the oscillators a, 0, ¢ of fig. 1: and
B, those with the Hertzian osciiJators.

A. Cylindrical Oscillator (fig. 1, a).

In Pl. VII. fig. 7, a, b, care shown curves obtained with the
eylindrical teenie which was made of sheet platinum on a
wooden form with well- shaped hemispherical ends. Here,
as always, the greatest variation in potential was at the end
of the wire. It gradually fell until a minimum was reached
at approximately 20 cms. from the end, and after another
rise it dropped again to a minimum at approximately 60 cms.
Each of the last two curves gives a half-wave-length of
40 cms., the first one 38 cms., or a mean wave-length for the
oscillator of approximately 79 cms.

In every instance the actual readings are shown.

Linear Oscillator (fig. 1, ¢)

Curves obtained with this oscillator are shown in Pl. VII.
fig. 7,d,e. Curve (d) is the mean of two sets of readings with
five swings of the pendulum. The mean of five sets, eack of
two swings, gave the same minima, though the curve was
not so good. Curve (e) is a repetition of the second portion
of the readings; itis the mean of two sets of five swings each.

Here hae minima are easily seen at 19, 59, and 9Y ems
respectively, from the end; and the w ave-length is thwe
approximately 50 cms.

Spherical Doublet (fig. 1, 6).

Curves for this oscillator are given in Pl. VII. fig. 8. It was
much more difficult to get consistent series of readings with it.
Curves (a) and (b) are for the 10-cm. spheres. The half-_
wave-lenuths deduced are respectively 19 and 19°5 cms., with
a mean wave-length of 88°5 cms. Curves (c) and (d) are for
the 30-cm. spheres. The half-wave-lengths from these are
61 and 62 cms. respectively, with a mean wave-length of
125 cms.

These curves are not as smooth as the former ones, but

Potential along a Wire transmitting Electric Waves. 339
Potential along a Wire t tting Hlects

are perhaps as good as one should expect with so dead-beat
an oscillator.

From the results with the 10-cm. spheres the ratio of
wave-length to diameter is 3°85, while with the 30-cm.
spheres this ratio is 4:1*. The theoretical value given by
J. J. Thomsonf is 3°6. Further exploration of the wire
revealed no more minima.

B. The Hertzian Oscillators.

With the Hertzian oscillators the results were quite dif-
ferent from those just given, and indeed they differed con-
siderably amongst themselves.

The first oscillator tried had sheet-zinc plates 40 cms.
square, with the straight wire between them 60 cms. long:
and the wire transmitting the waves was 860 cms. long. One
minimum was very well marked, but there were no more
clear ones. Then a second oscillator, with 20-cm. plates, and
otherwise of just half the size of the former was tried, but
the minimum, instead of being half the distance from the
end, was much farther from it. This led to the making of
additional oscillators, with plates 10, 15, 25, 30, 35, 50 cms.
square respectively, and with the wires ‘between of propor-
tional length. Tie spark-knobs were 19 mm. in diameter,
the same knobs being used with all the oscillators.

Using these oscillators, readings were taken with wires
from 100 to 860 cms. long ; and the results obtained are
exhibited in the accompanying table and curves. In the
table the positions of the minima are given by stating their
distances in centimetres from the free end of the wire. There
was always one more marked than the others, and this one,
indicated in the table by more prominent type, will be reterred
to as the chief minimum.

* It may be interesting to compare values of this ratio obtained by
other experimenters. Some are given in the following table, taken from
a paper by Hull in the ‘ Physical Review,’ vol. v. p. 231, 1897 :—

Dam. : . \/Diam. Experimenter. |
in mn. | in mm.
80 | 200 2°50 | Righi
eed) | 106 2°83 | =
8 26 B25 | Ff
78 L8-4 2°36 | Bose
19'3 | 91 4-71 | Hull
| 9°3 | 43 4-62 f
| 79 | 40 518 | :
| | |

Bad le Ale Thomson, ‘ Recent Researches,’ p. 370.

340 Mr, C, A. Chant on the Variation of

In Pl. VII. fig. 9 are shown readings and curves obtained
with the 20-cm. <oscillator, with various lengths of wire, and
in fig. 10 are similar readings with the oscillator of double
the size, 2. e. with 40-cm. plates ; while in fig. 11 is shown a
series of Tras successive curves given by the 20- em. oscillator
with the same length of wire. These ‘illustrate the method

moderately well.

Remarks on the Table and the Curves.

A glance at the table will show that the oscillators used
ean be divided into two distinct groups, the first including
the four smaller ones, and the second the three larger ones,
while the oscillator with 30-cm. plates lies between the two
groups. The results with each group are consistent amongst
themselves, while the 30-cm. oscillator behaved in a very
irregular manner.

For the first group (the smaller ones) the positions of the
minima for any particular length of wire are independent of
the size of the oscillator, 7. e. they depend only on the wire’s
length. In this case the oscillator does not torce its period
on the wire.

In the second group, on the other hand, the positions of
the minima depend only on the size of the oscillator, not at
all on the length of the wire.

The conclusion seems natural that, in this latter case, the
distance of the minimum from the free end is one quarter ot
the wave-length of the oscillating system. The values of this
quarter-wave-leneth deduced from the table are :—

For 35-cm. oscillator... 132°7 ems. (mean of 11 results).
pe 20 i AAT et aes 21. a iaee
reise, . 55 A oe ie 6. ae

Now it is possible that the proximity of the wire to the
oscillator may have the effect of virtually increasing the size
of the oscillator, and if such is the case all the quarter-waye-
lengths so determined are too great. According to Poincaré’s *
deduction from the homogeneity of the fundamental equations,
the wave-length of an oscillator or resonator varies directly
with its Tate dimensions. In fig. 12 the points A, B,C have ~
abscissze proportional to the dimensions of the three larger
oscillators and ordinates proportional to the quarter-wave-
lengths given above. It is seen that they lie very approxi-
mately on a straight line, but this line does not pass through
the origin. Let us now draw a line parallel to it and passing

* Poincaré, Les Oscillations Electri ques, Art. 53.

Potential along a Wire transmitting Electric Waves. 341

through the origin. The ordinate B/N of this line, corre-
sponding to the 40-cm. oscillator, has a length of approxi-
mately 103 cms. Thusif the principle of direct proportionality,

Fig. 12.

stated by Poincaré, held without limit to its application, the
arrangement of the wire as in the experiments, should be
equivalent to adding 44 ems. to the quarter-wave-length of
each of the three larger oscillators. On the other hand, the
fact that varying the length of the wire from 3 m. to 8°6 m.
had no effect on the position of the minimum, seems to show
that the wire did not act in the manner referred to. In
other words, the quarter-wave-lengths given are proper to
the oscillators. ;

Experiments with the first and second Hertzian oscillators
referred to above, gave the following values for the quarter-
wave-length : —

For 40-cm. plates, straight connexion 70 cms.,.. 154°4 cms.
30 ,, spheres, _ ,, 45 ae Lee loao..

These are practically identical.

For all wires of 3 metres and upwards in length there is
a well-defined minimum between 10 and 15 ems. from the end
next the oscillator. In figs. 9, 10 (Pl. VII.) is shown a portion
of each curve near the oscillator in continuous line, and also
in broken line. In this neighbourhood the oscillator exerted
a strong action directly on the detector. In order to allow
for this, readings were first taken as usual (shown by con-
tinuous line); then the wire was removed and readings
taken at exactly the same points. These latter were then
‘subtracted from the former, and the broken line shows the

Phil. Mag. 8. 6. Vol. 5. No. 27. March 1908. 2 A

342 Mr. ©. A. Chant on the Variation of
TABLE OF
E
ao 2 . ° aah oe
‘32 Distance, in centimetres, of minima |
On |
x) 5 | / |
S8| Wire Were Wire Wire Wire Wire | Wire | Wire |
R 860 ems.) 85U ems. | 840 ems.} 830 cms. 820 cms. 810 cms. | 800 ems. 790 ems.
= aaa | | | 187...635 ...780
Gad. 78l
10 | 625?...780 |
cms. 187
193
645 ...781 |
ye 188...635 ...780
185...618?...780
15 182
cms |
200 (|192 | 182...710|190. 675. 820 198 208...G45 188. .620 2. .790 193...638 ...780
25 | 200 205...650 190. .650 ...790
ens |
Be Metis! st) wh od ie 8 OR ORE Ria e |: is Lie |
| ISOM ee 655...780
25 | | | | 66s Wee 630...780 |
cms. | | 190
|---| ____|---______ id i a
| | | | MBEAN ......|187-1 |
cee ee a SS SS SS EEE SE, ee ae ee —— ———
| 730...280...585...780 |
| | 140...220...620...780
30 | | 130
cms. | |
| | | |
| | 182 sss 680...775
35 | | SHS) ecccccese 620...770.
a Io
_ | | : |
1148...735?\150.. 7402|145...750|150...745 |150...7202]150...645|150...650...790 150. 350. 6252. 780 :
40 148...655 150. .345..—- .. 780
cms. |
| )

Potential along a Wire transmitting Electric Waves. 343

Minima.

from free end of wire.

700 ems.

i Wire
a

183
178
182
1S6

SP aig do ania 240. .690)/177..
245...345. .542. 690/175.

iG).

170 NG
£75

————— | |.

150...3860...550...688)154..
142.,.355?. 550...690|146...
L4h gs
150..

170
170
L772
170

7 Sa GT ne a ae TaN DME te ai GeO ToaoD

Wire
600 ems.

Wire

500 ems.

.460...590 |207

..480...590 |195..
A50...590 1195...
188 ?
LOD *

430 ...590 152..
430 -...590!250..

440 ...590'154

170
\L77

430?...590 150..

...000
+7

9
9

@eccce

BaD es
4099) |.

335 ?...

.. 490;
400)
369 ..

490

..490)
..490

490

WakSoc
152..:
TOOT

152

Wire
400 ems.

197
197
199
203

205
wy
200
203

202...390
210...590
206...390

Wire Wire
300 ems. | 200 ems.

154,..290) 150
155...290) 148
152

143...290) 140
150...290| 138
150

er |

Wire
100 cms. |

nee

85
85

3Ad4 Prof. A. Schuster on the

result. Here it is assumed that the action of the oscillator
and of the wire singly are equivalent to the two together.
To examine this minimum more closely readings were taken
at intervals of one centimetre. There is no doubt of its
existence; it is about 10 cms. from the end for the smaller
oscillators and slightiy farther for the larger ones. I find it
difficult to give the significance of this.

Other minima were found, but they were not so well
defined. They are, no doubt, due to natural oscillations of
the wire, but they are hard to identity.

For the wires 300 and 400 ems. long the chief minima are
at the middle points.

The question of the dependence of the positions of the
minima on the detector is interesting and important; and
that there is no such connexion was shown in the following
way. <A second helix, similar to that of the detector, was
soldered to the free wire running up beside the one bearing
the wing, thus practically doubling the capacity and in-
ductance ; but there was no displacement of the minima.
The period of the detector must be many times that of the
oscillators.

In the near future I hope to apply the magnetic detector
to the exploration of much longer wires, in which case the
phenomenon of standing waves should be more distinctly
shown.

University of Toronto.

XXXII. On the Spectrum of an Lrrequiar Disturbance.
By Arraur Scuuster, F.R.S*

{* the February number of the Philosophical Magazine
Lord Rayleigh quotes under the above title the following
remark, which | made in a paper on the “ Periodogram of
Magnetic Declination as obtained from the Records of the
Greenwich Observatory during the years 1871-1895 :”
“Absolute irregularity would show itself by an energy-
curve which is independent of the wave-length, 7. ¢., a straight
line when the energy and wave-length or period are taken as
rectangular coordinates, while the perfect regularity of homo-
geneous vibrations would show itself as a discontinuity in the
energy-curve.”’
Discussing the same problem, Lord Rayleigh arrives at
the different conclusion that the energy of an arbitrary dis-
turbance is proportional to dk or kdk, according as the

* Communicated by the Author.

—_—=

Spectrum of an Irregular sturbance. 345

velocity-curve or the displacement-curve is taken to be
arbitrary. Here & is the frequency, or the inverse of the
period. I arrived at my own conclusion by translating the
results of an investigation, in which Fourier’s analysis was
employed, into what I thought to be its complete optical
analogy. The definitions that I gave of what I called the
Intensity of the: Periodogram are, I think, quite clear and
definite, but the optical and mechanical analogy is not as
good as I thought. This depends on the fact that I took the
periodic time to be the independent variable instead of the
frequency. It does not matter which we take, if we deal
only with a number of separate periods, each having finite
amplitude, the ordinates in that case measuring energy, but
if the periods approach each other indefinitely and the energy
between any two of them is to be represented by the area
included between the corresponding ordinates, the curve and
the axis of abscissa, the abscissa must represent frequencies
unless some correction is made to the ordinates.

I was therefore wrong, when translating my results into
optical language, to compare the ordinate of the periodogram,
as I had defined it, with the intensity of a luminous disturb-
ance, and Lord Rayleigh’s criticism is quite justified.

It may be desirable to alter my definition so as to make
the optical analogy complete, though practical considerations
have to be taken into account.

Whether frequencies or periods are best plotted depends
on individual cases, but if we take the period we may still
preserve the optical analogy which in that case would be
with the spectrum of a diffraction-grating. It would only be
necessary for this purpose to divide the ordinates by the
squares of the periods. This would notinvolve any additional
arithmetical labour, unless the Fourier coefficients are ob-
tained by mechanical means. As Lord Rayleigh points out,
meteorological irregularities should be made to correspond to
velocities im the mechanical analogy, and this I had realized.

I should like, in conclusion, to refer to a subject intimately
connected with the matter under discussion. We constantly
meet with the assertion that Réntgen radiations are due to
impulses and not to regular oscillations. Ihave no objection
to this statement if its meaning is clearly understood, but
generally it is put forward in such a way as to imply that an
impulse i is something smaller, or even something of a different
order of magnitude, than a periodicity of short wav e-length.
The statement that Rontgen rays are impulses differs from
the statement that Rontgen rays are short waves, only in so
far that the impulse theor y asserts that there are long waves

346 Prof. J. J. Thomson on the Charge of

present as well as short ones; but supposing that a violent
disturbance, lasting an indefinitely short time, leaves the
inner side of a Roéntgen tube, where it is generated, it will
quickly become modified. Before it has traversed the glass
walls, the impulse has already spread out owing to the absorp-
tion of some of the periods in the glass, and if this modified
impulse is further sent through a screen like a thin sheet of
aluminium or black paper, all the visible rays are cut off, and
the invisible ones down to at any rate very short lengths.
The Roéntgen radiation that affects a fluorescent screen or a
photographic plate therefore can only contain waves which
are either exceedingly short or very long, provided it con-
sists of transverse waves at all.

That an impulsive motion of zether cannot possibly remain an
impulsive motion, after traversing media with selective absorp-
tion, or media in which dispersion takes place, should be clearly
understood. I may, perhaps, in connexion with this, quote
a sentence from a letter I wrote to ‘Nature’ a few weeks
after Rontgen’s discovery was first announced. At that time
there was no theory put forward, except the original one of
Rontgen, that the rays were due to longitudinal vibrations.
The absence of interference was considered to be an objection
to any undulatory theory.

“The absence of interference would not, however, be
sufficient to show that the radiation is not of the nature of
ordinary light, but only that it does not possess sufficient
regularity, or, in other words, that the disturbance is not
sufficiently homogeneous. That this is the case is not at all
impossible, for the radiation is produced by an impact which,
in the first instance, may be an impulsive motion propagated
outwards, and, after passing through the screen, would only
possess such regularity asis impressed upon it by the absorp-
tion of the longer waves” *.

I think that the theory of impulses, as well as its limita-
tions, is clearly expressed in this passage.

XXXITT. On the Charge of Electricity carried by a Gaseous
lon. By J. J. THomson, Cavendish Professor of Experi-
mental Physics, Cambridget. |

ie the Philosophical Magazine for December 1898, I
gave a determination of the electric charge carried
by an ion in a conducting gas. The method employed in
this investigation was as follows :—If » is the number of
charged positive and negative ions per unit volume of the
* ‘Nature,’ vol. liii. p. 268.
* Communicated by the Author,

Electricity carried by a Gaseous Lon. d47

gas, e the charge carried by an ion, w the mean velocity ot
the positive and negative ion in a given electric field, the
current through unit area of the ionized gas in this field will
be neu; hence if we measure this current we can determine
the value of ne, as u the velocity of the ions in a field of
known streneth has been determined by Zeleny and Ruther-
ford. The number of ions m was measured by depositing by
C. T. R. Wilson’s method a cloud on the ions and deter-
mining the number of particles of water vapour in unit
volume of the cloud.

Since these experiments were made, the progress of our
knowledge of the electrical properties of gases has made
several improvements in the method possible. The discovery
of radium has furnished us witha constant source of radiation
very much easier to work with than the variable Réntgen rays,
which were the source of ionization in the earlier experiments.
The introduction of the Dolezalek electrometer, which can
be made to give a deflexion of 20,000 or more scale-divisions
for the potential-difference of one volt, makes the determi-
nation of the exceedingly small currents passing through the
ionized gas much more accurate than was possible with an
electrometer of the type used in the earlier experiments,
which only gave a deflexion of 50 divisions for a volt ; and
although the Dolezalek electrometer has a much oreater
capacity than the older form, the difference is not sufficient
to neutralize the advantage gained by the increased sensi-
tiveness.

The consideration which influenced me most in repeating
the experiments was the increase in our knowledge of the
laws governing the deposition of the cloud round the charged
ions. Lhe cloud is made by cocling the air by a sudden
expansion. I had noticed in the earlier experiments that
when this expansion was increased so that the ratio of the
volume of the air after expansion to that before exceeded the
value 1°3, there was a noticeable increase in the number of
particles in the cloud. Mr. C. T. R. Wilson, who has made
(Phil. Trans. exciii. p. 289) a systematic study of the relative
efficiency of negative and positive ions as nuclei for conden-
sation, found that while a cloud begins to be deposited round
negative ions when the expansion is 1°25, it is not until the
expansion is equal to 1°31 that the positive ions are caught
by the cloud; thus if all the particles are caught by the
cloud, the number of water particles in the cloud formed with
the larger expansion when both positive and negative ions
are caught ought to be twice that with the smaller when only
the negative ions are caught. In my earlier experiments the
increase in the number of ‘particles with the larger expansions,

348 Prof. J. J. Thomson on the Charge of

though marked, was not so great as this, pointing to the con-
clusion that all the positive ions had not been caught by the
larger expansion.
It is obvious that since the moisture begins to deposit
first on the negative ions, unless the rate of expansion 1s very
rapid, the drops formed in the earlier stages of the expansion
round the negative ions will have time to grow and form
convenient nuclei for further condensation, so that as the
expansion increases, the tendency will be for the moisture to
deposit on the drops already formed rather than to form new
drops round the positive ions. ‘I hus with slow expansions we
should expect the number of drops formed to be more nearly
equal to the number of negative ions than to the sum of the
positive and negative ions.

The results of the present experiments show that this was
the case in the expansions used in the earlier experiments.
The value of x determined in those experiments was but little
greater than the number of negative ions; as ne is the quantity
determined by the electrical experiments this caused the value
ot e to be nearly twice its real value.

The results of Mr. C. T. R. Wilson’s experiments give us
the means of testing whether the expansion is rapid enough
to catch the positive as well as the negative ions, for if we
determine the number of drops in the cloud when the ex-
pansion is less than 1°31, and again for expansions considerably
greater than this value, and find that the latter number is
twice the former, we may feel sure that the large expansion
has been rapid enc-ugh to catch the positive ions. This test
has been applied throughout the experiments described in
this paper.

The apparatus for producing the cloud was of the kind
used by Mr. Wilson. The expansion is produced by the motion
of a light glass piston P which slides freely up and down the
larger tube C, the lower end of the piston is always below
the surface of a layer of water at the bottom of the tube. The
inside of the piston is put in connexion with a vessel E by
means of tube F’, which passes up through the layer of water.
H is a large vessel exhausted to as low a pressure as possible;
H and E are connected by the tube G, the end of this tube
in E is closed by an indiarubber pad which can be quickly
removed hy means of the rod R; when this is done (the
piston being at the top of its range) the pressure of the air
drives the piston down, and the air in C and the vessels con-
nected with it expand. The amount of this expansion can
be adjusted by altering the height to which the piston is
raised before the expansion begins.

Electricity carried by a Gaseous Ton. B49

In order to make the expansion take place with sufficient
rapidity the piston was made of very light glass. The vessel H
was exhausted until the pressure in it was but little greater
than that due to the water vapour, and especial care was
taken that all the tubes, through which air had to rush during

the expansion, were of as wide a bore as possible and without
any constrictions ; when these precautions were taken, it was
found that the expansion was rapid enough to catch all the
positive ions. This is shown by the following results, which are
a sample of those obtained in a large number of experiments.

Jonization produced by a sample of radium A placed at a
height 10 cms. above the top of the vessel in which the
cloud is formed.

Pressure of atmosphere 768 mm. Temperature 19°5.

MR tala he eon Number of drops in cloud
Expansion. lioncan fall 1 ages reckoned per c.c. of the volume

| ‘ SiN of the gas before expansion.

1346 O°7 sec. 6:6 x 10"

1:333 OS) he; Ga,

1°32 Ons is, hy ae

131 Soi. 48,

1:29 il igi D005

1:28 (a SOL re,

1:27 t te 3°55 ,,
| 1:257 oh ae at ee

350 Prof. J. J. Thomson on the Charge of

Thus we see that when the expansion is greater than 1°33,
the number of nuclei caught by the cloud does not depend
upon the amount of the expansion. When this is between 1°33
and 1°29 this number diminishes, until when the expansion
is 1:29 the number caught is only half that at the higher
expansions. The number now remains independent of the
expansion until this falls below about 1:27; for expansions
smaller than this the number of nuclei caught falls off rapidly
with the expansion. We conclude from this that for ex-
pansions greater than 1°33 all the ions positive as well as
negative are caught by the cloud; then when the expansion
is smaller than 1°33 and greater than 1:29 some, but not all,
of the positive ions and all the negative ions ; for expansions
from 1:29 to 1:27 all the negative but none of the positive
ions are caught in the cloud; and that when the expansion
falls below 1:27 only a fraction of the negative ions are
caught.

The values of the numbers given in the third column of
the preceding table were calculated by the following method:

ro) co)

let g be the volume of water deposited through the expansion

per unit volume of the expanded gas (this was calculated by
the method given in the earlier paper), ’ the number of
drops per unit volume of the expanded gas, a the radius of
4a

one of these drops; then g=n/ = a’.

a
If vis the rate at which the drops fall, then
Oe
ue a
e fe

where yw is the coefficient of viscosity of the gas. In the case
of air w=1°8 x 10~ and v is therefore equal to 121 x 10*a?;
hence
n= a WSs TOs ee
Ar

The number of drops reckoned per unit volume of the gas
before expansion is n’X expansion. The velocity of the drops
was determined by measuring the time taken by the top of
the cloud to fall through two consecutive centimetres. With
the drops used, these times were very approximately equal
to each other ; with clouds consisting of very fine drops
which fall slowly, the time taken to fall through the second
centimetre is often considerably greater than that for the
first, owing to the diminution produced by evaporation in the
size of the drops.

To facilitate the measurement of the velocity the inside of

Electricity carried by a Gaseous Lon. oom

the cloud-chamber was lined with damped black silk, a narrow
slit being left to allow the cloud to be observed. The bottom
of the chamber was a plane piece of glass, and the fog was
illuminated by a vertical beam of light reflected from a
mirror. The top of the cloud-chamber was made of sheet
aluminium °3 mm. thick, this allowed the rays from the
radium to pass through. Two different samples of radium
were used: the one called B was placed at a distance of
15 cms. above the top of the cloud-chamber, the other (a
weaker specimen), A, was 10 cms. above it. The radium was
spread over surfaces measuring 7 cms. by 5 cms., and was kept
in its place by a thin sheet of mica.

The electrical part of the apparatus included a guard-ring
condenser, the upper plate of which was a circular piece of
aluminium of the same thickness and cut from the same
plate as that forming the top of the cloud-chamber; the
lower part of the condenser consisted of a circular plate of
aluminium 2°47 cms. in radius in one piece of apparatus, 4°55
in another, surrounded by a guard-ring also of aluminium ;
the distance between the upper and lower plates of the con-
denser was lcm. The radium was placed above the upper
plate of the condenser and at the same distance from it as in
the cloud experiments, 2. e. the sample A was placed 10 cms.
and the sample B 15 cms. above the plate. The lower cir-
cular plate was connected with one pair of quadrants of a
Dolezalek electrometer, the wire making the connexion being
led through a metal tube connected with the earth. The
radium was surrounded by lead guards so as to confine its
radiation to the neighbourhocd of the condenser. The radium,
the guard-ring condenser, and a second condenser used to
determine the capacity of the system were placed inside a
box lined with metal. The top plate of the condenser was
maintained at a constant potential ; the lower plate, which
was In connexion with the electrometer, was initially put to
earth. When the earth connexion was then broken, a current
of electricity passed between the plates through the air ionized
by the radium; this current charged up the electrometer, and
the needle was deflected. Knowing the deflexion of the elec-
trometer produced in a given time, the quantity of electricity
received by the lower plate in that time can be ealculated, if
we know the capacity of the electrometer and its connexions.

If wu is the mean velocity of the positive and negative ions
under the electric field applied to the air between the plates,
nthe number of ions (positive and negative) per c.c. of the
air, e the charge on an ion, A the area of the lower plate,
the quantity of electricity received by the lower plate in unit

et Prof. J. J. Thomson on the Charge of

time is neuA. If C is the capacity of the electrometer and
its connexions, this quantity of electricity will produce a
potential-difference of newA/C between the quadrants, the
deflexion of the electrometer is proportional to this difference
of potential ; hence to deduce the value of ne from the read-
ings of the electrometer, we require to know the value of ©.
This was found by connecting with the lower plate of the
condenser another condenser of known capacity 0’, and again
measuring the difference of potential between the plates after
the current has been flowing for one second; this is equal to

neuA/(C+C’); hence if 6,, 6, are the deflexions of the electro-
meter before and after C’ was inserted, we have

Stan!
ma i ae
or ‘
Eee!
Cae a

The effective capacity of the Dolezalek electrometer depends
mainly upon the charge on the needle, and may therefore
vary considerably from time to time, thus in these experi-
ments C ranged from 200 to 900 cms.: it is therefore very
necessary to determine the value of C for each observation.
The proceeding adopted was to take, say, six consecutive
readings with the condenser ©’ (whose capacity was ‘001
microtarad) out (in three of these the upper plate was at a higher
potential than the lower plate; in the other three the sign of
the potential-ditference was reversed) ; then six with it in, and
then another six with it out.

The high effective capacity of ihe Dolezalek electrometer
makes it less sensitive for measuring small quantities of
electricity than for potential-differences.

The value of » in the electrical experiments is the number
of ions per c.c. of the gas when exposed to the electric field ;
in the cloud experiments the value found for n is the number
when there is no electric field. The electric field tends to
drive the ions out of the gas, so that the number in the electric
field will be less than the other ; when the field is strong the
difference is very marked, but with the weak fields (about
3 of a volt per cm.) used in these experiments the difference
is Inappreciable; we can test whether the field is weak
enough to ensure this by measuring the currents under dif-
ferent electric fields: since u the velocity of the ion is pro-
portional to the electric force, if the electrometer deflexion is
also proportional to this force, x will be constant, i.e. will
not alter with the force. The electric force was reduced to

»)

Electricity carried by a Gaseous Lon. 3D3

one-half its value, i.e. | of a volt per cm., and the electro-
meter deflexions again determined : as these were found to be
just half the value with the double force, it was concluded
that with the weak fields used in these experiments the value
of n was sensibly the same as that without fields.

To test whether the secondary ionization due to the inci-
dence of the radiation on the aluminium was appreciable, the
observations were repeated with the lower plate covered with
wet tissue-paper. It was found, however, that the results
obtained with the wet payer were the same as those without.

The following are the results of experiments made to deter-
mine the number of ions per c.c. due (1) to a specimen of
radium A placed 10 cms. above the top of the chamber in
Expansions greater than 1°33.

Time taken by L
| cloud to fall 1 cin. Hons yer Gs.
Pressure Difference in /Expan- _ : Saas eeeew
ofatmo-| Temp. pressure be-| sion. | | |
sphere. | and after ex-. | Radium Radium | Radium | Radium
| pansion. Ale, vir | eB A. iB:
173 19°5° C., 193 | 1343 | 9°65 see. | 186 see. |0'3 x 10* | 17x 10*
793 19 | 185 1-335 | 10 Py Ooo ye hO”
1495 | 19 184 1300) O20 seine. Wh Oro xalO:
got > (To | 185 1:33 | 10 1825 |6:66x10*/16°3 x 104
02 19 193 1:343| 95 © | 17-25 |63x10* |15°5 x 104
768 19°5 193 1-344) 975 {185 |64x10* |16-9x10*
| | Mean ...|6°5 x 10? |16-42x 10!
ene 2-4! me P | Negative ions
Expansions less than 1°33. | pond
Mecimetommn. Ie 168 y | R877) 7 13. | 338x104) 86x10!
773 S| 163 | LEE SE 135 =| 26104) 89x 104
72 19 | 167 Ac2Se il | 12. bod 108) 8:2 <1
| ee aa =
| | Mean ...)| 30x 10"| 8:5 x 10+
|

which the cloud was produced, (2) to another specimen (B)
placed at a height of 15 cms. above the cloud-chamber.
The first table contains the number of positive and nega-
tive ions caught by expansions greater than 1°33, the second
the number of negative ions caught by expansions less
than 1°33.

If we take the mean of the results, we find the radium A
produces at a distance of 10 cms. 6°25 x 10# ions per e.c., w hile
radium B produces 16°75 x J0".

354

The results of the determinations of ne, where n is the
number of ions per c.c.,and ¢ the charge in electrostatic
measure on an ion, are given in the following table. D is
the deflexion of the electrometer in scale-divisions for the
potential-difference of 1 volt, C is the capacity of the electro-
meter and its connexions, 6, the mean of the positive and
negative deflexions in one minute of the electrometer when
there was a potential-difference of 4 of a volt between the
plates of the condenser, the gas between the plates being
exposed to the radiation from the radium A at a distance of
10 cms., 8, the same quantity when the gas was exposed to
the radiation from B at a distance of 15 cms. The values of
ne are deduced as follows: if A is the area of the plate
attached to the electrometer, w the mean velocity of the posi-
tive and negative ions under a potential-gradient of a volt
per cm., the quantity of electricity given to this plate in unit
time under 4 of a volt per em. is equal to 4newA, this pro-
duces a potential-difference of 4neuw A/C in electrostatic
measure between the plates ; the potential-difference in volts
is, however, 6,/60 D, hence we have

i: NEU A oF I
5 Come SUm:
From Zeleny’s experiments u for moist air is 1-4 em./sec.,
A=19:1; we have thus the data for determining ne :—

Charge of Electricity carried by a Gaseous Lon.

|
~ | ne ne
D. | C. ers a C. for radium A. | for radium B.

| 7400 | 483 | 63 | 170 252x10-6 | 68x10-6
| 6550 | 640 | 30 * 20°7 x 10-6 |
BOO, | S00 +2) 2h |b 1k Oe 58x10-6 |
8800 | 930 | 28 78 185x 10-6 52x10-6 |
| 57°6 x 10-6 |

Mean... 20°8x 10-6

hus, since for radium A ne=20°8 x 10-6 and n= 6°25 x 10%,
the value of e=3°3'x 10-":

For radium B ne=57°6x 107-6 and n=16:75 x 10+, thus
eon 107

The mean of these values gives 34 x10—!° as the charge
in electrostatic units of the gaseous ion. This is only about
half the value 6°5 x 10-!° I found in the earlier experiments.
The difference is, as I have already explained, due to the ex-
pansions in the earlier experiments practically catching only
the negative ions ; this made the calculated value of 7 little

On Resolving Power of Prism Trains. BD5

more than half the true value, while it made the value of e
twice as great as it ought to have been.

If we know the value of e, we can at once deduce the
number of molecules in a c.c. of gas at 0° C. and 760 mm.
pressure. Tor if N is this number, then, since e is the same
as the charge on the hydrogen ion in the electrolysis of
solutions,
| Ne= 1 22bcLoe
since 6a eer. N= S26 aloe:

This number is well within the limits of the various deter-
minations made by the methods of the kinetic theory. The
above method for determining N has the advantage of not
involving a knowledge of the shape of the molecules, or any
assumption as to the nature of the effects produced when two
molecules come into collision.

In making the experiments described in this paper, I have
had the help of my assistant Mr. Everett.

XXXIV. On the Effect of Absorption on the Resolving Power
of Prism Trains, and on Methods of Mechanically Compen-
sating this Eigect. By F. L. O. WapswortH*.

[Plate VIII.}
[ previous investigations + of the resolving-power of prism
spectroscopes, it has been generally assumed, Ist, that
the illumination is uniform over the wave-front passing

* Communicated by the Author. The general investigation on resolv-
ing-power, of which the present paper forms a part, was begun nearly
eight years ago, but the work has been much interrupted and delayed by
other more imperative and immediate demands upon the writer’s time
and attention. The publication of various parts of the work has there-
fore been more scattered and irregular than might otherwise have been
the case. Since this paper was written, Prof. Campbell, with whom I
fortunately had an opportunity of diseussing it, has called my attention
to a paper on the same subject that was published about a year ago by
Dr. Reese of the Lick Observatory Staff. On examining this paper
(Astrophys. Journ. xii. p. 199, April 1901) I find that Dr. Reese has
deduced the general equation corresponding to (11) of this paper (for
6,=0), but has confined his investigations of the effects of absorption
to the particular case where the value of 8 is very small. Hence his
conclusion (p. 206) “ that the resolving power of the Mills Spectrograph
is diminished by less than one half of one per cent. by the absanatini, of
the prisms ” is incomplete, and for that reason erroneous and misleading
as a general conclusion. I have therefore allowed my own paper to
stand as it was originally written, acknowledging Dr. Reese’s priority
of publication as above.

+ See Rayleigh, Phil. Mag. vol. viii. pp. 261-264; vol. ix. pp. 49-56 ;
vol. xlii. p. 167; Ene. Brit. vol. xxiv. pp. 480-439; Schuster, 2béd. vol,
xxii, pp. 373-374; also papers by the writer, Astrophysical Journal, vol,
i. p. 52; vol. ii. pp. 176 and 321; vol. iv. p. 54; vol. vi. p. 27; vol. xvi.
p. 1; Phil. Mag. vol. xli. p. 317.

356 Prof. F. L. O. Wadsworth on the Eqfect of

through the prism-train ; 2nd, that the material of the latter
is of the same temperature and refractive index throughout.

The general theoretical results agree so closely with those
obtained in practice that it is certain that the error, if any,
introduced by either of these assumptions must be small
under usual conditions. It is not, however, @ prion certain
that this would be true when the absorption of the glass, or
the differential temperature-change in different parts of the
prisms, becomes abnormally large, as it may do in certain
regions of the spectrum, and under conditions of use of the
instrument such as are met with in astrophysical work. The
tollowing investigation was undertaken in order to determine
the actual magnitude of the effects to be expected from large
variations in absorption and opticaldensity over the transmitted
wave-front.

The most general expression for the distribution in
intensity in the image of a point formed at the focai plane
of a telescope is

2 a. 2a : 2
=] en ae de dy | >.

where 7 is the amplitude of vibration of any element dx, dy
in the wave-front: p is the distance of this element from a
point p in the focal plane at which the intensity is desired.
In reducing this general expression to the form usually
given, the following assumptions are made +t :—
1st. That the amplitude of vibration is constant, 7=const.
2nd. That the wave-front passing the diffracting aperture
is truly spherical, 7. e.,

x = Op ae ~ i ies
3rd. ‘The heht which unites to form the image 1s strictly
monochromatic, 7@. e., \=const.

Under these assumptions (1) may be reduced at once to
the form given by Lord Rayleigh,

eee) i 2a) Qary ‘
— ere || sin ic a ae dy |

ee [feos + ay ae dy |’; ie

where ¢, 7 are the coordinates of any point in the focal-plane
image.

5 Rayleigh, article ‘“‘ Wave Theory,” Enc. Brit. vol. xxiv. p. 430.
’ + See also Popular Astronomy, “Problems Relating to... Resolving

Power of Telescopes,” vol. v. pp. 528-536; and Astrophysical Journal
vol. xvi. pp. 266 e¢ seq. ;

Absorption on the Resolving Power of Prism Trains. 357
If we retain 7 as a variable function,
cates ‘ \ { 9
d= (200) nN oe gig had)

but consider the second and third assumptions as correct, we
obtain similarly

: of (ts Be Acs 277 2
P= r2f2 || fey) <in( zy : + AF dx dy |

‘ i [fee Cos ( + F) la dy |’ Te

In the case of the prism spectroscope the aperture of the
prism-train is generally rectangular, and if all parts of the beam
of tight falling on the first prism-face are of uniform intensity,
the diminution in the amplitude of vibration due to the
absorption of the glass of the train will be uniform along any
line parallel to the refracting edge of the prisms. Along
oa line at right angles to this the change will be expressed by
the law

B
: > —— (d—/
Oh ae i aes CoN renee 5,

where z and 2, are the amplitudes of vibration of the ray after
traversing thicknesses of / and (, centimetres of glass, and 8
is the coefficient of absorption.

If we choose the two lines just defined as the axes of 7
and w respectively we have for d(ay) in (3)

Hy —O Cuma Mensa | een eo oO)

since the length of path, J—(), through any given point in
the prism-train is directly proportional to #, the distance of
that point from the central ray. |

The functin oe~®* is independent of y, and, for a rectangular
aperture, the limits of integration for y in both terms of (4)
are constant. Hence we obtain at once for the distribution
in intensity along the axis of € in the focal plane

+5 4b
pa ot [| ; Blot 2m / ; a OR 2 Bee 2m€ | 1 2
Ge yore Cm Sl ete _ e-Be eps —? & dx
ti aN u ref LL) M

eg —
»)

tg cl? AQ 9 _
For convenience put
2a7ré
+ =k.
Vi

Phil. Mag. 8. 6. Vol. 5. No. 27. March 1903.

Iw
a
ad

358 Prof, F. L. O. Wadsworth on the Hqfect of

Then integrating each of the two terms of (7) by parts we
obtain

Bo _BB Ih Boe VEO) eee
C=k(e2?—e z-) cos 7 —B( e+ anh sin | :
9 (8)
Bb Be vs tage eld BD tee kb |
S=i{e2 ie a ete +B(e? -e 4 COS iy }
and therefore
4 Bb 4 e—Bb__ 2 cos kb
PeC+ = eee
é ‘ k? + B? ©)

Resubstituting for & its value in terms of &, and also ex-

._ kb a5
pressing cos kb in terms of sin= we finally obtain

2
Cb oe Be . , Web
neq?” +e me et
9 Oa

ie = dor =
¢ ewe re TED 2
(Boy? +4( 4% )

When the origin of coordinates is not at the centre of the ©

horizontal aperture, and the limits of integration, },; and

—bo, are unequal, we obtain similarly
=i, a [ e-2Pes as p2Bbo__ 9 Cos k(b +.) eB) |
Nir (k? + B?) : 1 2
(11)
When there is no absorption B=0 and i=1, and both (9) and

(10) reduce at once to the usual form for rectangular aper-
TUTE: 2a'Cny
TED

si Bde ST AG
hve eo.
Cy)
For very small values of B the distribution in intensity is
practically the same as when there is no absorption. For

very large values of B, on the other hand, the term ¢®’ remains
the only one of importance in the numerator, and we have

pei bd? ebb

2
Gs Eb?
é B 2, doa
(Beye + a(S)

. (10)

2
I;

(12)

(13)

Absorption on the Resolving Power of Prism Trains. 399

In order better to show the transition between these two
extreme cases, the values of the function i? have been com-

puted for six intermediate values of B as follows :—

, b= OF oa

Bb=1°3862,

Bb 21002.

Bb =2°(726,

Bb=4-6052,

and Bb=7°825.
Piege oe Ue

In these computations the quantity 2. ak
determined simply by the intensity of illumination in the
incident wave-front and by the dimensions of the instrument,

whose value is

Tape. |.

2
i for different values of Bd.
a Ssin= a
7, 2 =—- | a se
Ao oan | }
Bb="5754.| 1-3862. | 2°1972. | 2°7726. | 4:6052. | 7-825.
ai = alee e paeeaes Wins aoe Naps corer!
0-00 | 1:0000 | 1:0000 | 1:0000 1-0000 | 1:0000 | 10000 1-0000
0107 | -9675 ‘9681 9696 | 9739 | -9766 | -9862% | -9925
0-207 | -8751 ‘8769 “8870 | -8997 | -9100 | -9486 | -9745
0-307 | -7368 | “7411 | -7598 | -7880 | 8114 | 8791 | -9459
O47 | “5754 ‘5792 6086 | ‘6535 | -6900 |. -7988 | -9079
05 7 | -4053 ‘4138 ‘A597 | -5182 | 5628 | -7102 | -8620
06 7 | 2545 2646 3105 +| -s8265' | 16 4! 6207 | 8128
ig | 1353 1462 0a5) | 2 2a2n | sels | saa 17590
O87 | -0547 0654 1140 | -1916 | -2558 | -4624 | -7079
09 x | -0119 ‘0217 0663 | -1882 | -1989 | -4003 | 6571
10 = | -v000 ‘0084 0464 | 1089 | -1629 | -3494 | -6079
11 = | -0080 0146 0452 | 0968 | +1492 | -3087 | -5€21
12m | -0243 “0292 0528 | -0935 | -13803 | -2752 | -5194
13 7 | -0392 0428 ‘0605 | -0923 | -1922 |). 2477 | -4798
147 | 0468 ‘0497 0632 | -0886 | 1139 | -2232 | -4432
15 7 | -0450 ‘0472 0587 | -0805 | -1026 | -2008 | -4095
16 7 | -0358 0381 0486 | -0686 | -0889 | -1798 | -3773
17 mw | -0229 ‘0250 USE OSE A OBR) EIGN eves
18 7 | -0108 ‘0130 0239 | -0484 | -0626 | -1441 | 3233
19 x | -0027 “0049 0155 | -0344 | -0529 | -1298 | -3002
2-0 r | -0000 ‘0020 0120. | -0297 | 0462 | -1182 | -2789
22 x | 0072 is ee im 0422 | -1O11 | -2429
24 r | -0159 ay Bis a 0402 | -0885 | 2116
26 | 0136 te 26 ie 0347 | -0764 | -1871
28 m | -0045 rs hala Ma ‘0270 | -0651 _| -1655
30 7 | ‘0000 ans Sey I, ree 0210 | -0562 | :1470
32 7 ¥ bs Caan Shih Wit "Pel Se O4O UVP TSn7
3° | -043 | -1169|
40 x i) Wrass md an ‘088s |
50 x aa ee wd ‘0582 |
6:0 7 | Rog Ce Pa ei ae OSES!

‘>

300 Prot. F. L. O. Wadsworth on the Eject of

is so chosen that the intensity I? at the centre ot the diffrac-
tion image, £=0, is the same (unity) in each case. The

. e j e a
abscissee are expressed in terms of the angular coordinates —

4
which are determined by the relations
E d
a= Ayp= 75>
I b
and therefore
TED a
= a — Tt =i ° . . . . 14 :
AT ay ( )

The comparative values of IZ for values of « ranging from
0 to 6a), and for the values of ‘Bo given above, are tabulated
in columns 3, 4, 5, 6, 7, and 8 of Table I. (Pp. 359) and plotted
as full-line curves in fig. 1 (Pl. VIII.). For comparison the
value of I? for B=Ois also tabulated in column 2 of this table,
and plotted as a dotted curve in fig. 1.

An inspection of this table, or the corresponding curves of
fig. 1, shows that the effect of mcreasing absorption is to
change the form of the curve P=/(a), Ist, by gradually
obliter ating the points of maxima and minima on each side of
the centre, and, 2nd, by gradually increasing its apparent
width mm. We have to consider this change i in form (a) on
the resolving-power of the instrument, () on the visual or
photographic appearance of the spectral lines.

(a) The visual criterion for resolving-power is that two.
lines of equal intensity may be considered as definitely

“resolved”? when the illumination at the centre of their
superimposed diffraction images is not more than 0°81 of the
illumination at the centres of the images themselves. In
the case of an instrument unaffected by absorption eb
11), this corresponds to a separation of the two lines by a
amount

X
Cj = 2) = —

b
as defined by (14

In the \ease of two equal lines separated by an 1 angalar
interval o the relative intensities in the physical image of
the double source at the points corresponding to the centres.
of the lines themselves and a point midway between them

will be

T= ee os

Absorption on the Resolving Power of Prism Trains. 361

and the lines will be resolved or not according as L-, is less
or greater than 0°81 [%.

Applying this criterion to the case of the images I? shown
in fig. 1, we find for a constant separation c= the follow-

ie
mr,
a5

—

ing values of

For Bob= “5754: Eye ly "R2-
ee a eee

I? "9054
ey es » eS) Cj Ue Re ee le te sede “SN

PB 10204

Bb =2: ¢ 2 —_—_ = a “2?
197 P 11089 J2+
: NAO
Bo=2-7726 Lg aa 97.

[2s a OD

|? 1°4204 es
—1:°6052- MO a —= | *(
Bb=4°6052: P = Oe 1:05 +

Bb=782): =a =h0i+

which shows that the effect of absorption is to decrease the

resolving-power of the instrument by an amount depending
both on the value of B and of 5.

To find the separation necessary for resolution we must
select a value of & such that

Ee ODE (pe oe Ae GG)

Jf we put
, epee P41)

(Bis)2=4F2,

and
7 oO
. ») — ivy
apo if”

we obtain from (9) and (15)

D D+sin? 2x thn sais
DeMi es co eRe MEDD Eatin 4,
(EH? +- 2”) E + FRe ar 2 OCR Sime Wye. (LO)

362 Prof. F. L. O. Wadsworth on the Effect of

from which we can determine 2 and o necessary for resolu-
tion for any given values of Bb. We thus obtain

ory ebb “Diot a= l-007a,
Bo=— 13002 o=1°042,
Bip 2 192 oj edalig,,
Bb=2 0020 o—lhsa,
Bb=4°6052 o=1°')4ay
B= Eo2 o= 2°56,

These relative values of Bb and o are plotted (circles) in
fig. 2 (Pl. VIII.). As is there shown, the relation between
these quantities can be closely represented by the dotted
curve, the equation of which is

G=a){1-+:0253' (Bb)?! . . . en

an expression which is simpler and more convenient for
computation than the more exact formula (16).

An inspection of the curve in fig. 2 shows that for small
values of Bd, z.e. for small absorptions, the actual resolving-
power of the instrument o is very nearly the same as the
theoretical resolving-power a,. For large values, however,
it is very considerably reduced ; nearly one-third for a value
of Bd equal to 4. |

To obtain a better idea of the physical conditions corre-
sponding to the different values of Bé considered above, it is
desirable to express these values in terms of the intensities at
the centre and edges of the transmitted wave-front. We
have from (5) and (6) |

a = ¢= Br)
1

Since the intensities at any two points are proportional to
the square of the amplitudes of vibration, we have for the
centre of the transmitted wave-front r=0, and the edge

b ,
w= 5) the ratio

and therefore for the different values of Bb already con-
sidered

Absorption on the Resolving Power of Prism Trains. 36

JIAO 3y2

em 1? a,
nae a | INE : :
S=g =(;) 29-1972
ey 2,

= =(7) — 27726
0

=i Ae

pS Nt fa Bee (a — \2
RecN ia) Haye
te al / 2

or for the extreme cases the intensity at the edge of the
beam traversing the base of the prism-train is fifty-six per
cent. and one twenty-fifth of one per cent. respectively, of
the intensity at the centre.

2
To find the relation between the quantities Bd, 5 , and 8
?

20
the coefficient of absorption of the glass, we have similarly

from (5) and (6)

= P=).
Also from the geometry of the prism-train
Nn Vea em a2
bilo | pyeO sim ty

for a single prism of refracting angle @ placed at minimum
deviation. For N similar prisms placed en train we have
similarly

BE eh TT esi 6/2
b=) 5 hte VEIN o2

and therefore in general

Poe nee doled soy

V1 —n? sir? $/2 3

from which we can determine the corresponding values of

Bd and 8 for any given spectroscope. Some examples may
be of interest.

For the Bruce spectrograph of the Yerkes Observatory,

364 Prof. F. L. O. Wadsworth on the Effect of

which is one of the largest and most recently constructed
instruments of this class, we have for b. d, N, and n the
following values* :—
b=95'l cms.
o=63° 35’ (mean value).
Nes.
n= 7 bos tern — 9007
1678 ., AX=4300
1693.7, Wh s90G7,.
Introducing these values and solving for Bd we find
Bb=C x ae for X=9900
SA 2400
17°8 A=3900

The absorption of the glass of which this prism-train is
composed (0°102) has been determined by Vogel and Miller.

The values of 8 computed from their results are as follows:—
For wave-length 5500, @6=:021
F. yh 4300, B= "Oil
ot x D900. Baar

For the visua] region of the spectrum, therefore, the value
of Bd for this spectroscope is about *34, and the corresponding
value of o,as given by (18), is less than 1°003 a,, ¢. e. the
resolving-power is diminished less than one-third of one per
cent. by the result of absorption.

In the photographic region of the spectrum, however, the
case is quite different. At wave-length X1=4300, which is
about the middle of the photographic region, the value of
Bb for the Bruce spectroscope is 17:2 x -071 =1°22, and the
corresponding value of o is 1°04, i.e. the resolving-power at
this point in the spectrum is reduced about four per cent. by
the result of absorption. At wave-length A=3900 the value
of Bb is 6°59, the value of @ is 2°10 a@,, and the resolving-
power is therefore diminished by more than fifty per cent.

For prism spectroscopes of larger size or greater resolving-
power than the one above considered the eftect of absorption
may become serious, even in the visible part of the spectrum,

* “The Bruce Spectroscope of the Yerkes Observatory,” E. B. Frost,
Astrophysical Journal, vol. xv. pp. 12-17, Jan. 1902.

+ Estimated by exterpolation from the values given by Frost.
{ Astrophysical Journal, vol. v. p. 82 (1897).

Absorption on the Resolving Power of Prism Trains. 368

particularly if a denser glass than 0°102 is used. Prism
spectroscopes have been constructed having an aperture of
from 2:2 ems. to 2°5 ems., and prism- -trains of from 10 to
13 dense flint prisms*. These prism-trains have been
constructed of very dense flint-glass whose coefficients of
absorption are probably considerably higher than those for
0°102, which is unusually white and tr ik ae Assume
the coefticients to be only 33 per cent. (1/3) larger. Then,
since the ratio Bb=£8 is roughly only ete as large for
the Bruce instrument as for the Young and Grubb instru-
ments, we have for the latter:

In the visible spectrum

Bons OO" G—T02 0 2,.
In the photographic region
4=4300 = BE BT re = 1°35,
A=3900 BUX20:0 og = 11:0 a,

In this last case the resolving-power of the spectroscope is
reduced more than 90 per cent. by absorption in the neigh-
bourhood of the H and K lines.

It is evident from these results that it is useless to increase
the theoretical resolving-power 7 of our prism spectroscopes
beyond a certain point. For every value of @ there will be
a certain limiting value of a, and hence of 7, for which the
practical resolving-power of the instrument as aftected by
absorption (which we will call Rg) will be a maximum. To
find this value we must transform equations (18) and (19) so
that all variables are expressed in terms of r and Rg.

From the well-known relation

5 ain A
bil Ay iv} AX
we have obviously
Be)
ga we ena
We have also the relation
SI y)
Nb sin p/2 Be SN oe - 68. dy (20)

V1 —n? sin? $/2 2° dn
* Young, ‘ Nature,’ vol. iii. p. 110; Grubb, Monthly Notices R.
vol. xxxi. pp. 56-88.
+ See Astrophysical Journal, vol. i. p. 55 (1895).

366 Prof. F. L. O. Wadsworth on the Effect of
From (18), (19), and (20) we then obtain at once
.
we i Lo
ine — cae an ( )
*: 3( aan
which is similar in general form to the expression for the

purity of the spectrum with slits of finite width*.
To find the value of 7 for which Rg is a maximum we have

1=-0063(80*r)

oes) see dn'/ ) 0, ee
Ee aL coa(asrr)
ry aS dn. 3)
or for Rg=max.
ale oie ee 23)
P= {8 dag (23)
and for the corresponding maximum value of Rg
aT coating val
Rg(max.) = (529) em 9 Tm eal (24)

that is, the maximum practical resolving-power that can be
attained with a prism spectroscope is one-half what we could
attain with the same spectroscope if there were no absorption.
For the flint glass 0°102 which we have been considering,

the value of the ratio

dr
for wave-length 1=38900 is about 4250. The value of @ for
the same region is, as we have seen, about °37. Hence for
this glass we have

Rg(max.)— 72000,

for Pn —~ 144000.

The relation between + and Rg, as given by (21), is
tabulated in Table II. and plotted in Curve 1 of fig. 3
(Pl. VIIT.). It will be seen that the increase in Rg is very
small (less than 7 per cent. of the maximum) between the
points r=100000 and +,,=144000; and it would therefore
in general be inadvisable to go beyond the first point, if we
proposed to work in the neighbourhood of the H and K
lines with a prism spectroscope of dense flint glass. The
theoretical resolving-power of the Bruce instrument for this

din

region is about 1538000, { f(t, —1) b, and is therefore

* See Phil. Mag. vol. xlil. pp. 333-339,

Absorption on the Resolving Power of Prism Trains. 307

TasueE II.

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125,000 | © 71675 |
150,000 72490 | 122990 | 137070
200,000 = 68880 =| 142460 = 169820
300,000 «6760 157140 | 217830
400,000 | 46440 152720 | 239440
/ 500,000 | 38750 | 141850 | 244200
| 600,000. | 33060- | 129420 239160
| 800,000 | 25440 107200 | 217280
Pe NODO000' "a, | 90100 | 192700

\ |

considerably larger than can be used to best advantage. ‘The
Young spectroscope has a theoretical resoiving-power 7 of
nearly 300000 in the same region of the spectrum, but as
will be seen from the Table or the Curve the effect of
absorption cuts down the practical resolving-power to about
57000, actually less than that which an instrument of only
one-fourth the size would possess. |

It is at once evident from these results that if high-power
prism spectroscopes are to be used in the investigation of
the photographic region of the spectrum, the use of the extra
dense flint glass, so commonly employed in the past, must
be avoided, not only on the score of light-efficiency, but, as
now appears, on the score of photographic resolving-power
and purity as well. The use of lighter flint reduces the
theoretical resolving-power, 7, of any given prism-train by
decreasing the value of the dispersion-coefficient = ; but this

/
may be easily and even advantageously compensated by
increasing the refracting angle @ of the prisms. The
advantages of this latter construction on the score both of
light-efficiency and economy of material were pointed out by
the writer several years ago*, and it has been adopted in all
the large spectroscopes recently constructed at Allegheny +.

* Astrophysical Journal, vol. ii. p. 264 (1895).

+ Among others may be mentioned the spectroscope of the Phila-
delphia Observatory, the spectroscope of the Lowell Observatory, and
the spectroheliograph of the Philadelphia Observatory (just completed).
Prof. Lord, of the Emerson McMillen Observatory, has also recently
replaced the battery of dense flint prisms first constructed for his star
spectroscope with one of light flint; and I believe Dr. Gill, of the Cape
Observatory, is likewise considering this change.

368 Prof. F. L. O. Wadsworth on the Hgfect of

To show the advantage of the lighter glasses on the score
of photographic purity the values of Rg have also been com-
puted for the dense flint, 0°93, and the light flint, 0°340, of

| an %
Schott’s table. The constants x, 8, and aL for wave-length
3900 for these two glasses are as follows :—
LA (A Ne Tae alg og
0°93 23900 = L°OO 5 aN == O00: Be 14

0-340 — ngq90= 1°61 ; Fy 73100: B=-08.

C
The values of Rg for these values of = and 8 are tabulated

in columns II]. and IV. of Table IL., and plotted as curves
II. and III. of fig. 3 (Pl. VIII.). The points of maximum
for these curves are found at
,, . 315000 for glass 0°93,
ni 488000.2 5) 0 gs ead;
and the corresponding values of Rg (max.) are

157000 for 0°93,

244000 Woe we Ore 0
As in the preceding case the form of the curves is such that
it is not desirable to go to the extreme maximum values of
of Rg, but to stop at points corresponding to »~200000
and 350000 respectively.

For the visible portion of the spectrum the values of

dn I ‘
n, >, and 8 for the first glass considered, 0°102, are as
dr = ‘

follows:—

A WG659 2 0 aan

dr
aN eae
="OOOLS:
B dn
Hm T4O000;

Reg (max.) ~ 370000.

The above results show that while the Bruce spectroscope
is quite efficient for the visible part of the spectrum, it is
quite otherwise for the photographic region in the neigh-
bourhood of the H and K lines. Such an instrument would
not be well suited, therefore, for solar work, particularly of a
spectroheliographic nature.

Absorption on the Resolving Power of Prism Trans. 569

For regions of the spectrum lying below wave-length 3900,
materials having a smaller coefficient of absorption than light
flint or even crown-glass must be used. In the case of
glass, indeed, we soon reach a limit beyond which a further
reduction in density will be actually disadvantageous. As
will be seen from (21) and (23) we reach an absolute. maximum.
for R, when the quantity

Pus

dn
becomes an absolute minimum. For the various flint glasses
already considered, the absorption-coefticient § decreases
dn
more rapidly than the dispersion-coefficient =—; hence the

dn.
quotient of these two coefficients decreases with diminishing
index of refraction. |
But as we pass from the flints to the crowns the reverse
takes place, and the value of @ decreases less rapidly than
the dispersion. Hence we soon reach a point at which the
quotient

is an absolute minimum for glass. Thus for the crown 0°203
examined by Vogel we have in the neighbeurhood of the
H line
hey an
eon Loon, LOSU5:" and? (5° Ss"004.
ae | i=
Hence for crown 0°203

8 > = (000035

which is nearly 25 per cent. larger than the corresponding
quantity (0° 000026) for the light flint 0-340. Hence, in spite
of its diminished absorption cr rown-glass would not beas good
a material to use for the prisms as light flint. ;

We might perhaps find a flint for which the quotient of the
two Coetieienten is somewhat less than in the case of O:340.
It is, however, safe to say that the value of this quotient
eon be snntieelh reduced, and that the maximum practical
resolving-power which we can attain in spectroscopes with
glass prisms will not exceed 250,000 units in the photographic
region of the spectrum, nor 400, 000 in the visual region.

‘In order to attain still higher resolving-powers we must
use other materials than elass. Of those available for this

370 Prof. F. L. O. Wadsworth on the Ejfect of

purpose quartz, rock-salt. and fluorite are among the best.
Unfortunately I have not been able to find any reliable data
on the coefticients of absorption of these materials for different
wave-lengths. Although they are considerably less than
those for glass for both very short and very long wave-lengths,
they are sufficiently large to exercise an appreciable effect on
the resolving-power in these ultra-visible portions of the
spectrum. It is also necessary to remember that certain
kinds of glass, as well as other materials of which prisms may
be constructed, frequently show strong selective absorption ;
and certain regions even in the visible part of the spectrum
where this occurs may exhibit a lack of apparent definition
in consequence. In fact, in all discussions involving questions
of resolving-power, the possibility of the effects of large local
or general absorptions must be kept in mind.

()) The second effect of absorption which we have to con-
sider is that on the general form and apparent ‘‘ width ” of
the individual spectral lines. This effect is in many respects
more pronounced and striking than that on the resolving
power just considered; for as will be seen by an inspection
of fig. 1 (Pl. VIII.), the apparent width is increased in a
much greater ratio than the resolving-power is diminished by
increased absorption.

As long as there is a well-marked minimum on each side of
the centre, we may consider the edges of the spectral image to
be defined by the position of these minima; or, in other
words, consider that the apparent “ width” of the line is
mgm, (fig. 1). For the value @=0 this width for an infi-
nitely narrow slit and monochromatic radiation is of course 2a.
The effect of an increasing absorption is to increase all the
ordinates of the diffraction pattern relatively to the central
one (for 2=0); but the ones in the neighbourhood of the first
minima are increased proportionaily more than the others, so
that these points of minima are gradually obliterated, and
become indistinguishable for values of Bd greater than 1°5.
The edges of the line then become less and less sharply defined
and clearly marked. Their apparent position depends some-
what on the absolute as well as the relative intensity at
different parts in the diffraction pattern ; but in general they
may be taken to lie near the limits + m defined by the relations

2
I +m) =a Li a ‘04 a 3
j. e. near the points at which the intensity of illumination in
the image first falls to less than 4 per cent. of the intensity at
the geometrical centre.
Assuming this criterion, we have for the relation between

Absorption on the Resolving Power of Prism Trains. 371

Bd (or 8) and w, the apparent ‘ width,” tke following values
(from Table I. and fig. 1):—
For Bb= 000 w=mpmy= 2°00 a,

= “iw = 2-044),
Bb=1°386 w=mn,=2'16 4,
Bo 2127 w = 3°66 a,

W= MyM, = 48 a,
Bb=461 w=m3m3 ~~ T 6a,
B= 3a) Ww De Nek eny

The apparent width of the line for Ae last value ot Bd is
therefore nearly seven times as great as the theoretical width,
2a, for zero absorption. This “large increase in w, together
with the accompanying reduction in the practical res olving-
pee Rg, is quite sufficient to explain the apparent haziness
aad lack of definition frequently observed in certain portions
of a spectrum formed by prisms with strong selective
absorption.

The effect of absorption on the form and distribution in
intensity in the spectral image, and hence on the resolving-
power of the prism-train, may be entirely eliminated by
mechanical diaphragming of the prism aperture. By referring
to equation (7) we see that the form of the expression for E
is the same as would be obtained if the illumination were
uniform over the wave-front, and the latter were limited by
an aperture whose length (along the w axis) is 0, as ee
but whose width at any point is the ordinate to the exponential
curve

= Crag ear he thee 9 sku telat cheat wel 25)

If, therefore, we limit the sponte of the prism-train by a
diaphragm whose width is y—*, the illumination remaining
the same as in (7), we obtain er the distribution in intensity
in the image of the spectral line

6) = =F ¢ .
l ya 4 > 2n E Sate
8 —Bx /Ba
“ Gn? eb? cos — a a
2 ale aft |
uy 2 uf
na . 9 WED
pe . ») ‘ *o 979 SIn- ;
ly A? 2 Dork 2 42@262 Xf a
= 5978 cos —- vde| = => WM FORs

372 Prof. F. L. O. Wadsworth on the Effect of

which is the same as obtained with rectangular aperture of
height d, unaffected by absorption, save that the absolute
aS thins at every point in the pattern are diminished in the
ratio

Too? &q2a?

ee OD

Since the intensity in the transmitted wave-front at the

thin edge of the prism is the same as in-the incident beam
nO %.

(J=0), we have, by making «= — . in (6),

iver’ =1,. or ae! Se

Also if we choose « in (25) such that the greatest width of
the diaphragm is equal to d, we have
Bb

db =ae2.
or (=a en ar ule (ya) Vegetal (295
Hence we have from (27), (28), and (29)
Too?

P =f ae UE ee (30)

For the Bruce spectroscope before considered the value of

Bi for wave-length 3900 is, as already computed,
Belle O25)"
ae ee
3 2000 002.

Although so much light is lost in diaphr: agming the aperture
as above ~ described, ae intensity in ene resultant spectral
image will compare somewhat more favourably with that
eared under the actual conditions of absorption with full
aperture, because the “‘ width ” of the line is so much reduced
when the diaphragm is used. The intensity at the centre of
the diffraction-image with full aperture bd (see 10) is
P22 pRB a, Boa

2 = ie “a ~ ‘ one Witt x 5 ° 3 . (31)
Me (Bb)? |

The ratio between this intensity and the intensity of
the image formed by the same instrument. unaffected by
absorption, will be

2 — Bb
0 é \

Tap leite hat... BB)

Absorption on the Resolving Power of Prism Trains. 373
For the same case considered before for which Bd is 6°59,
we have

I,? AY

Finally, for the ratio between the intensities with and
without a diaphragm we have from (30) and (32),
nro ee CBOs
Wet 6?! er = 2
which gives us for the Bruce instrument in the H regions

eS
ZOOM eta ae die eae Ph aha Ge (2)

oc.
I,

(33)

The curve bounding the edges of the diaphragm for any
given case is given by the equation [see (25) and (29) |,

+pN __ Sin 9/2 ph by
y =t¢ Bi V1 —n2 A 2 ) ‘ : ; (34)
For the above case
gee ec
Vv 1—n? sin? d/2 ‘
jae

If with these values of band B we make d=0 and compute
y for different values of #, we shall find the form of the
required diaphragm to be that shown in fig. 4 (Pl. VIIL.).
The widths at the two ends are 0-008 em. and 5:1 cms. respec-
tively, with the wide end toward the base of the prism.

When so placed this diaphragm will entirely eliminate the
effect of the variable absorption, but only, as indicated by
(33) and (33a), at a very large sacrifice of intensity of
illumination, This device can therefore be used only when
we have abundance of light. In other cases the only means
we have of reducing the effect of absorption for any given
material is to decrease the resulving-power of the prism-train
either by reducing the aperture or the number of prisms,

or both.

General Conclusion.

The results of the preceding investigation show that in the
case of prismatic spectroscopes we are confined to certain
resolving-powers. We are limited in one direction by the
physical properties of the glass now at our disposal, in another
by the dithculty, we might almost say impracticability, of ob-
taining blocks of crystalline minerals of larger than a certain
size, and in a third by lack of sufficient illumination.

Phil. Mag. 8. 6. Vol. 5, No. 27. Alarch 1908. 2C

374 Prof. Carslaw on the Use of Contour

Our only means of obtaining more powerful instruments
seems to lie, therefore, in the further development of the
grating-spectroscope. The maximum resolving-powers that
have thus far been attained with the latter class of instruments
are somewhat less than 400,000 units *, about the maximum
which, as we have now shown, is attainable with prismatic
spectroscopes in the visible region of the spectrum. As the
writer has already shown + instruments having at least three
times this resolving-power are not only exceedingly desirable,
but absolutely necessary to the successful investigation of
certain spectral phenomena. We must therefore aim to
ultimately produce gratings at least 40 cms. diameter. A
machine designed to rule gratings of this size was begun by the
writer seven years ago (1896), but owing to the many inter-
ruptions to which reference was made at the beginning of the
article, work on it was only recently completed f. The con-
struction of a machine of about the same size was begun in
1899 by Professors Michelson and Stratton at the University
of Chicago; but work on this has also been much interrupted
and delayed by the resignation of Professor Stratton to accept
the directorship of the new National Bureau of Standards at
Washington. More recently still Jewell, at Johns Hopkins,
has been remodelling one of the Rowland dividing-engines to
rule 10 in. (25 cm.) gratings.

It is to be hoped, therefore, that through the united efforts —
of all of those now working on this problem, gratings of a
considerably larger size than we now have may soon become
a commercial possibility.

Allegheny Observatory, November, 1902,

XXXV. The Use of Contour Integration in the Problem of
Diffraction by a Wedge of any Angle. By H. 8. Carsiaw,
Professor of Pure and Applied Mathematics in the University
of Sydney, .\.S.W.S

N the Appendix on Diffraction to his Adams Prize Hssay |
Macdonald gives a discussion of the two-dimensional

* See paper on ‘“‘ Resolving Power of Telescopes and Spectr
for Lines of Finite Width,” Phil. Mag. vol. xliii. es 520, Mab 1807.
+ Loc. cit, The large solar grating-spectroscopes of the new
Allegheny Observatory are designed for gratings of 25 cms. and 40 ems
aperture Report of Director, 1900.
¢ See Report of the Director, Allegheny Observatory, 1900, p. 22.
The final setting up of the new engine has been still further delayed by
the delay in the completion of the new Observatory and Laboratories
§ Communicated by the Author. :

| ‘Electric Waves,’ by H, M. Macdonald, Camb. 1902,

Integration in the Problem of Diffraction. d19

problem, where the boundary is formed by two planes
inclosing an angle a. As a special case his formula yields
the solution given by Sommerfeld* for the semi-infinite
plane.

The method by means of which Macdonald obtains the
solution of this problem depends upon a general theorem,
proved earlier in his treatise. I propose in this note to give
another demonstration, using the method of contour in-
tegrals. This method has been employed with very great
success in the theory of potential, by Dougall J, and. the
proot which I give here would occur to any one reading his
most important ‘and suggestive paper (¢f. §§ 17, 21).

Taking the origin in the edge of the wedge, which occupies
the space a< O<: 27, and considering the « case in which the
electric force is parallel to the edge of the wedge, the problem
reduces to the solution of the equation

Ou Oru

on") ay”
where, in addition, it is required that w shall vanish at the
boundary @=( and @=a, and that it shall become infinite

as log eh when R=0, at the point (7”, @’).

,+h?u=0,

lf the space were unbounded we should take as our solu-
tion

w= Uo (eku)
where

R?=r? +7? — 277’ cos (6-6),

and U,(¢) is the Bessel’s function of the second kind, elven
by the equation

Meer oe (siz, (2)—e-* J, ()).

2 sin nar

The addition formula for Uo(4R) is well known, and will be
used later, namely

U (ER) =Jo( kr’) Up (kr) + 23 na (kr”)U (kr) cos n(O—8’)

* Sommerfeld, “ Mathematische Theorie der Diffraction,” Math. Ann.
Bd. xlvii. ( (1896) ; cf. also a paper by the Author in Proc. Lond. Math.
Soc. vol. xxx.

+ Dougall, “The Determination of Green’s Function by means of
Cylindrical or Spherical Harmonics,” Proc, Edin. Math. Soe. vol. xviii.

(1900).
2C 2

376 Prof. Carslaw on the Use of Contour

in the case when +>; while when 7<7/, 7 and 7 must be
interchanged.

The method of this paper consists in obtaining a contour
integral for this expression, U(kR), and then adding to i
terms which introduce no singularity, and cause the boundary
conditions to be satisfied.

Piss:

THE FEAL AXIS 110 THE TH-PLANE

posse Riel AS

FATH(C) IN THE 2-PLANE

Consider the integral

‘ag m(ar— 8+ a) U(r) J, (kr)dm,

sin mq
taken in the m-plane over the path (C) of fig. 1.
When m is large we have the Bia’ values

use) =(3) a ne

using the asymptotic value for II(m)*, so that we see that
In(2) vanishes at infinity, when the real part of m is
positive. |

In the same way, using the relation,

ys Von. em =a alos moon m—m?

bO| &

W(m) Wf—m)= as

sin mr’

* Of. Whittaker’s ‘Modern Analysis,’ § 110.

Integration in the Problem of Diffraction. O17

the approximate value of J_,,(z) is given by the equation

ENT Sih oae jp. ———
5) | ae (z) = (5) —. Av 2arm . em log Li
a MTT

and this does not vanish at infinity, when the real part of 1
is positive. :
However, since

UO= gee (I-n()— eT) )

2 sin m7

the expression for In(2') Un(e) ) simplifies, and we find its
approximate value to be given by

ind Tip

Jm(2)U,, (2) = male jie

Hence this product vanishes at infinity, when the real part
of m is positive, provided that 2><’.
Further, it is readily shown that

cos m(7—O + 6")

~ sin mar

vanishes at infinity, when 0<@0—0@'<2c7. Thus

pdb st. cos m(a—O + 6’)
5 DS ON
Cc

Sin m7

‘ aff
In(ko')U_ (kr )dms (j a a

over the path (C) of fig. 1 is equal to the sum of the residues
of this function. Therefore

a eos ua 8 Ee )

17r sin 1077

cee ( ne a
over the path (C’) of fig. 2 is equal to

= [ Ty(to" Uhr) + 23,9, (tr) U, (kr) cos n(8— a’) |,
the path (C') differing from the path (C) by the removal of
the small semicircle at the origin.

We have therefore obtained the following expression tor
U,(kR) as a contour integral :—

ie COs me T— 0+ 6') im p>?! ),
an eer eae LT Clen Un (Arjan, a>6')

378 = Contour Integration in the Problem of Diffraction.

while when r<7’, or 0<6', we have only to interchange r
and 7’, or 8 and @’, in the above expression.

io, 2
Fig. 2.

THE REAL AXIS 11 THE T-PLANE

FatH (C') in THE WePLANE

To deduce the solution of the diffraction problem, where
the boundary is given by the planes 02=0 and @=a, we have
to balance the expression just obtained by the addition of
solutions of the differential equation

On Ol!
da? * Oy
which remain finite in the space considered, 0<@<a, and

cause the boundary conditions to be satisfied.
It will be seen that

ak 0,

1 a sin m0
i ( : cos m(1—0+6') —cos m(m7—a+t 6) .— —
t Jol sIn ma
sin m(a—@)4 Im (kr!) Um(kr dm
—cos m(7— 6’) —. ( ‘| m ) m (Arr
sin ma sin mar

satisfies all these conditions when 7>7’, and a >@>6', while
when 7<7", or 6< 6’, we shall have only to interchange r and
7’, or 8 and @, in the above.

To prove this we note first that the different elements of
the integral satisfy the differential equation, and that the
boundary conditions are satisfied. Further, that no new
sources are introduced by the additional terms, since the in-
tegrals they give converge for all the values of 7 and @ in
the space considered, unlike that for the first term, which
has a singularity at the point (7”, 6’). |

Notices respecting New Books. 379
This expression simplifies, and may be written

.( sin m(a2—8) sin m@ ‘i; r>r'
2i(_ sin ma Jn(hr')U,, (kr)dim, a>O>0!)

and as there is now no pole at the origin in the m-plane, we
may take the path (C) instead of (C’).

Hence we obtain our solution in the form of an infinite
series, by the use of Cauchy’s residue theorem, this solution
being given, for all values of @ in the space 0<@<a, by;the
equations

a oe Re gate ial Una(kr) Jnn(kir’), r>r’. . (1)
a a a a a

T= cue sin —@sin — 6 Une(kr’) Ine(kr), <r’. (2)
a a a a 5

This result agrees with that given by Macdonald*, and
may be compared with the solution of the same equation in
the n-fold Riemann’s space, given by Sommerfeld f.

This method may be extended to the corresponding three-
dimensional problem, and it can also be employed in the
cases where the diffraction is caused by a Sphere or Circular
Cylinder. Several interesting results in these cases have
been already obtained by me, and I hope to publish a full
discussion of these problems at a later date.

Glasgow, January 1905.

XXAVI. Notices respecting New Books.

The Meteorology of the Ben Nevis Observatories. Part Il. Containing
the Observations for the Years 1888 ...1892, with Appendices.
Edited by ALEXANDER Bucaan, LL.D., F.RS., and Rosert
Trattt Omonn; forming Volume XLII. of the Transactions of
the Roval Society of Edinburgh. 1902. Pp. xiv+552.

Ah PREVIOUS volume (vol. xxxiv.) of the Edinburgh ‘ Transac-

tions ’ gave particulars of the earlier meteorological observa-
tions taken on the summit of Ben Nevis and at its base, at the
Public School, Fort William, from December 1883 to the end
of 1887. The present volume brings down the complete obser-
vational record to the end of 1892. During the final years ot
this period the Fort William data are from the Observatory
opened there in July 1890, which possesses a superior set of
self-recording instruments.

* Loc, cit. p. 190, + Loc. cvt. p. 356 (13),

380 Notices respecting New Books.

A short preface, pp. v to x, gives an account of the: position
and management of the observatories; whilst an introduction,
pp. 1 to 8, describes very briefly the instrumental outfit and the
nature of the observations. The data for each of the five years
1888 to 1892 are in the first instance treated separately. Thus
for 1888 we have for Ben Nevis itself tables for each month,
including hourly readings of the barometer, wet- and dry-bulb
thermometers, rainfall, sunshine, direction and force of wind (scale
0 to 12), and amount of cloud (scale 0 to 10). These tables give
also particulars for each day of the mean barometric pressure and
cloudiness, the maximum and minimum temperatures, the maximum
wind-torce, and total amounts of rainfall and sunshine. Following
the Ben Nevis tables are corresponding but more restricted tables
for Fort William. There is then a summary of mean monthly and
annual diurnal variations for Ben Nevis, and a transcript of the
entries made during the year in a log-book kept at the summit
observatory. The log treats in considerable detail of fogs, auroras, ©
halos, thunderstorms, and other miscellaneous phenomena.

The records for the subsequent years 1889 to 1892 follow similar
lines ; only, after the institution of the low-level observatory, the
Fort William data appear in greater detail, and corresponding
tables for the base and the summit stations appear side by side in
adjacent pages. The five years’ records occupy over 400 pages.
They are followed on p. 419 by a table summarizing the snowfall data
on Ben Nevis from 1883 to 1892; and after this area set of rather
incomplete records obtained with a Robinson cup-anemometer, a
type of instrument difficult to work at the summit. On pp.436 to445
are a series of important tables, giving mean: diurnal variations of
barometric pressure, temperature, &c., for each month of the year,
based on the observations of a number of years. From the title of
the volume one would have supposed that no data later than 1892
would have been available; but the tables just referred to utilize
the observations taken up to the end of 1896.

The remainder of the volume forms an Appendix, consisting
mainly of miscellaneous meteorological papers, some apparently
new, others abstracts of papers previously published. Only a few
of them are exclusively confined to Ben Nevis data. Dr. Buchan
and Mr. Omond discuss the differences between the diurnal
variations of the barometer in bright and in cloudy weather at
some nine stations. Mr. Buchanan has a general discussion of
the effects of fog on Ben Nevis meteorology. Mr. Aitken has a
report on observations of atmospheric dust. The remaining papers
are due to Dr. Buchan and to Messrs. Omond, Rankin, and
Mossman. Most are mainly observational or statistical in cha-
racter, but several—e. g. papers by Dr. Buchan on the influence °
of high winds onthe barometer, and by Mr. Omond on differences
between the Ben Nevis and Fort William barometers when both
are ‘ reduced to sea-level ”—are more theoretical.

Notices respecting New Books. 381

A table of contents, pp. xiiiand xiv, andan index, pp. 951 to 352
make the book easily consulted.

The preparation of the tables in a volume such as this He prerents
an enormous amount of labour of a kind calculated to damp the
ardour of any but the most enthusiastic workers, and Dr. Buchan
and Mr. Omond well deserve the thanks of meteorologists. They
are to be congratulated on the beautifully clear way in which the
tables are printed, and on the success of the various devices for
guiding the eye to take in the prominent features. The reader of
the Ben Nevis “ logs” must also bear a tribute to the great zeal
shown by the observers at the summit. The freezing-up of instru-
ments, blocking by snow, and other exceptional conditions, render
the use of ordinary self-recording apparatus impossible, so that
all the hourly records—except those of sunshine—are from eye
observations. In the .winter months, during high gales and
drifting snow, few people would envy the Cheever Ww hee duty
takes him out of doors in the midnight hours. When it comes to

a critical estimate of the value of the observations, there is a little
more room for doubt. The non-instrumental estimate of such a
constantly fluctuating element as wind-force, the record of rainfall
or melted snow during storms, the use of the sunshine recorder in
alternating ciear and. snowy or fogey weather, are attended by
uncertainties from which the records at low-level stations are
comparatively free. Such sources of uncertainty should, however,
be largely eliminated when it comes to mean monthly or annual
diurnal variations. In the comparison of the data at the base and
the summit there are uncertainties arising from the great difference
in the environment of the two stations. The station at the base
hhas its wind and even its sunshine record considerably interfered
with by surroundiug high grounds ; whilst some of the records at
the summit are influenced by the want of symmetry in the shape
of the mountain, there being an enormous precipice on one side of
the observatory, at no very great distance. This want of symmetry
must add to the difficulty of judging how far meteorological con-
ditions at the summit are comparable with those that would exist at
the same level in the free atmosphere if the mountain were non-
existent. In some of the discussions in the latter part of the
volume evidence of greater familiarity with physical principles and
results, and with the theory of instruments, would give the reader
more confidence that the point of view selected is the one most
likely to lead to a clear issue. There seems a slight slip in the
theory of the table on p. 545 for eliminating from diurnal variations
any “non-cyclic” change taking place progressively. The table
ascribes to an interval of 23 hours the change that really answers
to 24. The consequent error w ould, however, very seldom be of
practical moment. - C. C.

382 Notices respecting New Books.

Franges @ Interference et leurs Applications Métrologiques. Par
J. Mach pre Liérrnay, Professeur a la Faculté des Sciences de
Marseille. Paris: C. Naud. 1902. Pp. 101. (‘Scientia ”
Series, No. 14.)

Iy this interesting and up-to-date brochure the author gives a
comprehensive account of the production of interference-fringes,
their properties, and application to the exact measurement of
length. ‘he last chapter in the book gives a brief account of some
determinations of the mass of a cubic decimetre of distilled water
at 4° C.; and perhaps no better evidence of the value of optical
methods of measuring lengths could be obtained than the following
concordant results of three recent determinations of this quantity :—

Mace de“Lepinay')s.2.. 2.41. ees 999-954 grammes
Fabry, Macé de Lépinay and Perot .. 999-974 mA
Chappuis 36 so. OLS eee eee 999-976 x

L’Electricité Déduite de UV Expérience et Ramenée au Principe des
Travaux Virtuels. Par M.-E. Carvatto. Paris: C. Naud.
1902. Pp. 91. (“Scientia” Series, No. 19.)

Tuts little book—one of the latest additions to the well-known
‘‘ Scientia ” series—forms an excellent introduction to some of the
more difficult portions of Maxwell’s great treatise. It is mainly
concerned with the application of Lagrange’s dynamical equations
to electrical problems. The principle of virtual work is employed
by the author to establish Lagrange’s equations, and the treatment
ot this subject appears to us to be clearer than any we remember
having seen elsewhere. The discussion of the applicability of
Lagrange’s equations to electrical problems is very thorough, and
the interesting case of Barlow’s wheel, to which the equations are
not applicable, is fully discussed.

Uiated States Magnetic Declination Tables and Isagonic Charts for
1902. By L. A. Bauer, Chief of Division of Terrestrial Mag-
netism US. Coast and Geodetic Survey. Washington, 1902.
Pp. 405, with 2 Charts.

TERRESTRIAL Magnetism has long formed part of the work of the
U.S. Coast and Geodetic Survey, but it has recently been consti-
tuted a separate division of the survey under the supervision of
Dr. Bauer, well known as 'the Editor of the journal ‘ Terrestrial
Magnetism.’ Judging by the present volume—the first drawn up
under Dr. Bauer’s regime—there is every prospect of increased
activity in magnetic work in the United States. The first part of the
volume gives a lengthy historical account of the origin and progress
of the subject, commencing with a réswmé of what is believed to

Notices respecting New Books. 383

have been known by the Chinese and early Greeks and Romans, and
following the course of discovery down to the present day. On
pp. 28 to 30 is a summary of old observations of declination, taken
prior to 1600 at different parts of the world, including an obser-
vation by Frobisher at a somewhat mysterious “ Fair Island (S.W.
of Scotland).” Dr. Bauer has many complimentary references to
early English observers, including Norman and Gellibrand ; but
he evidently thinks (cf. p. 35) that so far as Terrestrial Magnetism
is concerned Gilbert’s work has been overrated. The latter part
of the historical introduction gives tables and curves of secular
change in all parts of the world, also particulars as to diurnal and
annual inequalities of declination at various stations in America
and elsewhere, and includes a brief discussion of magnetic storms.
Under the heading of ‘‘ Magnetic Observatories,” pp. 56-61, we
have an illustrated account of the new American Magnetic Obser-
vatory at Cheltenham, Maryland; this includes a full description
of the elaborate arrangements for securing small ‘diurnal variation
of the temperature. The equipment of this observatory comprises
magnetographs both of the Adie (Kew) and Eschenhagen patterns.
Several of the photographic traces obtained at Cheltenham in 1902
are reproduced, including one which shows a magnetic disturbance
whose beginning is supposed to synchronize with the eruption of
Mt. Pelée (Martinique) on May 8th. Following this, pp. 62-65,
are some small scale magnetic charts, including early ones by
Hansteen, Halley and Duperrey, others by Neumayer, and some
by the British Admiralty for the epoch 1905. There is also a
general description of magnetic surveys, including that of the
United Kingdom by Riicker and Thorpe, with a reference to the
proposed Norwegian expedition under Amundsen during the
present year to the neighbourhood of the north magnetic
pole.

The remainder of the volume deals more directly with the
special work of tine U.S. Coast and Geodetic Survey. It describes
the Survey’s type of magnetometer-theodolite, contains instructions
-as to the taking of observations, and gives many particulars as to
secular change of declination in the United States and outlying
territories. These secular change data are used in reducing to the
epoch Jan. 1, 1902, an enormous mass of observations of decli-
nation in America—some in British territory,—particulars of
which occupy pp. 117-266. Then follows a minute description
of the position of all stations occupied between 1881 and mid-
summer 1902. At the end of the book are two isogonic charts
for the epoch Jan. 1, 1902, one for the United States proper,
with adjacent regions in Canada and Mexico, the other for Alaska.

C.C,

XXAVIT. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
(Continued from p. 175. |

November 5th, 1902.—Prof. Charles Lapworth, LL.D., F.R.S.,
President, in the Chair.

jes following communications were read:— ~~ :

#1.‘ The Fossil Flora of the Cumberland Coalfield, and the Palaeo-
botanical Evidence with regard to the Age of the Beds.» By E. A.
Newell Arber, Esq., M.A., F.G:S.

2. ‘Some Remarks upon Mr. E. A. Newell Arber’s Commu-
nication: On the Clarke Collection of Fossil Plants from New
South Wales.” By Dr. EF. Kurtz, Professor of Botany in the
University of Cordoba, Argentine Republic. —

- 3. ‘On a new Boring at Caythorpe (Lincolnshire). By Henry:
Preston, Esq., F.G.S.

This boring, after piercing Northampton Sands, passed through
199 feet of Upper Lias, 19 feet of Marlstone, and into the Middle
Hiassic Clays. With the aid of other shallow wells in the Lincoln-
shire Limestone, the author shows that this rock has a decided dip
to the west down the face of the escarpment, as though it had
settled down upon the eroded surface of the Upper Liassic Clay.
This settlement is probably the cause of a continuous spring flowing
from the junction, and it has given rise to an underestimate of the

thickness of the Upper Lias.

November 19th.—Prof. Charles Lapworth, LL.D., F.R.S.,

President, in the Chair.
The following communications were read :—

1. ‘The Semna Cataract or Rapid of the Nile: a Study in

River-Erosion.’ By John Ball, Ph.D., F.G.S., A.R.S.M., Assoe.
M.Inst.C.E.

Inscriptions placed on the rocks at Semna, between the second
and third cataracts, under the 12th and 13th dynasties, serve as
a means of gauging the local changes due to river-erosion during
a period of about 4200 years. Horner, in 1850, came to the
conclusion that ;

‘the only hypotheses which could meet the requirements of the facts observed,
would be either the wearing away of a reef or barrier at the place in question—
a process requiring too long a period,—or the existence at some distant period
of adam or barrier, formed perhaps by a landslip of the banks, at some
narrow gorge in the river’s track below Semna.’

The author is in favour of the former explanation. The river,

Geological Society. 385

above and below the Kumna and Semna temples, has a width
of 400 metres, but between the two temples a narrow band
(200 metres wide) of hard red and grey gneiss contracts the river
at low Nile within a central channel about 40 metres wide.
Through this deep channel not less than 400 cubic metres of water
pass per second. The gneiss itself, dykes of syenite-porphyry,
hornblende-schists, and augitite are described; and it is shown that
the foliation of the gneiss is parallel to the channel, and probably
accounts for the direction of the latter. Rapid erosion with the
formation of pot-holes is observed to be now taking place; and
the author calculates that if 200 cubic metres (approximately
590 tons) of rock per year has been removed from the barrier,
the lowering of it would amount to 2 millimetres a year, or in
4200 years 7°9 metres, the depth of the present river below the
lowest group of inscriptions dating from the time of Amenemhat IIT.
The yearly discharge of the Nile past Semna is nearly 100,000
million tons of water; and the author considers that the removal
of 500 tons of rock under existing conditions in a year is not
only not impossible, but highly probable, as all this erosion
only amounts to 5 milligrams of rock per ton of silt-laden water.
This erosion is compared with the classic instance of the River
Simeto in Sicily. At Assuan and Silsilla the river has suffered
considerable lowering within geologically recent times, probably
brought about by the removal of long pre-existent hard barriers.
The sluices of the new dam at Assuan may in the future give a
quantitative determination of silt-erosion in granite, and it would
appear to be not difficult to ascertain at Semna the rate of
pot-holing. The formation of new pot-holes 14 feet deep, in an
artificial channel in rock in Sweden, has been observed to take place
in 8 or 9 years, and the author hopes in future to attempt some
measurements of this kind at Semna.

2. ‘Geological Notes on the North-West Provinces (Himalayan)
of India.’ By Francis J. Stephens, Esq., F.G.S., A.I.M.M.

The country examined extends in a north-westerly direction
across the line of strike, from the borders of Nepal and South-
eastern Kumaon to north ‘of the Alakmunda River in the vicinity of
Badrinath, and the Marra Pass. The foothills consist of Tertiary
clays and sandstones, the snowy ranges of gneissose, granitic, and
metamorphic rocks of various descriptions. ‘ Between the snowy
ranges, or rather the most southerly range of the Himalaya chain,
a band of hills extends, for nearly 50 miles on an av erage, to the
foothills.’ These have hardly been oxppleneet though roughly mapped
on geological maps of India as belonging to a “Transition Series.
The whole area is rich in minerals. he author gives a brief
description of various rocks, met with mainly in this third belt.
They include slates with vein-quartz; mica- and graphite-schists -

386 Geological Socrety :—

dykes of dolerite; granites; clay-slates, sandstones, and schists,
with copper, lead, and tin ; limestones, serpentines, and hornblendic
rocks, with talc, steatite, etc.; various schists, quartzites, and lime-
stones. The summary of the author’s observations leads him to

“suppose that there are at least three distinct limestone or calcareous series

in Kumaon and Garhwal, and that schists and quartzites, with several isolated
patches of granitic rock, form a large part of the remaining formations.

3. ‘Tin and Tourmaline.’ By Donald A. MacAlister, Esq., F.G.S.

Cassiterite hardly ever occurs without tourmaline, though the
latter is found without the former ; hence it appears that tourmaline-
producing constituents and influences are of wider range than are
those of cassiterite. Boron-trioxide is an extremely common accom-
paniment of voleanic action, and there can be no doubt that it has
acted powerfully in changing such original minerals as the micaceous
and felspathic ingredients of crystalline rocks. From a comparison
of formule representing tourmaline and felspar, it is evident that
the act of tourmalinization has been accompanied by a loss of soda.
The excess of this soda will combine with boric acid, forming meta-
borate and pyroborate of soda. ‘The former, acting on disseminated
tin-ore, might result in the production of sodium-metastannate and
borax. The metastannate is soluble, and capable of being leached
out of the magma, and, by a new reaction, tin-oxide may be
precipitated and concentrated, while sodium-metaborate may be
liberated. According to the cooling-curve of solutions, in all pro-
bability deposition of the oxide of tin would take place more
rapidly at a certain stage in the process of cooling than at others.

December 3rd.—Prof. Charles Lapworth, LL.D., F.R.S.,
President, in the Chair.

Lhe following communications were read :—

1. ‘Qn some Well-sections in Suffolk.’ By William Whitaker,
Begs pA. FRS., F.G-S:

Notes of thirty-one new wells have accumulated since 1895, some
of them giving results which could not have been expected. A trial-
boring for the Woodbridge Waterworks Company gave a depth of
1334 feet down to Eocene beds, and a thickness of Crag about double of
any before observed in the neighbourhood. An analysis of the saline,
hard, water yielded is given. Three explanations are suggested :
a channel, a huge ‘ pipe’ in the Chalk, or a disturbance such as a
fault or a landslip; but the author is not satisfied with any of them.
Two borings at Lowestoft show that Crag extends to a depth of
240 feet in one case, and over 200 feet in another: confirming
estimates of Mr. Harmer and Mr. Clement Reid. In one of these,
Chalk was reached at 475 feet. Three other wells in the neigh-
bourhood confirm the great depth of the newer Tertiary strata.
Sections are also given from the following places :— Boulge,

————

Cellular Magnesian Limestone of Durham. DoT

iEicham Street, Ipswich (corroborating the evidence for a deep
channel filled with Drift given by the section at St. Peter’s Quay,
New Mill), Shotley, Stanofelal and Brettenham Park. The last
shows the greatest thickness of Drift recorded in the county,
namely, 312 feet.

2. ‘The Cellular Magnesian Limestone of Durham.’ By George
Abbott, Esq., M.R.C:S., F.G.S.

The Permian Limestone covers about 1} square miles near Sun-
derland; it alternates with beds of marl containing concretionary
limestone-balls, and attains a thickness of 65 feet orso. The cellular
limestones frequently contain more than 97 per cent. of calcium-
carbonate. -Magnesium-carbonate occupies the interspaces or ‘ cells’
of this limestone, and also the spaces between the balls. he hundred
or more patterns met with in it can be arranged into two chief
classes, conveniently termed honeycomb and coralloid, each
with two varieties; and each class has four distinct stages, both
classes having begun with either parallel or divergent systems of rods.
The second stage is the development of nodes at regular distances
on neighbouring rods; and these in the third stage, by lateral
growth, become bands. Finally,in the fourth stage the interspaces
become filled up. The upper beds are usually the most nearly
solid. In the coralloid class the nodes and bands are smaller and
more numerous than in the honeycomb class. In both classes tubes
are frequently formed. The rods have generally grown downwards,
but upward and lateral growth is common. A section of Fulwell
Quarry is given.

December 17th.—Prof. Charles Lapworth, LL.D., F.R.S.,
President, in the Chair.

The following communications were read :—

1. ‘Note on the Magnetite-Mines near Cogne (Graian Alps).
by Prot. 12) G. Bonney, 1).Se., LILAD., FR.S., E.G:8.

These mines have been worked probably since Roman times, but
are now almost deserted. They are situated in the Val de Cogne,
one of the larger tributaries to the Val d’Aosta from the Graian Alps.
The author, in company with the Rev, KE. Hill, last summer
examined two localities where the ore has been worked. At
one, the Filon Licone, the mass of magnetite is probably about
80 or 90 feet thick and some five times as long. At the other
place, the Filon Larsine, the mass apparently is not nearly so
thick. The ore is a’ pure magnetite, jointed like a serpentine,
a thin steatitic film being often present on the faces. At both
localities the magnetite is ‘found to pass rapidly into an ordinary
serpentine, the transitional rock being a serpentinized variety of
the cumberlandite described by Prof. Wadsworth in his ‘ Lithological
Studies.’ The serpentine is intercalated, like a sill, between two

388 Geological Society.

thick masses of cale-mica-schists, with which green schists (actino-
litic) are as usual associated, no doubt intrusively. All these
represent types common in the Alps. The author discusses the
relations of the magnetite and serpentine, which, in his opinion,
cannot be explained either by mineral change or by differentiation
in situ, but indicate that a magnetitic must have been separated
from a peridotic magma at some considerable depth below the
surface, and the former, when nearly or quite solid, must have
been brought up, fragment-like, by the latter; as in the case of
metallic iron and basalt at Ovifak (Greenland). .

2. §The Elk (Alces machlis, Gray) in the Thames Valley.’ By
Edwin Tulley Newton, Esq., F.R.S., F.G.S.

3. ‘Observations on the Tiree Marble, with Notes on others trom
Tona.’ By Ananda K. Coomiraswamy, Esq., B.Sc., F.L.S., F.G-.S.

The gneiss near Balephetrish has a general south-westerly and
north-easterly trend, and the limestone occurs in it as lenticles
of various sizes, having a similar foliation. Descriptions of pink,
grey, and white varieties of the limestone in this locality are given.
The inclusions comprise those of gneiss containing quartz, felspars,
hornblende, augite, scapolite, and sphene as characteristic minerals,
and mineral-aggregates consisting of sahlite, coccolite, scapolite,
sphene, apatite, calcite, and mica. The contact-phenomena are not
specially well displayed, but several instances are described ;- and in
these the minerals of the modified gneiss interlock with those of the
modified limestone, and there is no actual line of junction seen
under the microscope, although an abrupt change is evident. The
dynamic phenomena include the rounding of the minerals (frequently,
however, an original character) and the formation of ‘augen.’ The
carbonates are present as a fine-grained granular matrix, the result
of the breaking-down of larger grains, probably at a temperature
not above 300° C., as indicated by the experiments of Adams &
Nicolson. Although there are exceptions, gneiss-inclusions aud
mineral aggregates have usually been protected from the effects of
extreme pressure. The description of minerals includes carbonates,
pyroxene, amphibole, forsterite, scapolite, sphene, mica, apatite, and
spinel. White, greenish, and black marbles are described from Jona,
where they are associated with actinolite-felspar schists and others ;
they are included in the gneiss. Sedimentary rocks suggestive of
Torridon Sandstone occur along the eastern shore of Iona.

January 7th, 1903.—Prof. Charles Lapworth, LL.D., F.R:S.,
President, in the Chair.

The following communication was read :—

‘On the Discovery of an Ossiferous Cavern of Pliocene Age at
Dove Holes, Buxton (Derbyshire).’ By William Boyd Dawkins,
M.A., D.Sc., FLR.S., F.G.S., Professor of Geology in Owens College,
Victoria University (Manchester).

Phil, Mag. Ser. 6, Vol. 5, Pl. V.

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Phil. Mag. Ser. 6, Vol. 5, Pl. V,

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TH E

LONDON, EDINBURGH, anv DUBLIN

PHILOSOPHICAL MAGAZINE

AND
JOURNAL OF SCIENCE.
[SIXTH SERIES. ] \

APRIL 1903, 4 ‘A | yi
7" Oa EST Gee ape
XXXVIII. The Conductivity produced in ae by Yy *e a
of Ultra-Violet Light. By Joun 8. Townsenp, J/.A.,
Wykeham Professor of Physics, Oxford*.
[Plate IX.]

}* a former paperf on this subject, | gave an account of

some experiments which were made with a view to
finding the nature of the conductivity which is obtained when
ultra-violet light falls on the negative electrode in a gas.
The results confirmed the theory “of. the genesis of ions S by
collision which had been previously deduced { from experi-
ments with Réntgen rays and from Stoletow’s experiments.
It was also shown that the negative ions thus produced in a
gas are identical with the negative ions set free from the
electrode by the action of the ultra-violet light. The gases
which were examined were air, carbonic acid, and hydrogen.

I propose in this paper to give the results of some experi-
ments which | have made with hydrochloric acid gas and
water vapour, and to compare the results with those obtained
with the other gases. In all cases the same general theory
affords an explanation of the phenomena, and we are led to
conclude that negative ions are generated in air, carbonic
acid gas, hydrogen, water vapour, or hydrochloric acid gas,
which are all identical with the negative ions set free from a
zinc plate by the action of the ultra-violet light.

* Communicated by the Author.
+ Phil. Mae. June 1902. t Ibid. February 1901.

Phil. Mag. 8. 6. Vol. 5. No. 28, April 1903. 2 D

390 Prof. Townsend on the Conductivity produced

The experiments with hydrochloric acid gas were con-
ducted in precisely the same manner as has been already
described for the first three gases. In order to use water
vapour it was necessary to alter the arrangement of the ap-
paratus, since the pressures cannot be found with a McLeod
gauge, and it is undesirable to introduce the vapour into the
Toepler pump. :

Plate IX. fig. 1 shows the apparatus which was used
for adjusting and measuring the pressure of the water
vapour. The parallel plates for measuring the conductivities
were set up in the air-tight vessel A, which was connected
with one side of the oil manometer M by the tube T. The
bulb B containing water was joined to a side tube provided
with a stop-cock $8, through which the water vapour was
admitted to the apparatus. The other side of the manometer
was connected through drying-tubes to the McLeod gauge
and the Toepler pump. Sulphuric acid was used in the
tube D, near the manometer, and phosphorus pentoxide in
the second tube D,. |

The oil used in the manometer was that which is supplied
for lubricating the Geryk vacuum-pump ; it had a specific
gravity °87, and a small vapour-pressure which may be
neglected in comparison with the pressure of the water
vapour in any of the experiments. The oil floated on a
mercury column in the tube U, which was connected by
flexible tubing with a mercury reservoir.

In order to remove the air from the apparatus the stop-
cock S and the manometer were opened, and the pressure
was taken down to a few millimetres of mercury. The stop-
cock was then closed and the pressure was further reduced
to about a tenth of a millimetre by the Toepler pump. The
exact value of the pressure could be found by the McLeod
gauge,

In order to reduce the pressure of the air in A and B to
about 1/1000 millimetre, the oil was raised in the manometer
so as to stop the connexion between the two sides of the ap-
paratus. The stop-cock S was then opened and the vapour
from B was allowed to pass into A until the surface of the
oil in the tube H, was about fifteen centimetres lower than
the surface in H,. After closing the stopcock the mercury
reservoir was lowered carefully in order to allow the gas on
the left of the manometer to bubble through the oil in the
column H, until the difference in level on the two sides of
the manometer was reduced to about one centimetre. The
mercury reservoir was again raised and the process was re-
peated, until the pressure of the air in A was reduced to the

vin Gases by the Aid of Ultra-Violet Light. 391

desired amount. The sulphuric acid and phosphorus pent-
oxide absorbed the water vapour on the right of the mano-
meter, and the air which was also carried through was
estimated by the McLeod gauge. The air was pumped out
by the. Toepler pump when the pressure exceeded about a
tenth of a millimetre of mercury. It was found that the
air was very rapidly removed from the vessel A by the above
process.

The pressure of the vapour in A was adjusted to any re-
quired value by closing 8, and allowing the excess of vapour
to pass through the oil column in aa The pressure ex-

pressed in millimetres of mercury is +h’, where fh is

is: 56
the height of the column of oil in H, above the column in H,,
and h’ the pressure of the air on the right of the manometer
as found by the McLeod gauge.

It was easy to measure the height # within half a ini:
metre, so that the pressure was tound to a thirtieth of a
millimetre of mereury, which is about the accuracy required
when the pressure of the water vapour was not less than one
millimetre of mercury.

The experiments were made with the pressure below the
maximum pressure at the temperature of the room, so that
the water vapour did not condense and injure the ebonite
insulation in the electrical part of the apparatus.

The condensation on the surface of the glass vessel A and
the tube T gave rise to some inconvenience in adjusting the
pressure. Thus the pressure in A does not attain its final
value immediately after some vapour is admitted from B, or
removed through M. In the former case vapour would con-
dense slowly on the glass, and the pressure would gradually
fall a little for some time after the change in pressure had
been made. The reverse took place after some vapour had
been removed. It was not possible, therefore, to make a
large number of experiments at precisely the same pressure.

The conductivities were measured in the manner described
in the previous paper, and the values found are given in the
following tables. The pressure P is given in millimetres of
mercury, - and the experiments are numbered according to the
pressure at which they were made. The electric force X is
given in volts per centimetre. The corresponding conduc-
tivities tor the different distances between the plates are
given in the columns nj, ns, n3, &e., the suffix denoting the
distance between the plates in millimetres. The ratios of the
conductivities are given in the column R.

2) D-2

392 Prof. Townsend on the Conductivity produced
Taste I.—HCl.

eet -
ie) Sich 1750 | 28°77 | 42:5 | - 1:48 |
fee. | AS 1750 | 56. | 407 | me 7-28 |
aes RS 2 1050 | 82-5 | 565 | 98 2 1°74, 1°73 |
pr ahe.|cbor2 1575-119 18 | 9251] 4 ee04 | ae
(ce | 350 | 82 4) = Sou | 74 | 152,153 |
ete ord 575 | 46 | 187 | 735 <406, 3°94 |
peste bie Sal 706 | 32-3 | 101 | 335 eee 3:14, 3:31 |
Ne es es 2 | 875 | 51:5 | 268 | 1600 -. 52, - Soa
ES eae B50 .| 2a lees. 81 | 220. |. 276, 2570ea
oo .. 302) | S25) 465 | 438 Wao | + | 282, 2°76
omc S02 700 | 765 | 361 |.) See
Go. Vie 350 | 36 153 | 656 | 426,43 |
Gu. 472 525 | 54 | 176 | 590 | ee 326, 335g
Fes lad ber 700 | 80 | 388 | eae 4-85
F val 2°98 350!) 308 At 21eh) ge | 880 | 4-66, 4:83
Wily ENS 525 | 205 | 59 | 176 |:-531 | ...1) 2S
Fo a\-. £98 700 | 266 | 98 | 361 |1570 | _... | Saja
TY OS © 050 S00 eee iy ed | 476
NS. ch) 595 | Sah 29 ‘aya 495 | 404,424 |
ee eee 595 | 525 38 | 217 | |1460 | 57, 673
heey. 595 , 700 | 46-5 | 122 | 350 | | 2-62, 2°86
} 8 | 895 | 1050) GL | deo) | | | 2-95
| | \ }
TasiE [1.—H,O.
| | |
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| ey ade | ».4 2, Ny Nz, | | Ms. -| R |
| —— = = | | es
ae ee ee fw | 56 | 1:10
ey 108 700 | 88 a) F308 ia peers
de 3.1 (91058,5)))-1050°) 168, | S628 eerie est 8 | 3°85
|) Zen] 6S | 350) 535) | 279] 22 .| 114-1 ae
| 2..., 65 | 700} 115 | 313 | 870| ... | | 2:73, 2-78
sre eS) Ul e75.) 166 ONS eee ote 432 |
3...) 336 | 350] 59° |> 2 |-148)> 2. | 302) | © oan eee
31 $42 | 700) 123° | .....| 443). oo oie
4...) 214) 350] 545) ... | 185 |... | 60l.| S300
4} 298 |''700} 99 | 348 | 1200) | [1 | “Sa aee
Bye 2841 9 B7H2)-129) | 155° Le Ee Sees
Ashe O37) |) B25) |, 72°°| USF | 494) seal he eee
5...| 1:08 | 350] 495) ... | 158) ... | 512 | 319,324 |
5...) 113 | 700) 68 | 172 | 427) ... | ... | 253,249 |
5...) 117 | 1050; 87 | 260 | ... A | ay SO eg
| | | So

When the increase in conductivity obtained by separating
the plates is due to the genesis of new ions by the motion of
negative ions through the gas, the theory indicates that the

ratios 2, =, &e., should be equal. In most of the cases

2
given in the above tables this condition is satisfied. When
the value of the electric force X is sufficiently large, other

in Gases by the Aid of Ultra-Violet Light. 393
lonizing actions are called into play as the distance between
the plates increases, so that the ratio . increases as the

d
distance between the plates increases. A few examples of
this are given in the table for hydrochloric acid gas. Thus

in the experiment P=5'1, X=875 the ratio 2 exceeds the
i 2
ratio = by an amount which cannot be attributed to experi-

ey teey
mental error. Another example is to be found when P=-98
and X=700; the ratios 2 and es are equal to one another,

i UD)
and are both less than the ratio -'. I am at present
n

e : 3
engaged in making some further experiments in this direction,
which I hope to have ready soon for publication. —

When the distance between the plates does not exceed a
certain limit, depending on the values of X and P, the ratios

e e,e No Ne e
of the conductivities —“, —, &c. are equal, and the inequa-
fds 4 fs

lities n,<ny <n; &e. can be accurately explained by attributing
the increases in conductivity to the action of the negative
ions alone. All the experiments for any gas can then be

represented by a single curve. The theory shows that =
should be a function of —, « being the number of ions

generated by a single negative ion in travelling through one
centimetre of a gas at pressure p under the electric force X.
The values of « can be found from the experimental results
by substituting the numbers found for n in the formula

. Nes . ° e
— =e! oy — =e**?, The points whose coordinates are

~ and are marked on the accompanying diagrams (figs. 2 & 3,

p
P]..1X,), and it can be seen that a single curve passes through
all the points. This shows that a, X, and p, as determined
experimentally, are connected by an equation of the form

ne =) which affords further confirmation of the theory.

p
: It was found necessary to give each curve in two parts
since the variables extend over such large ranges.

I have already shown how some physical properties of
gases and ions may be deduced from these results, such as
the mean free path of an ion, and an approximate value of
the size of a molecule. The first of these quantities may be

394 Prof. Townsend on the Conductivity produced

found by finding the number of molecules that a single ion
encounters in going through a centimetre of gas at a given
pressure ; this will be the maximum value to which @ ap-
proaches as the electric force increases. A simple investiga-
tion of the curves obtained for ultra-violet light will be
sufficient for this purpose. 3 7

Let an ion be travelling in a gas under an electric force X.
The velocity with which it encounters a molecule depends on
the free path which it traverses previous to the collision.
Let it be supposed that two new ions are formed whenever
the velocity at collision exceeds a certain value, so that an
ion will acquire the requisite velocity under a force X, if it
travels along a path # such that Xx=or>V, where V de-
notes a constant difference of potential. Let the gas be ata
pressure of one millimetre, and let N be the number of en-
counters that an ion makes with molecules of the gas when
it travels through a distance of one centimetre. The mean

free path will be = and the number of paths which exceed

the distance x will be Ne~**. When X2=V new ions will be

produced, so that the number of ions which a single ion

generates in going through one centimetre will be Ne ~* -

This is the value of « corresponding to X when p=1.

Hence the equations of the curves should be of the form
NV |

a=Ne *, where N and V are constants to be determined
by any two points on the curves. This simple formula gives
the values of @ fairly accurately for the larger forces, and
the following tables show how it may be applied to the. gases
which have been examined. :

Thus for air when N=15:2 and V=25 we obtain the
following values of a2 (Table III.). The values of « taken from
the curves (in the former paper) are given in the same table,
the pressure p being one millimetre. |

The values of «# corresponding to the larger forces are thus
seen to agree with the numbers obtained from the simple

NV |
formula N=e X, so that N represents the maximum value
of a, or the number of collisions which an ion makes in going
through one centimetre at one millimetre pressure.

Since the formula is not in agreement with the experi-
mental results for the smaller forces, it is necessary to modify
the original hypothesis in order to obtain an explanation of
the results over the whole range of forces. e

in Gases by the Aid of Ultra- Violet Light. 395
TABLE Hi.

vee N= = 15:2, V=250.

‘ X: “1400, 800. | 600. 400, 200. | 100. | 70.
|

= $a

a obtained four the

"a given by 2nd for-_ heres
or reer | 115 | J |
ae | |

Hydrogen, N=): i V=25 1.

(os)
Or
Na}
by
o
Ss
S
bo
fo

x "1200. 400. | 300. | 200. | 100. | 50. | 30.

a Deeiined from the

curve for Hy...... | 51 | 41 | 86 | 28°] 1-37 '| -36'| -08
ay | | |
pee Wee 2500.10. 50 | 40) 85!) 98! Par] -85' |) -05

Carbonic acid gas. N= 18:9, V=22'9.

Xs, 1200.| 800. | 600. | "400. 300. | 200.| 100.;} 50.

a obtained from the |
eurve for CO,...| 13°38 | 11 9.) 64) £8 ) 2:8 | 82.) 15
|

a=Neo * oo... 182 | 11 | 92 64) 45 | 218] -25 | -003

Hydrochloric acid gas. N=22°2, V=16°5.

Xx. 1500.} 1000.| 700.| 400.| 300. 200. 100.| 70.

eicemined from the - k
curve for HCl... | 17°5 | 15:4 | 13 SO. Ge) | 4515 p12 | -40
Ny a
Xi
apa NiSle 1 see a o's 17°5. | 15:45) 13°23) §9 | 6D | 3:5 “O77 | “12
eT a ee eee abc) ie ge) Leh
Water vapour. N=12°7, V=20.
Heid an Ne marie. aa Lr l
X. 900. ; 500. | 300. | 200. | 100. I GOL
a obtained from the | ; | | |
curve for H,O...| 94 "3 51 So. / LO paoae
PSN |
x | | : =
Ga INGtt oF Nettaceee | 9-4 73 1 So. Bor are

396 Prof. Townsend on the Conductivity produced

It has been assumed that two new ions, one positive and
one negative, are produced by a collision on all occasions
when the velocity of the negative ion exceeds a certain fixed
value. It is probable that there are other circumstances
besides the velocity of the negative ion which determine what
takes place on collision, so that ions may be produced on
some occasions when the negative ion collides with a. mole-
cule with a comparatively small velocity. A comparison
between the numbers obtained experimentally and_ those

NV
given by the formula a=Ne * shows that this is the more
correct explanation. Thus with air it is only the larger
values of a that are accounted for by supposing that the
negative lon requires a velocity corresponding to a fall of
potential of 25 volts. It is evident, from the values of a
obtained experimentally for the smaller forces, that new ions
are produced when the velocity is much smaller than this.
Taking the value 15°2 already obtained for N, we may arrive
at a more correct formula if we include some encounters in
which the velocity is as small as that corresponding to a fall
of potential of about 10 volts. Let C, be the average number
of new ions arising from C collisions, in which the velocity
is intermediate between the velocities corresponding to 10
and 20 volts. Let C, be the number arising from C col-
lisions when the velocities are intermediate between those
corresponding to 20 and 30 volts. It may be supposed that
for voltages above 30 the velocity acquired will be sufficient
to produce new ions at every collision.

The number of collisions, which occur in one centimetre

when the velocity is intermediate between those corresponding
10N 20N

to 10 and 20 volts, is N(e~ ay —< =) On the average

the number of ions arising from these collisions will be

Cie 10N 20N
5 Xp ee Be ):
OC
Hence «a is the sum of three terms
CR ae ss 20N, 20N 30N 30N
1 ——— see 9 Fee c aya ees = — i
a=—-Nie xX —€E x}+eN(¢ xX -—€é x )+Ne nas

The number N has been already found, and it only remains

C C
to deduce — and — from the experiments. It will be found

C C

that the formula gives results in good agreement with those

in Gases by the Aid of Ultra-Violet Light. 397

found for air when

MJ
ear
The numbers corresponding to the various forces are given
in the last line of the above table for air.

In the case of hydrogen the experimental results are fairly
well explained by supposing that ions are produced on some
occasions when the velocity corresponds to about 20 volts.
For the other gases it appears that collisions in which the
velocities correspond to about 5 or 10 volts give rise to new
lons on some occasions.

From this theory it is possible to find only an upper limit
for the energy required to ionize a molecule. An accurate
value of the latter quantity cannot be found from the ex-
periments. ‘There is only a very small probability of a positive
ion producing others by collision when it has the kinetic -
energy acquired in passing between two points differing in
potential by 10 or 20 volts. The positive ions are therefore
not so efficient for generating ions as the negative ions, so
that it is reasonable to suppose that ions may be produced by
other processes, which are more efficient than ihe negative
ions. |

Since I first brought forward evidence to show that ions
are produced by negative ions when their velocity on col-
hision with a molecule is comparatively small, a number of
papers have been published, in which the principle has been
applied to the ordinary continuous discharge in a tube con-
taining gas at a low pressure. In one of his papers on this
subject J. Stark* refers to my work, and states that the
velocities which I gave in my first paper are too small. Ac-
cording to Stark a negative ion must travel between two
points differing in potential by 50 volts, in order to acquire
sufficient velocity to produce new ions on collision, because
there is a fall of potential of 50 volts near the anode when a
ecntinuous discharge takes place in air. Evenif it be granted
that the fall of potential at the electrode is to be explained by
this property of a moving negative ion, the phenomenon gives
no reason for supposing that new ions are not generated by
collision when the velocity of the negative ion is less than
that corresponding to 50 volts. |

The lengths of the mean free paths, in centimetres, of a
negative ion travelling in a gas at one millimetre pressure is
given in the following table. The mean free paths are the
reciprocal of the above values of N.

* J. Stark, Annalen der Physik, 1902, Band vii. p. 487.

349, and N=15'2.

398 ~~ Mr. 8. W. J. Smith on a

If it be supposed that a collision occurs between a negative
ion anda molecule, when the ion approaches within a distance
R of the centre of ‘the molecule, then R is determined by the
equation 7R?n=N, where x = the number of molecules
per c.c. of a gas at a millimetre pressure. The following

values of 10° x R in centimetres were found, taking n equal
to 2x 10°—760.

The radius S of the sphere of action deduced from: ex-
periments on viscosity is given in the third line of the table.
‘The values were obtained from the numbers for 7S?No given
by Meyer (Meyer, ‘ Kinetic Theory of Gases,’ p. 300), Ny the
number of sprees in a c.c. of. gas at 760 mm. pressure
being taken equal to 2x10'* as in the above calculation

for R.

Airs de Hie | Os:

HCl. | HO. |
| Mean free path | | | a)
| 1 066 “182 053. | = -045 ‘079
N | |
108xR ~ | 136 | “82 -1.1-62 164 | 194
10°xS 172 |1:296 |207 | 200 — | 1-99

| | |
J = Sis s eal

The quantity 2S is the smallest distance between the centres
of two molecules during a collision, and is not the same as
2R. The latter quantity 1 is deduced from the maximum value
of a, so that in this case we are considering collisions which
would give rise to new ions if the negative ion were travelling
with a certain velocity. It appears from the above numbers
that a negative ion may pass inside the sphere of action of a
molecule with a ee re without producing new ions.

XXXIX. A Portable Capillary Llectrometer. ee . :W...oB

SmitH, 1.A., Demonstrator in Physics, Royal College of
Science, Tiondan®
[Plate X.]

HIS instrument is a modification of the form of capillary
electrometer represented in the first figure, and con-
sisting of two wide tubes joined across bya capillary tube
which is cylindrical, and may be horizontal or may slope up-
wards at any angle from} towardsa. The apparatus contains
mercury and sulphuric acid of about maximum conductivity
distributed roughly as shown. A spring-key, like that repre-

* Communicated by the Physical Society: read December 12, 1902.

Portable Capillary Electrometer. 399

sented in the figure, 1s commonly used with the instrument,
and keeps the platinum terminals P; and P, at the same
potential unless the lever S is depressed. When the lever

Fig. 1. | Fig. 2.

Uy
4

B/,

CL Lh highidka
DORR I

y 75%
peeseees
RK

i agreed the potentials of the terminals become EH, and
E., which may, for example, be the potentials of two points
in a potentiometer circuit. It is the function of the instru-
ment to determine whether these potentials are the same or
different.

The nature of the modifications made in the present electro-
meter is shown in the second figure.

a prevent evaporation of the sulphuric acid solution,
without preventing free motion of the liquids within the
apparatus, the wide tubes are closed at the top; but are
Jones oe by another tube opening into them as shown.

1 ‘i ts arrangement the apparatus is made air-tight, and
can, if desired, be made air-free by exhaustion of the appa-
au before sealing. It is obvious also that the apparatus
can be upset without spilling of the liquid. The two limbs

400 Mr. S. W. J. Smith on a

are of equal size, and the capillary passes from the middle of:
one to the middle of the other. The apparatus contains:
approximately enough mercury to completely fill one limb,
and about half as much sulphuric acid solution. By suitably
adjusting the distribution of the mercury and the solution in
the two “limbs, the apparatus can be arranged for use with
the capillary tube either horizontal or tilted upwards at a
considerable angle. The maximum angle of tilt available is
increased by increasing the lengths of the limbs in com-
parison with the length of the capillary. it is easy to
construct an electrometer which can be used with the capillary
at almost any inclination between horizontal and vertical.

The distribution of the mercury can be altered most easily
by means of a cross-piece provided with a tap, as represented
in the figure by dotted lines. When the tap is open there
is free communication between the mercury in the two limbs,
and the relative amount in each can be altered by tilting
the apparatus. When the tap is closed the two quantities of
mercury are insulated from each other. The addition of this
arrangement tends to complicate the construction of the
instrument, and, although it is very convenient in practice,
it is not indispensable. Any desired changes in the distribu-
tion of the mercury and the solution can usually be effected
without much trouble, by means of the capillary and the
upper cross-tube.

To prevent the platinum wires forming the electrodes being
wetted by the acid solution, if the apparatus should acci-
dentally, or during transit, be laid on its side or turned up-
side down, the lower ends of the tubes may be drawn out,
as shown at P,’ and P,’ in the second figure, and slightly
constricted ae the ends of the platinum terminals. This
precaution may be dispensed with if the electrodes are formed
by welding pieces of platinum foil, which are afterwards
amalgamated, on to the ends of tne wires P, and P,. The
apparatus can then be turned upside down and shaken, so.
that the amalgamated foil becomes wetted by the acid, with-’
out any further ill-effect being produced than an ccenmineel
slight wandering of the zero of the instrument for a short
time after it is righted again.

The usual spring-key has several disadvantages. Thus, if
it is made of brass, the contacts frequently become unsatis-
factory through surface tarnishing, and if, to avoid this, the:
bearing surfaces are made of platinum the key sometimes
shows ‘pronounced thermoelectric effects. Further—and this
is a point of some importance in a portable instrument—the
key cannot conveniently be fastened on to the same stand as

Portable ‘Capillary Electrometer. AQ1

the rest of the instrument, for, unless the stand and the
support on which it rests are very rigid, the pressure
necessary to depress the spring produces sufficient movement
of the meniscus, by change in the inclination of the capillary
tube during the act of depression, to render the detection of
minute changes of surface-tension impossible.

The mercury-key, represented in the second figure, is
free from these disadvantages. It consists, as shown, of a
U-tube closed at one end and communicating at the other
with a pneumatic-pressure ball and containing mereury in
the bend. Three platinum wires are fused into the tube and
connected as shown. It is obvious that the same change of
contacts is produced by squeezing the ball B, as by depressing
the lever 8 in the spring-key. The mercury in this key
takes the place of the lever in the spring-key, and the two
different contacts between it and KH, and Ii, respectively are
here quite definite and practically independent of the amount
of pressure exerted upon the ball B. I[further, the contacts
are not exposed directly to the laboratory atmosphere. The
thermoelectric effects are very small since the changing con-
tacts take place between platinum and mercury which are
almost identical thermoelectrically. The warmth communi-
cated to the key from the hand of the operator can be
neglected, and the heat produced by the compression of the.
air in the key need only be very small. The key can be
fixed to the same stand as the rest of the apparatus, for even
if the pressure which changes the contacts is applied as
suddenly as possible the maximum vertical pressure upon the
stand is only a few grams, whereas in the case of the ordinary
spring-key it may be 500 grams or more.

By adjusting the length of the mercury column in the key
so that it is only slightly less than the length of the U-tube
between the two extreme platinum wires, the change of
potential at P, from HE, to EH, and conversely, can be made
almost instantaneously. Hence measurements can be made
with the instrument even if the zero is altering fairly rapidly.
With a key of this kind it is also obvious that the observa-
tion of the meniscus through the microscope can receive a
very near approach to undivided attention.

Commutatorsand keys which make a set of connexions in
a prescribed order can be constructed on the same principle
as the pneumatic key above described. The third figure (p. 402)
represents a combined commutator and electrometer key:

The U-tube to the left is the key already described, and the
double U-tube to the right is the commutator. The positions
of the different wires are so arranged with respect to the

402 Mr. 8S. W. J. Smith on a

levels of the mercury, that it requires greater pressure to
change the contacts in the double U-tube, than in the tube to
the left. The first effect of
pressure is to throw the electro-
meter into the potentiometer
or other circuit, connecting P,
with H, and P, with E,. On
increasing the pressure, the con-
nexions in the double U-tube
are reversed and FP, is con-
nected with E, and P, with
E,. Hence, when the contacts
change in the commutator, we
get a motion of the electrometer
meniscus corresponding to ap-
proximately twice.the difference
of potential between EH, and
E,, and so, in this way, the
sensitiveness of the instrument
is doubled.

While it is clear that to get
the minimum thermoelectric
effect in mercury-platinum keys,
it would be necessary to use a
method of changing the con-
tacts in which compression of E, E,
air in the key does not take place, yet the thermoelectric
electromotive forces which occur in the pneumatic keys
described are much too small to produce an observable effect
upon the readings of the most. sensitive capillary electro-
meter*.

The sensitiveness of the electrometer, using the simple key
first described, is such that when the diameter of the wide
tubes is about 1 cm. and the diameter of the capillary is
about 1 mm.,a movement of the meniscus perceptible with
certainty in a microscope magnifying 100 times is produced
by a potential-difference equal to ‘0001 volt. The actual
extent of the movement is somewhat variable, and amounts
usually to about ‘01 mm. The following numbers, obtained
with apparatus previously described (Phil. Trans. A. 1899,
vol. excill. p. 63), show the effect of comparatively large

Wels
Hier 3.

* Since this paper was read I have found that mercury keys (similar
in principle to those referred to above) in which the thermoelectric
effects are reduced to a minimum are described by Kamerlingh Onnes,
Leyden Communications, No. 27, p. 31, 1896.

_ Portable Capillary Electrometer. 403

polarizing electromotive forces upon the surface-tension be-
tween mercury and sulphuric acid solution of density 1:17 :—

EMF. Volts. Surface-Tension.
0) Y
00-0202 L021 ¥ |
0-0404 1-040 y |
0-0605 1-059 ¥
0-0807 1-080 y
01009 1-097 y

y is the “ naturai” surface-tension between the mercury and
the solution. Its approximate value is 300 ergs per sq. cm.
Judging from these numbers, it would seem that the surface-
tension is altered by about one part in 10,000 by a polarizing
E.M.F. of -0001 volt. In the case in which the capillary-
tube is horizontal and the wide tubes are vertical, the relation
between the motion of the meniscus dz and the corresponding
change in surface-tension dy is expressed approximately by
ap g 6x = Ac by

if we assume that the capillary and wide tubes are of uniform
cross-section—a being the area of cross-section of the capil-
lary, ¢ its circumference, A the area of cross-section of the
wide tubes, and p the sum of the densities of the mercury
and the solution. From this formula it would appear possible
to produce a much larger movement of the meniscus than
‘01 mm. by means of a potential-difference of ‘0001 volt by
using a very narrow capillary, especially if the cross-
section of the capillary were elliptical instead of circular.
It is found in practice, however, that the motion of the
meniscus under minute polarizing forces is controlled very
largely by stickiness and accompanying changes in the
angle of contact between the liquids and the glass, and
by variation in the cross-section of the tube at the place
where the meniscus rests. The sensitiveness of the instru-
ment to small electromotive forces is practically as great
when the diameter of the capillary is 1 mm. as when it is
very much less. A very narrow capillary is less easy to
manipulate than a comparatively wide one (about 1 mm. in
diameter) and is only advantageous when it is desirable that
the capacity of the instrument should be as small as possible,
or that its action should be as rapid as possible. In the latter
case the length of the capillary should also be small.

If the capillary-tube, instead of being horizontal, is inclined
at an angle @ to the horizontal, the equation given above
becomes

ag{(pr+p2)a/A . cos 8+ (p;—pz) sin 0} d2=c dy,
in which p, is the density of the mercury, and p, that of the

404 A Portable Capillary Electrometer.

solution. From this equation it follows: (1) that if @ is posi-
tive (mercury thread sloping upwards towards the meniscus)
the sensitiveness is not increased appreciably by making A
very large in comparison with a, unless @ is very small ; and
(2) that if @ is negative (meniscus at lowest part of thread)
the mercury becomes unstable when @ is numerically greater
than tan! (p; + ps)a/(p,;—p2)A, 2. e. when @ is numerically
greater than a/A approximately, since in order that the
polarization may be practically confined to the capillary
electrode, the ratio a/A must be small. It also follows
that if it were proposed to design an instrument which should
have the utmost sensitiveness possible, attention would have
to be paid to the straightness of the capillary as well as to
the uniformity of its cross-section. It is not necessary,
however, to take the precautions here indicated in order to
obtain the sensitiveness already quoted ; it may be obtained
with almost any capillary-tube chosen at random, and with
@ having such a positive value that the restoring force for a
small displacement is considerable enough to render the
instrument easy to work with.

_ The sensitiveness of ‘0001 volt, which is obtainable with-
out any difficulty if the mercury is clean, is sufficient for a
great many measurements in which the electrometer can be
employed, and for these the electrometer (which for the pur-
pose in question is really a surface-tension galvanometer) is
more convenient than an ordinary galvanometer with a sus-
pended magnetic system. The electrometer is much more
easily set up than an ordinary galvanometer. ‘There is no
suspension, no lamp and scale, and, practically, no levelling ;
but it is advisable when working with the instrument that
the potential of E, should never be more than a few tenths
of a volt less, or more than about a volt greater, than the
potential of H,. These conditions of working are, in general,
not difficult to satisfy. If the potential-ditterences applied
exceed either of the limits above mentioned, it is sometimes
necessary to run some of the mercury through the capillary
tube in order to get the instrument again into its best working
order. The capillary electrometer is already used almost
universally in physico-chemical laboratories, and the modi-
fications herein suggested may, perhaps, have the effect of
slightly extending the sphere of its usefulness. The accom-
panying Plate X., taken from a photograph, represents one
form of the instrument described. Its size is about two-fifths of
that of the actualinstrument. The arrangement of the different
parts will be obvious from the description already given.
The illumination of the end of the mercury-thread is effected
by means of a concave mirror attached to the base of the
instrument.

[ 405 J

XL. On the Connevion between Freezing-points, Boiling-
points, and Solubilities. By Meyer WILpDERMAN, PA.D.,
.S¢..( Oxon.) *.

i Comptes Rendus, xx. p. 1349 (1890), Guldberg gave
the connexion between the lowering of freezing-point
and lowering of vapour-pressure of solutions. In a similar
manner van’t Hoff and Roozeboom connected two vapour-
pressure curves meeting at one common point (the point of
transition), belonging to two hydrates of the same salt, or to the
same substance in two different allotropic states, &c. (see van’t
Hoff’s Studien zur chemischen Dynamik, translated by Ernst
Cohen, pp. 235, 247, also 226). In this paper the connexion
between the freezing-point, boiling-point, and solubility curves
will be considered.
Le Chatelier and van’t Hoff have deduced the following
thermodynamic equations for the solubility curve, which are
analogous to those of Clausius for the vapour-pressure curve:—

Ee Ge as ; ,
TW Br? where p is the concentration, T the absolute

q . = e dlo 4 (é
temperature, g the heat of solution (Le Chatelier) ; eal = ne
; 52
where p is the osmotic pressure of the solution (van’t Hoff).
Taking into further account the connexion between the con-
centration of the solution, C, and its osmotic pressure, p, we

eale,C ¢ et GAO eG)
get ae = ye for non-electrolytes, and Wy oP for

electrolytes, (A), where g is not independent of tem-
perature ; putting g=q,+al, the above equations assume
the form

den gt+al dlg,C _ g+aT

Oe hy aes oPOwN STL
The considerations involved in the deduction of the above
equations show that they will, as a general rule, apply best
to dilute solutions, 7. ¢., of substances of small solubility, and
that they will require some modification when we pass to the
consideration of substances of greater solubility. Van’t
Hoff t, in his illustration of the fact that d calculated and
observed gives satisfactory confirmation of his equation,
selected for this reason a number of substances of small
solubility and temperatures where the solubility was the
least. Le Chatelier further showed that from a consideration

* Communicated by the Author.
Q? . we . =
T Studien zur chemischen Dynamik, p. 215.

Phil. Mag. 8. 6. Vol. 5. No. 28. April 1903. , 2 E

406 Dr. Meyer Wilderman on the Connexion between

ot equation (A) it follows that the solubility curves should

be of the form shown in fig. 1; 7. e., the curve must. first

temperatur z asymptotically to

the abscissa of temperatures, 7 eo ae

(z), reach a maximum (8), r

then again decrease, having

temperatures again asymptotically the abscissa. The solu-

bility curve sone thus decrease above and below the tempe-
In the next place we have from van’t Hoff’s thermo-

dynamic deductions the following relations for the /freezeng-

increase, starting at the lower Rie

then have a point of inflexion

then another point of inflexion (y), approaching at higher
rature belonging to £.

point curve, where the solidified solvent and the solutions of

‘ : : a eae T,—T)N.
different concentrations are in equilibrium, oe = ) -
(T.—T)NA , 21,
for non-electrolytes, and n= 3772 for electrolytes,
+0

where x is the number of molecules dissolved, N the number
of molecules of the solvent, X the latent heat of melting,
which is also a function of temperature. TT, is the freezing-
point of the pure solvent, T is the freezin g-point of the
given solution. This law, which holds good strictly for
dilute solutions, becomes for several reasons more complicated
in the case of more concentrated solutions. But even in
very_ concentrated solutions, so far as experience goes, the
greater the concentration of the solution, the lower is its
freezing-temperature.

In the third place we have to consider the botling-point curve,
where the solvent or solutions and their vapour are in equili-
brium. Attention should again be restricted to solutions of
non-volatile substances. Here we have the followi ing thermo-
dynamic relations existing between the concentrations of the
solutions, and the rise of boiling-point, analogous to that for

—= / Vi
freezing-point (Arrhenius) »= (I—T,) Nl

T—T,)N. 2ITy”
( 5 a7 7s tor electrolytes, where T)’ is the boiling-

fornon-electrolytes

and n=

point of the pure solvent, J is the latent heat of evaporation,
which is also a function of temperature. This equation holds
good tor dilute solutions, and becomes more complicated for
more concentrated solutions. But in case of non-volatile sub-
stances in solution, even for the most concentrated solutions,
the greater the concentration of the solution the higher is ie
boiling-point.

Freezing-points, Boiling-points, and Solubihties, 407

Since the solubility (or the concentrations of the eee
substance) decreases above and below Tg, at B, where =)
on the one hand, and on the other hand on the freezing-pornt
curve the concentrations always increase with the decrease of T,
and on the boiling-point curve the concentrations always in-
crease with the increase of T, we have the general result for all
non-volatile substances that the solubility and the freezing-point
curves as well as the solubility and the boiling-point curves must
always cut each other.

Fig. 2 gives an illustration of this. At the point T,, which
is common to the solubility and freezing-point curves, the

Fig. 2.

C(ConcewTR,) Ay

T ( TEMPERATURES)
ICE PURE WATER ‘
OA BSOLUTE To To

dissolved substance in its solid state, the solid solvent, the
saturated solution (and vapour) are in equilibrium. At
the point T,,,, where the solubility and boiling-point curves
intersect, the dissolved substance in its solid state, the saturated
solution and its vapour are in equilibrium. Ports T, and
T,, are the freezing-point and boiling-point of the saturated
solution in the presence of an excess of the dissolved substance
in the solid state, and are as characteristic as the freezing-
point and boiling-point of the pure solvent. The points T, and
T,,, are the only points where the concentration of the
solubility and of the freezing-point curves as well as the
concentration of the solubility and of the boiling-point curves
are the same.

It is evident that, once having the points T, and T,,,, we
can connect with each other the concentrations of the solu-
bility, freezing-point and boiling-point curves, the latent

2K 2

408 Dr. Meyer Wilderman on the Connexion between

heat of melting, latent heat of solution, latent heat of
evaporation, &c., and calculate, e. g., solubilities from freezing-
points or boiling-points, &c. I shall now proceed to do this
in a few cases under the assumption that q, \, / do not vary
with temperature, which, however, is never quite the case.
I choose for this purpose boric acid and chlorate of potassium,
for which the values of g prove to change little with tem-
perature. It is evident that better results would be obtained
if the variation of g, /, \ with temperature were taken into
account in the calculation of the same. Hox

From the equation of the solubility curve nt = mis and
TPE = ap we set for the temperature T, (where the solu-

bility and freezing-point curves cut each other) and any

WC i 7) gee.
other temperature T the equation lg G = 3% 9-302 a( Ty )

Ti.
Laan ibe al —g (hog
for non-electrolytes (I.) and IgG = OxExI9-B026 (a 7)
for electrolytes (I.’) (van’t Hoff’s law).

In case of electrolytes we shall assume that 7 remains the
same for all concentrations and all temperatures, taking for
the same the average of z at T, and T. In reality this is
never the case, but as the values of 2 vary in more con-
centrated solutions only little, and, as far as experiment goes,
also not much with the temperature, we may make here this
assumption for the sake of simplifying the calculation.

In Table I. are given the solubilities, freezing-points,
and boiling-points observed by Arrhenius, Raoult, Beckmann,
Gerlach ; van’t Hoff’s 7’s, as obtained from freezing-
points and electrical conductivity ; T, and T,,, the points of
intersection of the freezing-point and solubility curve, as well
as of the solubility and boiling-point curves, as found by
myself or other observers.

In Table II. the values of g are calculated for boric acid
(non-electrolyte) and for ClO3K (electrolyte) through the
whole length of the solubility curve under the assumption
that g does not change, or only very little, with temperature.
This is pretty well the case with boric acid, and is less the
case with potassium chlorate ; the values of g for ClO;K con-
tinuously diminishing with temperature. The value of g cale.
falls for potassium chlorate between 0° and 100° from 10°49 to
9°4, if the total region from 0° to T° is taken. This drop in
the values is naturally still greater when small intervals are
successively taken. At higher temperatures the drop in the

409

ities.

ts, and Solub

ing-pon

ts, Bo

—puin

ing

~
~

Free:

Borie Acid, B(OH).

Temp.
Ge

Solubility.
Grams
substance
per 100
grams of

water.

1:9(5)t

2-9

4-0

7-0

98
11-0

16°8
340

—- | —— S- — —___—__—.

100°185
100°380

* Arrhenius.

Preez.-pt.
Grams
substance t.
per 100 | Freezing-
grams of | points.
water.
1-706% 1:02
1-024 1:02
0-41 1:02
Grams is
substance.) Boiling-
Boiling-pt.| point.
2°38 1:079
4°88 . 1:077
7:42 1-057
12°19 1-043
17°27 1:042
t Gorlach,

le
Solubility.

1 to 1°02

{ E, Beckmann.

Potassium Chlorate, C1O;K.

Solubility. | Kreez.-pt.
Grams Grams |
Temp. | substance | substance i. i. A ane
t. per 100 per 100 | Freezing- | Solubility. ,,,.
gramsof | grams of points.
water, water.
O
—0:408 1-532 1:465
—0:2079 0-766 1-798 V=2Zie
—0°'1058 0380 1831 - 0°797§
—0:05371 0:1915 1-859
0 a3t | (1°70)
10 Ls - LT =278 |
20 72 (1:66) —( 797
30 sr :
40 14-4 (1:62)
50 19°5 (1:62
60 aes | 99
70 32'0 I> “C60)
80 39:0 | (1°59) AD 4 ia
90 waa | a +105°
100, 56°0 | (1°54)
Grams is
substance. | Boiling- |
Boiling pt.| point. |
100'5 6°5 || L8iZT |
101-0 13°2 1-786 | 0a et
101°5 . 20:2 1-751 +273°
1020 27°8 1:696
102°5 39'8 1-647
103:0 44-6 1586
§ My own observations, || Landolt’s Tables.

410 Dr. Meyer Wilderman on the Conneaion between

TABLE II.
Boric Acid, B(OH); :—
View.
Between 1000
on _ 2X 273X283 x 23026 | ZA 6-1
O>andlO? i597: — i0 1-95
2 x 273 X 293 x 2°3026 , 40 =.
fe} DOC - — =
0° and 20°: 4g oi lg E05 SS7/
2X 273 x 313 x 2°3026 , 7:0 x ae:
Os — =— 5! =:
0° and 40°: g 40 ] 195 5 1000
} BR ste ee s instead of 5:4 obs.
Oandn0o: ig — 2X 278X323 X2'3026 ),98 _ 5°7 (Julius Thomsen).
50 1:95
2x 273 X 333 X 2°3026 ,_ 11:0
2) a = 1 a my 54
0° and 60°: ¢ 60 g 1-96
2x 273 x 353 x 2°3026 ,_16°8 x
io} QO. = sat eye 2
()°randes0? = 9 20 Ig 5-95 5)
2X 273 X 373 X 23026 | _ 34-0
Oia Cx = lg. = 58
0° and 100°: ¢ 100 e 7-95 5
Potassium Chlorate, ClO;K :—
a
Betweer. 1000
€ e 9: € 92
0° and 20°: pee 3026 le 7 = 10-49
20 3:3
an 2-209 : .
O° and 40°: q= 2x1 66 X 273 x 3138 x 2°3026 lg 14-4 = 1045 instead of
40 33 Fis
| 0° and 50°: g —2X 166X273 323 x23026 1,195 _ ing Pie
5 ge 50 eae (Julius
Thomsen
941-RR -2N9e ; ’
OPand 709% ¢ = 2% 1°65 x 273 x 343 x 2°3026 12220 = 1003 Thermo-
70 33 chemie Un-
DY RAR VON: >: ae tersuch ung,
0° and 80°: g —2X 1645278353 2'3026 | 39:0 _ 9.79 “val. tid)
80 33
2X 1°62 x 278 x 373 x 2°3026 , 56-0
° Oke ye a, :
0° and 100°: g a a aaa Ig == 9°4

Van't Hoff’s Equations for Solubility -—
si y

digC_ sg

VES 2r

ETON g

aT 21"

(Borie acid).

(C10,K).

Freezing-points, Boiling-points, and Solubilities. 411

values of g seems to be much greater than at lower tempera-
tures. This may be due not so much to the fact that y
actually decreases with the rise of temperature to such an
extent, as to the difficulty of getting reliable data for the
solubility curve, especially at too high temperatures”.
Indeed, from the run of the existing solubility and boiling-
point curves of ClO;K it appears that the curves cut each
other at T,,,=103°8, but in reality mach higher concentra-
tions than that belonging to 103°°8 have been observed for
the boiling-point curve. When the value of T,, is found
quite independently, namely, by a determination of the point
where the saturated solution boils in the presence of an excess
of salt, it at once becomes evident that the solubilities as
found by the present methods give, especially at higher tem-
peratures, too low values. This point T,,, is found to be for
C1O3K at 105° (Gerlach), not at 103°°8.

Again, from the equation for the freezing-point curve
C= (To —T)N.r.m (T)—T)N.l.m

De c ile

(electrolytes) we get for the temperature T, (point of cutting of
the solubility and freezing-point curves) and any temperature
T”, if we assume that ) remains the same for all temperatures,
2) 2 ee for non-electrolytes) (II.) and ee
opat—T, TS SOPRA O Ny =)
(for electrolytes) (II.’).

Connecting (I.) and (I1.), and (I’.) and (II.’), we get :--

(non-electrolytes) and C’/=

Bese) Was fel be \ ol toe Re
EO iempann too D026 \lisolk, |, y= = 1,

(for non-electrolytes) (A), and

C sol. — 1 if (T.—T”)2
Joni Tots = f ( pus ed, PEAT Ty Seiad REAL
8 (Orsi e <2 <9°3026\T sol. ve Ig (T)—T,)? (as):

Here van’t Hoff’s 7, belongs to T,, 7” to T’. These equa-
tions give the connexion between the concentration of the
freezing-point curve, taken at any temperature T”, the concentra-
teon of the solubility curve at any other temperature, the heat of
solution g, which we here assume to remain constant, and the
temperature T,, which ts the point of cutting of the solubility
and of the freezing-point curve, the concentration at T, remain-
ang unknown. T, is found experimentally when we start
with an oversaturated solution, cool it in the presence of

* See my paper “ On Real and Apparent Freezing-points, Solubilities,
&c.,” Phil. Mag. xly. p. 204 (1898) and August 1902, p. 270.

412 Dr. Meyer Wilderman on the Conneaion between

the dissolved solid, continuously stirring the solution and
separating the dissolved substance during this. .The
cooling and stirring are continued until, in the presence
of an ice-crystal, the saturated solution begins to separate
ice. The ice is then melted and the experiment repeated
more carefully, the point of the first formation of ice being
carefully w watched.

In the case of electrolytes the value of 2, belonging to T, ought
to be known, but it can, for our purpose, be assumed to be equal
to (2) at any other point on the freezing-point curve not very far
removed from T,. For non-electrolytes, where the laws of os-
motic pressure dir ectly hold good. the molecular fr eezing-point
depression is, for one and the same solvent, the same for all

feel atin

dissolved substances, 7. e. —"——— o1 T,— 7 is constant, and
(C) =

T. a se 7 for water, M being the molecular weight of

the dissolved substance, therefore for any le (C) —lg (Ty>—T”)

and we get instead of (A) :

i
18-7

—¢ IL eeeal
2 x 23026\T ip )+ Ia ( nae as

tor all non-electrolytes in water, Wc.

Thus it is enough, in the case of non-electrolytes, to know the
temperature (I',) at which the saturated solution of the substance
freezes in the presence of an eacess of the same, and the heat of
solution of the substance in the given solvent (q), to be able to
calculate its whole solubility curve. In case of electrolytes the
additional knowledge of van’t Hoff’s 1 ts necessary.

In Table IIT. the solubilities are calculated from freezing-
points for boric acid (non-electrolyte) and potassium chlorate
(electrolyte). For boric acid the results are also given,

when le a4 instead of the observed lg(C)—lg(T)—T”) is

taken. Considering that the values of g and ) were assumed
to be independent of temperature, and that the solubilities at
higher temperatures are for reasons indicated before not very
correct, the obtained results are certainly as good as we could
possibly expect them to be.

Again, from the equation for the boiling-point curve:

, (T—Ty’) N.dm (T—T)’)N.l.m

=~ oT for non-electrolytes and C= 27,2

for electrolytes, we get for the point of cutting T,,, and any
other temperature q between Ty’ and T, if we assume that

we may put a constant le

low » (A")

Baa

///?

Freezing-points, Boiling-points, and Solubilities. 413
TasuE IL1.—Solubilities calculated from Freezing-points
M
and g, T,, or from q, 87 iis

Boric Acid, B(OH)s.

(4’)

(4) (C) sol.
< Ig (C) soi. =

& Ciep. ~

|
VW | M
Bs g ih 1 dh fr.p.—To qd i es alti, ae pasifus

2X 23026 & m3 a) LS it ats 33-3006, x) Hg(T, —T) 41g 1-37

5400 x 0:585 0318 | M 62

= pe ieee 9. A

Ig Co= 90973 272-415 x 23026 —/8 0-585. isteqes Tae

+lg 1:024 |
Between Calc. Obs. | Calculated. Observed.

—0'585 and 0°: Co = 1:92 instead of 1: Co = 1:98 instead of 1°9
eo = Cio = 2°79 a 2°9 | Cio = 2°81 5 29
eee 0 - C29 —' 386 a 4-0 C29 = 3°89 oh 4:0

Pe eO0e: Cig = 695 a 70 Cap = 701 ~p 70
Peeeeo0>-. C50 — 9:09 BS 9°8 C50 = 9:16 +5 9°8
eee c0-: Ceo = 18:04 GS Cs0 =18'63 p: 16°8

Pee eos: Cioo=27'°8 A ot! Ci00=28 03 ve 340!

Potassium Chlorate, ClO3K.

(C) sol. _ q aad (T''frp. To) 4,
cB) le Oirip< = 7 2xcix ea: = aa —'s tT)
10000 x 0-797 0-408 x 1:70
o —— BSS ES : == | O° —— == o 15 y
18 Co= 2X 1-70x 272-203 x 278 x 23026 180797 x 1-765 +18 18
Calculated. Observed.
Between —O0°797 and 0°: Cy = 3°21 instead of 3:3
” ” 202 : C20 == (GD! a6 TZ
” ” AOS: C40 == | PLY 99 14°4

” 1 50° : C50 =17-°01 ” 19°5
” ” 70°: C70 =28:°90 ” 320
99 ” 80° 5 Cso =36°85 + 39°0
” ” 100° : Ci00=57'61 ” 560
If 2, is assumed to remain, as at 0° for solubility, =1-70 for all temperatures.

Calculated. Observed.
(B') Co = 3°21 instead of ‘3
C29 = 6°63 f 72
Cao = 15:23 3 14-4
C50 = Id-14 Ke 19°5
C7o = 31°84 ai 32'0
Cge = 41°35 . 39:0
Cioo= 69°85 “ 56-0 !!

If 7, is taken as the average of the zs belonging to the two limits of tempe-
rature (i.¢. to T, and to 0°, 20°, 40°, 50°, 70°, 80°, 100°). After (C)sol. is
calculated by the formula B, the (C)sol. are very approximately known, and
the zs belonging to the (C) sol. at the given temperature can be well estimated,
when the ?’s obtained from freezing-points and boiling-points are known. In
this way the results obtained for the solubilities become more accurate.

414 Dr. Meyer Wilderman on the Connexion between

om Ty aes for

/ does not change with venice that ~~—- ci = oy

ay
44 for electro-

OO ee Ci)

(Cra i ( Mil Se .
lytes (ILI.’). For the solubility curve we shall have for the

/d/

non-electrolytes (III.), and

same T’,, ah any other temperature between T,,, and T,,
Oe + =U, fe l ) ; Rp

lo (C) = 2xP3006 TT, for non-electrolytes (1.)

Sage es aie I /

and lg oe Can sable = for electrolytes (1.’).

Assuming that 7 does not change for concentrated or satu-
rated solutions, and that g does not change with tempena
we get
C sol. —y¥ ( iL ) T’—T,’
ls (C)bp. ~ 2xzs00\T—T,)— Sa sty? ©

tor non-electrolytes, and

oO Csol. — =u. 1 = =) te: te

(Vos: 2 x 273026 X7,, (i a (T,—To 2”
for electrolytes (B’).

This equation gives the connexion between solubility at any
temperature T, the boiling-point at any tenperature TL”, the
latent heat of solution q. and the temperature T,,, which ts the
point where the solubility and the boiling-point curves cut each
other, the concentration at T,, remaining unknown.

In the case of non- electrolytes, since the molecular rise of
the boiling-point is the same for all substances when the

same solvent is used, lg (C”)—lg(T’— —T)))=le 55 for

water, i.e. we are able to calculate the whole scabies
curve, if T,,, and g are known, using the equation

///

z rs a¥.
rT) +lg ae ) +lg x

HOS O30) (By:

Dix 2 Sas
In case of electrolytes the sdditional knowledge of van’t
Hoff’s 2 is necessary.

In Table IV. the solubilities are calculated from boiling-
points for boric acid and ClO;K: in the first case lg =
instead of the observed lg(C”)—lg (T’ —Ty’) is used. Con-
sidering that the values of g and / were assumed to be
independent of temperature, and that the solubilities at
higher temperatures are not very easily correctly determined,

Freezing-points, Boiling-points, and Solubilities. 415
Taste 1V.—Solubilities calculated from Boiling-points
and q, T,,,,0r from q, Ss le
Borne Acid, B(OH)s.
a3 7 UES |(4’)

(C,,)b.p. — lg C sol. =

pee 5s 7) dee ie 1 - M
22-3026 \T, ~ T,, len ay Fa T, — py Fle Ly. To) +18 Fo

1 3400 x 2°3 Ls 0:98 io ae
8 0100 = 9373x3753 X23026 — 18 23 85g = 859
+ lg 12°19
Between Calc. Obs. Calculated. Observed.
102°°3 and 100° : C100=27°34 instead of 34! C1900 =26:23 instead of 34!
4 Pecos: Oso =18:16 LOS) Cs9 =17°41 - 16°8
29 ” GO: Céo ea LI 38 ” 11-0 C60 =10°90 5 11:0
i Pera> 2 C50 =" 8:93 3 9°8 C59 = 85h ti 9°8
”? ” 40°: C4so = 684 9 70 C40 = 6:95 ” 70
Es Pee = C20 =. oto ‘A 4-0 Beo = 3:64 y £0
i FOS S'Cio = 3°05 as 2°9 Cio = 2°92 - 2:9
a Pee Co, = 1-9 - Ale) Cor =e-83 + sige)
eon Chlorate, ClO3K.
C sol. = Gio? iM
@ "ep = 3G, x20 (x, - --) 7 8 @ ts,
— 10000 x 5:0 0-5 x 1°53 ie
Ig C100= 95.753 873x378 23026 ~ B5-0x1:812 + 16 65
Calculated. Observed.
Between 105° and 100° : C1io0=68'48 instead of 56:0!
Re 80°: Cs0 =41-68 i 39:0
* 702 (C70 =31-82 oy 32:0
vA 50°: C50 =17°15 S, 19:5
ks 40°: Cao =12°78 4 14:4
* 20°: C20 = 6:26 x 72
” 0°: Co = ATE 2 33

(T"—T,)')=0°°5. (C,,) b.p.=6° 5. ole
If 2 s0l.=1°53, 2. e. taken as a constant for the whole solubility curve
and = toz,,, at 105°.
T,,, = 105° +-273°.

Calculated. ; Observed.
(B') Cio0 = 6871 instead of 56:0!
Cso = 43°09 a 39:0
Cio = 35°21 Lp 32:0
C50 = 18°42 a 19°5
C40 = 13°83 . 14-4
Goo (SOLE af; T2
Cos ote ss 33
(I"—T"> \e=O°'D. Gy c= UESHRE (C,,) bp. = 69°5. T,,, = 105°+278°.

2 gol. is taken as the average of 7,,,=1°53 at 105°, and the 2 sol, of the ethos
limiting temperature (100°, 80°, 70°, 50°, 40°, 20°, 10°); ¢=1-54, 1:59, 1°60,
1:62, 1°66, 1:70. This mode of calculation is done after the results have been
calculated by means of the formula B, 7. e. the values of C sol, very nearly found,

416 Dr. Meyer Wilderman on the Connexion between

the obtained results are as good as we could expect them to
be,

In equation (A”) lg is7 e oasTe (for water), i.e.
07

(A) may be written

—g E . M.A
iC ar T ~w)tle (Ag —T) +18 oooT2

which is the connexion between solubility C at any tempe-
rature Tg, , T,, and Tp. In the same way in equation (B”)
aul Je vy
8 59 =e £0-02T,2 (for water), and (B’”) may be written :

iC ee > M.!
Ig [C]= 2x 5026 (T} ~ 1 :-) +e is To | +18 pote ‘02T. 72

which is the connexion between solubility [C] at any tem-
perature [T], g, /, T,,, and ao Taking the same point on
the solubility curve, C=[C], T=[T], we get

qd 1 HL a" TT l ae
2x 25006, ~T Jaleoe tle 7

J4/

This equation gives the connexion between all the constants =
the heat of solution q, the latent heat of melting i, the latent
heat of evaporation l, freezing-point and boiling-point of the
pure solvent Ty and Ty’, and the freezing-point and boiling-
point of the saturated solution of any given substance in the
presence of an excess of the dissolved substance in the solid (or
liquid) state T, and T,,,.

Example: Boric acid in water: g=5400 (J. Thomsen),
f= 310-9, L,= 272-415, Th =213,_ 1, =313° (at 760 mmamean
1=536°35 (Regnault), X=80 (down to 79, according to
different investigators).

We get for the above equation (C) :

1°18=1°15 (when ) =80 cal.)
1°18=1°16 (when A=79 ceal.).
Calculating any of the above constants, if it be unknown,
from the rest, we get
g=5263 instead of 5400 obs. (when X=80)
[=574°9 instead of 536°35 obs. (when 7»= 80)
\=74'61 instead of 80 (79) obs., Ke.

Thus we can calculate the solubility curve when fle and
,, or T, and q, or T,,, and g are known.

Freezing-points, Boiling-points, and Solubilities. 417

Ty, To’, %, 2 are the same for the same solvent, are different
for different solvents, and the freezing-point and boiling-point
eurves are (for non-electrolytes) in the same solvent inde-
pendent of the nature of the dissolved substance. On the
contrary, 7, T,, T,,, are characteristic of both, of the solvent
as well as of the dissolved substance. Hach substance in
solution has in every solvent its own solubility curve.

B. In a similar manner to the above figure 2, the
figure 3 may be formed, representing, instead of con-

centrations, the vapour-pressures of three curves at different
temper atures.

Cig See Soe eee

OaBsoe. T, Te To! + T (TEMPERATUPES)

T,—9 absolute represents the vapour-pressure curve of ice,
fee, that, of pure water, 1’, 17, 1’”, U””%, Se. are: the
vapour-pressure curves of the unsaturated solutions. Since
the vapour-pressures of an aqueous solution are known to be
smaller than that of pure water, z.¢. the vapour-pressure curve
of a solution runs below that of water, Guldberg drew from
this as early as 1870 (C. R. lxx. p. 1849) the conclusion that the
lreezing-points of the solution must be below that of the pure
solvent. Itis evident that in the same way we may show that
the boiling-point of the solution must be higher than that of
the pure solvent. As at the boiling-point the pure solvent
and the solution have a vapour-pressure equal to that of the
given atmospheric pressure, we have to draw a line T)’—T,,
From the ordinate To (say “for 760 mm.) parallel to the ab-
scissa; T,—T, is to represent the vapour-pressure curve
belonging to the concentrations of the solubility curve, which
for different substances will have a different form. As the
curve of the saturated solutions meets with the curve of
Te the curve T, T,,, will intersect the whole series

fT’, 1”, 1’, 1”, &e., starting for the solution having the

ro)

418 On Freezing-points, Boiling-points, and Solubilities.

concentration C, (belonging to T,) and continuing up to the
solution having the concentration C,,, (belonging to T,,,):
C. Only within Ty T,T,,, To’ To and on T, 0 abs., and
not beyond the same, is real equilibrium possible, as may be
seen from the above figures (2 and 3). The system which is in
equilibrium at T) (fig. 2) cannot be in equilibrium at any point
on eT, say (5), since the solution will have to contain more salt
than it possibly can below T, (this quantity is given by (5’)
on BT,); it cannot be in equili ‘brium at any point on PT, say
on (6), because solutions containing the amount of salt of (6)
can only be in ee with ice at a higher temperature,
corresponding to (6’) on the freezing-point curve. In the
same way the system which is in equilibrium at T,,, cannot
be in equilibrium at anv point on yI,, say at (7), since for
this a concentration higher than that which the system can
dissolve at this temperature (given by (7) on 61’,,) will be
necessary ; it cannot be in equilibrium at any point on 6T,,,
say at (8). because solutions having the concentration of (8)
can be in equilibrium with their vapour at the given atmo-
spheric pressure only at (8’) on yI/,,, 2.¢ ata lower tempe-
rature. That systems cannot be in equilibrium beyond the
lines Ty’, Lee T,,To', To'l,, T,0 abs., has been already
generally shown in another place * : when the effect of cooling
or heating by the surrounding medium was cons sidered.
Though it has been shown in the above papers that the
equilibrium of the systems represented by the above diagrams
are never in reality reached in nature, the above diagrams lose
nevertheless nothing of their meaning and theor etical content.
The observed equilibria of systems are always more or less
removed from the real points of equilibrium, and the apparent
points of equilibrium often fall outside the region of
POET /T,'To, T,0 abs., but apparent equilibrium is not real
equilibri ium, but only A state of the system, when a reaction is
still going on in the same. At apparent equilibrium one or
more ~ parts of the system may even completely disappear
and the system may be transformed into another one, quite in
conformity with the meaning of Gibbs’ “ Rule of Phases.”
The region included in T of /T,,1,/T, is further most in-
teresting on account of the fact that we can here describe any
amount of reversible cycle processes, starting from any point
and returning to the same in different ways, e.g. starting at T,,,
we can pass along the solubility curve, then along the freezing
point curve, then along the curve of pure water or of an

% See ‘On real and apparent Freezing-points, Boiling-points, Solu-
bilities,’ Phil, Mag. xlv. p. 204 (1898), and August 1902, p. 270.

Radioactivity Excited in Atr at the Foot of Waterfalls. 419

unsaturated solution, then along the boiling-point curve back
to the point T, Oe. It is well worth while looking into.
whether it is not possible, by means of such cycles, to dis-
close some new thermodynamic connexions between the
different phenomena included in the above diagrams.

Davy-Faraday Laboratory of the Royal Institution,
June 1902.

XLI. Induced ee Eacited in Air at the Foot »,
Waterfalls. By J. C. McLennan, Associate Professor of
Physics, University of Toronto * ~

1.—Introduction.

NHE fine drops of spray into which water is broken on

passing over waterfalls was found by Lenard + to
communicate, on striking the wet rocks at the foot of the
fall, a negative charge of electricity to the surrounding air
and a positive charge to the water.

From a number of laboratory experiments with jets im-
pinging on metal plates he obtained the same results with
pure water, but found that the presence of any impurity
greatly lessened the effect. With certain solutions—notably
sodium chloride in water—the action weakened with an in-
crease in the strength of the solution, and was finally reversed,
a positive charge being communicated to the air and a nega-
tive charge to the liquid.

The splashing of rain he found imparted a negative electri-
fication to the surrounding air, while the breaking of waves
on the sea-shore electrified it positively.

The experiments of J. J. Thomson { and of Hlster and
Geitel§ have confirmed these observations, and, while showing
that the sign and the amount of the electrification im-
parted varied both with the liquid and with the gas in which
the splashing occurred, yet the splashing of pure water in air
always gave a negative electrification.

A little over a year ago Elster and Geitel || found that, if
a negatively electrified wire were exposed for some hours in
the open air or in a very large room, it became temporarily
radioactive. Since then a number of observations have been
made upon this effect, and the consensus of opinion appears
to be that it is due to the presence in the atmosphere of some

* Communicated by Professor J. J. Thomson.

+ Lenard, Wied. Ann. xlvi. p. 584 (1892).

fio dreads Thomson, ‘Discharge of Electricity through Gases,’ p. 17.

§ Elster and Geitel, Wied. Ann. xlvii. p. 496 (1892).
|| Elster and Geitel, Phys. Zeit. No. 40, p. 590 (1901),

A420 Prof. McLennan on Induced Radioactivity

peculiar constituent similar to the emanation from thorium,
which has been shown by Rutherford * to induce radioactivity
in any body with which it comes in contact, especially when
that body is negatively electrified.

The difficulty of determining and of regulating the atmo-
spheric conditions for observations upon this excited or
induced radioactivity suggested the desirability of resorting,
for purposes of experiment, to a locality where exceptional
electrical conditions were known to exist permanently in the
atmosphere. Niagara Falls, according to Lenard’s results, is
preeminently such a locality, and, through the kindness of
the Hon. Thomas Walsh, Superintendent of the Niagara Falls
National Park Reservation, the author was enabled in Sep-
tember last to carry out a short series of observations upon
excited radioactivity at the foot of the Falls. The general
result of the investigation was that during the course of the
experiments the amount of radioactivity induced in a wire
exposed at the foot of the Falls was found to be very much
less than that in a wire exposed in the same manner in
Toronto.

2.— Apparatus.

In these observations the measurements were made with a
quadrant electrometer of the Mascart type as constructed by
Carpentier. The silk suspension in the original apparatus
was replaced by a phosphor-bronze strip less than 0-025 miili-
metre in thickness, which was attached at its upper end to
an ebonite rod to secure insulation. The needle was kept
charged by a battery of small storage-cells similar to those
installed in the Reichsanstalt. The deflexions were measured
by the movement of the image of an incandescent-lamp
filament upon a transparent scale placed at a distance of one
metre from the electrometer.

With a potential of 480 volts applied to the needle, the
sensibility of the instrument was such as to produce a
deflexion of 1600 millims. on the scale for a potential-
difference of one volt between the quadrants. In measuring
the induced radioactivity, bare copper-wire No. 24 was ex-
posed in the open air by means of specially-constructed
insulating supports (fig. 1) attached to a series of bamboo
poles erected at convenient distances. The wire was charged
by a small Toepler Holtz Hlectrical Machine driven by a
water motor, which maintained a potential of from eight to
ten thousand volts.

The insulator shown in fig. 1 consisted of a brass tube

* Rutherford, Phil. Mag. xlix. p. 1 & p. 161 (1900).

Ck eee

Excited in Air at the Foot of Waterfalls. 421

about 20 centimetres long, closed at one end and having a bell-
shaped opening at the other. Into this tube an ebonite rod
was screwed which could be easily removed when it was
necessary to renew its surface. Hooks fastened to the tube
and to the ebonite rod provided for the support of the insu-
lator and the suspension of the wire.

Fig. 2.

wb
9 gttZ
02

———————e
~
~
H —
7B
i
MM
,
i}
{ ae
; ~
t =
~
~A
4
é
i
Qe
Coo
H \ Kgo
j
t
——

(LIZA 7A
"zat
ran)

In the experiments at the foot of the Falls, it was found
that with these insulators a wire could be easily maintained
at a potential of 10,000 volts for hours even in a drenching
spray.

The exposed wire was tested for induced radioactivity by
means of the apparatus shown in fig. 2. A is a galvanized iron
cylinder about 30 ems. high and 20 ems. in diameter, resting
on an insulated platform and having a movable cover pro-
vided with a flanged opening into which was fitted an ebonite
plug about five centimetres in diameter. A brass tube C
was passed through this plug and into ita second ebonite plug
was tightly fitted. This second plug carried a brass rod D
from which B a brass reel was suspended, and on this reel

Phil. Mag. 8. 6. Vol. 5. No. 28. April 1903. 2 EF

422 Prof. McLennan on Induced Radioactivity

the wire to be tested was wound. The brass tube C, which
was earthed throughout the measurements, served as a guard-
ring and prevented any leak from the vessel A to the rod D
across the ebonite plugs.

The saturation current due to spontaneous ionization of
the air in the vessel having been first determined by con-
necting the supporting rod D to the electrometer in the usual
way and applying a potential of 100 volts to A, the exposed
wire was then wound on the reel, inserted in the vessel, and
the saturation current again ascertained. Any increase
observed in the ionization current was taken as a measure of
the radioactivity induced in the exposed wire.

As it was impossible, in setting up the apparatus in two
different localities, to be certain that it was of exactly the
same sensibility,a standard of ionization was deemed necessary
for purposes of comparison. A radioactive substance which
the writer had in his laboratory at the time of making the
experiments was chosen, and a small quantity in a glass phial
being found to give a constant ionization current when placed
in a given position in the chamber A, this current was adopted
as a standard and the ionization currents measured in the
various tests were expressed in terms of it.

3.—LHaperiments.

Both before proceeding to Niagara, and after returning, a
series of exposures was made in the quadrangle of the Uni-
versity at Toronto. Copper wires, approximately 30 metres
long, were exposed for periods of two hours at a potential of
8000 to 10,000 volts on a number of days. After a wire had
been exposed it was placed in the ionization chamber, the
saturation current measured, and its radioactivity, thus ascer-
tained, was expressed in terms of the standard radioactive
substance.

The resulting values, taking the standard saturation current
as unity, showed considerable variation in the amount of
radioactivity excited, the highest value observed being 1°75
and the lowest 0:6. The intermediate values ranged between
these limits, but were quite irregular and seemed to depend
more upon the existence of wind and its velocity than other
changes in the weather. The occurrence of showers did not
exert a noticeable effect on the amount of radioactivity ex-
cited. It was frequently observed that exposures made in
the morning gave greater induced radioactivity than those
in the afternoon, but that exposures made after sunset gave
values generally equal to, and sometimes greater, than those
of the morning.

Excited in Air at the Foot of Waterfalls. 423

The following numbers, which represent the observations
made upon one day, are typical and show this variation :—

Exposure 9 A.M.—11 a.m. Hxcited radioactivity °8
mn 1 P.M.— 3 P.M. 34 Ms "6
a 6 P.M.— 8 P.M. i is 1:0
x4 9 p.M.—11 P.M. be i, 1-1

The observations were made in Toronto between Sept. 5th
and 12th, and between the 19th and 23rd, those made at
Niagara occupying the interval. The values in the two series
at Toronto exhibited similar variations and were confined in
both cases within the limits mentioned. The weather through-
out, except for a few showers, was uniformly fine.

In conducting the experiments at Niagara Falls, the electro-
meter and its attachments were set up in the basement of the
landing-station at the foot of the inclined railway. It was a
iarge room having stone walls and a cement floor, and being
fairly dry, was well suited for making the tests. The elec-
trical machine which was intended for charging the wire was
also located in this room, and the wire to be exposed was led
from it out of a window and suspended in three stretches of
about 30 metres each, the insulation being secured as already
described.

The situation was admirably adapted for making the ex-
posures, as the wire could be led within a metre or two of
the vast mass of falling water. The first length of wire was
generally enveloped ina very fine spray, that which surrounded
the second was heavier, while the downpour upon the third
resembled the heaviest rain.

A point of peculiar interest in connexion with the first ex-
posure was that the wire, upon suspension in the spray,
immediately became negatively electrified to a potential ot
about 7500 volts. This voltage was maintained with but
little variation both day and night during the period covered
by the experiments, and the sign of the electrification was
invariably negative,

The results of a number of tests with the different sections
of the wire showed, that the removal of the third generally
caused a drop in the potential of the remaining sections from
7500 volts to about 5500 volts, while the first section, when
exposed alone, gave a potential varying from 3000 to 4000
volts. From this it was evident that the spray was the cause
of the electrification, and that the potential of the wire was
largely determined by its density.

On account of the permanency of this electrification of the

2F 2

424 Prof. McLennan on Induced Radioactivity

exposed wire, the electrical machine necessary in the Toronto
experiments was not employed.

In testing for induced radioactivity, the wire was expered
for periods of about two hours and was removed in sections,

each section being replaced by a new length. The same

method of testing was used as in Toronto, and the results
expressed in terms of the standard radioactive substance.

Exposures were made on four different days with the
following results, A, B, and C denoting the sections of the
wire of which A was that nearest the obser ving station, and
C that nearest the Falls :—

Induced Radioactivity.
Saturation current of

|
|

Date. | Section of
| standard substance=1.

wire tested.

[Sept 2th: 2.258 | 0-1
O31
None observed.
0°16

None observed.
Not exposed.

| Sept. 18th......... |

Sept. 16th ......... | 0-18
0-14
O11

Sept: 1/th 0.5 015
0-12

None observed.

ORF OFF OP OP

From these numbers it willbe seen that but little variation was
_ observed in the radioactivity excited in the sections A and B.
In C, however, which was nearest the Falls, measurable radio-
activity was present in only one of three exposures.

Ordinarily this section was drenched by masses of falling
water in addition to being surrounded by fine spray such as
enveloped the rest of the wire. But on Sept. 16th the air
currents, during exposure, were such as to drive aside the
sheets of water and permit only the fine spray to come in
contact with the section.

As already stated the spray enveloping the section B was
generally heavier than that in contact with A, but the con-
dition was not permanent as the spray was blown about by
gusts of wind whose direction was continually changing in
the gorge.

The chief interest attaching to the results was that the
radioactivity excited was much less than that in Toronto. It

Excited in Air at the Foot of Waterfalls. 425

will be noticed that the greatest amount of radioactivity
observed at Niagara Falls was 0°3, while the least observed
in Toronto during the period covered by the experiments was
0-6. The numbers also show that on the average the radio-
activity excited at Toronto was at least from six to seven
times greater than that induced at the Falls.

The observations were not made in the two places at the
same time, and a direct comparison is therefore impossible,
but as there was no break in the weather during the progress
of the experiments, and as the values found in Toronto before
going to the Falls were almost the same as those obtained on
returning, one is warranted in concluding that the air at the
foot of the Falls permanently possesses less power to excite
radioactivity than the air of localities at some distance.

While the experiments were in progress the spray was
frequently examined for radioactivity. This was done b
collecting a quantity, evaporating it, and testing the con-
taining vessel. In no case was any trace of radioactivity
observed.

Assuming then that excited radioactivity is caused by the
presence in the atmosphere of some peculiar constituent, the
experiments which have been described would seem to show
that this constituent is present to a much less degree in the
atmosphere in the neighbourhood of waterfalls than in places
remote from them.

That it is possible to reduce the amount of this constituent
present in the atmosphere is shown by some experiments
recently performed in the Physical Laboratory at Toronto.
The windows and doors of a large room, which had been well
aired, were closed and, while of course they were not made
air-tight, it may be assumed, as they were close-fitting, that
the quantity of outside air which they admitted was relatively
small. An electrical machine at one end of the room was set
in action and a number of zine disks attached to a wire lead-
ing from its negative terminal were suspended for an hour
simultaneously at different points in the room. Upon testing
these disks for radioactivity by the method employed by
C. T. R. Wilson* it was found that radioactivity excited in
the disks regularly increased with the distance from the
machine.

It was also found, when a series of disks were consecutively
exposed for an hour in a fixed position in the room after it
had been well-aired and closed, that the radioactivity excited
regularly diminished with the time. The admission of a
considerable volume of fresh air, as by the opening of a

* ©. T, R. Wilson, Proc, Roy. Soc, vol, lxviii. p. 154,

A426 Prof. McLennan on Induced Radioactivity

window, immediately caused an increase in the amount of
radioactivity excited in the exposed disks. It was evident,
therefore, that the electrical machine in action served as a
means of removing from the atmosphere surrounding it the
constituent upon whose presence the excited radioactivity
depended.

In seeking for an explanation of the diminished radio-
activity excited at the Falls, the experiments just described
suggest the presence of an agency having an effect similar to
that of the electrical machine on the air in the room.

The negative electrification of the wire when in the spray-
area pointed to the presence of this agency in the spray itself.
The time at the writer’s disposal did not permit of a direct
investigation into the charge carried by the spray, but the
negative electrification of the wire, which it will be remem-
bered was always present and always increased as the wire
was extended into the heavier spray, seemed to find its only
explanation in a similar electrification of the spray. This
being so, it follows at once that the vast quantity of the spray
produced by the Falls would act as a huge negatively-charged
body in attracting to it from the surrounding atmosphere
the constituent responsible for the excitation of induced
radioactivity.

In this way a satisfactory explanation is afforded of the
relatively small amount of induced radioactivity excited at
the foot of the Falls. This explanation requires the spray
itself to be radioactive, but when the enormous volume of
the spray and the very limited amount of induced radio-
activity observed in the locality are taken into account,
together with the known decay of induced radioactivity, it
would appear reasonable to conclude that experiments con-
ducted with very much larger quantities of spray than those
in the writer’s tests would be necessary to obtain observable
results.

From Lenard’s observations one would have expected a
positive electrification to be developed on the exposed wire by
the splashing of the spray, but the opposite was found. Some
experiments on dropping water through ionized gases recently
made by Schmauss*, give some aid in explaining this anomaly.
He found that when water was dropped through air ionized
by Réntgen rays, it acquired a negative charge from the gas,
and he explained this fact by a reference to the experiments
of Rutherford f and of Zelenyt, in which it was shown that

* Schmauss, Wied. Ann. [9] i. pp. 224-237 (1902).
+ Rutherford, Phil. Mag. xliii. p. 241 (1897).
{ Zeleny, Phil. Mag. xlvi. p. 120 (1898).

Excited in Air at the Foot of Waterfalls. 427

a stream of air, when it was ionized by Rontgen rays and
directed against an insulated conductor, imparted to it a
negative charge owing to the greater velocity of diffusion of
the negative ions. These experiments, in which the gas was
in motion and the insulated conductor at rest, Schmauss con-
sidered the converse of his own.

Now, in the experiments we are considering, we have
water dropping through air which is known to be spontane-
ously ionized. From the results of Schmauss, we should
expect the spray to take up a negative charge from the air.
This, if sufficient to overcome the Lenard effect by which a
positive charge is developed through the impact of the spray
on the wire, should leave the wire negatively charged, and
this was the uniform result of the observations.

4.—Radioactive Rain and Snow.

In order to ascertain, if possible, the effects of variations
in the weather upon the radioactive state of the atmosphere,
the writer made a series of daily observations in the month
of November. During this period both rain and snow storms
occurred. The falling of rain was not found to produce any
marked change in the radioactive power of the atmosphere,
although, as already shown by C. T. R. Wilson*, the rain
itself when tested was active. The falling of snow, however,
_ was accompanied by a very considerable drop in the value of
the excited radioactivity. For example, on Nov. 25th the
air was dry and cold, and the morning exposure gave a value of
0°92, that for the afternoon exposure being 0°66. The next
morning snow began to fall heavily, and an exposure was
made in it for two hours. The resulting value for the excited
radioactivity was 0°3. The snow-fall continued throughout
the day, and the value for the afternoon exposure was again
0-3. This storm was general throughout Ontario, and the
snow, which fell to a depth of about three inches, remained
for some days on the ground and did not entirely disappear
until Nov. 30th. Tests made for radioactivity in the interval
showed values ranging from 0:2 to 0°4. On Dec. Ist an
exposure made about noon gave a value of 0°9. On this day
the weather was again mild and the snow had disappeared.
Exposures made in the mornings of Dee. 2nd, 3rd, 4th, and 5th
gave the values 0°8, 1:1, 0°9, 0°9 respectively.

The weather continued mild until Dec. 5th, when the tem-
perature dropped below 0° C. On Dee. 6th the cold weather
still prevailed and an exposure made from 1 to 3 o’clock in
the afternoon gave a value of 0°92. Shortly after 3 o’clock

* C. T. R, Wilson, Proe, Camb, Phil. Soc, vol, xi, Pt. 6, p. 428,

428 Radioactivity Excited in Air at the Foot of Waterfalls.

a light fall of fine snow began, which continued throughout
the night. An exposure was made from 3.30 to 5.30 P.M.,
and also one from 9 to 11 p.m. The resulting value for the
former was 0°2, and for the latter 0°32.

As the numbers just given indicate, the falling of snow on
both occasions was accompanied by an immediate drop in the
excited radioactivity. It will also be noticed that while the
ground was covered with snow from the first fall the dimin-
ished activity continued. The snow on both occasions was
collected as it fell, melted and evaporated, and the residue
found to be highly radioactive. Snow which fell in the
first storm was tested after it had lain two days on the
ground and was found still to possess about 1 per cent. of its
original activity.

These results, it will be seen, lend support to the theory
that the constituent of the atmosphere to which the excitation
of radioactivity is due is an emanation from the earth’s sur-
face. It would also seem from the values found for the
induced radioactivity that this emanation is cut off to a con-
siderable extent when a wide area of the earth’s surface is
thickly covered with snow.

The limited number of observations made hardly justifies a
definite conclusion as to the manner in which rain and snow
become radioactive ; but it is possible that water-vapour in
moving through the air, whether in the form of clouds or
otherwise, gains a negative charge in the same manner as the
spray at the Falls, and consequently becomes radioactive.
This view is supported by the results of some experiments
recently made by the writer. Water-vapour was condensed
from the atmosphere upon the surface of a number of cylin-
ders containing a freezing-mixture of ice and salt. The
water thus obtained was evaporated in a metallic tray
and the residue tested for radioactivity. Such tests were
made daily for a period of two weeks. In most of them no
radioactivity was observed, but in several slight traces were
noticeable, and on four occasions the radioactivity excited
was very marked. The experiments were all conducted with
equal care, and no cause was apparent for the different results
of the observations.

The thanks of the writer are due to Mr. J. S. Plaskett,
B.A., for assistance in conducting the experiments, which at
Niagara were attended with considerable difficulty, and to
Mr. J. C. Rothery, Superintendent of the Niagara Falls’ Park
and River Railway, for facilities afforded in transporting the
apparatus.

Physical Laboratory, University of Toronto.
. December 8th, 1902.

f 429 4 | :

XLII. A Determination of the Charge on the Ions produced
in Air by Réntgen Rays. By Haroutp A. Witson, ellow
of Trinity College, Cambridge*.

| oe experiments described in this paper were undertaken

with the object of making a fresh determination of the
charge on one ion. This charge will throughout this paper
be denoted by e.

Prof. Townsend (Phil. Mag. Feb. 1898), in a paper on
the “ Hlectrical Properties of Newly Prepared Gases,” has
described a determination of the average charge on the
droplets composing the cloud formed when newly prepared
oxygen is bubbled through water. This charge was found
to be about 3 x 10-"° electrostatic units of electricity. There
are some reasons for supposing that each droplet contains
one ion, and consequently ‘lownsend’s result may be regarded
as a determination of the charge on one ion. The result
which I have obtained is in very good agreement with his.

Prof. J. J. Thomson (Phil. Mag. Dec. 1898 and 1899) has
given two estimates of ¢, the first depending on a determina-
tion of the average charge on the droplets of a cloud formed
by condensation of water-vapour on the ions produced in air
by Rontgen rays, and the second on a similar determination
for the ions given off by a zinc plate under the action of
ultra-violet light. The mean result of the first research was
e—o) < 10519 and or the second e=6'°8 x 10-" f.

Since from the value of e the number of molecules in a
cubic centimetre of a gas can be immediately deduced, and
also since the absolute value of e is of considerable interest
in itself, a fresh determination by a different method appeared
to be worth making.

The method I have used depends, like Prof. Thomson’s, on
the fact discovered by C. T. R. Wilson, that the ions pro-
duced in air by Réntgen rays act as nuclei for the cloudy
condensation of water-vapour when supersaturation exceeding
a definite amount is produced by a sudden expansion.

* Communicated by Prof. J. J. Thomson.

+ Since this paper was written Prof. Thomson has informed me that
he has lately made a fresh determination of e by his original method,
but with an improved apparatus, and he has very kindly consented to my
mentioning the result he has obtained, here. It ise=3'8 x 10-12, and so
agrees very well with the mean result of my experiments, viz. 3°1x 10-10,
It appears that in his earlier experiments the cloud was formed mainly
on the negative ions and not on both positive and negative ions as was
supposed at the time, consequently the result obtained was nearly twice
too big.

{ Phil, Trans, A. 1897, p. 265, and A. 1899, p. 403,

430 Mr. H. A. Wilson: Determination of the Charge

The droplets of the cloud produced presumably each con-
tain one or more ions. Let a droplet containing one ion, and
consequently having a charge e, have a mass m which can be
determined by observing its rate of fall (v, say) in air. If
now a vertical electrostatic field of strength X is applied to
this droplet, there will be a vertical force on the droplet equal
to Xe due to the field, so that the total force on the droplet
will be Xe + mg, where g is the acceleration due to gravity,
and reckoning Xe positive when it is in the same direction
as the weight mg. Now the rate of steady motion of a sphere
in a viscous fluid is proportional to the force acting on it, so
that the rate of fall of the droplet will be altered by the
electric field. Let it be now vy. Then we have

The relation between m and v, is given by the equation

Mao x Ome xe
so that

e=3' Ix Om = (V2— 0) 042.

Thus if X is known measurements of v, and vy are sufficient
to determine e¢ absolutely. This is the method which I have
employed.

It was found that, using strong Réntgen rays, some of the
droplets in the cloud had bigger charges than others. In
fact there sometimes appeared to be several sets of droplets
having charges nearly in the ratios 1: 2:3. It appeared,
therefore, that some of the droplets contained one ion, some
two ions, and so on. This agrees with Prof. Thomson’s ob-
servation that when the strength of the Rontgen rays was
increased beyond a certain amount, the number of droplets
in his clouds did not increase proportionally to the number
of ions present at the moment of expansion. Prof. Thomson
therefore used weak rays so that in his experiments each
droplet probably only contained one ion, which is a necessary
condition for the success of the method he employed.

The principal advantages of my method are that it is not
necessary to estimate either the number of drops in the cloud,
or the number of ions present at the moment of its formation,
or to make the assumption that each droplet contains only
one ion. Both these estimations involve assumptions which
in practice can only be approximately true, and there is

* J. J, Thomson, Phil, Mag. Dec. 1899, p. 561,

on the Ions produced in Atr by Réntgen Rays. A431

always a danger that some of the drops in the cloud contain
more than one ion.

The apparatus used is shown in the accompanying diagram.

It consisted of a glass tube AB about 4 cms. in diameter
and 10 ems. long. Its lower end was closed by an india-
rubber stopper and its upper end joined on to a short length
of narrow tubing. Two circular brass disks, C and D, each
4°5 cms. in diameter, were supported one above the other in

U
M a: ope Ex 70 INJECTOR PUMP
a.

this tube as shown; the cloud on which the observations
were made was formed between them, and they could be
maintained at any required difference of potential up to
2000 volts by means of a battery of small secondary cells.
A glass tube Hi was sealed on to the side of AB and served
to connect the space between the disks with an apparatus for
producing a sudden expansion of any desired amount. A
small mercury manometer (H) was used to measure the
expansion,

432 Mr. H. A. Wilson: Determination of the Charge

The expansion apparatus used was kindly lent to me by
Mr. ©. T. R. Wilson, and it was similar to those he has
described in the papers referred to above. The apparatus
was arranged so that the valve V, the opening of which pro-
duces the sudden expansion, could be pulled back suddenly
by means of an electromagnet (M). This enabled the valve
to be pulled away every time in exactly the same way.

The space in the tube AB below the disks was filled with
water so that the air between the disks was thoroughly satu-
rated with moisture. This air was rendered “ dust free” in
the usual way, by repeated expansions with intervals in
between to allow the clouds formed to settle. The apparatus
was then ready for a measurement of ¢.

A Réontgen-ray bulb was worked near AB, so that the
rays passed between the disks. Then the battery circuit
through the magnet was closed and a sudden expansion so
produced. A cloud was thus formed between the disks, and
the time which its upper surface took in falling from the
upper disk to the lower disk was measured. This gave x
the rate of fall without an electric field. The experiment
was then repeated, but immediately after the expansion the
disks were connected to the battery, and so v, the rate of
fall in an electric field, was obtained.

It was found that if the rays were kept on all the time
during an experiment, then very large values for the charge
on each droplet were obtained. A field of a few hundred
volts per centimetre was then sufficient to cause many of the
droplets to rise instead of falling. It soon became clear that
the fresh ions formed after the expansion attached themselves
to the droplets, so that the longer the rays were kept on after
the expansion the bigger the charge on the droplets became.
A switch 8 was therefore put in the primary circuit of the
induction-coil used to excite the Rontgen bulb and arranged
so that the armature of the magnet turned the switch, broke
the circuit, and so stopped the rays a small fraction of a
second before the expansion was produced.

The disks C and D were also connected to a commutator
which first connected them together, and then on being
turned connected them to the large battery used to charge
them up.

A narrow beam of light was passed between the disks C
and D to illuminate the cloud and enable its upper surface
to be observed. The falling of the cloud was watched
through a small hole on a level with the disks, and about
twenty centimetres away from them in a direction nearly
perpendicular to the beam of light. A second screen was

on the Ions produced in Air by Réntgen Rays. 433

put up close to the apparatus having a vertical slit in it
through which only the central portion of the illuminated part
of the cloud could be seen. This slit and the beam of light
were each about half a centimetre wide, so that the portion
of the cloud which was observed was that occupying a vertical
prism half a centimetre square at the axis of the tube AB
between the disks.

The disks were never more than one centimetre apart, and
consequently very little circulation of the air could take place
between them. When a cloud is formed by expansion in a
large vessel, the walls of the vessel heat up the air near them
which produces a circulation of the air upwards near the
walls and downwards in the middle. If this sort of thing
happened in these experiments, v, and v, would both be
obtained too high; but it was found that when the disks
were not more than a centimetre apart the circulation which
occurred near the glass walls of the tube did not extend to
the centre, and the surface of the cloud between the disks
remained plane as the cloud fell.

The disks were always connected together until the expan-
sion had taken place, when, if it was desired to determine v,,
they were immediately connected to the battery by turning
the commutator lever. If they were connected to the battery
before the expansion took place no cloud was obtained because
the field removed the ions as fast as they were formed.

In making a measurement of e the time of fall from the
upper disk to the lower one was measured with a stop-watch,
alternately with and without the electric field. 2, and v,
were then calculated from the mean results for the times of
fall.

C. T. R. Wilson (Phil. Trans. A, 1899, p. 440) found that
with an expansion of nearly 15 cms. of mercury only the
negative ions acted as nuclei, but with greater expansions
condensation occurred on both positive and negative ions.
These results were easily verified with my apparatus. With
an expansion of 15 cms. charging the upper disk negatively
caused the whole cloud to fall more quickly than it fell when
the disks were uncharged, while charging the upper disk
positively reduced the rate of fall of the cloud. It was clear,
therefore, that the droplets were negatively charged.

Also with considerably larger expansions than 15 ems.
some of the droplets fell more slowly and some more quickly
when the disks were charged than when they were not
charged, showing that both positively and negatively charged
droplets were present. However, there always seemed to be
more negatively charged droplets present than positively

434 Mr. H. A. Wilson: Determination of the Charge

charged ones, and unless the expansion used was nearly
enough to produce a fog even in the absence of any ions,
the positively charged droplets were not very easy to observe.
There seemed, in fact, to be a large excess of negative ions
present between the disks and not equal numbers of positive
and negative ions. ‘The explanation of this is, no doubt, to be
found in the secondary radiation emitted by brass under the
action of Rontgen rays. This secondary radiation has been
proved to consist of negatively charged corpuscles, so that
an excess of negative ions in the air near the disks might
have been expected. The excess would, however, not have
been expected to be as great as appeared to be the case. It
is perhaps possible that when both positive and negative
ions are present together, condensation takes place mainly on
the negative ions, although when either kind are present
alone, there is very little difference between the supersatura-
tions required to produce condensation on the positive or
negative ions.

An expansion of from 16 to 17 cms. of mercury was always
used in the experiments described below, and all the results
are for the charge on the negative ions.

All the droplets did not always fall at the same rate when
the electric field was applied. This appeared to be nearly
always the case, but was especially so when strong rays were
used. There appeared to be several sets of droplets, each
set falling all at the same rate. The rate of fall of the most
numerous set indicated that the droplets in it had the smallest
charges. The observations given below refer to this set only,
the other sets will be considered later.

Since the cloud begins to evaporate soon after it 1s formed,
it is very important to get the measurement of its rate of fall
over as quickiy as possible. I therefore generally oaly
allowed it to fall about half a centimetre, and applied the
electric field in the direction which increased the rate of fall.
Another reason why a very small distance between the disks
had to be used, was that the available P.D. was only 2000
volts, so that unless the disks were near together, the electric
field between them was not strong enough to appreciably
alter their rate of fall. For these various reasons nearly all
the observations were made with the disks as near together
as possible, because it was clear that reliable results could
not otherwise be obtained. For the same reason the maximum
P.D. available was used in nearly every case. It would of
course have been more satisfactory if observations could have
been made with a greater variety of distances between the

on the Ions produced in Air by Réntgen Rays. 455

plates, and through a larger range of P.D., but to accomplish
this with the battery available was not possible.
The following table contains the results of a set of obser-
vations :—
Distance between the disks d=0°45 cm.
Potential-difference used 1800 volts.

Time of Fall without P.D. Ditto with P.D.
X=0. X=13'3 E.S. units.
Secs. secs.
(1) 23°6 CA ETS
(6) 9) (4) 16°9
(5) 23:9 (G@) alee)
(7) 23°8 (8) 17-2
Mean...23°65 Mearns? 2

The numbers in brackets refer to the order in which the
observations were made. ‘The above results give

0°45

cm.
0°45 cm.
YVe= 717.99 =0°0262 coat

Consequently, since

e=3'1x 10-9 = (¥— V1) U42,

we have
a1 x 10>? 981 x 0:0072 x (0;019):
e=
11395}
x Oe) B.S. uMits:
Also

max N=" o7— 8 1x 10>? sram.

The method of experimenting can be varied by measuring
the velocity of fall first witb the field in one direction and
then with the field in the opposite direction. If v, and vy
are the velocities, then

taking v, to be the velocity when Xe acts in the downward
direction. The mean of v, and v3 gives the velocity when

<0:

436 Mr. H. A. Wilson: Determination of the Charge
In an experiment made in this way the following numbers

were obtained :—

Distance between the disks 1°0 em.

P.D.=2000 volts.
Time of Fall.

X=+6°7. (= —6'7.
secs. secs.
(1) 18-4 (2) 21°6
(3) ow (4) 2771
(5) 19°4 (6) 22°4
(7) 24°2 (8) 27°8
(9) 27°0 (10) 32°6
Mean...22°94 Mean...26°3

These numbers give
em

V2 = 0°0436 —
sec.

v= 0°0380
SCG.

Also
21K 4
74 oe z (vg—v3) (vo+vs)*,
so that
e=2'6x10-° E.S. units.
and

m=8'1 x 10-9 x (25) 2:5 x 10-4 gram.

As already mentioned the cloud soon begins to evaporate
after it is formed, so it is important to get the measurement
of its rate of fall over as quickly as possible. It was, there-
fore, found most satisfactory to use the rates of fall with
X=0 and with X positive, making the rate of fall greater
than when X=0.

In making a series of measurements an observation with
X positive was always made as quickly as possible after one
with X=0, in order that the strength of the rays and other
conditions should -be as nearly as possible the same in both
eases. Although the individual observations in a series, say
with X=0, often vary a good deal, yet there is usually a
corresponding variation in the observations with X positive, -
so that the value of ¢ obtained from the mean results for the

on the Ions produced'in Air by Réntgen-Rays. 437

series is not necessarily affected by any error due to these
variations.

The following tables contain all the other results obtained
except a few done at an early stage, before the apparatus
had been got to work satisfactorily, none of which are
included.

d=0°50) em. a— 075 0 emr.
P.D.= 2000 volts. P.D.=2000 volts.
th. te. ieee fs
a0) (v= "4183.) Can ee se)
SeCS. Secs. secs. Secs.
232 9°6 7 18°3 10°8
ele Tes 20°3 | 15°6
11-4 9°3 182 17°6
12:0 oa, - 18°0 13°8
10°6 9°6 18°4 15:4
Mean 11:4 Mean 9-4 | Mean 18°64 Mean 14°64
v,=0°0439 ve=0°05380 =| + %=0°0268 v=0:0341
Ne 2-80) Lt m= 1°36 x 10-1!
OBA SO Mae C2IM GSMO
=e) emir | d=0°55 em.
P.D.= 2000 volts. P.D.=2000 volts.
is to. ty. t,.
c= 01) (X=+13:3.) (320) SLITS
secs. Secs. secs. Secs.
14:9 13°2 15°6 130
D0 11°4 ee IL)
14:9 ee? 16°0 LDA
14:0 WO 7-0 138
—_——. —— 17°4 AST:
Mean 14:7 Mean 11°87 18:4 E5s0
%=0084 % =0-042 Pig i
m=1°95 x 10-8 16-0 12°3
o= 3-4 x 10-1. 16°9 Tost
LOST L2"6
Mean 16°84 Mean 13°37
v,=0:0327 v=0:0411

Ria LO
e=3'°81 x 10—%

Phil. Mag. 8. 6. Vol. 5, No. 28. April 1908. 2G

438 Mr. H. A. Wilson: Determination of the Charge

d=0°4 em. ad=0°40 cm. |
P.D.=2000 volts. P.D.=2000 volts.
a A ty. e
(K=0)). oem (X=0) = Sige
secs, Secs. Secs. secs.
21-5 1G-at Jie 12-4
21°9 13:0 20°4 1372
20°9 12:0 20°6 130
21-0 12°0 sees oe
19-4 12-0 Mean 20°7 Mean 12:9
4i6 °° At v,=0°0193 v,=0-0310
— moe ~12
Mean 21:05 Mean 11°80 pene,

#=0°0190 2=6°0340
m=8'l x 10-!" |

é=3' 8 xa”. |
d=(:4 em. d=-+0°40 cm.
PD. =2000 volts: P.D.= +1500 volte
Ay A i a
(X=0.) (X= +16°7.) (0) (X=+12°5.)
secs. secs. secs. secs.
20-0 12 33°6 20-0
20-4 12-0 | 33:0 20:0
=== a 30°5 20:0
Mean 20°2 Mean 12:0 31°6 20°4
v,=0°0198 v,=0°0334 29°4 19°6
m= 8°64 x 10-4 ral a
e=3°5x 10-22. Mean 31'6 Mean 20:0
v,=0:0126 +,=0-0200
| m=44 x 10-"
| e=2:04x 10-2,
d=()'44 cm. P.D.=2000 volts.
A te.
(X =0.) (X=4+15-2.)
secs. secs.
21-3 15°4
22°6 18°2
23°4 16°7
23°6 1-2
17°6
16°4
14°6
14:4
14°9
Mean...22°85 Mean...16°10

v= )OIIS t=O 02ZT2 m8 xl0-= e=23x%N0e 2

on the Ions produced in Air by Réntgen Rays. 439

The following table contains a summary of the above
results :—

om ee OX ie Oe mM. é.
0°45 13°3 19x10-2 | 262x10—2| 81%10=12|) 23x 10-10
1:00 OEM I ce teaare AOD a; 25 “r 2°6 43
0°50 13°3 AO 5 53 5s 236 ;, 4°4 “y
0°50 13:3 Za, DE ity, IS: Gye 27 9
0°50 13°3 34 4:2 ‘ LOD a a4 op
0°55 1271 Deo 55 A Ts UNS }33. ep 38 9
0-40 16:7 1 eo! a4 “i os 38 9
0-40 16-7 L933 31 9 Shey 3°0 +3
0°40 16°7 1:98 .;, 3°34 8:0) oy 3D 3
0°40 12'5 E26 5, ZOD | 5 44, 20 2
0-44 152 OSes, Th Son 2°3 “5
Mean ...-.. 3:1+10—10

It will now be convenient to consider the less numerous
sets of droplets which fell quicker than the principal set on
which the above observations were made.

When no field was applied the whole cloud fell at the same
rate and its upper surface was sharp. No sign of any sepa-
ration into sets could be detected. When the field was applied
the cloud fell quicker than before, but otherwise its appear-
ance was at first the same. After a few seconds, however,
the surface of the cloud began to separate into two ; appa-
rently some of the cloud falling quicker than the rest. The
line of separation between the two sets was fairly sharp.
Sometimes three such sets were observed.

The following numbers were obtained in one series of
experiments with the disks 0:4 cm. apart :—

xX—0)

X=+12'5. X=+12°5, X=+12'5.
Principal set. Second set. First set.
secs. secs. secs, secs.
33'6 20:0 154 11:0
33°0 20:0 15:0 10°6
30°5 20:0 14-0 10:0
316 20°4 108
29+4 ds 10°4
Mean 31°62 Mean 20:1 Mean 148 Mean 10°56
v, =0°0126 v,=0'020 Pe UL v,=0°038

We might suppose that the subsidiary sets are produced
by two droplets coalescing under the influence of the field,
but it is easy to show by calculation, that a droplet with twice
the mass and twice the charge of the others ought to have

2G 2

440 Charge on the Ions produced in Air by Réntgen Rays.

fallen in about 6 secs. in the above experiment. If we
suppose that two droplets, one with a positive charge and the
other with a negative charge, coalesced, which of course is a
probable thing to happen, the resulting droplet with twice
the mass and no charge ought to have fallen in 11:2 sees.,
which is very nearly the mean time (10°6 secs.) taken by the
quickest set to fall. However, it is not easy to see how
droplets coalescing could produce a set of drops having a
sharp upper limit, for we should expect coalescence to occur
from time to time during the existence of the cloud. The
existence of a sharp upper surface to the set seems to show
that all the droplets forming it were formed at the moment
of the expansion.

Another possible explanation of these sets seems to be that
when the cloud is formed some of the droplets contain more
than one ion. IJ£ two ions were very near together during
the expansion they might easily give rise to only one droplet.
An objection to this view is that such a droplet ought to be
larger than one containing a single ion. This objection,
however, falls to the ground when the magnitude of the
effect of the charge on the equilibrium size of the droplets is
remembered, for it is known to be very small.

If we suppose that the droplets in the three sets are all of
the same size, but have different charges, then it is easy to
calculate these charges. The results of this calculation for
the observations given above are

Principal set, charge per droplet 2°04x10-%
Second set, 5 Bah
First set, 3 6°94

If, then, the principal set has one ion per droplet, the second
has two, andthe first about three. é

It has been shown by Townsend (Phil. Trans. A. 1899,
p. 129) that the charge on an ion produced in air by Réntgen
rays or by other forms of radiation is equal to the charge on
the hydrogen ion or atom in solutions. According to the
result of the present experiments it consequently follows that
the charge on one hydrogen atom is 3°1x 10-" ES. unit or
10-*° of an electromagnetic unit. One E.M. unit of elec-
tricity deposits from a solution 0°01118 gram of silver in
electrolysis, and consequently — = 1043 x 10-* gram
of hydrogen. It follows that the mass of an atom of hydro-
gen is approximately 10-*x 10~°=10-* of a gram. The
mass of a molecule of hydrogen is therefore 2x 10-4 of a
gram, so that since the mass of one cubic centimetre of

The Radioactivity of Uranium. 441

hydrogen at 0° C. and 760 mms. of mercury pressure is
9x 10~ gram, the number of molecules (N) in one cubic

L ox Ome
centimetre of hydrogen is =———, or approximately
N=4 x 10%, Ae

The mean result of the present experiments, viz. e=3°1 x 10-°
of an electrostatic unit, cannot be very far from the truth.
I think that it may be considered established by these experi-
ments that e lies between 2 x 10—"° and 4x 10-1! ES. unit.

The values of N which have been obtained from the kinetic
theory of gases vary between rather wide limits. The value
obtained depending usually on the radius assigned to a mole-
cule of the gas under consideration. O. H. Meyer (‘ Kinetic
Theory of Gases,’ p. 333) gives the value N=6'1 x 10%,
which is based on the assumption that the average radius of
a molecule of airis 10-*cm. IfN=4 x 10° then the average
radius of a molecule of air must be 1:2 x 10-% cm.

A great many different lines of argument (see Meyer’s
‘ Kinetic Theory of Gases’) lead to values for the radius of a
molecule or sphere of molecular action near to 10—* em., but
the magnitude of this quantity certainly cannot be considered
to be established except within limits not very near together.
The agreement between the value of N obtained from the
present experiments, and the values deduced from the kinetic
theory of gases, may consequently be considered as good as
could have been expected.

In conclusion I wish to say that my best thanks are due
to Prof. J. J. Thomson for much valuable advice during
the carrying out of these experiments in the Cavendish
Laboratory.

XLII. The Radioactinty of Uranium. By EK. RuTHERFORD,
M.A., D.Sc., Macdonald Professor of Physics, McGill
University, and F. Soppy, M.A. (Ozon.)*.

i tao radioactivity of the element uranium has been ex-

amined in the light of the theory put forward by the
the authors to explain the radioactivity of thorium. The
constant radiating power of that element was shown to be
caused by an equilibrium process, in which the decay of
activity with time was balanced by the continuous production
of fresh active matter at a constant rate. This explanation
embraces equally well the radioactivity of uranium, although
the changes that occur differ widely in degree and complexity
from those that maintain the radioactivity of thorium.

* Communicated by the Authors.

442 Prof. Rutherford and Mr. Soddy on

The case of uranium presents some very. interesting features
for, unlike thorium, this substance produces neither an ema-
nation nor excited activity, and the experimental analysis of
the processes that occur is in consequence extremely simple.
It will be recalled that the main difficulty in the case of
thorium was to separate and distinguish between the various
changes that are occurring simultaneously, and to eliminate
the effects of the production of the emanation and excited
activity from the effects of the primary change which gives
rise to the production of Thorium X. These difficulties are
absent in the case of uranium.

It was shown in 1900 by Sir William Crookes (Proc. Roy.
Soe., 1900, vol. Ixvi. p. 409) that the activity of uranium to
a photographic plate is caused by the presence of a minute
amount of a foreign substance to which he gave the name
Uranium X. This substance, like uranium, is precipitated
from its aqueous solution by means of ammonium carbonate,
but, unlike uranium, is not redissolved by an excess of the
same reagent, being left behind with the iron and similar
impurities present as a minute insoluble precipitate. The
uranium obtained from the solution is completely inactive to
the photographic plate. The uranium X left behind in the
precipitate is intensively active, and may be obtained, weight
for weight, many hundred times as active as the original
uranium. It, in fact, possesses in concentrated form all the
activity that the uranium has lost.

Becquerel, independently ( Comptes Rendus, 1900, vol. cxxxi.
p- 137) reduced the activity of uranium by successive pre-
cipitations in its solution of small quantities of barium sul-
phate. After several precipitations the activity of the
uranium was found to be much enfeebled, whereas the first
barium sulphate precipitates were more active weight for
weight than the original uranium.

It has been shown by one of us (Soddy, Journ. Chem.
Soc. Trans. 1902, p. 860) that in the interpretation of these
results it of great importance to distinguish between the
photographic and electrical effects. For the uranium radia-
tion consists of two types :—(1) the @ or easily absorbed rays;
(2) the 6 or penetrating rays which are readily deviable in
a magnetic field. The former contribute by far the greater
part of the electrical effect, the latter practically all the
photographic effect. Uranium freed from uranium X by
the methods of Crookes and Becquerel, although inactive to
the photographic plate, possesses a nearly normal activity
when examined by the electrical method. The uranium X, on
the other hand, although intensely active photographically,

the Radioactivity of Uranium. 443

possesses comparatively little activity when tested in the
ordinary way by the electrical method. But its radiation,
when tested in a magnetic field, is found to consist almost
entirely of deviable rays, whereas the uranium from which
it has been separated gives no deviable rays at all (Rutherford
and Grier, Phil. Mag. 1902, iv. p. 323). The conclusion was
drawn that the chemical separation had effected the separation
of the matter causing the photographically active or 6 rays
from the uranium, but had not all affected the easily-absorbed
or a rays of the latter. All-attempts to alter the amount of
arays from uranium resulted in failure, and this radiation
appears to be derived from a specific and non-separable
activity of the element uranium itself. The magnetically
deviable and penetrating @ ray, on the other hand, which
causes the photographic effect, is entirely produced by a non-
uranium type of matter, uranium X.

Becquerel (Comptes Rendus, 1901, vol. exxxill. p. 977) has
shown that uranium rendered photographically inactive in
the manner described recovers its activity with time, and
after the lapse of a year is again as active as at first. The
barium sulphate, on the other hand, which had been rendered
active by precipitation with uranium, completely lost its
activity after a year. As this behaviour is exhibited by
thorium and thorium X respectively, it seemed likely that the
phenomena would prove susceptible to the same explanation
in the two cases. Experiments were therefore undertaken to
examine the rate of loss of the activity of uranium X with
time, and the rate of recovery of the activity of uranium freed
from uranium X. The problem resolves itself into a measure-
ment of the amount of penetrating rays given out in the two
cases after recular intervals. ‘The electrical method was
employed, a very sensitive electrometer being necessary for
the measurement of the somewhat small effects involved, and
the observations were continued over a period of 160 days.

At the beginning of the period the uranium that had been
freed from uranium X by the various methods gave practically
no § rays, although less than one per cent. of the normal
amount could have been detected. The activity of the
uranium X, on the other hand, steadily diminished, until at
the end of the period it possessed less than one per cent. of
its original activity. The result is shown graphically in the
figure. The initial value of the activity of the uranium X is
taken as 100, and the final value attained by the uranium is
also made equal to 100. It will be seen that the activity of
the uranium X decays very approximately in a G. P. with
the time, and is, on an average, reduced to halt value in about

444 The Radioactivity of Uranium.

22 days. The uranium recovers its power of giving # rays
just as fast as the uranium X loses its power, and for equal -
times the proportion of the total activity recovered by the

Time in Days
uranium is equal to the proportion of the total activity lost
by the uranium X. The laws of decay and recovery are
represented therefore, as in the case of thorium, by the two
equations

et ee

I, —— » ' > ie. ~ te -l > cones. (1.)
it =

i, =l~—e o> tiwtyyiwieg Gel (II.)

1, in eagh case representing the maximum activity (this being
in the first equation the initial, and in the second the final
activ ity’), and I; the activity after time t, X being the same con-
stant in each case. When t is expressed i in days the numerical
value of X is approximately 0°031. In the case of thorium
the half value is reached after 4 days, and the value of A is
about 0°173.

As in the case of thorium, uranium that has partially re-
covered its activity gives on repeating the separation a new
quantity of uranium X proportional to the amount of activity
recovered. The constant activity of the @ rays of uranium
is therefore maintained by the continuous production of
uranium X at a constant rate, and represents the equilibrium
point where the decay of the activity of the uranium X present
is balanced by the steady production of fresh uranium X.

On the Radioactivity of Radium and Thorium. 445

The case of uranium is especially interesting on account
of two points. The existence of non-separable activity con-
sisting entirely of a rays, as in the case of thorium. The
non-existence of « rays in the radiation of uranium X.
This is probably an example of a general law that each type
of radioactive matter when got by itself, free from the
matter which produced it on the one hand and the products
ot its further change on the other, gives rise to homogeneous
rays, and that in all cases the a ray ‘is the first to be produced,
the 8 ray only resulting in the final stages of the disintegra-
tion. Uranium gives more definite evidence on this point
than thorium, because the period of the change is long enough
and the experimental analysis simple enough to enable the
chemical separation of the different types of matter involved
to be fairly complete. The suggestion was put forward in
the first paper on thorium (Phil. Mag. 1902, iv. p. 392) that
the non-separable activities of thorium and uranium re-
spectively might possibly be caused by the simultaneous
production of a second type of matter in the changes in which
thorium X and uranium X are produced. Later (zbzd. p. 584)
it was shown that this explanation is not necessary when
radioactivity is considered as an accompaniment of the change
occurring. ‘This explanation has now been adopted, but a
fuller discussion of the nature of radioactive change is reserved
until after the case of radium has been dealt with.

McGill University, Montreal, Feb. 20, 1903.

XLIV. A Comparative Study of the Radioactivity of Radium
and Thorium. By KE. RutHerForp, M.A., D.Sc., Macdonald
Professor of Physics, McGill University, and F. Soppy,
MEAS (Oxon. ™.

Sal HE elements thorium and radium are very closely

allied in radioactive properties, notwithstanding
the enormous difference that exists in their relative activ ity.
Both produce radioactive emanations, and both emanations
in turn excite activity on surrounding objects, which in an
electric field is mainly concentrated on “the negative electrode.
In the details of their properties, however, ‘they differ very
widely; so that the behaviour of a radium: compound, com-
pared with that of thorium under similar circumstances, often
exhibits very striking peculiarities. The explanation alr eady
advanced for the case of thorium elucidates satisfactorily
everything that has so far been observed for radium; and,

* Communicated by the Authors.

446 Prof. Rutherford and Mr. Soddy on the

knowing the time constants of the processes involved, it is
possible to predict from general principles the whole course
of any series of changes of the radioactivity of radium under
any given conditions. The main point of distinction is in the
rate at which the emanations in the two cases lose their
activity. The intensity of the radiation from the thorium
emanation falls to half value in one minute, while that of the

malinnm emonotion falledo dale yaluelm about tons days. In
one case, therefore, the change occurs about 6000 times faster
than in the other.

On the other hand, the excited activity from radium decays
much faster than that produced from thorium. The former
is almost inappreciable a few hours after the removal of the
exciting cause, whereas the latter continues for several days.
In the case of radium the emanation and the excited activity
produced by it contribute the major proportion of the total
activity, while in the case of thorium these effects are, for
various reasons, not so marked.

The experimental analysis of the processes that give rise to
the radioactivity of radium have so far not given any evidence
of the existence of a stage corresponding to that of thorium X
in the case of thorium. — It will be recalled that the first stage
in the disintegration of thorium is not directly into the
emanation, but i into an intermediate system named Thorium X,
which then gives rise to the emanation by further change. In
the case of radium it has not yet been found poss sible to
separate any system intermediate between the radium and the
radium emanation. From analogy to thorium one would
expect that a Radium X or RaX, analogous to ThX, existed ;
but the quantity of radium at our disposal has been ‘too small
to enable us to obtain a definite answer to this question.

After the removal of the emanation and excited activity
radium retains about 25 per cent. of its normal activity, which
is not affected by chemical processes, and constitutes a “ non-
separable ” activity, analogous to that possessed by thorium
and uranium. But whether thisisin reality the non-separated
activity of ‘Radium X” superimposed on the true non-
separable activity has not yet been determined.

In the present paper the radioactivity has been examined
in detail, and the results are in accordance with the view that
the radium is changing spontaneously at a constant rate into
the radium emanation, whose further changes give rise to the
phenomenon of excited activity. In addition, the compa-
rative study of the two emanations has settled some points
left over in the discussion (Phil. Mag. 1902, iv. p. 582) of the
nature of the emanating-power of thorium see 3).

Radioactivity of Radium and Thorium. AAT

§ 2. Rate of Decay of the Activity of the Radium Emanation.

It has long been known that the activity of the radium
emanation decays very slowly, and special methods were
found necessary ‘for its determination. The emanation mixed
with air was obtained from a solution of radium chloride kept
-inaclosed bottle, and was stored over mereury in an ordinary

gas-holder. From time to time equal quantities were mea-
sured off by a gas pipette and delivered into the testing-
vessel. The latter consisted of an air-tight brass cylinder
carrying a central electrode insulated by an ebonite stopper
provided with a guard-ring connected to the earth. A
sufficient voltage to obtain the saturation-current was applied
to the outside of the cylinder, and the inner electrode was
connected with the electrometer, with a suitable capacity in
parallel. The contents of the gas-holder were thoroughly
mixed by shaking, and a definite volume measured off by the
pipette and blown into the cylinder which was then closed
air-tight. The ionization-current immediately after the intro-
duction of the emanation furnished the measure of the activity
of the latter. The measurements were repeated at suitable
intervals over a period of 33 days before the effect became
too small to be accurately determined.

The fellowing table expresses the results :—

Time in Hours. Relative Activity.
0 100
20°8 85°7
187°6 24:0
3594°9 6°9
921°9 1°5
786°9 O-19

It will be seen that the activity falls in a geometrical pro-
eression with the time and decays to half value in 3°71 days.
If I, is the original activity and I, the activity after time ¢,

Taking as the value of X the mean value deduced from the
last four observations of the above table, we find

M216 LOS

when ¢ is expressed in seconds.

In these measurements the effect of excited activity was
eliminated by taking the current immediately after the intro-
duction of the emanation into the cylinder. Ina closed space
the ionization-current steadily increases after the introduction

463, rea

448 Prof. Rutherford and Mr. Soddy on the

of the emanation, very rapidly at first and then more gradually
until it attains a maximum after 5 or 6 hours nearly twice
as great as at first, and then decreases according to the above
law of the decay of the emanation. If when the maximum is
attained the emanation is blown out of the testing-vessel the
excited activity remains, representing about one-half of the
total activity, concentrated on the negative electrode. In
the actual measurements it was usual to take a series of
readings at regular short intervals after the introduction of
the emanation. The proportion of the current due to the
emanation could be easily deduced from these readings, for
the proportionate increase due to excited activity is for any
given interval independent of the quantity and “age” of the
emanation, and is the same throughout the whole series of
measurements.

During the progress cf the work a very similar result to
the one above given for the rate of decay of the radium
emanation has been published by P. Curie (Comptes Rendus,
1902, cxxxv. p. 857) under the title “ On the Time-Constant
characteristic of the Disappearance of Radioactivity induced
by Radium in a Closed Space.’ It is an interesting example
of how a measurement of the rate of decay of the excited (or
induced) activity in a closed space containing the radium
emanation gives in reality the rate of decay of the latter, and
not of the excited activity at all. The latter decays at the
same rate in the free air as when sealed up in glass.

M. Curie measured the penetrating radiation emitted from
a sealed glass tube containing the radium emanation; and
since the latter gives no penetrating rays (compare § 5), the
effect measured was solely due to the excited activity on the
walls produced by the emanation. As we have seen, after an
initial period of some hours this effect attains a maximum,
and then represents the equilibrium-point when the decay of
excited activity is balanced by the continuous production of
fresh active matter from the emanation. As the activity of the
emanation decays, so also does its power of exciting activity
decrease in like ratio. Hence the excited activity in a closed
tube containing the radium emanation furnishes a measure of
the activity of the emanation itself. After the initial period
of a few hours has elapsed, its constant of decay is the same
as that of the emanation. If at any time the emanation is
blown out of the tube, the rate of decay changes at once to
the time-rate of decay of the excited activity, as M. Curie’s
experiments themselves show.

M. Curie performed his experiments under the most varied
conditions and the rate of decay of the activity was unaffected

Radioactivity of Radium and Thorium. 449

in all cases, as we have already shown for the thorium
emanation. M. Curie, however, apparently overlooked the
initial period of increase, and states that the rate of decay is
uninfluenced by an alteration of the time of “ activization ”’
(or exposure to the original radium) from 15 minutes to one
month. As we have seen, for any period under 5 or 6 hours
the excited activity will increase at first instead of decaying,
and for a period as short as 15 minutes this effect would be
very marked. This increase of activity, due to the steady
production of excited activity when the emanation is trans-
posed from one vessel to another, is of course only one example
of many similar ones that have now been accumulated. But
it would be difficult to get in any single experiment a better
illustration of the real nature of the phenomena occurring in
radioactivity. A quantity of the emanation is removed from
the radium that produced it, and, mixed with air, is stored
like an ordinary gas over mercury in a gas-holder. Several
weeks after, it may be, a portion is removed to a new vessel,
when its activity is found to rise steadily to double its original
value in the course of a few hours, showing that all the time
it has been manufacturing out of itself the fresh active matter
which causes the excited activity. When the maximum is
reached, it is not because the process of manufacture has
stopped, but because an equilibrium has been reached between
the rate of supply of new active matter and the rate of decay
of that already deposited.

§ 3. The Occlusion of the Emanations.

In the solid state radium compounds give out so small an
amount of emanation that special methods must be employed
to detect it. As in the case of thorium compounds, heat or
moisture, but especially solution in water, increases the
emanating-power of radium; but these effects are far more
marked in the latter case. The same considerations apply
equally to the power of radium to excite or induce activity on
bodies in its neighbourhood; for the activity excited under
any conditions is proportional only to the amount of emanation
present. ‘These variations in the power of exciting activity
in radium compounds were observed by Dorn and by M. and
Mme. Curie.

Radium compounds can be de-emanated by ignition, and
the de-emanated compounds recover their power as soon as
they are brought into solution, exactly in the same manner
as we have shown for thorium compounds (M. and Mme.
Curie, Comp, Rend. exxxiv. p. 85, 1902). It may be stated

450 Prof. Rutherford and Mr. Soddy on the

generally that the emanating-powers of both radium and
thorium are ata practical maximum in solution.

The question arises as to what the variations in emanating-
power (2. e. the amount of emanation produced per gramme
per second) aredue. It was pointed out in the case of thorium
that they can be interpreted in two ways. Hither an alte-
ration in the velocity of the reaction producing the emanation
occurs, or the same amount is produced in all cases but the
time taken for the emanation to escape from the compound is
ditterent under different circumstances. This question, which
is of comparatively secondary importance in the case of
thorium, becomes of paramount importance in the case of
radium. For since the radium emanation loses its activity
only after a period of several weeks, the view that the
emanation is being continually produced at a constant rate
necessitates the conclusion that there must exist in a solid
non-emanating radium compound a large amount of emanation
stored up or ‘ occluded” in the compound. This will be
given up when the substance is dissolved, so that there should
occur a sudden “rush” of emanation from the solution very
much greater than the amount subsequently produced.
Assuming that in a solid radium salt no emanation escapes,
and that in the same salt when dissolved the emanation
escapes as fast as it is formed, it is easy to calculate the ratio
of the amount given off on the solution in the first “ rush” to
the amount given off in any subsequent period.

Let gy=the number of particles of emanation produced

per second by a given amount of radium.
N,=the number of particles stored up in the same
quantity in the solid state.

N, represents the equilibrium state when the rate of pro-
duction of fresh particles of emanation is balanced by the
rate of change of those already present. If the process of
production were stopped, the number N,; left after the time ¢
would be given by

Ne Nie
where A is the constant of decay of the activity of the
emanation. The rate of change

aN: r
oe —AN;:.
At the equilibrium point therefore
Jo ee
Neeelinr
ae = = 463,000,

substituting the value of \ found in § 2.

Radioactivity of Radium and Thorium. 451

The amount of emanation stored up in a non-emanating
radium compound should therefore be nearly 500,000 times
the amount produced per second. This result was tested in
the following way. ‘03 gr. of solid radium chloride, of
activity 1000 times that of uranium, was placed in a Drechsel
bottle, and. sufficient water drawn in to dissolve it. The
released emanation was swept out by a current of air into a
small gas-holder and thence into a large testing cylinder.
The maximum ionization current observed immediately after
the introduction of the emanation is proportional to No.

A rapid current of air was then drawn through the radium
solution for a few minutes, and the Drechsel bottle was then
closed air-tight for a definite time, viz. 105 minutes. At the
end of this period the accumulated emanation was again swept
out as before and transferred to the testing vessel. The new
ionization current represents N, the amount of emanation
produced in the time ¢.

N,, the amount occluded, gave 4°46 divisions of the electro-
meter per second with a capacity -494 microfarad in parallel.

N,, the amount produced in 105 minutes, gave 5°48 divs.
with a capacity ‘00526 microfarad.

Thus N,

Assuming there is no decay during the interval,

N= 105 x 60d0-
r : UV
Thus No _ 480,000,

Making the small correction for the decay during the
interval ¢

No
Yo
We have previously shown that from theory
IN Gane
—? = — = 463,000.
qo *

The agreement between theory and experiment is thus as
close as could be expected, and is an interesting example of
the way the processes occuring in radioactive bodies may be
brought to the test of quantitative experiment.

This experiment proves conclusively that the production of
emanation occurs at the same rate in a solid non-emanating
radium compound as in the solution. In the former case it is
occluded, in the latter it escapes as fast as it is produced.

= 477,000,

452 Prof. Rutherford and Mr. Soddy on the

An experiment gave as the value of the emanating-power
of solid radium chloride in a dry atmosphere less than half
per cent. of the emanating-power of the solution; or to express
the result in another way, the amount that escapes per second
is less than 10~$ of that occluded in the compound. Moisture,
however, Increases it many times.

Exactly the same consideration applies to the case of
thorium. If the manufacture of the thorium emanation pro-
ceeds under all circumstances at the same rate, the solution of
a solid non-emanating thorium compound should also be
accompanied by a “rush” of emanation at first greater
than the amount obtained subsequently. But here the very
rapid rate of decay of the emanation will make the effect less
marked. For the case of the thorium emanation

ae ele
Jo *

It has been shown that thorium nitrate in the solid state
only possesses 54, part of the emanating-power of the same
compound in solution. A quantity of finely powdered thorium
nitrate was dropped into a Drechsel bottle containing hot
water and the emanation immediately swept out into the
testing vessel by a rapid current of air.

The ionization current in the vessel rose to a maximum,
and then fell again immediately to a steady value, showin
that the amount of emanation released when the nitrate dis-
solves is greater than the subsequent amount produced by
the solution. The rapid rate of decay renders a quantitative
comparison difficult. By slightly altering the arrangement.
of the experiment, however, a definite proof was obtained that
the rate of production of emanation is the same in the solid
compound as in the solution. After dropping in the nitrate,
a rapid air-stream was blown through the solution for
25 seconds into the testing vessel. The air-stream was
stopped and the ionization current in the testing vessel im-
mediately measured. ‘The solution was then allowed to stand
for 10 minutes undisturbed, in which time the accumulation
of the emanation in the Drechsel bottle again attains a
practical maximum and again represents the steady state.
The air-stream was then blown through as before for 25
seconds, stopped, and the ionization current again taken.
In both cases the electrometer recorded a deflexion of 100
divisions in 6°8 seconds. By blowing the air continuously
through the solution the deflexion observed when a steady
state was reached was 100 divisions in 12°6 seconds, or
about one-half of that observed after the first “ rush.’’.

Radioactivity of Radium and Thorium, ADS

In the case, therefore, of both thorium and radium the
manufacture of emanation takes place at the same rate in
non-emanating as in highly emanating compounds.

_ The effect of heating solid non-emanating radium com-
pounds is precisely analogous to the effect of dissolving
tnem. It has long been known that the emanating-power
of solid radium preparations is increased to the order of a
hundred thousand times by heat. As in the case of solution,
the occluded emanation is liberated ; and when this has passed
off the effect again falls to a value approximating the true
emanating-power, 7. e. the amount of emanation produced
per second.

A compound like thorium oxide, possessing in the solid
state one-third to one-fourth of the emanating-power of the
amount of thorium in solution, has its emanating-power
increased 3 or 4 times at a dull red heat. A compound like
the hydroxide or carbonate, on the other hand, which pos-
sesses as much emanating-power in the solid state as when
dissolved, does not suffer much increase of emanating-power
with rise of temperature.

The changes of emanating-power that are produced in
thorium and radium compounds by ignition, moisture, solu-
tion, &c., are therefore to be ascribed solely to changes in
the rate of escape of the gaseous emanation into the sur-
rounding medium from the substance producing it. This
result is of great importance in the general theory of radio-
activity, for it brings into conformity what might otherwise
have been regarded as an exception to the view that the
processes which maintain radioactivity lie outside of the
sphere of known molecular forces.

Attention may here be drawn to the fact that the general
phenomenon of occlusion of a gas by a solid is not connected
at all with the radioactive properties of the matter in question,
although in the present instances radioactivity has furnished
a convenient means of accurately studying the problem. The
helium is given off from the mineral fergusonite, for example,
in part when it is heated, and completely by dissolving the
mineral.

It is therefore to be expected that if any of the unknown
ultimate products of the changes of a radioactive element are
gaseous, they would be found occluded, possibly in consi-
derable quantities, in the natural minerals containing that
element. This lends support to the suggestion already put
forward (Phil. Mag. 1902, iv. p. 582) that possibly helium is
an ultimate product of the disintegration of one of the radio-
active elements, since itis only found in radioactive minerals.

Phil. Mag. 8. 6. Vol. 5. No. 28. April 1903. 2 Eh

454 Pyof. Rutherford and Mr. Soddy on the

§ 4. The Influence of the Emanation on the Radtoactivity

of Radium.

The converse of the changes that occur when a solid radium
preparation is dissolved in water has now to be considered.
One of the earliest facts observed in connexion with radium
was the steady increase of its activity after preparation
(Giesel, Wied. Ann, vi.a p. 91, 1899). Consider the case
of a preparation of radium that has been kept for some
time in solution in the open air and then evaporated to
dryness. The emanation that before escaped is now cccluded,
and the gradual accumulation of the emanation and of the
excited activity it produces causes a gradual increase of the
activity of the preparation until a maximum is reached some
weeks after. A solid compound of radium, on the other
hand, that is dissolved and then immediately evaporated to
dryness, loses its occluded emanation, but retains the excited
activity that the latter has produced. Hence in this case
there will occur a fairly rapid decrease at first as the excited
activity decays, followed after a few hours by a slow increase
as before, due to the production and occlusion of fresh
emanation.

Again, apart from the consideration of the possible exist-
ence of RaX analogous to ThX, the general analogy to
uranium and thorium would lead us to expect that the
removal of the emanation and excited activity will not
entirely remove the radioactivity. A certain proportion of
the total, constituting a non-separable activity, will remain.

These considerations are borne out by experiment. Radium
chloride was dissolved in water and a current of air aspirated
through the solution. After a few hours the radioactivity of
the salt obtained from the solution was found to have been
reduced to a minimum ; and longer aspiration over three
weeks did not affect it. This is the non-separable activity.
The solutions were evaporated to dryness, and the course of
the recovery of the activity observed over a period of three
weeks, after which the activity remained constant, at about
four times the original value.

The following table expresses the results :—

Activity Percentage

Time in Days. Activity Recov ered.

0 25-0 0
0°70 33°7 11-7
1:77 42-7 23-7
475 68-5 58-0
7°83 83:5 78-0

160 96-0 95-0

21-0 100-0 100-0

of Normat

Activity

Radioactivity of Radium and Thorium. 455

In the second column the final activity is taken as 100:
In the third column the proportion of the lost activity
regained is tabulated. These results are shown graphically
(curve A). The curve B shows the decay of activity of

Time in Pays
the emanation drawn from the table in § 2. The two
curves are quite analogous to those obtained for the decay:
and recovery of UrX and ThX respectively. The proportion
of the activity regained after an interval ¢ is given by

where 2X is the coefficient of decay of activity of the radium
emanation. ‘The curve of recovery of the activity of radium
can thus be deduced if the rate of decay of the emanation is
known. In these experiments the non-separated activity was
25 per cent. of the final activity. The activity of the emana-
tion, together with the excited activity it produced, made up
the other 75 per cent.

The above equation is only approximate owing to the
existence of a period of retardation of a few hours, due to the
time taken for the excited activity to reach a steady value
for any given quantity of emanation present. It is, how-
ever, too small to affect the results appreciably and may be

neglected.
Somewhat similar experiments were performed tor thorium.
A sample of thorium hydroxide of high emanating-power
was ignited over a blast-lamp and converted into the de-
emanated oxide. Its radioactivity was found to rise in

2H 2

456 Prof. Rutherford and Mr. Soddy on the

consequence about 20 per cent. in three days, and remained
constant at the higher value.

In the converse experiment the thorium hydroxide was
kept for three days in liquid air, 7. e. under conditions where
its emanation is condensed and produces the excited activity
in the compound itself. It was spread on a plate and its
activity found to decrease about 12 per cent. after afew days.
These results are to be expected if the rate of production of
emanation is constant and independent of chemical or physical
conditions. When the emanation is prevented from escaping,
its activity, and also the excited activity produced by it,
cause an increase in the intensity of the radiations emitted.
in the second case, the activity decreased, since some of the
emanation escaped from the compound at ordinary tempera-
tures, and, in consequence, some of the excited activity
deposited in the compound gradually decayed.

8 5. The Radiations of Radium.

Radium, like thorium and uranium, emits two types of
radiation, the @, or easily absorbed rays (deflectible in very
intense magnetic fields), and the 6, or penetrating rays,
readily deviated ina magnetic field. It also emits some very
penetrating rays. which, however, have not yet been fully
investigated. The non- separable ‘activi ity of radium, which
remains after the emanation and excited activity have been
removed, consists only of a rays, the @ radiation being less
than 1/ 200 of the amount normally present. In this respect
the three radio-elements are analogous.

The radiation from the radium emanation was tested by
introducing it in a cylinder made of copper-sheet -005 cm.
thick, which absorbed all the « rays and allowed the rays
to pass through with but little loss. The external radiation
from this cylinder was determined at intervals commencing
about 2 minutes after the introduction of the emanation.
The amount at first observed was extremely small, but in-
creased rapidly and reached a practical maximum in 3 or 4
hours. Thus the radium emanation also only gives @ rays,
the 8 rays appearing after the latter has changed into the
excited activity. On sweeping out the emanation from the
cylinder by a current of air there was no appreciable decrease
of the radiation immediately, but the radiation commenced
to decay rapidly with the time, falling to half value in about
30 minutes. <A similar result has been obtained by P. Curie.

Attention has been called (Rutherford, Phil. Mag. Jan.
1903) to the irregular character of the curves of decay of
both thorium- and radium-excited activity, as measured by

Radioactivity of Radium and Thorium. ADT

the a radiation, and the view was put forward that this stage
probably represents a double change in the case of thorium,
and a treble change in the case of radium. In the latter
there is (for a short exposure to the emanation) a very rapid
decrease for the first 10 minutes to about 20 per cent. of the
original value, then a period of very slow change, and then
a more regular decay in which the remaining activity falls to
half value in about 30 minutes.

Now the decay curve of the @ radiation of the radium-
excited activity shows a fairly regular decrease to half value
in 30 minutes. Hence there is strong evidence that the 6
rays are not given out in the first change of the excited
activity, but only in the second or third change.

Radium therefore fully supports the view already advanced
that the @ rays are in all cases the first to be produced, the 8
rays only resulting in the last stages of the process that can
be experimentally traced.

‘6. The Chemical Nature of the Radium Emanation.

The experiments already described on the chemical nature
of the thorium emanation were repeated for that of radium.
Asin the former case all the reagents tried were without effect.
The emanation passed unchanged through phosphorus pent-
oxide, sulphuric, nitric, and hydrochloric acids, and over red-
hot lead chromate and metallic magnesium. Water does
not dissolve the emanation appreciably, and the activity of
the water is solely due to the presence of the excited activity.
The emanation in both dry and moist atmospheres is un-
affected by passage through a platinum tube electrically heated
to the point of incipient fusion. An interesting effect, how-
ever, was observed as the temperature approached a white
heat in this experiment,

The ionization current due to the emanation decreased with
rise of temperature, but returned to its original value when
an increased voltage was applied sufficient to give a saturation
current through the gas. This effect is due to fine platinum
dust given of from the white-hot platinum, and is quite
analogous to that of tobacco-smoke observed by Owens (Phil.
Mag. 1899, xlviii. p. 377) in this laboratory.

The condensation of the radioactive emanations of thorium
and radium at the temperature of liquid air (Proc. Chem.
Soc. 1902, p. 219) will be dealt with in detail in a separate
communication.

McGill University, Montreal,
Feb. 20, 1903.

[ 458 4]

XLV. The Problem of Columbus. By H. W. Carman,
B.Sc., University College, London*.

[Plate XI. ]

t; ha an ordinary hard-boiled egg be laid on its side on a

horizontal plane and be then given a spin round the
vertical its axis will rise and at last stand up on its end, still
spinning ; in this position it will remain until its motion
fails and it falls down. This problem I term Columbus’s
Problem. To a first approximation it would appear as if the
dynamical problem could be treated as identical with that of
a body symmetrical about an axis and with a hemispherical
end moving on a perfectly rough horizontal plane.

The only references [ have been able to find to the motion
of a body of this nature are first, in Jellett’s ‘Treatise on
Friction, where the case is discussed in which the spin
round the long axis of the egg is taken so large that all the
other motions are small in comparison with it. A second
reference occurs in Routh’s ‘Advanced Rigid Dynamies,’
Article 244, Example 4, where the equation of angular
momentum (my Equation 12) is given.

There are several investigations of the more general problem
of a solid of any shape moving on a plane. In Poisson’s
Traté de Mécanique the small oscillations of a body on a
smooth plane are treated of. In the 5th and 8th vols. of
Crelle’s Journal M. Cournot considers the case of a body on
a perfectly rough and also on an imperfectly rough plane,
but he confines himself almost wholly (1.) to showing that
there are sufficient equations obtainable to determine the
coordinates of the body, and (ii.) to the consideration of
initial motions.

It therefore appeared of interest to examine whether the
problem of the egg could not be completely solved in the
most general case. This solution is effected in the following

ages.

i 2. Let O be the point of contact at any time, C the centre
of the hemispherical base, and G the centre of gravity
of the egg. Let OCZ be the vertical through O, OX the
projection of CG, the axis of the body, on the horizontal
plane, and OY a perpendicular to OX in this plane. Let
OC=a, CG=hA; let the moment of inertia of the body about

* Communicated by Prof. Karl Pearson, F.R.S.

The Problem of Columbus. 459
CG be C, and about any perpendicular to CG through G be A.
Let 2 ZOG=6 and the angular velocity of the plane ZOX

about OZ be wy. Let R be the normal reaction at O and
F’,, F, the components of the friction along OX, OY. Take

GA the perpendicular to GC in the plane ZOG, GB the per-
pendicular to this plane, and GO’ the axis of the body as
principal axes. They wiil coincide in direction with OX,
OY, OZ when 6=0. Let the spins of the body round them
be @, @:, w;, and the spins of the axes round their instan-
taneous positions be 6, @, @;. Also let the velocities of G
parallel to OX, OY, OZ be w, v, w.

3. Then we have clearly

ee! Tl sles oe)

460 _ Mr. H. W. Chapman on
Also by the modified form of Euler’s equations,

——— — A@3w.-+C0,.0,= moment of external forces about GA,
ie — 06,3 + AP,o; = ss 35 33 GB,
on — A6,w, + A0,0.= ss 39 39 GC’.
These give by (1)
—Awsin 6—2A6W cos 6+ Co; 6 =F (h +a cos 0), ae
A6+ Cov sin 6—Aw? sin 6 cos @= Rh sin @— F, (a+hcos 6),
(3)
Co,—F ja sin@,. . Yaa (4)

Next consider the accelerations of G referred to OX, OY,
OZ. This system of axes has a spin round OZ, so we get

du ee te e
dt a iY ie . . « . . ° (5)
dv ie ih :
dt + up = VW (6)
dw oe

ye = M — J ; A 3 2 (7)

We have also the geometrical equations arising from the
fact that O has no velocity, since the surface is supposed to
be perfectly rough.
Velocity of O along OX=velocity of G parallel to OX
+velocity of O relative to G
parallel to OX
=u--@(a+h cos 8),
. ron (1) @—(a-- cos 0)0. ~. ’e

Pare of O along OY=velocity of G parallel to OY
+velocity of O relative to G
parallel to OY
=v+ @,(h4-a cos 8) 4- Wil 8 sin 6,
-. from (1) v=wWsin O(h + acos@) —a;asin @ (9)
and clearly w=—Asm00. . . . . 1210}
4. As the plane is perfectly rough we can use the equation
of energy. This is

4M(u? 4+ v2? + w?) +4(Ao,’? + Aw,? + Cow;”) + Mgh cos €=constant.

the Problem of Columbus. AGL

_ Using (1), (8), (9), (10) this becomes

3M[(a+hcos 0:20? + Iwrsin O(h+a one 6) —«,;a sin 6?

+1? sin?66” | +4A (62+ sin’@) +40w;?+ Mgh cos @= constant.

; A
ie) cag + (1 +2" cos 6+

1) t 6 oe +e0s 8) + Hee
— esp sin%6{ + Cos a) + *( a f sin?) 4% os OG = Kam

K being the initial value of the left-hand side of the equation.
Multiply (2) by asin @ and (4) by (h+ a cos 6) and subtract;
then . t “ ae
Co;(h+4 cos$) —Co 3a sin 06+ aA sin?é + 2aA 0 sin Ocos 0=0:

Integrating and dividing by a
Co,(- + cos @) + Aw sin?@=A= vo" + cos @o) +Amsin’@, (12)

where 3, 2, @) are the initial values of @3, wy, 6.

This is the equation of angular momentum round the
vertical through O.

5. Substituting from (8) and (9) in (6) :

wr sin 0(h+a.cos 0) +W cos O(h +a eos 6) —anv sin?6

_ Gat sin 0-—-a cos0ws + + (a+h cos 6) b= i By,

4
Sea vee prom 3

ze “ir sint4( = €0s @) + 270 sin 6 cos a(~ + cos @)

=o ay + sin?) +3 sin 8 cos 00,

er
*

h : uae Ara eet MI ie AiG in? )
i + cos a: sin ie dey en +sin2@

j
Ce ics <in*@)

462 Mr. H. W. Chapman on
C h : C 3
*. Integrating, — x @3 i + cos 0) = on( oat +sin’@ )+ constant,

»{A0

: a; 2 y
a th sind+ O(% +008 @) t a?

a2 | ayy tA sin? + +cos 0 Je (13)

We get from this

| | if
Ue «eM + A sin’@-+ o(; + cos 6)
d\@s| 12 |sin | A. cos 0— o(- + cos 8) }

| A sin?™ + (= + cos 6) be
*. | @3 | decreases as @ increases if
A COs @>0(" + cos 0),
é.(A—C) ccs g>O2. |

We have then four cases :

G.) A>C andwe 3:

If (A—C) cos 6, >C" we shall have |@3| decreasing as 0
increases until (A— C) cos 0= Cage when it will be at a

minimum, and then as the top an further down it will
increase again.

If (A—C) cos @>C and the top is rising, || will
increase as long as the top rises.

If (A—C) cos &< oe and the top is descending, | @; | will
increase as long as the top descends.

If (A—C) cos ®< of and the top is rising, | @s; ie will
decrease until (A—C) cos d= oz , and then increase again

if A— coce ;1fA—C< oe it a decrease all the way up.

the Problem of Columbus. 463
Gi.) A<C and h>O. The condition is never satisfied if
eae If fee the conditions of the problem are not

satisfied unless the body is spherical. In this case the top
behaves as in (i.), changing the signs of (A—C) and cos @.

(iii.) A>C,h<0. The condition is satisfied as long as
N20 < = lp @> = oy it is as in the first case, changing the
signs of cos @ and h.

“(iv.) A<C,A<0. This is similar to the first case, if we
write C—A fon A—C and |h| for h.

In any case the position for which | 3| is a minimum, if
a possible one, does not depend on the initial motions. Also
3; cannot become zero or change its sign, for the roots of

AC as h BBE ie ; ae
2M + Asin 6+C(— + cos @) =() are clearly imaginary, the

left-hand side being the sum of three positive quantities.
6. Substitute from (12) in (11) for wsin?é ;

(ng eos) } [d= Can( eos) |

a‘sin- G

Ae 0
us DRe (5 + evs 6 a adh = pe) +; x 42 Se :4)

} A ZG) ee
+64, sy t1+2/c0s 0+ n) aK he noes
h 2
2 a ft :
ke [eG + cos @) | one +e0s8) 20 (7 + cos 8)
— A* sin? a A
Dro, (tee -— tC O(| +e0s8) s
ae + Sin” 0) us aM | » en |
& eM A sin? 6

‘ 2 }
+ 6° is +1+ .,.
a” M. an a

A h Q
| aml +( € + Cos yf:

AZ sin?

=K— cos —

464 Mr. H. W. Chapman on

2 2

OF oe + Asin? 9+0(7 +cos 6 | lo Len +Asin?6 }
a’ M sale a

gin

: ear Se lee AAs h a

2ro (7 +0058) Py ae a+0(; +e0s8) }

A? sin? 6

deta ay) ey h? C h iu
A*sin? 0 @ (ca Pt ee +27 cos)
oh h ae pike } | A h 2
+n Le(> + cos a _ + A? sin? @ +07) 2M + (; +2058] |
+ Asin? @ ie cos — K)
a

ae ee ali 2
—2)rn "(i + cos 9 ay tA sint6+0(7 +005 ) . (14)

The positive value of the root will be the right one if we
take n of the same sign as @;, and therefore as w;. This can
be done as the sign of 7 is still at our disposal.

If we put cos =p, the equation becomes

A he h AX? h?
A oat 2M ea aes 7) ie yt e+ Cm)

2
+ An?—A’°K + 2u | 2 (? + Cn?) + ghee |

z 3 2
+e? (A? + Cn?--- An? + A?K) —2 ue be

=2)n An) / AC rarok +204 (C= A)p* (15)

The height of the centre of gravity of the egg above the
horizontal plane is a+hw. Hence (15) is the fundamental
equation giving the vertical motion of the centre of gravity.
This defines the nutation.

the Problem of Columbus. 465
h Q
7, From (12) Awsin? (=’—Co she + cos }5

Cn( 7 + COs Bi

-, by (18) Aw sin?6=)\— sc aa =. (16)
=, +A sin a+0(7 + cos co 6)
a” M
When cos 9=y is known in terms of the time, (16) will
give y and therefore w in terms of the time. Thus (16)
defines the precession.
Now we see from (16) that if @ becomes zero we must
either have wsin @ infinite or
Cn GG : +1)
ie AC aie,
aM c(, a
But if sin @ were infinite the kinetic energy would be-
infinite, as we see from its expression in {11) ; for the only

negative term in that expression is — Qo sin? 0 (« + cos O ) ?

which cannot become infinite, for wsin?@ is not, neither
1s 03

. the ege cannot stand up on end unless

r AC ro(4 +1) =On(7 +1).

aM
The right-hand side of (16) is an even fnnction of @, so
that if it he expanded in terms of 0 we see that the terms
containing @ will disappear, and ab sin 6 will tend to the limit

zero, and af to a finite limit if the above condition be
satistied.

8. The integral of the equation (15) cannot be expressed
in known functions, but the following considerations will
throw some light on ‘the nature of the motion :—

ZghA? = =
pw — W(X? + Cr? — An? + A?K) — auf “Q2 + Cri) + 22S a
| An

“a

|
| — An? +A°K —(Q24Cn')% _
|
|

Wy +2yn(< tM (ex 1 Noe F208 p+ (C —A)2)

he ae

p= +t as
AY ag ti+ 4 F By ee ne

466 Mr. H. W. Chapman on

When p=p, this must be satisfied identically, so that the
right-hand side must become + (u.2)*; thus the positive sign
is the proper one if bb, is positive, and the negative one if Ly
is negative.

If »,=0, let us differentiate (15) with respect to ¢ and
divide by uw; this ones

RN. lie h ” ha? -, Gh P : ghA?
é 2 peat ee a 5) yetigieas 2D +) ay 2 ee '
2A (er tlee 420m uso" 4247 O84 On) 4%, }
+ Qu? + Cn? — An? + A?K) — a We
AG). Ser eae
== 2NM i Cee Ge pat 2
eM Cie Ca Ee
h ht
2An(~ tu) {O° 4(C—Ajat
Aerob wa | ues i
A Su ee oh ee . 2 Se

If we put w=y,, » vanishes and we get the initial value of
y. The sign of this is clearly the one to take in (17).

Now the roots of the expression under the radical in the
numerator in (17) are clearly irrelevant ; this is at once seen
from its form in 6.

Also the root of the denominator is irrelevant, being
clearly < —1.

From this we see that to every possible value of pw there
correspond two and only two values of w,and these are equal
and opposite, and we can only pass from one to the other by
w passing through a root of the numerator of (17).

There are three cases to be considered. <A root, to be
relevant, must <1 in absolute value and be placed so that
is moving towards it.

(az) The numerator has a real and relevant root, and the
first root it reaches is single. Then if this root is a, put
w=aty, x being small. Then toa first approximation y= Bx®
where # is a constant.

This gives y2=4At, so that ~ reaches the root in a finite
time; the motion is then reversed and it goes back again till
it reaches another root.

(8) The first root réached is double. Then to a first
approximation

X=rx ;
Bit= log x ;

the Problem of Columbus. 467

so that y can only become zero after an infinite time and the
axis of the body approaches asymptotically to a certain cone.
lf the root be of higher order still,

2
// ee
B = a 29

and there is again asymptotic approach to a cone.
(y) There is no relevant root.
This is impossible, for we have the numerator in (17) posi-

tive in every possible position, otherwise 4 would become
imaginary.
When p=1 itis

-ve(t jefe)
+2An ( Fee lg/ ae +0(2 +1)
= ae my t G +1)'—n(* +1) veh

When p= —1 it is

A A i] 2
Te a =) , (1) ver.
These are both negative or zero.

So that there is always a relevant root.

We also see that the egg cannot stand up unless

as a. : +1) - vOn(“ +1)=0.

This is the condition found in art. 7, it will be observed that it

is independent of the value of u,.

We see by this that if the top be started with mw between
two roots, it will oscillate up and down between the two cones
defined by these roots, or else approach one of them asym-

ptotically.
If it be started at a single root we have w,=0, but py will

clearly not be 0, for this would involve (s) =0, if N is
L=Ko

the numerator in (17), and the root would be double,
lf it be started at a double root 4) =0 and b=0, so we have

468 Mr. H. W. Chapman on

a case of steady motion; itis necessary to consider the Ligon
of this.
If the root we start with be «, put nee EN and we have

V= f(a) + Vf (a) + ai “(@).
W=f' (a) + Vf"(a).
But f(@=

Then, on solving this in the ordinary way, we see that the
motion is stable if f(a) is negative and unstable if f”(a) is
positive.

9. The case in which the root considered is w= 1 requires

special attention. In this case the vanishing of w does not
imply the vanishing of 6, for »=—sin 60, and thus
sin @=0, so that ~=0 whatever 9 may be. Consequently,
although the value of w turns back the body itself need not,
but may pass through the vertical position.

We will therefore go back to the equation for @ and make
@ small.

It can be written

sin? 0¢?=f(6), where f(@) is obtained from (14).

7(@) is clearly an even function of 6, so we have, neglecting

66 and 6°, :
G6? =7(0) + 5 Cf") + “f(0)
=C,+ Ci. + C,%, say
Put C=.
Then we have
du

Vi Aakenee: ct

| du
2t+e= SEES a
e/ VC, +Cow+ Cyu?

A its #2
i | a/c (ees = ) ae
4

u+ = Me Ci ee ect VC,(2t +e)

if Cy is positive,

This will give

the Problem of Columbus. 469

and Bi a = ype ae Sun 4/ = =O Oats

if C, is negative.
We see that in either case for the approximation ever to be
Co, i

C,?

valid we must have small, as is otherwise obvious, for

C, must be smail.

‘This ensures NW (= C2" or ) being positive, which is also

seen to be necessary,

In the first case we see that uw cannot remain small, This
therefore gives the motion near the origin, but need not be
further considered,

In the second case we see that for the approximation to
hold always, both

C, /C2—4C,C,

- aC, 30)
and ahs a 2x MC —40C, must be small,
74 OF 20) :

?.e, C, and C, must both be small.
This j is really a case of the last article, the egg oscillating
between two cones both near the vertical.

If C,=0 we have
ape + nee ZONE

Hy OS Ne alee)
and C, is negative, so

Cy : eae i
pee ON psi (0, (Ones)

c—

eed T
- af /—C, oe

Real ss -sin (we Cae ea

This will be always valid near the vertical, iy we see that
in this case the body oscillates through the vertical inside a
cone whose semivertical angle is given 1 by the next root.

T£ C, is small the approximation is alw ays valid. We see

by (17) that when C,= =0, 2.¢.
AC” tc
r Mt ee — +p +1) = = Cn ( 0 1 ),

Aw sin? @ takes the form 676? +
Phil. Mag. 8. 6. Vol. 5. No. 98. April 1903. oF

470. Mr. H. W. Chapman on

Therefore neglecting 6* and substituting in above equation
we get

t
v= = + constant,

rz
. 0= Gy se Vv a constant),
2

This is a well-known equation, and when 6,=A —C, we
see that the curve traced out by the axis isa circle on one
side of the vertical.

10. There are some cases where the equation (15) can be
solved in elliptic functions.

The first is the degenerate case when

oo +208 p+ (C— — A)? is a perfect square.

The condition for this is

4) (ay i ‘05.

This necessitates C er giving a flattened top, not an egg.

The case is real and, it is interesting to note, depends only
on the structure of the top, not on the initial conditions.

11. Another case is when a@ is small so that a? can be
neglected. In this case we must remember that )?, n°, K
have a in their denominators, while the coefficient of yu has
no term with a denominator of order higher than a?.

The only terms with a’ in the denominator occur in the
constant term, and these must disappear since they only occur
in terms independent of w, and must disappear when w=py ;
for the equation (17) is then satisfied identically, so that the

right-hand side must reduce to w,, and there being no term

2 he

in — in the denominator there cannot be in the numerator.
at

This reasoning will not apply to the terms containing =
for some of them occur in the coefficient of s.
These are on the left-hand side of (15)

eae.
i ( C2a,2h? ee a VM i 2C*hw,” (27 + ")
2. ee

a [Fe eee

———

the Problem of Columbus. 471
And on the (ae side they are contained in

C 20)
a it ae es i? a eie(t 4 +p) aE +08 Ba lhe | ee ee bela
4 q +08
L

AC
M

ae the terms in = out of this we have

Saye

a Te RO eee

+ Ch? &

ie
Therefore the term in 5 vanishes.

Thus the term in es in the absolute term disappears as the
as
one in 7 did.
Accordingly if we multiply by @ we shall get rid of all
terms with a@ in the denominator.
Now, in expanding the right-hand side, we find that pw is

never multipled by a power of a less than its own by more
than two, for if we multiply by a? we get

2rn(h+ ona) * +h? + 2uChw+a}(C—A)u?+ At

and and n only contain a once each 1 in their denominators.

Ther eae if we expand as far as pe we keep all terms con-
taining a’; and there is no expansion in terms of mw on the
left-hand side, and no power of mw higher than the third.

It follows from this that if we neglect a’ the equation can
be solved in elliptic functions.

This gives a closer approximation to the case of the ordinar ay
top than the usual one where the lower end of the top is
taken as a point, i.e. a is neglected altogether.

As such a top is usually spun, w; is large and m small, and
0, is fairly small. In such a ease the condition of art. 8 (vy dis
nearly satisfied, so that such a top will stand nearly upright
even without slipping.

12. The expressions for the reactions can be obtained from
the equations of motion.

From (4)
r Co. n| A cos O— -o(4 +e038) (0
M it asng AC

|
{
a <
i

I ie Asin? 0+0(/ teos8) fo

Clearly this can never become infinite.

—, Js. >) A
2. 27 ( + 2 2 2
ASEAN Mwy +h ( ‘ Chay ' IC? hoz (21° + wt)
= == - Sat i X 4

AG2 Mr. H. W. Chapman on
From (5)

2 =(a+hcos 0)0 —h sin 062 —y sin 0(h+<a cos 6) —ora sin 6,

This also can never become infinite, as will be seen by
considering the expressions for wy, 9, @:

>
3°

For the motion to be physically possible, ae Fe: must

always < some fixed quantity v, depending on the nature of

SE? + BY?
the egg and plane. We have seen that a cannot
become large by the numerator becoming large ; it remains
to see whether it can become large by the denominator
becoming small.

From (7) we have
R=hpt g.

We must therefore see if hy -++g can be made to become small
without F\’+ F,? also becoming small.
Equation (18) gives
BY eo Ne |e ee SS hirerowm (ik ghh?
(en es eS puis Q Se NO pe) as Ba 2 2 haere
(sy t+ 5 +2 hu) w= — bane Lh oe tony + SEE

— u(r? + Cn? — An? + A?K)

27): a A Me fee he i,

te Han eM Tat Cat 20 CH t(C A)u
h h ‘.

ea ee an

EE he h ;

Suppese / positive, and put 3; negative and m flarge
enough to make A positive. Take w=0.
Then we have

pri h? a ieee: h A
A? (on +1+ a) (hutg)=-— ee (A? + Cn?) +A%9(4

. >
is 1)
+ (negative terms).

We can clearly make this as small as we like by choosing
w; and m properly.

We have still to see that this is a possible position under
the circumstances.

the Problem of Columbus. 473

The necessary condition for this is that the numerator of
(17) should be positive when w=0.

The only positive term in this is A’K, but this contains a
term with @, in it; we have assumed nothing about (, so we
can make K as large as we please.

This condition is also sufficient; for having py at our dis-
posal, we can take it between 0 and the next root.

Also we see that pw need not be small at-this point, so that
6 need not be; F, will thus not become small: so that we can

VF?+E,?.
R

choose our initial conditions so that > any number
we please. It follows from this that with any material in
actual nature, under certain initial conditions, the egg must
slip at some time, and accordingly this solution will then fail.

13. To illustrate the motion I took a numerical example.
The egg was taken as a hemisphere with half a prolate
spheroid with major axis double of its minor, and its minor
axis equal to the diameter of the hemisphere, all supposed
homogeneous. In this case we have

eles
ier

2 9
= MER ar

When we form equation (15) we see that a divides out of
ae : g

every term except those containing g, and there we have -:
oh 6 a

for convenience of calculation I took a=4'90 ... ems., so that
2 =200, taking one second as the unit of time; I also took

Bee

As the top is not a complete sphere, fie must be positive
for the solution to apply.
_ Referring to (18), we see that the condition for this is

rr ers
AC. a;
Xr —-
n Mal a ve a An ‘ c Fe

7 +A + C

“es

"02 t Cn?)— > 0.

474 Mr. H. W. Chapman on
This gives .
mee GAA hh? h ghA2
eb a Spi ts hee te aie 2) a oF ees .
Naa(“ayp tA +20 a) — > 08+ Cn) — 2 50;
ECD

A Wig AC ee h Fie
Ws (An = re Co; Nee +A+2C =) eet A2m?+- 2AC 7 nes

phe —,,AC h? ghA?
+ Con + Oar (yp tA +Ci2) } > Se
_ Wesee from this that if #, and uo=0, the top must fall if
@,;=0 andh be positive. It is therefore necessary to give
the body an initial roll as well as an initial spin. The con-
dition becomes, supposing @; not zero,

h 2 iales C ghae |
= | An? + Atma,( ayy +1)>° arin

eae

ie h h
Ms (ce + 1) me m >

Putting in the values for h, a, C above we get
1:4 mw;—°375 m2 >75.

This shows that to represent a real case we must have m
and w, rather large as the spins of tops usually go. Take

m=10, w3;=10 radians per second.
These give
r~=8'094, K=145, n?=97°94.
And equation (16) gives
65°21p?—103°15y? — 143-738 ~— 59°46 + 8°956('375 + p)
oe x V¥313°4 + 96u—83p?
; 7826 +3261.
This of course has a root ~=0, and the next root is w="328,...
which corresponds to a rise of the axis through about 19° 9’.
On tracing the curve and integrating it by graphical
methods we get fig. 1 (Pl. XI.) which gives the period of the
nutation. The integration was done by two methods, shown
in. fio, 1% firstly, by inverse summation, 7. e. the curve was
divided up by ordinates and the height of the mid-ordinates
set off along a vertical as MIT=NP, a polar distance MO
was taken and pp’ drawn between the extreme ordinates
perpendicular to OII. It can be seen that the curve thus
obtained is such that the ordinate is proportional to t. The

the Problem of Columbus. Ad 5,

other method was Prdéll’s method ; in this ordinates are taken
as before and from the top of the mid-ordinate a constant
length QG is set off to the base-line; qq’ is then drawn between
the extreme ordinates perpendicular to QG. The time in this
case is proportional to the are of the curve. These two
methods both give about °685 second as the complete period
of nutation; the resulting curves are shown in Pl. XI. fig. 1.
In fig. 2 the precession is dealt with, y is found in terms of yu,
the equation being

3959(:375 +
65 94yp(1—p?) = 8-094 — ( H)

M9794 +3 — "2539p?
is found in terms of ¢ from fig. 1, and thus af and ¢ curve is
constructed. This is integrated by the ordinary sum-curve
method, and the amount of precession during a period of the
nutation found. 3

‘Fig. 3 is a polar diagram in which the ray is taken pro-
portional to sin @ and the angle to y. It starts on the outer
circle at C,, touches the inner at C,, and meets the outer again
at C’, the period of nutation being a little more than that of
the precession. It is the projection on a horizontal plane of
the motion of the centre of gravity relative to the centre
of the hemisphere.

The coefficient of friction necessary that the egg may begin
without slipping is easily found. Initially we have 0=0,
@=0; so we have

Je — (),
Ey

= ab, — mh— masa

rs : utd
= — apy — VA — Mas,

R 2

M —— hyo + q.

Working out Ub from (18), we get : = "128.

This shows that slipping:would take place as . rule, but
that it is perfectly possible to get surfaces rough enough
to prevent it. We find w)=11'47; thus the wy terms ‘are
much less important than the others, so that slipping would
be less likely if m and @, were smaller; but this would
involve a larger radius for the hemisphere.

14. The results obtained in this paper show :—(i.) That the
axis of an egg-shaped body would certainly not rise towards the
vertical unless, when its axis is horizontal, it receives not only

476 Messrs. Runge and Precht on the Position

a spin about the vertical, but also a rolling motion round its
axis. (ii.) That even when so spun it is very improbable
that its axis would rise to the vertical.

_Itis found, however, that eggs with their axes horizontal

generally do rise to the vertical without any delicate adjust-
ment of their initial spins. We are therefore forced to
conclude that this rising is in some way connected with the
phenomenon of limiting friction. To test this, an egg was
cast in rough cement and spun on a rough stone. It was
found that while the smooth wooden eggs rose with great
ease, this-cement egg only rose with difficulty, and usually
remained oscillating between two cones as required by the
theory for a “perfectly rough” egg. I hope to deal later
with the Problem of Columbus, supposing the egg to be only
imperfectly rough; but the analysis promises to a of amuch
more complex kind.
- JI have to thank Professor K. Pearson, who first suggested
the problem to me, for a-great deal of. kind assistance and
advice during the course “of the inv estigation. I must also
thank Mr. W. Arnold Ogden, Demonstrator in the Department
of Applied Mathematics, University College, for the trouble
and care he took in plotting the curves ‘for the numerical
example and in graphically integrating them.

XLVI. The Position of Radium in the Periodic System
according to its Spectrum. By C. RuNGE and J. PRecut*.

HE spark-spectrum of radium may be splendidly observed

by using the bromide recently prepared by Herr Giesel.

A few milligrammes, which Herr Giesel was good enough
to place at our disposal for this purpose, enabled us, when
using a small amount of dispersion, to produce a decidedly
more perfect spectrum than any hitherto observed ; and with
greater dispersion, to investigate the lines which are capable
of being easily photographed, with respect to their behaviour
in a magnetic field. Asa result we found that the strongest
lines of radium are exactly analogous to the strongest lines
of barium and the corresponding lines of the related elements
Mg, Ca, Sr.. As shown by Runge and Paschen f, these lines

may be grouped into three pairs, called by them, on account

* Translated from the Physikalische Zeitschrift, 4 Jahrgang, no. 10,
pp. 285-287.
+ Runge and Paschen, Ber. d, Berl. Akademie, June 26, 1902,

of Radium in the Periodic System. AT7

of certain analogies with the spectra of the alkalies, the line-
pair of the primary series, the line-pair of the first and that
of the secondary series. In the line-pair of the first secondary
series there occurs by the side of the line of greater wave-
length a feebler line on the side of greater wave-lengths,
which Runge and Paschen term a satellite. Measured on
the scale of frequency, the two lines of each of the three pairs
are the same distance apart for any one element, provided
that in the case of the pair of the first secondary series the
satellite be taken instead of one of the lines. This distance
varies, on the other hand, from one element to another, in-
creasing in a perfectly regular manner with the atomic
weight, as will be seen below. In a magnetic field these
lines, as has been shown by Runge and Paschen, split
up im various ways into components, but in such a manner
that, referred to the scale of frequency, the resolution
of each line of any one element is precisely the same
as that of the corresponding line of each of the other
elements. :

Now we have found that this also holds for radium, so that,
Ra is to be classed along with Mg, Ca, Sr, and Ba in a group
of chemically allied elements—a conclusion which is sup-
ported by the chemical behaviour of radium, in so far as this
is known. ‘

The following table exhibits the correspondence between
the lines :—

ate Gn age he iene aes,

Jae Ganicy S| 2808 “| 8969 -)4216 | 4934 | 4682
Primary Series...... 1.) 2796 | 3984 | 4078 ABBA. ilk: SQ

Ais 3181 | 3475 | 4166. 4436
9798 | 3179 | 3465 | 4181 | 4341
| 2791 |. 3159 | 3381 | 3892 3650
| | |
| 2937. | 38787 | 4306 | 4900 5814
2929 | 3706 | 4162 | 4525 4583 |

Ist secondary Series

{
atl ss K H

The resolution of the radium lines in a magnetic field is
easily observable with the strongest lines. It is only the
resolution of the satellite and of the yellow line 5814 that we
have as yet been unable to effect.

For any one element the distances apart of the two lines of
each pair are, as already remarked above, equal if measured

A478 Messrs. Runge and Precht on the Position

on the scale of frequency. The same holds good for radium,
as shown by the following table :— :

Xr. | 8LO2 7K: Difference.

9-2F ‘ AR

Primary Series...... l see | aes | 4858'3
BA DRA):

ist secondary si ae ae 4858°5

ond (| 5813-9 17200°2
= - Z 1 4533°33 22058'8

4858°6

The variations in the numbers corresponding to the dis-
tances are sufficiently explained by experimental errors.
They correspond to very small errors in the wave-length
determinations.

From one element to another the distance: apart of the
lines increases with the atomic weight in the cases of Mg,

Ca, Sr, Ba :—

Atomic weight.' Distance.
SS eee
Mg ...| 24°36 Ser
exe io 923 :
| State 87°6 | 801
Ba) i: 137-4 | 1691

It is suggested to regard the atomic weight as a function
of the distance between the lines, and to extrapolate this
function for radium. It has already been pointed out by ©
Rydberg, Kayser and Runge, in their investigations on the
spectra of the elements, that within a group of chemically
related elements the distance apart of the lines of a pair
increases regularly with the atomic weight. They state that
in the case of alkali metals the atomic weight is very nearly
proportional to the square root of this distance. We wish to
draw attention to the fact that for the other groups in which
line-pairs have been observed, the relation between the width
of the line-pairs and the atomic weight is capable of bemg
expressed by a simple formula :—

In each group of chemically related elements the atomic
weight varies as some power of the distance apart of the two
lines of a parr.

of Radium in the Periodic System. AT9

The exponent is a proper fraction. This result may other-
wise be expressed thus :—

The logarithms of the atomic weights and those of the dis-
tances when plotted as coordinates lie on a straight line for a
chenucally related group of elements.

The following two figures illustrate this law.

LT ®
Aw)
Y

At)
AN)

N
or

pylon Taupo ayy fo uy7.tv.£0

LS 2.0 25 3.0 55 Pow

Logarithm of the line-distance (-01 scale-division
=2°3 per cent. of the value).

In fig. 1 it will be seen that among the alkalies potassium
alone falls slightly below the line passing through the re-
maining points. We do not mean thereby to suggest that
the directly determined atomic weight of potassium is in-
correct ; but it appears to us interesting that the straight-line
law is appreciably departed from precisely in the case of the
element whose atomic weight in the periodic system points
to an unknown disturbing cause, which produces the inversion
of the positions of argon and potassium.

As regards boron, gallium, and indium, the radiation of
these elements in a magnetic field has not been investigated.
On the other hand, there is no room for doubt as regards the
line-pairs corresponding to aluminium and thallium. The
same applies to the alkali group, where only the two yellow
sodium lines have been investigated in a magnetic field.

In fig. 2 is represented the same relation for Mg, Ca, Sr,
Ba, and Ra. The extrapolation gives for the atomic weight
of radium the value 258. Of course, the straight line may
be to some extent rotated and displaced without any great
departure from the points; but the figure shows clearly that
the value 225 as determined by Madame Curie is considerably
removed from the straight line.

In the following table the straight line is represented by a
formula, and the extrapolated value obtained by calculation.

480 = The Position of Radium in the Periodic System.

Fig’ 2.

2,5
FQ

+Ha accoran
lo Mme. Curie.

° pyre 22M OZ jo uly gi hoy

2 0!\-_— oat
20 COS 50 3S 4zO

Logarithm of line-distance (01 scale-division
=2°3 per cent.).

If x stands for the width of the line-pair, measured on the
scale of frequency 10°/A, then we have:—
reaper ie hs ere |
Calculated atomic

weight=antilog. | Observed
(-2005-+ "5997 log x)., atomic weight.

Me... 23-84 24-36
Gee 40-6 401
reget Ly) 87-5 | 87-6
epee ages teu P 487-4

The extrapolation for radium gives for its calculated atomic
weight the value 257°8. |

We do not venture to suppose that our value deserves
more confidence than that determined by Mme. Curie. It
must, however, be remarked that in view of the close re-
lationship of barium and radium, and the small quantities
with which the chemist is forced to work, the complete sepa-
ration of these two bodies is very difficult, and that if the
separation had been incomplete Mme. Curie would have
found too small a value for the atomic weight. According
to the crystallographic observations of F. Rinne, to be pub-
lished shortly, radium bromide and barium bromide are iso-
morphic, so that a joint crystallization of both substances (an
somorphie mixture) is, from & priori considerations, highly

Some Remarks on Radioactivity. 481

probable—on the assumption of similar solubility relations.
From this will be understood the great difficulty of separating
these substances by crystallization, so that even after fre-
quently repeated re-crystallizations the corresponding radium
compound may contain more or less barium. The same holds
for the relation of radium to calcium as well as to strontium
and magnesium.

The number 225 is in better correspondence with the
periodic system, in so far as it fits the gap between bismuth
and thorium in the proper column. According to the value
258, radium would have to be moved two rows further down
in the column Mg, Ca, Sr, Ba, and a number of new un-
occupied places would be created in the periodic system.

On the other hand, Rutherford’s remark may be adduced
in support of the higher value of the atomic weight. The
higher atomic weight is indicative of a more complicated
atomic structure, and therefore of an easier splitting up into
electrons. The element which gives off electrons most freely
should therefore also have the highest atomic weight.

The radium line 4826714, which is the most prominent of
all in a Bunsen-flame, is also after resolution in a magnetic
field found to be analogous to the strongest Bunsen-flame
lines Ba 5535, Sr 4607, Ca 4226. All these lines become
resolved into triplets, which in the case of the elements con-
sidered consist of equidistant lines, the frequency scale being
used.

Hanover, Physicai Institute of the Technical High School.
January 1903.

XLVII. Some Remarks on Radioactivity.

To the Editors of the Philosophical; Magazine.
GENTLEMEN,

- a recent number of the Comptes Rendus, Jan. 26, 1903,

there appeared a paper by M. Henri Becquerel, entitled
‘Sur la deviabilité magnétique et la nature des certains
rayons émis par le radium et le polonium,” and also one by
M. P. Curie “ Sur la radioactivité induite et sur ’émanation
du radium,” in the former of which certain criticisms of my
experimental methods, and in the latter of my theoretical
views were made.

I am very pleased that M. Becquerel, with the very active
material at his disposal, has confirmed in such a direct
manner by the photographic method the results which I
had previously obtained by the electric method *, showing

* Phys. Zeit. No. 8, p. 235, Jan, 15 (1903); Phil. Mag. Feb, 1903.

482 Prof. E. Rutherford : Some

that the a or easily absorbed rays of radium are deviated by
an intense magnetic field. In the course of his paper
M. Becquerel states, “M.E. Rutherford, avee une grande
habileté, et par une méthode électrique relativement grossiére,
a reconnu un phénoméne d’une extréme délicatesse. Cepen-
dant la méthode employée laisserait prise a diverses cbjec-
tions et a un doute sur lVexistence du phénoméme en
question si on n’en apportait pas d’autre preuve. L’une
des objections resulte de la disposition expérimentale qui fait
traverser des espaces laminaires par un rayonnement dont la
partie cathodique est rejetée sur les parois, et les rayons
secondaires qui en résultent peuvent donner lieu a des effets
dans le sens observé par M. Rutherford. Je me suis alors
proposé de mettre en évidence le phénoméne par une expé-
rience plus simple et plus stre. J’ai eu recours a Pune des
dispositions photographiques que j’emploie depuis longtemps
et qui permettent certaines distinctions qui n’apparaissent pas
toujours quand on emploie exclusivement la méthode élec-
trique.”

I fully recognize the great simplicity and utility of the
photographic method, so ably developed by M. Becquerel
himself, for determining the magnetic deviation of rays and
determining accurately the curvature of their path, provided
that the rays enutted are sufficiently intense to affect a photo-
graphic plate without too long an exposure.

The difficulty of obtaining satisfactory photographs in cases
of less active material is clearly shown by M. Becquerel’s own
experiments on the rays of polonium described in the same
paper. I have unfortunately not had at my disposal very
active preparations of radium, and in consequence have had
to adapt my methods to obtain effects from such active
matter as I possessed. It was for this reason that 1 employed
the electric method, which is capable of extreme refinement,
and can be used to compare rapidly the intensities of radia-
tions which would require very long exposures to act appre-
ciably on the photographic plate. As an example of the
comparative sensitiveness of the two methods I may recall
some of M. Becquerel’s own experiments (Comp. Rend. p. 209,
1902) in which he was unable to detect photographically any
action of the a rays from uranium, or any evidence of the
existence of very penetrating rays from it, although the times
of exposure in two experiments were as long as 20 and
42 days.

By the electric method the 2 rays from 1 milligramme of
uranium can be quickly measured; and I have recently
found that, using 100 grs. of uranium oxide, the existence of

Remarks on Radioactivity. 483

very penetrating rays can be detected in a few minutes,
through 1 cm. of lead, by the increased rate at which the
leaves of an electroscope fall together.

The objection raised by M. Becquerel that the effects ob-
served may have been due to secondary rays set up by the
(3 or “cathode” rays striking the metal boundaries is in
direct opposition to the data given in my paper. I have
there shown that 89 per cent. of the discharge in the electro-
scope was due to a rays, since the discharge was diminished
by that amount by placing a thin layer of mica ‘01 em.
thick over the active material. It is well known that such a
thickness of mica completely cuts off the a rays, but allows
the passage of the 3 rays through it with but little absorption.
The effect in the electroscope, due to the 3 rays and the
secondary rays set up by them, was thus only slightly altered
by the addition of the mica plate, and therefore could not have
been initially much more than 11 per cent. of the total. As
a matter of fact, I showed that the 11 per cent. was hardly
affected by an intense magnetic field, and was due chiefly to
the very penetrating rays from radium. With the uncovered
active specimen the rate of discharge in very intense fields
was reduced by 89 per cent. of the original, showing that all
the a rays were deviated in passing through the narrow slits.

Tt has been shown in previous papers that, with a thin layer
of active material, the ionization due to the 3 rays (including
that due to the secondary rays produced by them) is very
small compared with that due to the @ rays under ordinary
experimental conditions. On the other hand, the 6 rays are
photographically very active compared with the a rays; and
M. Becquerel, in several of his papers, has drawn attention
to the marked photographic action of the secondary radiation
set up by them. This may have led him to believe that their
electrical effect would be equally marked, but such is not
the case.

M. P. Curie in his paper, after giving some experimental
results showing that the decay of activity of the radium
emanation is unaltered by variations in temperature between
450° C. and —180° C., proceeds as follows :—

‘“Pour expliquer les phénomeénes de 1a radioactivité
induite et la transmission de l’activité par les courants des
gaz, M. Rutherford a admis que le théorium et le radium
emettent une émanation radioactive qui provoque la radioac-
tivité des corps sur lesquels elle vient se fixer. C’est cette
émanation qui entretient l’activité induite dans une enceinte
fermée activée. M. Rutherford semble croire a la nature
-matérielle de ’émanation et, dans ’un de ses Mémoires les

484 Prof, E. Rutherford : Some

plus récents*, il considére comme vraisemblable qu’il s’agit
Vun gaz de la nature de ceux du groupe de l’argon. -

«Je pense qw il n’y a pas actuellement de raisons suffisantes
pour admettre existence d’une émanation de matiére sous sa
forme atomique ordinaire. Nous avons antérieurement, M.
Debierne et moi, vainement cherché des raies nouvelles dans
les gaz radioactifs extraits du radium. Hntin l’émanation
disparait spontanément en tube scellé. Je considere aussi
comme peu vraisemblable que les effets qui accompagnent
Vexistence de ’émanation aient leur origine dans une trans-
formation chimique. On ne connait en effet aucune réaction
chimique pour laquelle la vitesse de réaction soit indépendante
de la temperature entre —180° et +450°.”

Since the discovery of the thorium emanation, I have always
taken the view that the emanation consists of matter in the
radioactive state present in minute quantity in the surround-
ing gas. The experiments of Miss Brooks and myself
(‘ Nature, p. 157, 1901) showed that the radium emanation
mixed with air diffused very slowly. By comparing the rate
of interdiffusion of the emanation into air with that of known
gases, it was deduced that the emanation particles behaved
like heayy gas molecules of molecular weight probably
lying between 40 and 100. I have long recognized that the
electrical and other effects produced by the emanations can
be manifested by an extremely minute quantity of radio-
active matter in the gaseous state. Tor this reason I am not
surprised that MM. Curie and Debierne have failed to obtain
evidence by the spectroscope or balance of the existence of
the emanation. At the same time I do not doubt that with
sufficient quantity of active material the presence of the
emanation will ultimately be detected by these means. I
do not consider that the emanations remain permanently in
the gaseous state, for it seems probable that the emanations
gradually change into the matter responsible for excited
activity, which is deposited on the walls of the containing
vessel. Recent experiments by Mr. Soddy and myself show
that the thorium emanation behaves chemically as an inert
gas, and in this respect resembles the gases of the argon
family. M. Curie has, apparently, not observed a recent
paper by us (Proc. Chem. Soc. p. 219, 1902) in which
it is shown that if the emanations of thorium or radium
mixed with air, oxygen, or hydrogen are passed slowly through
a spiral tube immersed in liquid air, the emanations are con-
densed in the tube, and the issuing gas is completely free

* Rutherford and Soddy, Phil. Mag. Noy. 1902,

Remarks on Radioactivity. 485

from activity. On removing the spiral from the liquid air,
the whole of the condensed emanation (allowing for the
decay of activity in the interval) is released at a fairly definite
temperature and appears again in the stream of gas. A more
detailed account of these investigations will shortly appear
in this journal. |

These results, in my opinion, conclusively show that the
emanations are gaseous in character, for it is very difficult
to explain such phenomena except on a material hypothesis.

In addition, I have recently shown that it is extremely
probable that the greater proportion of the radiation from the
emanation is materialin nature, and consists of heavy charged
bodies projected with great velocity, whose mass is of the
same order as that of the hydrogen atom. In view of these
results, which so strongly confirm the theory of the material
nature of the emanation, the alternative theory proposed by
M. P. Curie that the emanation consists of “ centres de con-
densation d’énergie situés entre les molécules du gaz et qui
peuvent étre entrainés avec lui,” appears to me unnecessary.

The interesting result, obtained by M. Curie. of the expo-

entia] law of decay of the radium emanation under all
DB aieiins: is only one of many others that have now been
accumulated. I quite agree with M. Curie that such results
cannot be satisfactorily e explained on the laws of ordinary
chemical change, but the difficulty disappears on the view
already put forward by Mr. Soddy and myself (Phil. Mag.
Sept. and Noy, 1202) that the radioactivity of the elements
is a manifestation of sub-atomic chemical change, and that the
radiations accom pany the change.

There is no @ prior’ reason to suppose that temperature
would affect the rate of atomic disintegration ; in fact the
general experience of chemistry in failing to transform the
elements is distinctly opposed to such a view. It is there-
fore not surprising that, if radioactivity is an accompaniment
of sub-atomic change, the process should be independent of
the ordinary chemical and physical agents at our disposal.
These points, and many others bearing on the same question,
are discussed in more detail in a joint paper with Mr. Soddy

now in the course of publication.
Iam, Gentlemen,

MeGill University, Yours very truly,
Montreal, Feb. 28, 1903. B®. Ruraerrorp

Phil. Mag. 8. 6. Vol. 5. No. 28. April 1903. ag Se

Be aes

XLVIII. New Magneto- Optic Phenomena exhibited by Magnetic
Solutions. By Dr. Quirino MAJoRANA*,

1B UIDED by the analogy between magnetic and elec-

tric phenomena, I wished to determine whether a
magnetic field was capable of rendering a magnetic substance
doubly refracting, as an electrostatic field is capable of doing
in the case of a dielectric (Kerr’s phenomenon). I was thus
led to the discovery of the following three effects :—

(1) Magnetic Double Refraction.

(2) Magnetic Dichroism. |

(3) Certain rotations of the plane of polarization of light,
which I have called Bimagnetic Rotation.

2. Magnetic Double Refraction—LExperiments on highly
magnetic substances, such e. g. as thin transparent sheets of
iron, or solutions of ferric chloride, did not yield any appre-
ciable results. But solutions of ferrous chloride were rendered
feebly doubly-refracting when placed in a very intense mag-
netic field. The experiment was conducted in the following
manner. ‘The liquid having been placed in a magnetie fielu,
a ray of light was allowed to pass through it in a direction
normal to the lines of force. The liquid was placed between
two crossed nicols whose principal sections made angles of
45° with the lines of force. On exciting the field, the light
re-appeared. With a field intensity of 18,000 c.¢.s. units, if
the liquid was placed in a tube 7 cms. long, the double re-
fraction represented at most 2 to 3 hundredths of the wave-
length of yellow light. On the other hand, dialysed iron or
colloidal solution of ferric oxide was frequently strongly active.
The degree of activity varied aczording as the substance was
more or less freshly prepared. Thus freshly prepared dialysed
iron is entirely inactive, while if it is kept for a long time
(ten years or more), the double refraction, under the experi-
mental conditions indicated above in connexion with ferrous
chloride, reaches a value of 12 wave-lengths of green light.
Dialysed iron thus aged was obtained from old bottles of
fer Bravais in a druggist’s shop.

The magnetic double refraction exhibited by dialysed iron
presents numerons peculiarities. Jt may be either positive or
negative ; but if the specimen of the liquid is very old, the

* Communicated by the Author. This note forms a brief réswmé of
some researches of mine described more in detail in the Rendiconti della
Accademia dei Lincei. at the meetings of May 31, June 15, August 3
and 17, 1902. I think that some observations contained in a short
notice of Dr. J. Kerr (Report Brit. Assoc. 1901, p. 868), with which I
became acquainted after the publication of my researches, must be
referred to the phenomena there described.

New Magneto-Optic Phenomena. 487

double refraction is positive in a weak field, decreases gra-
dually, and ultimately becomes negative under the action ot
a strong field. It therefore has a point of inversion,
corresponding to a field of given intensity, for which the
double refraction becomes equal to zero. If the point of
inversion is very low, 7. e. occurs at a weak field intensity,
then the foliowing Jaws hold with a considerable degree of
approximation. The magnetic double refraction is :—
(1) Directly proportional to the concentration of the
liquid.
(2) Directly proportional to the thickness of liquid
traversed in a direction normal to the lines of force.
(3) Directly proportional to the square of the field
intensity.
(4) Inversely proportional to the square of the wave-
length of the light experimented with.

3. Magnetic Lichroism.—Dialysed iron strongly absorbs
light. It is therefore easy to foresee that by reason of the
phenomenon of double refraction described above, the ab-
sorption of a polarized wave will undergo different modi-
fications according to the azimuth of the plane of polarization,
when the magnetic field is excited. Itis thus that I was able
to establish the existence of a series of phenomena to which [
propose, with good reason, toapply the term Magnetic Dichroism.
These phenomena are entirely analogous to these presented by
dichroie crystals (e. g. tourmaline), with the sole difference
that they are only observed when the circuit of the exciting
current is closed. The more important results are:—

In the case of the magnetic dichroism exhibited by dialysed
iron, it always happens that when one wave is propagated
through the interior of the liquid with a velocity less than
that of another wave (on account of different azimuths of the
plane of polarization, or different directions of propagation),
it also suffers less absorption. Photometric measurements
have shown that the absorption suffered by vibrations propa-
gated in a direction parallel to the lines of force is the same
as that suffered by vibrations propagated normally, the plane
of polarization being parallel to the tield.

4. Bimagnetic Rotations.—This phenomenon is exhibited
by solutions of ferric chloride prepared from certain hydrated
oxides of iron.

With the arrangement described in connexion with double
refraction, the solution of ferric chloride replacing the dialysed
iron, it is cbserved that when the field is excited between the
two crossed nicols at 45” to the field, the hght reappears; and
that itagain disappears when the analyser is rotated through a

488 New Magneto-Optie Phenomena.

small angle. In another experiment with the polarizer
turned through 90° from its original position, the pheno-
menon is still exhi bited, but the rotation (whose absolute

value is the same) is in the opposite direction. If the plane
of polarization is parallel or normal to the field, no effect is
obtained. I have called this rotation of the plane of polar-
ization bimagnetic, in order to distinguish it from the magnetec
rotation of Faraday, the term being intended to emphasize
the fact that the first phenomenon is different from the second,
and depends on the maguetic property of the liquid used as
well as on the ma onetic field. The bimagnetic rotation may
be positive or negative, according as the plane of polarization
is rotated so as to recede from or to approach the lines of
force.

I must refer to my original publication for the method of
preparing the active liquid. Here it must suthce to mention
that in general this may be prepared by oxidizing, in the wet
way, small pieces of iron, and then acting on them with a
dilute solution of ferric chloride. According to the nature
of the iron oxide employed, the rotation is positive or
negative.

The maximum rotation observed by me was at most 4° 30).
The following is a theory of this effect which has been sug-
gested to me by Prof. Voigt. The incident vibrations which
are propagated at an angle of 45° to the field may be resolved
into two components, one normal and the other parallel to the
field. Itseems that the magnetic action results in producing
a different absorption of these two components, which on
leaving the liquid give rise to a resultant vibration in a plane
different from the original one.

The following are a few details regarding this pheno-
menon :—

(a) The bimagnetic rotatory power is different for different
colours, according to a law which I have not succeeded in
formulating, and which varies from one liquid to another.

(6) The rotation is proportional to the thickness of the
liquid traversed, provided the rotation be not excessive.

(c) It increases with increase of field intensity, rapidly at
first, but beyond a certain not very intense field strength
becomes almost constant.

(d) All the specimens of liquids endowed with the power
of bimagnetic rotation lose this property to some extent.

5. I have finally tried to determine whether magnetic
double refraction is an instantaneous or a gradual phenomenon.
I believe I may conclude that it is really instantaneous, since
samples of dialysed iron became double refracting in a field
generated by the discharge of a leyden-jar.

r 489 ]

XLIX. Note on an Elementary Treatment of Conducting
Networks. By L. R. Wiveerrorce, M.A., Professor of
Physics at University College, Liverpool *.

T may be worth while to point out that the well known

reciprocal relations between the parts of a conducting

network can be readily established without an appeal to the
properties of determinants.

Let A, B, ©, D,..., bea number of points connected by
conductors AB, AC, AD,..., BC, BD, ..., CD, .,., of resist-
ances Rap,..., and suppose that currents Qa,..., are led
into the network at the points A, ..., from without, subject
to the condition Qa+Qpt+ ...==0, and that internal electro-
motive forces, E,g, .... act in the conductors in the directions
Ab,.... Let the currents in the conductors be Cap, ...,
and let the potentials at A,..., be Va,.... The fact that
there is no continuous accumulation of electricity at any point
gives us a series of equations whose type is :—

OCB AS ORC ee Tl shh Sara ER)

and the application of Ohm’s law gives us a series whose
type is

Rap Cap= VA— Ver Hap, « . «+ (2)
Suppose now that a different system of external currents,
Q’a,.-., and internal electromotive forces, E’ap, ..., are
applied to the same network, and let the consequent currents
and potentials be denoted by accented letters. Hquations
similar to (1) and (2) will, of course, hold for these quantities.

Multiplying each equation of series (2) by the correspond-
ing current in the second system and adding, we cbtain :—

Rap Cap C’ap=>C’ap (Va— Vp) + SHap C’az.

Now, remembering that C'ym=—C’mn, the coefficient of
any potential Vy on the right-hand side of this equation is
easily seen to be O'mat+C’mpt+..., and thus is Qu. The
equation thus becomes :—

>Rap Caz Clap==2Va Qlat SHap C’as.
By a similar process we obtain
>Rap Caz Clap=2ZV'a Qa + 2Eap Cap.

[If the accented system is made to coincide with the unac-
cented system, we obtain Rag Cap=2Va Qat+ Hap Cap,
the equation of activity. |

* Communicated by the Physical Society: read Jan. 23, 1908.

490 Notices respecting New Books.

From the general equation :

=Va Qlat+>Hap C'ap==2V'a Qa t+ SH’az Cap
the required reciprocal relations follow at once.

(i.) Let every Q and Q’ be zero, and every H except Hap,
and every Ii’ except H’cp.

Then: Eap C’ap=E’cp Cep, and if Hagp=+E’ep then
Cop=+C’ap, or, in words, if an E.M.F. in one branch
produces a certain current ina second branch, then an equal
E.M.F in the second branch will produce an equal current in
the first ; and, according as the direction of the latter H.M.F.
is the same as or opposite to thit of the former current, the
direction of the latter current will be the same as or opposite
to that of the former E.M.F. Again. if Cop is zero, C’ap
will be zero, which leads to the definition of conjugate
conductors.

(ii.) Let every E and E! be zero, and every Q except Qa
and Qp (which will be —Qa), and every Q/ except Qc and
Q’p (which will be —Q'c).

Then: (Vo—Vp) Q’c=(V/a—V’s) Qa, and if Qa=Q’o,
Vco—Vp= V’a—V’,; that is, if a certain current led in at A
and out at B produces a certain excess of potential of C over
D, an equal current led in at C and out at D will produce an
equal’ excess of potential of A over B.

L. Notices respecting New Books.

Report on the Total Solar Eclipse of January 21-22, 1898, as ob-
served at Jeur in Western India. By Kavasst DaDABHAI
NarcaMvana, V.A., F.R.AS., Director of the Observatory.
Bombay: Printed at the Government Central Press.

(eae Report was published at Poona in November 1901.

Prof. Naegamvala thinks it necessary to account for the delay
in its appearance, which was due to his desire to compare the
spectrum of the “ flash,” which was for the first time adequately
obtained at the Indian Eclipse of 1898, with stellar spectra and
other related types. He has since been engaged in laborious
efforts to secure these for purposes of comparison with the eclipse ;
but finding that his progress was much hampered by certain mecha-
nical defects in the prismatic camera, he finally decided to publish
an account of his observations at Jeur without further delay. Asis
well known, he is Director of the Maharaja Taktasingji Observatory
at Poona, and feeling the importance of taking part in the obser-
vations of the eclipse in question, he memorialized the Government
of Bombay on the subject as early as February 1896. To prepare
himself for efficient participation, he accompanied the expedition
sent to Norway to observe the total eclipse of August 9 in that year ;

Notices respecting New Books. 491

and though the weather effectually prevented any results being
secured on that occasion, Prof. Naegamvala obtained the valuable
opportunity of examining the numerous instruments brought
together by five different parties of European astronomers. This,
of course, was of the greatest service to him in forming his plan of
observation and selecting his instruments for the Indian eclipse,
but unfortunately some improvements which were considered
desirable in his equipment were completed only just in time,
which is to be regretted because longer preparation in the matter
of adjustments would have secured greater precision when the
eventtul moment arrived. Nevertheless, results of great value were
obtained, the details of which are given in this volume, together
with the illustrations requisite to enable readers to follow a scheme

earried out with great skill. All the parties in India were ~

favoured with most propitious weather, and the eclipse was well
seen and observed, as was cabled to England immediately. (The
present writer had the satisfaction of announcing this at a
lecture delivered at South Norwood on the evening of the same
day.) Jeur (the site selected) is near the very centre of the line of
totality, and is a station on the Great Indian Peninsula Railway,
nearly east of Poona. A locality at the Southern Maratha line
would have been superior in several respects; but owing to the
fact that the plague was raging in that neighbourhood, Jeur was
preferred, and near it an observing camp was prepared, about
one hundred yards to the west of the spot selected by Prof. W.
W. Campbell, of the Lick Observatory. Great care was used in
training the assistants who went to take part in the work, and the
fiual result was highly satisfactory. To use the words of the Report
of the Council of the Royal Astronomical Society in February 1899,
«Prot. Naegamvala of the Poona College, assisted by a number
of his students, secured an excellent series of photographs both of
the corona and also of the chromosphere spectrum with the pris-
matic camera.” To appreciate these, the reader must refer to the
volume itself. Waly.

Die Internationalen Absoluten Masze, Inshesondere die Electrischen
Masze, fur Studirende der Electrotechnik. Von Dr. A. Von
WaLrenHOFEN. Dritte, zugleich als Einleitung in die Electro-
technik bearbeitete Auflage. Mit 42 eingedruckten Figuren.
Biaunschweig: F. Vieweg und Sohn. 1902. Pp. xi+3806.

THis book on units covers a very wide field. It is divided into
two parts, Part I. dealing with the subject of units, and Part LI.
consisting of a series of appendices, devoted mainly to the eluci-
dation of various points connected with magnetic and electrie
theory. This second part is also intended by the author to form
an introduction to electrotechnology. In our opinion, the treat-
ment of the subjects considered in Part II. is much too condensed
and scrappy to be suitable for a student, although to one already
acquainted with the subject it may prove a useful compendium.

492 Notices respecting New Books.

The proofs and explanations given are not always remarkable
for elegance of treatment. Thus, in dealing with the formula for
the E.M.F. of a dynamo, p. 61, the author establishes it by sup-
posing that the E.M.F. in each conductor follows the sine law, and
then caiculates the mean value of the H.M.F.! This ponderous
and clumsy treatment is not only unnecessary, but is positively
misleading ; for there is no dynamo in existence in whose conduc-
tors the E.M.F.-wave so much as approaches the sine law.

As a book of reference, the work should prove useful, for it
contains a large number of important data. In the section
dealing with inductance, in particular, we notice some very useful
approximate formule for the self-inductances of coils.

Cryoscopie. Par F.M.Raount. Paris: OC. Naud. 1901. Pp. mii
+106. (Scentia Series, No. 13.)

Tue work of the late F. M. Raoult is of such far-reaching im-
portance that his name is one of the most familiar to students of
physical chemistry. Happily for such students, he was enabled,
almost immediately before his death, to give the clear and
fascinating account of his important researches in the monograph
before us. We could wish for no better exposition of the subject.
After an account of some general principles in Part I. we are in
Part II. introduced to the experimental methods of cryoscopy.
Part III. deals with the cryoscopy of organic compounds, and
Part IV. with that of electrolytes—a subject which, in the early
days of the science, was beset with so many serious difficulties that
Raoult’s work was accepted with very considerable reserve, if not
diffidence, until the daring and brilliant speculations of Arrhenius
restored the confidence of the scientific public in the soundness of
Raoult’s generalizations.

The volume is embellished with a portrait of the author, and an
appreciative sketch of his career and work by his friend and pupil,
M. R. Lespieau.

Bericht wiber die Internationale Experten-Conferenz fur Weiter-
schiessen in Graz (XXXIX. Band der Jahrbiicher der K. K.
Central-Anstalt tir Meteorologie und Erdmagnetismus). Wien:
Wilhelm Braumiiller. 1902. Pp. iv+154.

ANYONE interested in either meteorology or folklore will find the
present volume interesting reading. Edited by J. M. Pernter, it
contains a number of valuable contributions from experts on the
various aspects of the modern system of battling with hail-storms,
which originated in Graz, and is now extensively practised both
there and in Italy. As to whether a hail-storm can or cannot be
averted by the firing of specially-constructed cannon is a question
still sub judice. But it is interesting to learn, from the opening
paper of this Report, that the belief in the efficacy of such a
method is of comparatively great antiquity.

\ Phil. - Ser. 6, Vol. 5, Pl. IX.
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PRECESSION DIAGRAM.

LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF. SCIENCE.

[SIXTH SERIES.] | . ie

a! "S, 4
LI. On the Measurement of Small Capacities and, Fuctaitis,
By J. A. Fuemine, D.Sc, PRS. Professor of. Mectrical »
Engineering in itieen sity C. oleae, London, aneté-W, C.° : gt
CLINTON, B.Sc., Demonstrator in the Pender Electvtent’” te

Laboratory, Uhetner sity College, London*
[Plate XII. }

MAY 1903. . a hy woe vi

HE measurement of small capacities and inductances has
become important in connexion with Hertzian Wave
Wireless Telegraphy. The experimental determination of
the electrical capacity of telegraph wires and of the overhead
wires used for the conveyance of high tension alternating
currents, is also called for in connexion with the calculation
of sending speeds and of voltage drop in a power line. The
advantage of possessing an appliance which will conduct this
work quickly and well has led us to design the instrument
which is here described.

It is generally admitted that for the measurement of small
capacities, when the dielectric is air or some other substance
not possessing the quality commonly called absorption, no
method is so easy to apply as that depending upon the rapid
charge and discharge of a condenser through a galvanometer.
This method is almost the only one applicable to the measure-
ment of the small electrical capacities of wires insulated in
the air, such as the aerial wires employed in Hertzian Wave
Telegraphy, or ordinary telegraph-wires, or small air-con-
densers, or in fact any form of condenser in which the

* Communicated by the Physical Society: read February 27, 1903.

Phil. Mag. 8. 6. Vol. 5. No. 29. May 1903. of

494 Prof. Fleming and Mr. Clinton on the

capacity is independent of the time of charging. This
method has been extensively employed, the only difference
being in the nature of the commutator for charging and
discharging the condenser. Maxwell suggested the use of a
tuning-fork as a switch, the vibrating prongs being furnished
with a stylus which made and broke contact with a mereur
cup, or vibrated:to and fro between two fixed contacts. The
great objection to this arrangement is the uncertain
duration of the contact. Hence other experimentalists have
employed an electrically maintained tuning-fork with a
vibrating contact used as a means of driving cynehean ee
an electromagnetic contact-breaker, which in turn makes a
better and longer contact between two stops alternately. A
device of this latter kind was successfully employed by
Protessor J. J. nena *, Dr. Glazebrook +, and Professors
Fleming and Dewar{ in various experiments connected
with the Se ieee of specific inductive capacity at low
temperatures

We have had considerable experience with all these tuning-
fork devices, but we have found them troublesome in practice,
especially when a large number of measurements have to be
made. In addition there is always an uncertainty as to the
actual duration of the contact, which makes it impossible to
determine by calculation whether the condenser is being
fully discharged at each vibration. After a great many
preliminary experiments, we finally devised the followin
appliance, which when properly made never fails to give
satisfaction and renders the measurement of small capacities,
even as small as one ten-thousandth of a microfarad, a matter
as easy as the measurement of resistance on a Wheatstone
bridge.

The instrument as constructed consists of a continuous
current electric motor of 2 HP.; but for certain purposes,
and where very small capacities have to be measured, it is
preferable to employ a motor of 4} HP. This motor is bolted
down upon a baseboard and has connected with it a starting
and regulating resistance. The motor is preferably 100 or
200 volt shunt wound motor. To the shaft of this motor is
connected bya flexible coupling the commutating arrangement,

* See J. J. Thomson, Phil. Trans. Roy. Soc. 1883, p. 718, “On the
number of Electrostatic Units in the Electromagnetic Unity of Elec-
tricity.”

+ Also R.T. Glazebrook, Phil. Mag. Aug. 1884, vol. xviii. p. 98, “On
a Method of measuring the Capacity “of a Condenser ” ; or Proc. Bam
Assoc. Leeds, 1890.

1 AD Fleming and J. Dewar, Proc. Roy. Soc. London, 1896, vol. lx.
p. 368, “On the Dielectric Constant of Liquid Oxygen and Liquid Air”

Measurement of Small Capacities and Inductances. 495

the function of which is to charge the capacity or condenser
to a given voltage and then discharge it through a galvano-
meter, repeating this process four times in each revolution of
the motor. This commutator is fixed on a shaft carried in well
lubricated bearings supported on two small A frames (P]. XII.
fig. 1). On this shaft are held, by means of ebonite bushes
and washers, three gunmetal disks or wheels, of which the
centre one is 1n shape like an eight-rayed star, whilst the two
outer ones are like crown wheels, each having four teeth.
The three wheels are so set on the shaft that the teeth or
projections of each of the two outer wheels interlock or fall
in the space between the teeth of the other, whilst the radial
teeth of the intermediate wheel occupy the intervals between
the teeth of the two outer wheels. The developed surface of
this triple wheel is shown in fig. 2. The whole outer surface
is turned true and forms a barrel about four inches in
diameter, and two and a half inches wide. On this barrel
rest three brass gauze brushes which are carried in well
insulated brush holders, and by means of three springs and
levers the brushes are firmly pressed against the barrel, the
two outer brushes resting on the continuous portions or
flanges of the two outer wheels A and B, and the middle
euch occupying the centre line and making contact either
with the wheel A or wheel B, or with the intermediate
wheel I according to their position. Tt will be seen then
that as the somnntie “on runs round, the middle brush is
alternately brought into metallic connexion with first one and
then the other of the two brushes on either side. The
function of the middle wheel (I) is to afford a stepping piece
and prevent any shock or jar as the middle brush passes over
from one connexion to the other. It also prevents the middle
brush from short-circuiting the two outer brushes at any
pa kG then one tenminaliof the galvanometer is connected
to the brush pr essing against the wheel A, and one terminal
of a battery is connected to the brush pressing against wheel
B, and one terminal of a condenser is connected to the middle
brush, the other terminals of the battery, galvanometer, and
acoMlenenet being connected together, it will easily be seen
that as the commutator runs an the condenser is first
charged at the battery, and then discharged through the
calvanometer. In the following experiments, speeds of 1200
to 1700 revolutions per minute were used. To count the
rotations of the commutator a worm on the shatt drives a
wheel of such gear that the latter makes one revolution for
every hundred revolutions of the commutator. This wheel
carries a pin which at each revolution causes a hammer to

2 L 2

496 Prof. Fleming and Mr. Clinton on the

strike a gong. Every hundred revolutions, therefore, of the
motor or commutator, the gong gives one stroke, and by
means of a stop-watch it is easy to take the time of ten
strokes of the gong ; in other words, to ascertain the time in
seconds of a thousand revolutions of the motor, and therefore
of the number of commutations per second. In the case of
the motor we have employed, 1000 revolutions take place
generally in 40 seconds, which is at the rate of 1500 per
minute, and therefore corresponds with 100 commutations of
the condenser per second.

We have tried various methods of making the rubbing
contacts and found nothing better than brass gauze brushes.
Carbon brushes were tried at one time and found to be
unsuccessful. It is essential that the commutator surface
should be kept bright and clean, and the brass gauze brushes
do this themselves when adjusted to the right pressure.

Associated with this commutator we have employed a gal-
vanometer of the movable coil type, either one made by
Crompton, or in some cases one made by Pitkin. By the aid
of this instrument, given a source of constant voltage by
which the motor can be driven steadily, such as a secondary
battery, the measurement of small capacities becomes an
exceedingly easy matter.

There is, of course, no novelty in the mere use of a
rotating commutator for the determination of capacities by
the above method. It was employed many years ago by
Dr. R. T. Glazebrook for this purpose. See ‘The Elec-
trician,’ vol. xxv. p. 616, 1890, on ‘“*The Air Condensers of
the British Association.””. One of us (Dr. Fleming) had,
however, employed the device several years previously for
the same purpose. Our only claim to novelty in this matter
is that of having worked out a thoroughly satisfactory form
of rotating commutator, which is designed more from the
point of view of an engineer than an electrical instrument
maker.

In the case of the measurement of capacity of insulated
wires or aerials, the aerial is connected to the middle brush.
one terminal of the galvanometer and battery respectively
are connected to the two remaining brushes, and the other
terminals of the galvanometer and battery are connected to the
earth (seetfig. 3). Under these circumstances, when the commu-
tator is in rotation, the galvanometer gives a perfectly steady
deflexion due to the passage through it of 100 discharges per
second from the condenser. In order to determine the
numerical value of the capacity, we have therefore to
evaluate the deflexion of the galvanometer and to determine

a . . 7
Measurement of Small Capacities and Inductances. 49

the ampere value of a steady current which will make the
same deflexion. This can be accomplished by putting the
galvanometer in series with a variable resistance, and placing
the two as a shunt on a known small resistance in series with
another variable resistance, and then placing on the terminals
of this circuit a cell of known electromotive force.

In the case of most movable coil galvanometers, the scale
deflexions are by no means proportional to the current, and
hence when measuring a series of capacities it is desirable
afterwards to plot a calibration curve of the galvanometer
scale, from which the condenser currents can be read off
directly in microamperes. This, however, is always easily
accomplished. In addition, we have to measure the potential
of the discharging battery. For most practical purposes
this can be done by a Weston voltmeter.

Thus let V represent the voltage of the battery charging
the condenser or aerial, C the capacity of the condenser in
microfarads, A the current in microamperes through the

galvanometer, n the number of charges per second, then

A=nCV
or C= Ain.
In order to avoid the necessity for standardizing the

valvanometer and measuring the voltage of the charging
battery, we have devised a method employing a differential
galvanometer which in principle is as follows :—The condenser
discharges, as above described, pass through one coil of the
differential galvanometer, the other coil being traversed by a
current taleemn from the same battery, and therefore having
the same voltage. This second coil is shunted by means ce
a shunt R and has in series with ita high resistance ». If
fen these resistances are arranged so that the galvanometer
shows no deflexion, we have ihe following equation for the
capacity :—
USS a Vv
Ge GS
tee GS
(G+) 10°
nr(G+S)+ nGs

This determines the capacity in terms of a conductance and
the reciprocal of a time, thus reducing the number of dimen-
sional quantities to be a neanod to the minimum.

In carrying out this method, it is perfectly impossible to
use any ordinary differential galvanometer, because with an

498 Prof. Fleming and Mr, Clinton on the

electromotive force of 100 volts or more between the coils
the resulting unavoidable leakage entirely vitiates the result.
We have therefore devised a differential movable coil gal-
vanometer which has been made for us by Messrs. James
Pitkin & Co., and is constructed as follows :—

In this galvanometer there are two sets of fixed field-
magnets, and also two movable galvanometer-coils completely
insulated from one another, but attached to the same stem,
which also carries the mirror. Very fine spiral flexible wires
convey the currents into and out of each coil. In order to
make the galvanometer differential and therefore show no
deflexion when the same current is passed in opposite directions
through the coils, it is necessary to be able to adjust exactly
the field-strength i in the air-gap of the fixed magnets. This we
accomplish by means of two curved pieces of soft iron FP,
which are moved by screws to or from the field-magnets N, S
(Pl. XII. fig. 4) so as to shunt more or less of the lines oF
flux passing between the pole-pieces of the magnet. In this
manner we find we can construct a movable coil differential
galvanometer which shows no deflexion when the same or
equal currents are passed in opposite directions through the
two coils, yet each coil is perfectly insulated from the other.

Employing such a differential movable coil galvanometer
In connexion with a commutator, we get rid of “all necessity
for measuring any voltage or electromotive force, and reduce
the measurement of capacity simply to a determination of the
speed of the commutator (which can be taken with great
accuracy by means of a stop-watch) and the known value of
the shunt and series resistances in connexion with one coil
of the galvanometer. Moreover, we can always tell from the
speed of the commutator exactly the time during which the
condenser is in connexion with the galvanometer, and hence
whether the time of contact is, as it should be, large compared
with the time-constant of the discharge circuit.

We have employed one or other of these methods in making
a number of measurements of the capacity of aerial wires,
such as are used in connexion with Hertzian Wave Tele-
graphy, and also in the investigation of the laws governing the
capacity of such wires when grouped tog ether in certain
ways, and we have employed the ari ‘angements for verifying
experimentally, as far as possible, the formule that have
been given for the capacity of insulated wires in various
positions in regard to the earth. Taking first the case of

co)

single vertical wires insulated in the air, measurements have

been made of the capacity of wires suspended vertically in
the open air, and also in the interior of a large Laboratory,

Measurement of Small Capacities and Inductances. 499

the dimensions of which are 18 feet high, 32 feet wide, and
44 feet long.

Some pr eliminary experiments in the open air showed that
the capacity of parallel wires suspended in the air, and
insulated, is by no means equal to the sum of their separate
capacities when in free space, even when the wires are not
very near together. A series of experiments was therefore
carried out in the Pender Laboratory with flat iron strips, to
investigate this fact more carefully. Hleven lengths of iron
strip one inch wide, the thickness being 0:05 inch, and
15 feet 4 inches long, were suspended vertically from the
ceiling of the Laboratory by silk strings passing over por-
celain buttons. To keep the strips straight they were fastened
to the floor through pieces of ebonite. Connexion was made
at the bottom end of each strip by a terminal to a straight
bare copper wire connected to the above described commutator,
so that the capacity of any one strip or of any number of
strips in parallel could be measured. In the first place, the
individual capacity of each strip taken alone and isolated,
was measured and found to be nearly the same in each case.
Hence in the tabulated results, the absolute values of capacity
are not given, but the capacity of each of the above strips. by
itself in the room, and held vertically, is taken as unity. The
voltage of the battery employed in charging the strips was
about 148 volts, and the number of revolutions of the com-
mutator 1200 per minute, corresponding to a frequency of
80. One terminal of the nenienied battery used for charging
was connected to the earth, and also one end of the galvano-
meter. The other ends of the galvanometer and battery
were connected to the outside brushes on the commutator, the
middie brush being connected to the insulated strip or strips.
A series of capacity measurements was made, taking the
strips one at a time, two at a time, three at a time, &c., and
at various distances apart, viz.: 12, 6, and 3 inches, and
also when close together. The results are tabulated in the
following table (p. 500).

The last column in the Table gives the figures showing
the sum of the individual capacities of the strips, and it will
be seen that the total measured capacity of n strips taken
together at a distance d inches apart is always very much
less than the sum of the individual capacities of the » strips,
that is, much less than n times the capacity of one strip, and
the figures show that as the strips are brought nearer together
this difference increases. When the strips are about 6 inches
apart, that is to say, separated by a distance equal to about

per cent. of their length, the capacity of the strips in

500 Prot. Fleming and Mr. Clinton on the

TapLE I.—Measurement of the Capacity of Flat Iron Strips
~ suspended in a large room, taken separately and together,
at various distances apart.

Measured Total Electrical Capacity with

distance between strips as below stated. Sum of the |

Number of

parallel is very nearly proportional to the square root of the
number of strips; thus, four strips have only twice the
capacity of one strip, and nine strips rather more than three
times the capacity of one strip. The same fact has been
observed by us in the case of the measurements of the
capacity of wires suspended in the open air. Taking for
convenience as a unit cf small capacity the micro-microfarad
(M.M.Fd.), i. e., the millionth part of one microfarad, we
have made measurements of the capacity of nearly vertical
insulated wires suspended in the air, with their lower ends a
few feet from the ground, and have obtained the following
results. In these measurements the capacity measured was
that of the wire or body under investigation, together with
that of a connecting wire, and that of the commutator
itself. This latter quantity is about 60 micro-microfarads,
and that of the commutator and lead used varied from 80
to 300 M.M.Fd., according to the length of lead. This
value is subtracted from the observed total value. The
capacity of a wire one-tenth of an inch in diameter and 111
feet long, with the bottom end about 5 feet from the ground,
was found to be 205 micro-microfarads. In the next place,
160 wires of the same kind and diameter, but 100 feet long,
were arranged in a conical form, so that the common junction
of all the wires was about 10 feet from the ground, and the
tops of all the wires were distributed around a square of
80 feet side, and at a height of about 112 feet from the
ground, the wires being therefore about 2 feet apart at the

Measurement of Small Capaciizes and Inductances. 501

top, and in nearly close contact at the bottom. Such an
arrangement of insulated wires was found to have a capacity
of 2685 micro-microfarads; in other words, about thirteen
times that of one wire, so that in this case the square-root
Jaw also holds very closely. In the same way the capacity
of four parallel vertical wires 111 feet long, and one-tenth of
an inch in diameter, arranged vertically at the corners of a
square of six feet in the side, was measured, and was found
to be 583 micro-microfarads ; in other words, about two and
a half times the capacity of one single wire of the same
kind in the same position. Similar measurements have
shown that 25 wires 200 feet long, arranged with their
bottom ends close together, and about ten feet above the
ground, and their top ends about two feet apart, had a
capacity not greater than five times that of one single wire
of the same kind in the same position. Hence it is clear that
in bunching together or placing in contiguity a number of
vertical wires in the air so as to form a radiator for use in
Hertzian Wave Wireless Telegraphy, account must be taken
of this fact, and the assumption must not be made that the
capacity of m parallel wires placed vertically in the air and
insulated, even approaches a value equal to the sum of their
individual capacities, unless the distance between the wires is
a large percentage of their length.

This effect was further examined in another series of
experiments made in the Laboratory. Two of the above-
mentioned iron strips, suspended and insulated as before,
were placed at different distances apart, and their united
capacity measured and compared with the mean value of
their separate capacities. Taking this mean value of the
capacity of a single strip as unity throughout, the results are
as follows :—

Tass I.
cet sdb 7 |
Horizontal distance | Horizontal distance | Capacity of the two |
between strips in between strips as a__ strips together, that

inches. Strips 174 percentage of their | of one strip being |
inches long, length. unity.
ee ee 22 ee oo reren st

90 | 49 8h

a7 3l | 1°85

30) 14 | L7G

Hy 9 | 1:57

13 7 1-60
4s 2°] 1-34 |

13 0-9 L'15

502 Prof. Fleming and Mr. Clinton on the

The discrepancies between parts of Tables I. and II. are to
be accounted for by the adoption of a different arrangement
of connecting wires in the two sets of experiments. The way
in which allowance should be made for the capacity of the
leads, when this is not very small compared with the capacity
to be measured, is at present under investigation, and the
above Table can only be taken, therefore, as showing that the
capacity of two vertical and parallel wires is not twice that
of one wire, unless they are at a distance apart of nearly one-
third of their length *

Similar experiments were made with two zine cylinders,
the diameter of each cylinder being 14 inches, and the length
of each cylinder 9 feet 12 inches, the capacity of each cylinder
taken alone in free space is taken as unity. If these two
cylinders were suspended one foot apart in the centre of the
large Laboratory above described, and hung vertically, their
total capacity only amounted to 1°46 times that of either
cylinder taken alone. A further experiment was made with
these cylinders. One of them was cut longitudinally and
rolled out into a flat strip, and suspended in the same position
vertically, the capacity of the original cylinder being taken as
unity. The capacity of the sheet when rolled out into a strip
was found to be 10 per cent. greater than in its original
form.

With the same appliances, a series of experiments was
made in the Pender Laboratory on the measurement of the
capacity of vertical wires of different diameters. Seven wires
of different diameters were suspended vertically by means of
silk strings from the ceiling of the Laboratory, and the
capacity of each wire was measured separately, a correction
being made for the capacity of the terminal, and of course
also for the fine wire or lead connecting the wire under
experiment with the commutator. The lengths of the wires
were about 12 feet in all cases. The following Table shows
the result of the measurements, the capacity of the wires
being given in micro-microfarads (M.M.Fds.), the fourth
column showing the capacity as calculated from the formula

Capacity (in electrostatic units) = oe where J is the
J €

length of wire and 7 is the semi-diameter in centimetres.

* It is clear that the capacity of the object measured, as it would be
free in space, is not obtained exactly by deducting that of the leading
wire alone from that of the leading wire and object when connected.
The assumption that it is so is only a first approximation to the truth.

Measurement of Small Capacities and Inductances. 503

TasrEe II11.—Measurement of Capacity of Wires of various
diameters suspended vertically in a large room.

| Meehan OF | Mean Value} Calculated | Difference in per
7 Length of — of Capacity value by | cent. between the
ca eee wire in feet. in M.M.Fds. | the formula observed and

“wa ee observed. above. calculated values.

‘0047 11°44 18:79 17°62 66

‘0075 12-23 21°36 19°59 9-0

‘0127 12:29 | 22°56 20°73 88

‘0182 22a 23716 21:38 itisil

‘0278 12:04 24:24 22-06 99

"0485 12°33 | 26°51 23°97 10°6

"1381 12:02 | 32°36 27:00 19°8

The above formula has been deduced on the assumption
that the form of a very long thin wire may be considered asa
limiting case of a prolate ellipsoid of revolution. It can he
shown that the electrical capacity (C) of an ellipsoid of
semiaxes a, b, and ¢ in infinite space is given by the ex-
pression ™ :

els

=3|" eee eee
| 2 Jo V (a2 +u) (6? +u) (2 +u)

If we put b=c in the above formula, it can be shown that

Hence the above expression gives us the capacity of . the
ellipsoid of revolution.

If the ellipsoid is very elongated so that 6 is very small
compared with a, then if e is the eccentricity of the principal
elliptical section, ¢ is nearly equal to unity, and J+e is
nearly equal to 2.

Hence (1+e)(1—e)=2(1-e) nearly
and a(1—e?)=2a(1—e) nearly.

Accordingly, since V a?—l?=ae, we can say that

a— Vo — 6° =b?/2a nearly,

and loo

= 2 log. 2a/b.

* See Article Zlectricity by Prof. Chrystal, 9th Edition of the
Eneyclopedia Britannica, vol, viii. p. 30.

504 Prot. Fleming and Mr. Clinton on the

Therefore the capacity of a very elongated ellipsoid of
revolution of which a is the major and } the minor semiaxis
is given by

2 log. 2a/b

If therefore we can consider a thin circular-sectioned wire of
diameter d and length / as an ellipsoid, we have its capacity
in electrostatic units given by the formula

tay (ST Be ese

2 log. 2l/d

where / and d are of course measured in centimetres. To
reduce a capacity expressed in electrostatic units to micro-
farads we have to divide by 9 x 10°, and therefore to convert
capacity expressed in electrostatic units to the same expressed
in micro-microfarads, we have to multiply by 14 or to increase
by about 11 per cent.

Hence expressed in micro-microfarads the above capacity

LSissoaa

\C (in M.M.Fds.) =,

C Gin E.S. units) =

, lx 108

2 x 2°303 x 9x 10° x logy2l/d
l

~ £1454 logy 2U/d°

An approximate formula for the capacity of a telegraph-wire
is also easily found. If an infinitely long filamentary wire is
uniformly charged with electricity so that it has g electro-
static units of char ge per centimetre of length, then from the
analogy with the case of an infinitely long straight current, it
is easy to show that the force due to the filament at any point
distant + centimetres from it, is 2g/r. Hence if the potential
at this point is V we have

i ie
dr -r
or V=—29 log r+ Ct,

where Cz is the constant of integration.

If we have two very long straight circular-sectioned wires
suspended in air parallel to one another, at a distance D,
the diameter of each wire being 27, and 7/D being a small
quantity, then it is easy to calculate the capacity of the
condenser formed of these wires, if we assume them to be so
far apart that the electrical charge on each remains uniformly
distributed round the surface of each wire. Let one wire

Measurement of Small Capacities and Inductances. 505

be called A, and let it be positively charged, and the other be
B, and negatively charged. Let V4 and Vz be the potentials
of these wires, and let the charge on each be ¢ electrostatic
units per centimetre of length, then their capacity per unit
of length (c) is equal to g/(Va — Vz).

Now from the expression for the potential of the electrified
filament we see that

Va= (-—2¢ logr+Ct) —(--2¢ log D+Ct),
Vp= —(—2¢ log r+ Ct) +(—2¢ log D+ Cte),
Va—Vs=4q(log D—log r) =4¢ log D/r.

The capacity per unit of length is therefore given by

1
c=—{——;_ (in electrostatic units).
4A log D/r ( )
If we employ ordinary logarithms and express the capacity
per unit of length in micro-microfarads (c’) this becomes

IMO?

oO 4x 2°303K9x1 0? logy) D/r
—_ ee
Skog ID

where d is the diameter of either wire, and D their distance
from centre to centre. The formula for the capacity per
unit of length of the single telegraph-wire of diameter d
supported at a height 4 above the earth, is easily deduced
from the above. For since the ground-surface must be a
zero-potential surface, the capacity c in electrostatic units
of the single wire per unit of length under these conditions
must be

Ae 2 u 1

‘~ Flog. 2D/d ~ Flog. 4h/d’

and the capacity ¢’ per unit of length in micro-microfarads
will be

aa 10°

~ 2x 2°303 x 9 x 10° logy, 4h/d

0°2415

(in M.M.Fds.).

Accordingly the capacity C of a telegraph wire / centimetres

506 Prot. Fleming and Mr. Clinton on the

long and d centimetres in diameter, and at a height h centi-
metres above earth, is given in micro- microfarade by the
formula

. 0724151
C= Tomsk Mle (M.M.Fds.)
or very nearly by
: l |
C= ae a (M.M.Fds.).

To test this last formula, an experiment was made in the
open air with a long wire held parallel to the earth’s surface,
on insulators at a height of about six feet above the ground.
The length of this wire was 500 feet or 15,240 cms. ‘The
height of the wire above the ground was 6 feet or 183 cms.,
and the diameter of the wire was ‘0645 inch, or 0°164 cm.
The observed value of the capacity of this wire zn situ was
1081 micro-microfarads. The value of the capacity calculated
from the formula

Oi Gn MIMAlaa) ee ee

logy) 4/ Ah/d
is nearly 1000 micro-microfarads, the difference between this
calculated and the observed value being about 8 per cent.

In the same manner the capacity of a vertical wire was
measured in the open air, and compared with the theoretical
value as given by calculation. Im this case the length of
the wire was 111 feet, or 3385 cms., and the diameter of the
wire was 0°085 inch, or 0°215 em. The observed value of
this wire when suspended vertically in the air with the
bottom end about six feet from the ground, is 205 micro-
microfarads. The value calculated by the formula

1
OMe Ee Sean logy 2u/d

is 181 micro-microfarads. The observed value is again
greater than the calculated value by about 10 per cent.

It will thus be seen that in all these cases the observed
value of the capacity of the wire, whether vertical or hori-
zontal, appears to come out, roughly speaking, about 10 per
cent. greater than the elena value. Appr oximately, the
same difference was found in the case of the capacity of a
zinc disk suspended in the Pender Laboratory. The disk
was made of sheet zinc circular in form, and 60 inches in
diameter. The calculated capacity of this disk in free space
is 48:1 electrostatic units, or 53°44 micro-microfarads*,

* The capacity of a thin circular disk when insulated in infinite space

is numerically equal to d/x in electrostatic units, where d is the diameter
of the disk in centinietres.

Measurement of Small Capacities and Inductances. 507

The measured capacity in micro-microfarads was found to
be 59°95, the difference being about 12 per cent. In all
these cases, except that of the horizontal wire, the dif-
ferences between the observed and the calculated values
appear to depend upon the proximity of neighbouring
objects or the ground, and upon the way in which connexion
is made to the commutatator. The capacity of a body
together with that of the connecting wire is not, strictly
speaking, the sum of the separate capacities of the body and
the wire measured zn situ. In an experiment with one of
the iron strips, an apparent decrease of 5 per cent. in the
capacity was found when the connexion was changed from
the bottom to near the middle. The mathematical formula
gives us the value of the capacity of the body in infinite
space, but its measured capacity is in practice its capacity
relatively to earth and depends on two things :—the proximity
of neighbouring earth-connected bodies, and the manner of
attachment to the measuring device. The first always in-
creases the capacity above the calculated value, while the
second decreases it. It appears that the net result in the
case of the capacity of a disk of about five feet in diameter,
when insulated and hung up in the middle of a room 40 feet
long, 18 feet high, and 30 feet wide, with the connexion
taken away from the bottom edge, is numerically in excess of
its calculated or theoretical capacity in free space by about
10 or 12 per cent.

Another interesting experiment was tried on the relative
capacity of two lengths of No. 30 copper wire, each 12 feet
long. One of them was preserved straight and suspended
vertically in the Laboratory as above described ; the other
was bent into a spiral about 2 inches in diameter, and 6 feet

in length over all, and then again into a closer spiral ? inch
in diameter, and 18 inches in length over all. Taking the

capacity of the straight wire as unity, the capacity Gr the
long coil of large diameter was 0°8, and the capacity of the
short coil of small diameter was 0°32, showing how much
the capacity of a wire of given length is decreased by coiling
it into a spiral. .

One of the uses to which the above-described commutator
can be put is that of determining the capacity of leyden-
jars in absolute measure ; at any rate, the capacity cor-
responding to frequencies in the neighbourhood of 100.
Instrument-makers still retain the absurd customof speaking of
leyden-jars as pint, quart, and gallon sizes, instead of marking
on them their capacity in absolute measure. Now that leyden-
jars are so much used in wireless telegraphy, the necessity

508 Prof. Fleming and Mr. Clinton on the

often arises for knowing their approximate absolute capacity,
and it is much to be desired that instrument-makers should

forsake the custom of denominating their different leyden-

jars in the present manner.

Incidentally, the apparatus may be used for more or less
accurate determinations of the electromagnetic constant “v”
One method by which a small capacity of known value can
be made with a fair amount of accuracy is as follows :—Two
cylindrical air condensers are constructed, each of which
consists of a cylindrical rod or thick-walled tube placed in the
interior of another concentric tube. Two condensers of this
kind are prepared, one about double the length of the other ;
one may be, say, a foot long, and the other fab feet long. The
tubes may be of the quality known as “‘ triblet-drawn ”’ brass
tube, one exceeding the other in diameter by about 2 milli-
metres. These tubes may then be cut up into the requisite
lengths. The ellipticity and variation of diameter in length
of such tubes are vei -v small indeed.

These pairs of tubes can then be formed into two air con-
densers by fixing the inner tube concentrically within the
outer tube by means of ebonite disks at the end. By the
adoption of known mechanical methods, the concentric
adjustment of the tubes can be made very accurately ,and the
radial thickness of the air space determined. In this manner
two cylindrical air condensers can be constructed identical
in every way, except that they differ in length.

If ¢ is the capacity per unit of length of the middle part of
the condenser, where the strain-lines are truly radial, and if
Lis the Jength of the condenser, then the capacity C of the
condenser is expressed by a function of the form C=a2+clL,
where 2 is an unknown quantity depending on the distribution
of the electric strain at the ends of the tubes. Hence if we
measure the capacity of the above two condensers by means
of the rotating commutator, and take the difference of these
capacities, this is the value of the capacity of a length equal
to the difference of the lengths of the condensers, and there-
fore the capacity per unit of ee of one of these condensers
is known, disregarding the uncertain distribution of the strain-
lines at the ends. If the device of employing a guard-ring
or guard-tube is adopted, then the capacity of the inner
portion of such a cylindrical guard-tube condenser cannot be
determined simply by charging and discharging that inner
portion through a galvanometer, without at the same time
charging and discharging the ‘guard- tubes through a by-
path, or else redistributions of electricity take place at each
discharge, which vitiate the result. This source of error was

Measurement of Small Capacities and Inductances. 509

pointed out and guarded against by Prof. J. J. Thomson
(1883) and by Prof. J. J. Thomson dnd Mr. Searle (1890) in
making this class of measurement.

Measurement of Inductance.-—If two such commutators as
we have described were mounted on the same spindle, with
the eight radial teeth of each centre wheel (I in fig. 1)
insulated from each other, and a second central brush added
in the correct relative position to the first, we should obtain
an instrument similar in principle to the secohmmeter of
Professors Ayrton and Perry ; but we have thought it worth
while, in order to get a simpler apparatus, to sacrifice reversi-
bility and construct simply a double contact-breaker on the
same lines. By making the apparatus substantial and elimi-
nating all insulating material, except air, from the rotating
drums, and abolishing all flimsy spring- _contacts, we have con-
structed an instrument which is much more satisfactory to work
with than the secohmmeter as made by the ordinary instru-
ment-maker (Pl. XII. fig.5). This double contact-breaker con-
sists of a steel shaft which carries on it two circuit-interruptors
constructed in the following manner :—Hach of these con-
sists of two wheels, like crown wheels, having four teeth, and
these two wheels are set on insulating bushes with the teeth
of one wheel interspaced between those of the other. The
shaft carries two such barrels (see fig. 5), and the developed
surface of these barrels is shown in fig. 6. The barrels are
formed of gun-metal, and against each barrel press two brass
gauze brushes carried on insulated brush-holders. One brush
bears on the continuous flange of one part of each barrel, and
the other brush alternately makes and breaks contact with it
by bearing on that part of the barrel occupied by the inter-
locked teeth. The two barrels can be set relatively to one
another in any position on the shaft. These two barrels serve
the purpose of making and breaking two separate electric
circuits in such fashion that at the moment when one circuit
is being broken, the other is complete, and at the moment
when the first circuit is being completed, the other is broken.
The arrangement is direct-driven through a flexible coupling
by a one-sixth H.P. direct-current shunt motor.

In the measurement of inductance this double interruptor
is employed like the secohmmeter of Professors Ayrton and
Perry. The coil of which the inductance is to be determined
is balanced on a Wheatstone-bridge, and the two interruptors
of the rotating appliance are inserted respectively in the
battery and galvanometer circuits, so that if the apparatus
is set rotating after the steady balance of the non-inductive

oD
resistance on the br idge has been obtained. it will eliminate

Phil, Mag. 8. 6, Vol. 5. No. 29. May 1903. 2M

S10 Measurement of Small Capacities and Inductances.

every alternate inductive electromotive force due to the
inductance of the coil, and cause the galvanometer to give a
steady deflexion. To evaluate this inductance in absolute
measure, we prefer the method described by Professor A.
Anderson*. In this method a variable resistance 7 is placed
in the bridge circuit in series with the galvanometer con-
nected to a Wheatstone-bridge, and a condenser of known
capacity (© is joined in, as shown in the diagram (see fig. 7),
and the double interruptor inserted in the battery and gal-
vanometer circuits. When the steady or ohmic reo of
the inductive coil has been determined in the usual manner,
the interrupior is set in rotation, and the value of the resist-
ance 7 in series with the ealvanometer is altered until the

galvanometer deflexion vanishes. This last change does not
upset the adjustment of the arms of the bridge already made
in obtaining the ohmic resistance of the coil. If P, Q, S are
the arms of the bridge, and R is the ohmic resistance of the
cou under test. of which the inductance is L, then the ohmic
resistance R and inductance L of the coil are given by the
equation

R=PS/Q,
L=C{r(R+8) +RQh+.

Fig. 7 shows the galvanometer and battery connected to a
change-over switch mm in order that they may be placed
relatively to the four arms of the bridge in the position
giving the most sensitive arrangement for the resistances
employed. We understand that ‘Prof. Stroud has employed
one of these arrangements for some time past in the measure-
ment of inductance, but no publication of it appears to have
been made prior to that by Prot. Anderson.

This method of measuring inductance by a combination of
the double interruptor, with the Anderson method, is one of
the most perfectly satisfactory methods that can be employed
in the laboratory. It is an absolute method in that it
requires no arbitrary standard of inductance, and yet, at
the same time, it requires no determination of a speed ; it
only assumes the possession of resistance-boxes and a known
capacity.

The value of small inductances, such as are best reckoned
in millihenrys, can be obtained most accurately by measuring
them as the difference of two larger inductances. Thus, for

* See Phil. Mae. vol. xxxi. p. 329 (1891); or ‘The Electrician,’ vol.
xxvil. p. 10.

+ For the proof of this formula for the inductance, we refer to the
original paper by Professor A. Anderson (doc. c7t.).

Special Epochs in Vibrating Systems. Fel

instance, if a coil is given of small inductance, its ohmic
resistance is first measured. It is then joined in series with
the coil of considerably larger inductance, and the inductance
of the two coils together measured as above described. The
larger inductance is then determined separately, and the
small inductance becomes known by the difference. In this
manner it is possible to determine with very fair accuracy
the inductance of quite small coils of wire.

In conclusion we have pleasure in mentioning the assistance
rendered to us in portions of this work by Dr. G. A. Hemsa-
lech, who devoted a considerable amount of time to the
experimental work at one stage of the investigation.

ILE, Note on the Sn Epochs in Vibrating Systems. By
James W. Prcx, M.A., Lecturer in Physics in the Un-
versity of Glasgow as

i a vibrating system there are two special states which

may occur, viz.:—(1) The system may be at rest in all
its parts at the same instant ; (2) The system may be in its
undisturbed configuration at the same instant in all its parts.

If these states occur at all, they will recur periodically. In

what follows the conditions under which such special states

will occur are found.

Call the time at which the system comes to rest simulta-
neously in all its parts the rest epoch; and the time at which
the system is passing through its undisturbed position in all
its parts the undisturbed epoch, both to be reckoned from the
initial time at which the system starts off with arbitrarily
given displacements and velocities. It will be shown that in
the general case when both the initial displacements and
velocities are completely arbitrary (consistent with the con-
ditions of the system) the two special epochs will not occur ;
but that by relating the system of initial displacements to the
system of initial velocities in a certain way the rest epochs
may be made to occur; by relating them in another way the
undisturbed epochs may be made to occur; and that the con-
dition which makes the one set of epochs possible makes the
other impossible, and vice versa.

Take any continuous elastic system finite in one dimension
(length /) and fixed at both ends. The general equation ot
its one-dimensional vibrations is

“¢
cya ve. Et RR ROR (5)
Ww sins y is the displacement coordinate at the time ¢ of the

* Communicated by Prof. A. Gray.

912 Mr. J. W. Peck on the Special

point whose undisturbed distance from a fixed end is w.
V is the velocity of the elastic wave in the system. If the
arbitrary set of initial displacements be given by /(x), and of
initial velocities by ¢(~), the value of y at time 7 is

Ee ITT mm Vt l . mrVet
> sin— | An cos a5 B,, sin a 2p

: l l ma l
or more conveniently in terms of the fundamental period T,
Se MIE 2mr7t ah . 2mtt
2 sin j | Am cos + mag bm sin —— |, - (3)
where

91 : ;
A= a f(#) sin “da,
i |

l f
Be - Ain 2 pe
oh

The following deductions from these well-known results are,
of course, applicable to a variety of special cases, e. g. trans-
verse vibrations in thin strings, longitudinal vibrations in
wires, rods, &c., torsional vibrations in rods.

It will be convenient to begin with two special cases :—

I. Suppose the system to start from rest so that ¢(a2)=0
for all values of x between 0 and J. The rest epochs are
given by

. 2mat
s = ()
in 7 :
or
kT
Liga) i sev. Sa (4)

where & is any integer. This gives these epochs for any
harmonic constituent m; and it is obvious that even in the
most general case both the sets of epochs occur always for
any harmonic constituent considered separately. But the
question is, whether among these epochs for any and every
constituent m are to be found those of the fundamental mode.
Only when this overlapping happens for every harmonic
mode, will the general rest epochs or undisturbed epochs
occur. Inthe present case itis seen from equation (4) above,
that / can always be chosen so as to be a multiple of m, what-
ever constituent is being dealt with, and therefore among the
rest epochs of any mode there will always be found those of
the fundamental. Hence in this case the general rest epochs
occur, and obviously at times T/2, T, 3T/2, &e.

LE pochs in Vibrating Systems. 513

But the general undisturbed epochs will in this case not
always occur. The condition is

2mat
gen
cos 7
or
Po (2k4+1)T

a his We sden heee a

giving the series of times for any harmonic m. But here the
eancelling of 24+1 by m can only oceur when m is an odd
number. Hence among the undisturbed epochs of any odd har-
monic are always found those of the fundamental ; but this
coincidence will not occur for the even harmonics. Hence
for a system starting from rest, the general undisturbed epochs
will only occur if the initial displacements be such that the
even harmonics are absent.

II. Suppose the system to start from its undisturbed con-
figuration, i. e. f(#)=0 for all values of x between 0 and J.
This gives exactly the reverse of the previous case. The rest
epochs do not in general occur ; but will, if the initial set of
velocities be such that the even harmonics are absent; while
the undisturbed epochs will always occur. This may be
shown by taking the special form of equation (3) for this case
and treating it as above.

III. The general case in which both the displacements and
velocities are given arbitrarily. Taking equation (3) above,
the condition that the rest epoch should occur is

L2MTt A, 20 TR

Bi wwe ae

Observing that A,, is a distance (or angle) and B,, a velocity
(linear or angular), denote 27A,,/Bn by the time tm. Then
equation (6) may be written

t _ are cot (Tm/Tm) +k

T 2Qarm

(7)

where T;, is the period for the mode m, and & is any integer.
This gives the times of recurrence of the rest epochs for any
harmonic m; but it is clear that in general the times of the
epochs for the fundamental will not be found among those of
the constituent harmonics: tor 7,, and T,, are quite inde-
pendent, the first depending upon the initial conditions of
displacement and velocity, the other only upon the elasticity
(or its equivalent), the inertia, and the extent of the system.

d14 Mr. J. W. Peck on the Special

If, however, the initial displacement conditions be related to
the initial velocity conditions so that
are cot T. =m arc cot T, (8)

for every harmonic, then (since the m disappears in equa-
tion (7)) the general rest epoch will occur; for evidently
among the rest epochs of each harmonic are found all those
of the fundamental. The first general rest epoch will occur
at time

arc cot (7,/T

a rh Xx T, 5. «ea on (9)
and the subsequent ones at times increasing from this by
multiples of T/2.

In the set of conditions

2 Unt \ T2 1J5)
are cot _ =¢ are cot— = arccot;- =... - (10
arc CO ae Loe T, (10)
it is to be noted that are cot _ is not to be taken as the
smallest angle with the given cotangent. Suppose 7 is
given, then arc cot et is to be chosen as follows :—If A, and

1
B, are each positive, first quadrant; if each negative, third
quadrant : if A, positive and B, negative, fourth quadrant ;
if A, negative and B, positive, second quadrant. If A, and

Bare such that are cot (formed in accordance with the

™m
. e ii e e
above rule) is m times arc cot T (formed in accordance with
1
the above rule) for every m, then the necessary condition for
the rest epochs is satisfied.
For the undisturbed epochs to occur we must have

2m7t As 2m Tm
tan ee — .
iT ibs ub Te :
or Tm
, are tan( — T ) 4+ hor
fe Sip wise m
- = meee

Hence, as before, these epochs will not occur in general

but will at times be given by

are tan( a i) +k
t= — a :

Tie a

20°

‘Epochs in Vibrating Systems. 515
provided

== ll Ota TB Sy GE Ss)

iain

are tan; =Lare tan
ee:
the angles being taken as before.

The times for the undisturbed epochs of a given harmonic
are obviously in quadrature with those for the rest epochs ;
but the set of conditions (10) which make the general rest
epochs possible are incompatible with those which make the
general undisturbed epochs possible, and vice versa. The
conditions (10) and (13) evidently agree with those of the
special cases I. and II. above. In I. all the angles of the
condition (10) become zero, and of the condition (13) 90°
or multiples thereof. The reverse holds in IL., and the
necessity for the absence of the even harmonics in the cases
remarked upon is shown by (10) and (13).

These results are all very clearly illustrated by the usual
graphical representation for simple harmonic motion.

Take a line XX’ to represent the rest position, YY’ the
undisturbed position. Represent each harmonic by a vector

Nia

from O rotating in the positive direction with a uniform
angular velocity m times that of the fundamental. The
general motion will then be represented by the group of
vectors (which are infinite in number though in any actual
system only the earlier ones in the harmonic series will be
appreciable) rotating simultaneously and starting all at once
from positions scattered round the circle. These initial posi-
tions will be determined by the initial conditions. A general

D16 Special Epochs in Vibrating Systems.

rest epoch will be indicated by all the vectors being found
simultaneously along XX’; and a general undisturbed epoch
by their being found along YY’. If OP,, be the position, at
the beginning of the motion, of the vector corresponding to
the harmonic m, the angle XOP,, is are cot (T/T).

Take, for example, the conditions (10). These indicate
that in the diagram the points P,, Py, Ps, &., must have
angles (reckoned backwards from OX) which are in the ratio
of the natural numbers. Then if all the vectors start off at
once with velocitivs proportional to their places in the
harmonic series, all will arrive at OX simultaneously, and
half a period (fundamental) later, all the odd ones will le
along OX’ and all the even ones along OX; 7. e. two rest
epochs (of different configuration) have occurred. But all
the vectors (starting off in this way) will never be found all
in the line YY’ unless in the special case in which the even
harmonics are absent.

It is clear that there are three types of possible configu-
ration at the rest epochs, and three types of velocity distri-
bution at the undisturbed epochs. This can be seen most
easily from the graphical representation. At a rest epoch, for
example, all the vectors may lie along OX, or they may all
lie along OX’, or they may lie some along OX and the others
along OX’. The first case occurs if condition (10) is satisfied
and the configuration recurs at intervals of the fundamental
period. The third case also occurs if (10) is satisfied and all
the rest configurations of this type are arrived at half a
period (fundamental) later than those of the previous type.
All the vectors corresponding to the odd harmonies lie
along OX’, ali those to the even ones along OX. The second
case will only occur as a result of (10) if the even harmenics
are absent. i

Similar results may be arrived at for the times and natures
of the undisturbed configurations. If condition (13) is
satisfied, the undisturbed epochs occur, and this is indicated
by all the vectors being found simultaneously along YY’.
The velocity distribution of the system when these epochs
occur is of three types, corresponding to all vectors along OY,
all along OY’, some in OY and others in OY’. It is also
seen from the graphical method that in general conditions (10)
and (13) are incompatible. But that if the even harmonics
are absent, either condition gives both rest and undisturbed
epochs.

Similar results to all these may be worked out for a
vibrating system free at both ends instead of fixed, as in this
case.

fs eaen 14

LITT. On the Thickness of the Liquid Film formed by
Condensation at the Surface of a Solid. By Dr. G. J. Parxs*.

T was known more than half a century ago ¢ that when a

solid is placed in a gas or vapour there is a condensation

of the latter on the surface of the solid, and in particular

that glass has the power of condensing water-vapour at
temperatures above the dew-point.

Aragot proposed to measure the amount of condensation
by the optical method of interference, and quite recently
Lord Kelvin § has suggested a method depending upon
electrical conductivity.

In almost every department of physical research glass
bulbs or tubes are used, and the presence of moisture on the
surface of the glass is a continual source of trouble. Prof. J.
Trowbridge || has lately called attention to this. matter in
connexion with spectrum analysis.

There can be little doubt also that many of the standard
results for the specific heats of finely divided or porous solids
are incorrect, for if a solid is perfectly dry, heat will be
evolved on wetting it { when it is placed in the calorimeter,
and if it is not dry then the specific heat obtained is not the
true specific heat of the solid ; in either case the specific heat
obtained will be too high. Thus, from the most recent deter-
mination of the specific heat of pure precipitated silica, well
dried and sealed in a bulb, the value appears to be -1808 **,
but the values previously obtained for amorphous silica are
much higher than this.

The present brief inquiry, which is not intended to be by
any means exhaustive of the subject, arose out of another
investigation, not yet completed, in which the author has
attempted to determine by direct experiment the surtace-
pressure of water and other liquids in contact with glass.

It was found that everything depended on keeping the
surface of the glass perfectly free from moisture until the
moment of the experiment ; and the author was thus led to
consider the quantity of moisture concerned in surface-
pressure, in the Pouillet effect, and in surface-action generally.

* Communicated by the Physical Society: read February 27, 1903.

{| Jamin et Bertrand, Phil. Mag. [4] vi. p. 157 (1853); Comptes
Rendus, June 1853, p. 994.

t See Phil. Mag. | 4] vi. p. 157 (1853).

§ Lord Kelvin, Phil. Mag. {6]iv. p. 181 (1902).

|| Trowbridge, Phil. Mae. [6] iv. p. 156 (1902).

q Parks, Phil. Mag. [6] iv. pp. 240, 251 (1902).

** Bellati e Finazzi, Att? cel R. Istituto Veneto, Tomo |xi. Parte

Seconda, p. 507 (1902).

518 Dr. Parks on the Thickness of the Liquid Film

In the first experiment some cotton silicate, similar to that
used in the author’s previous investigation *, was packed
tightly into a test-tube and the mouth of the tube was drawn
out to a fine neck, but not sealed.

The weight of the silicate was 3°37 grammes, the average
diameter of the cylindrical filaments was °00175 cm., the
sp. gr. was 2°7, and the estimated area of surface was
847 sq. cm. per gm.

Hence the superficial area of the silicate was 3°37 x 847=
2854 sq. cm., and allowing for the area of surface of the test-
tube, the whole area of glass surface amounted to about
2900 sq. em.

The tube was placed in an open beaker, and this was
covered with a large inverted beaker standing over some
water in a shallow tray and kept ina closed glass cupboard
at nearly constant temperature.

The vapour which filled the chamber slowly diffused into
the test-tube through the narrow aperture, and became
condensed on the surface of the glass. The experiment
continued for 16 days, the tube being weighed at intervals.
The outside of the tube was wiped with a clean cloth before
each weighing, so that the observed increase of weight was
entirely due to condensation by surface-action. The tem-
perature never varied much from 15°C. The following table
shows the results of the various weighings and the estimated
thickness of the film of moisture. The initial weight of the
tube and silicate when dry was 9°3402 grammes.

me Weight of tube | Increase of denne
3 and silicate. | Weight. fil

m (em.).
“WZhours ....... 93602 0200 69x10_,
he hey (fs shee ee 93644 0242 83x10_,
AGA Sos <.acck tect 9:3672 | “0270 93x UO
Tee ets tae 9°3710 ‘0308 10-6 x 10_¢
RE oy Stee ee 9°3774 W3i2 12°83 x10 :
Uo PE a A 9°3790 “0388 | 13410 ig

1G. 2. coger 9°3790 “0388 13-4x107

In another experiment the silicate was placed loosely in
the tube and the mouth of the tube was allowed to remain at
its ordinary width, about 1°5 em. The experiment was made
much more quickly. than the first one, but the final result
was the same.

* Phil. Mag. [6] iv. p. 246 (1902).

Thickness of film in millionths of em.

es
i=)

pai end a

formed by Condensation at the Surface of a Solid. 519

Temperature during experiment about 12°C.
Weight of silicate 1-10 om
Total area of surface of silicate and tube about 1000 sq. cm.
Initial weight of tube and silicate 7-9517 gm.
Weight after 4 days 7°9650 om.
Oe OSU
Tnenense of weight -:0133_,,
Estimated thickness of film 13:3 x 10-6 em.

Fig. 1.

.o)

ieee A a oe GF 1 See 9° 10) LI HIP sh tee oro MG™ ly) 18
Time, in days.

The cotton silicate thus covered with a film of moisture
showed no alteration in appearance even when examined
under the highest power of the microscope, but when the
silicate was placed in water no heat was evolved, though
when the same substance was thoroughly dried and placed j in
water the heat evolved amounted to ‘0011 calorie per sq. em.
Hence it may be inferred that the Pouillet effect for water
in contact with glass at 12°C. is confined to a film of
moisture the thickness of which is about 13°3 x 10-® em,

It will be interesting to compare with this result the results
obtained by other experimenters with different substances
and under widely different conditions. The earliest measure-
ment of surface condensation of which the author has been
able to find an account, is that of Magnus *, who, from experi-
ments on the expansion of sulphurous xel gas, found that
the amount of gas condensed on the surface of emcnre glass

* Magnus, Phil. Mag. [4] vi. p. 336 (1853).

920 Dr. Parks on the Thickness of the Liquid Film

rods was ‘0008 cub, mm. per. sq. mm., that is 80 x 10~* cub.
cm. per sq. cm. of surface.

It is not improbable that in these experiments the sulphur
dioxide was condensed by chemical combination with a film
of water previously existing on the surface of the glass, but
it may be noticed that the result obtained is of the same order
of magnitude as all the other results quoted in this paper.

Martini * found that some precipitated silica exposed to
aqueous vapour increased in weight by 80 per cent. without
any alteration in appearance: on putting this moist silica
into water no heat was evolved, though the heat evolved on
wetting the dry silica amounted to 19 calcries per gramme.
Martini does not state the area of surface exposed by the
powder, but the author has shown f that when dry silica is
wetted, the amount of heat evolved is about ‘00105 calorie
per sq. cm.; and hence we may take the area of surface of
the powder used by Martini as about 18,000 sq. cm. per gm.,
and the extreme thickness of the aqueous film would therefore

°§ oe
be 18000 =44 x 10~° cm.

It should be remarked here that when a powder is exposed
for a long time in an open tray it is likely to receive some
moisture by the ordinary process of condensation at tem-
peratures below the dew-point, and thus the more exposed
portions of the powder may receive excess of moisture.

Bellati and Finazzit have recently made an excellent
series of experiments showing the relation between the
amount of moisture absorbed by silica and the heat evolved
on putting the powder into water. The area of surlace
exposed by the silica is not stated, but the authors consider
with good reason that if the powder were perfectly dry the
heat evolved on wetting it would amount to 26 calories per
em., and hence we may assume the surface exposed by the |
powder to amount to about 25,000 sq. cm. per. gm.

In the following table the figures of the first two columns
have been selected from the original paper referred to, and
the other three columns have been introduced by the author
for the purposes of the present inquiry. An example will be
sufficient to explain the table and the diagram (p. 522). When
the dry silica has absorbed, say, 2°38 per cent. of moisture it

* Martini, Att? del R. Istituto Veneto, Tomo lix. Parte Seconda,
p. 624 (1900).

+ Phil. Mag. [6] iv. p. 247 (1902).

t Bellati e Fimazzi, Atti del R. Istituto Veneto, Tomo 1xi. Parte
Seconda, p. 514 (1902).

formed by Condensation at the Surface of a Solid. 521

is put into water and the heat evolved is found to be 18°29
calories per gm.

But if the silica had been perfectly dry the heat evolved
would have been 26 calories, hence the heat due to 2°38 per
cent. of moisture must have been 26—18°29=7°71 calories

per gm.
The thickness of the film of moisture is about
°J238 : tates
25000 =) BD) HO
and the corresponding amount of heat per sq. cm. is
iegieatas os Ak Oe paces
25000 — 3°08 x 10-4 ealories.

The results show that when the water film is only one
millionth of a centimetre in thickness, the heat evolved is
about one third of the whole amount, when the thickness of
film is two millionths the heat evolved is about one half of the
whole, and on further increasing the thickness of the film
the amount of heat evolved slowly approaches a maximum
which it reaches when the thickness is about 31°6 x 10-8, the
heat evolved being then -00105 cal. per sq. em.

Parts of Reduction of | Heat evolved |
moisture | Heat evolved) the heat evolved, Thickness of | per sq. em. by
absorbed by | per gramme | by previous | water film | a film of this
100 parts of of silica. absorption of | Tao Ae thickness
dry silica. (q) moisture. | 25000 ° 26—q
(2) (26—q) | 25000°
2:38 18:29 T71 95x10_¢| 308x10_, |
5°85 12°23 13-77 2:14x10_,| 551Xx10_
8-59 917 16°83 3-44x10_,| 673x10_,
12-92 7-61 18:39 517x10_¢| 7:36x10_—
18:83 6-50 19,50) aecos 10M 7 60>< 10m
27-36 525 20°75 109410. | 830x104
39:95 3°70 22°30 1598x10_.| 9892x1074
46°35 2-94 23-06 1854x107 | 922x1074
56-48 1-66 24-34 22:59x10_°| 9-74x107*
64-78 ‘90 2510 | 2591x107°| 1004x1074
76:94 19 25°81 30°78 10-° | 10:321074

Dr. C. Barus * gives some valuable data on the size of the
water particles produced by condensation on a solid nucleus.
In the experiments described it seems that the condensation
must in the first place be caused by the surface action of the

* Barus, Phil. Mag. [6] iv. pp. 24 to 29 and pp. 262 to 269 (1902),

Heat evolved per sq. em. X 104.

522 Dr. Parks on the Thickness of the Liquid Film

nucleus, though as the exhaustion of the chamber proceeds
the average size of the water particles increases by ordinary
condensation at temperatures below the dew-point. If we

10 20 30
Thickness of film x 10°.

subtract the average diameter of the nuclei from the average
diameter of the drops, and halve the remainder, this will give
the thickness of the film of water.

In the following table the first two columns have been
taken from the original paper of Dr. Barus, and the last
column has been inserted by the present writer. The results
tor the first six exhaustions only have been selected.

Dr. Barus remarks that “the use of Kelvin’s vapour-
tension equation breaks down quantitatively for the present
purposes in practice.” The reason for this will be clear
when it is remembered that Kelvin’s vapour-tension equation
is only intended to apply to a condition of equilibrium
existing between a liquid and its vapour ; but in condensation
upon solid surfaces another element must be taken account
of, viz., a force of the nature of an attraction between the
solid and the liquid or vapour, which causes a pressure,

fermed by Condensation at the Surface of a Solid. 523

Diameter of nucleus 260 x 10° em.

Number of Diameter of Thickness of
exbaustions. | water particle. filma.
6 —6

i aekias aoet eae 280X10_ 4 I< Nas
ae aM 31010, 25X10_¢
Liss 330X10_, 35X10_,
Ae ROS ae 360 x 10 és 50x10_.
Sean eee 390 X10_. 65x10_.
Crate awaken! 420x108 | 80x10 ©

Diameter of nucleus 360 x 107° em.

gems 370x105 | 5x10_,
Spee 39010_ 15x10_,
ae 410x10_, | 25x10_°
Ae os sade: 420Xx10_, 30x10,
Bish semis 440 x 10_° 40 x10
peel 460 < 10 50X10

probably a very great pressure, in the liquid at the surface of
the solid. The author hopes to be able at some future time
to give the numerical values of this surface pressure for
various liquids in contact with glass.

In now appears that in all cases where condensation of
moisture takes place ata solid surface, and at temperatures
not below the dew-point, the thickness of the surface film
varies from 10x10~° to 80x10-® cm. according to the
substances used and the conditions of temperature and
pressure, and for the water film on glass in saturated vapour
at 15° C. the thickness is about 13:4 x 10~® cm.

According to Prof. J. J. Thomson * the mean radius of
the drops formed by condensation in electrified gas is of the
same order of magnitude, being 81 x 10~° cm. for negatively
electritied oxygen, and 68 x 10—§ cm. for positively electrified
oxygen ; the size of the nucleus is not known, but it is

probably very small.

HLM. Dockyard School, Portsmouth.
November 1902,

* J. J.Thomson, ‘The Discharge of Electricity through Gases ’ (1900).

Lipset ay

LIV. On the Gaseous Constitution of the H and K lines of
the Solar Spectrum, together with a Discussion of Reversed
Gaseous Lines. By JoHN TROWBRIDGE*.

[Plate XID.)
DESCRIBED in the Phil. Mag. July 1902 and Feb.

1903 the discovery of reversed lines in the spectra of
gases, when the latter are submitted to powerful disruptive
discharges.

In this paper I shall show that the continuous spectrum
observed when glass tubes are employed is not due to the
ineandescence of the walls of the tubes; and also that the
lines obtained by me which apparently coincide with calcium
lines at wave-lengths 4227 and 3933, 3968 are not due to
calcium but are gaseous lines. The group of H and K lines,
therefore, of the solar spectrum, although being doubtless a
composite spectrum, has a strong basis of gaseous lines.
This seems more than reasonable when we consider that the
solar protuberances are observed through these lines; and
when we also take into account the rarefied nature of the
gas and the improbability of a metallic vapour like that of
calcium being projected so far from the limb of the sun.

It seemed necessary, in the progress of my work, to deter-
mine to what degree metallic electrodes influence the spectra
in Geissler tubes of the dimensions | have employed. When
long and powerful sparks are produced in air the metallic
lines disappear at a distance of less than two inches from the
terminals. The photograph, therefore, of the spectrum pro-
duced by a spark of three or four feet in length shows
nothing but air-lines when the slit of the spectroscope re-
ceives the light from the middle of the spark. This is true
even when sparks of eight inches are examined. The most
effective way, therefore, of sifting out air-lines from metallic
spectra is to employ long and powerful sparks. At one time
I believed that the oscillatory nature of the discharge in-
fluenced the nature of the spectra. 1am now of the opinion
that self-induction acts merely by diminishing the instan-
taneous energy of the discharge.

In the present paper I shall confine my attention mainly
to the immediate region of the H and K lines of the solar
spectrum.

In Geissler tubes, having capillaries not less than two
inches in length, the terminals being three and a half or four
inches apart, no metallic lines were observed under the con-
ditions of my work. Indeed, to produce metallic spectra at

* Communicated by the Author.

Constitution of H and K lines of Solar Spectrum. 525

such distances from the electrodes during the time of dura-
tion of the discharges would demand a prodigious velocity of
the particles. I have made a careful study of the influence
of metallic electrodes in the tubes employed by me and find
no spectra due to them.

In order to determine whether the walls of the glass tubes
could give lines due to calcium, I first placed aluminium ter-
minals on a sheet of glass of the same kind as that from
which the Geissler tubes were made; and having placed the
glass against the slit of the spectroscope, I passed powerful
discharges of the same nature and energy as were employed
in the study of the spectra of gases. The glass was badly
corroded along the path of the discharge, showing the same
corrosion which was observed in the capillary of the glass
Geissler tubes.

No continuous spectrum was observed and no calcium
lines. Similar discharges were passed through fifty ohms of
No. 36 iron wire ; the wire was barely raised to a dull red
heat. A photograph was taken of ten centimetres of such
wire, illuminated by the discharge from a Geissler tube
placed in the same electrical circuit. The photograph showed
the wire intact at the moment of the illumination of the tube.
It took time to communicate sufficient heat to melt the wire.
On the same photograph was shown the subsequent melting
of the wire. ‘That is the wire is seen intact, and also the two
ends of the wire contorted and burning. If the walls of the
capillary of the glass vessels are heated to incandescence the
time element must be large, for the gas must first be heated
by the discharge and then the walls of the glass by conduc-
tion and radiation. Thermodynamic considerations make it
impossible that the walls of the glass vessels are heated to
incandescence; moreover, Wiedemann* has shown that the
heat of electrical discharges in Geissler tubes has been much
exaggerated. A photograph was taken of the light from
a Geissler tube by means of a rapidly revolving mirror.
Beside the tube and in the same circuit was a spark-gap
between magnesium terminals. The duration of the light of
the Geissler tube was one-fourth of that of the spark between
the magnesium terminals in air. There was absolutely no
duration of the light of the Geissler tube due to a supposable
incandescence of the glass, The light in the Geissler tube
arising from powerful disruptive discharges is the strongest
and most instantaneous light which has been obtained, and
would be useful in the study of rapid motions.

If the glass is not vaporized by the discharges I have

* Wied. Ann vi. (1878).
Phil. Mag. 8. 6. Vol. 5. No. 29. May 1903. 2N

employed, the spectrum of calcium cannot be produced in the
capillary of the glass vessels. A direct test of the question
whether the reversed lines observed by me are due to the
glass is afforded by the use of quartz vessels, of which the
ends were closed by metal plates. There being a complete
absence of glass, and previous investigation having shown
that the metallic plates or terminals, and the luting employed,
gave no metallic spectra. In the case of quartz the powerful
disruptive sparks produced absolutely no corrosion of the
walls of the quartz capillaries ; and the reversed line at ap-
proximately wave-length 4227 and wave-lengths 3968, 3963
(H.H.) of the solar spectrum came out with the same in-
tensity as in the case when glass was employed. Moreover,
the strong calcium lines towards the ultra-violet, besides
those which apparently coincide with the H.H. lines of the
solar spectrum, were conspicuously absent.

The reversed lines which I described in my previous
article, and which are shown on the plates of that article,
are not due to calcium.

These lines may arise from an electrical decomposition of
residual air. It seems impossible to fill spectrum-tubes with
perfectly dry and pure hydrogen: traces of air must enter
from the purifying and drying apparatus, and the impurities
may be brought to light by powerful discharges. I have
shown in a previous paper that the electrical decompositions
in a tube apparently filled with pure hydrogen can produce
various spectra, among them that of argon. ‘The most pro-
mising method of obtaining pure dry hydrogen appears to be
by the use of liquid hydrogen.

In my paper in this Journal, Feb. 1903, I spoke of a re-
markable reversal of lines in the ultra-violet which were
obtained by the use of quartz tubes. Fig. 4 (Pl. XU.)
shows these lines with a companion spectrum of magnesium.

These reversed lines apparently coincide with spark-lines
of silicon in air; and one might conclude that the lines come
from a volatilization of the walls of the quartz capillary.
There is, however, absolutely no corrosion of the walls of the
quartz vessel. The surface of the quartz remains limpid and
clear. I have concluded that, just as in the case of the
supposed calcium lines discussed above, these reversed lines
are also due to a gas. In order to discover whether these
lines can be obtained from some gaseous constituent of the
air, I have studied the spectra obtained from powerful sparks
in air taken from a great variety of metallic terminals. The
spectra from terminals of pure platinum, electrolytic silver,
and iridium show strong lines which coincide, with the dis-
persion I have employed, with the great H.H. lines of the

of the H and K lines of the Solar Spectrum. VA

solar spectrum, and also with the gaseous lines I have ob-
tained in rarefied hydrogen*. Terminals of aluminium,
copper, iron, tin, magnesium, show these lines faintly. The
noble metals, which are least affected by the electric discharge
and which are therefore used for nonoxidizable contact in
electric apparatus, give these lines strongly. Is it not pro-
bable that when the electric discharges volatilize to a high
degree the metallic terminals, electric discharge prefers a
passage through the metallic vapour, and does not sufficiently
heat the air to bring out certain air lines? The method of
sifting out air lines from metallic spectra by observing the
lines which are apparently common to these spectra, and
setting down such lines as air lines, is a fallacious method.
Silicon is not easily volatilizable, and certain important
groups of lines attributed to that metal, obtained by the use
of the spark in air, may be atmospheric lines. I have ob-

tained traces of such lines which seem to coincide with the
_ gaseous lines I obtained with rarefied hydrogen in quartz
tubes by employing water electrodes. These electrodes were
made as follows:—two iridium terminals were placed on
pieces of kiln-dried wood four inches apart. The condenser
spark could leap only one inch. The wood was wrapped with
cotton, inclosing the metallic terminals, around the cotton
was wrapped chamois skin ; the clear space between the ends
of the wood thus protected was half an inch. The terminals
thus prepared were soaked in distilled water. A very powerful
spark was thus obtained in air which was entirely free from
metallic lines. With these terminals it is undoubtedly true
that the water-vapour conducted the main body of the dis-
charge, just as the metallic vapour does in dry air. The
edges of this spark show a strong red tint, and give the line-
spectrum of hydrogen. The centre of the spark is of a
brilliant whiteness. Strong bands appear in the position of
the reversed lines which I have obtained with rarefied hydro-
gen in the quartz tubes. I therefore believe that these lines
are gaseous lines.

I believe that these lines, and also the great H.H. lines of
the solar spectrum, are due to oxygen. At very high tempe-
ratures the oxygen atom set free from the salts of calcium
and its allied metals is free to vibrate in its own periods. It
does not seem improbable that many lines attributed to metals
may be oxygen lines; the metal releasing its hold of the
oxygen atom at very high temperatures.

* Compare with paper “On the Constitution of the Electric Spark,”
Arthur Schuster, F.R.S., and Gustav Hemsalech, Phil. Trans. Roy. Soe.
vol. exciil, series A.

2N 2

528 Constitution of H and K lines of Solar Spectrum.

When the liquid terminals described above are saturated
with chemically pure chloride of calcium, with nitrate of
strontia, with nitric acid, the great H.H. lines and the line at
wave- length 4227 are oreatly enhanced. This gives strong
colour to the above hypothesis. There is evidently an electro-
chemistry of the air which has been opened by the discovery
of argon.

The continuous ae observed with disruptive dis-
charges in gases occurs also when electrical discharges are
obtained in distilled water, and in certain other liquids.
Prof. Wilsing*, Prof. Hale+, and Sir Norman Lockyert have
discussed tie reversed lines observed under this condition.
The phenomenon of continuous spectrum and of reversals is,
I believe, of the same nature as the phenomenon observed by
ine in gases. The continuous spectrum is due to a sudden
compression of the medium under the powerful disruptive
electrical explosion, and the reversals are due to a polariza-
tion and not to a reversing iayer. The reversed lines ob-
served by me increase in intensity toward the ultra-violet,
and also are strengthened by repeated exposures. This is
the case also with the reversed lines observed under water.

The conclusions of my first paper in the Phil. Mag. July
1902 are therefore confirmed by further investigation. At
the basis of the great H.H. lines of the solar spectrum, there
are strong gaseous lines which I believe to be oxygen lines.
The reversed lines are not due to calcium but are due to
oxygen.

The accompanying Plate (XIII.) shows the normal spectra
which illustrate this article. Fig. 1 represents the gaseous
lines which closely correspond with the great H.H. lines of the
solar spectrum. Fig. 2 represents the spectrum of calcium
in the neighbourhood of the H.H. lines. It is seen that
strong lines of calcium are conspicuously absent in fig. 1.

Fig. 3 shows the gaseous lines obtained in a quartz tube
filled apparently with pure hydrogen. A strong group of
magnesium lines is added for comparison. These 1 magnesium
lines are the strongest lines of that metal between wave-
length 3000 and 2000.

Fig. 4 gives also the same comparison spectrum of mag-
nesium, and reversed lines of the gas contained in the quartz
tube.

In fig. 38 there is no continuous spectrum. The argument
of incandescent walls to account for the continuous spectrum
in the case of the employment of glass Geissler tubes, would

* Kayser, 1 C. 1 P. p. 228.
+ GOK. Hale, Astrophys. Journ, p. 15 (1902).
{ N. Lockyer, Proc. Roy. Soc. p. 70 (1902).

Influence of Magnetic Field on Thermal Conductivity, 529

require also a heat of at least incandescence to volatilize the
silicon in order to produce the bright unreversed lines seen
in fig. 38 at wave-length 2882, and wave-lengths from 2542
to 2507.

Jefferson Physical Laboratory,
Harvard University, Cambridge, U.S.

LV. On the Influence of Magnetic Field on Thermal Con-
ductivty. By Vincent J. Buytu, M.A. (Glasgow), 1851
Hahibition Research Scholar, Emmanuel College, Cambridge*.

ie a circuit composed of bismuth and another metal, the
thermo-electric E.M.F. is altered if the bismuth be
placed ina magnetic field. This alteration was observed by
Leduc} and by Righif, while using such.a circuit as a
means of measuring the difference of temperature between
two points of a heat-conveying bar of bismuth. Assuming
that the change represented a change in the temperature-
difference between the junctions, they deduced the result
that the thermal conductivity of bismuth was altered by the
magnetic field. But von Httingshausen and Nernst§ have
shown that such a change in the H.M.F. takes place without
any alteration of temperature-difference, and that it repre-
sents the “ longitudinal thermomagnetic effect,” which may
also be regarded as an alteration of the thermoelectric nature
of bismuth by application of magnetic field{]. If thermo-
electric junctions are to be used for observing temperature-
differences with a view to measuring the effect of magnetic
field on thermal conductivity, it is necessary that the in-
trusion of the von Ettingshausen and Nernst effect should be
prevented ; and this may be done either by keeping the
junctions out of electrical contact with the bar under test, or
by obtaining the temperature-differences by independent ob-
servations of the two temperatures in each case with reference
to a standard junction, It is the purpose of this paper to
describe a number of experiments made with a view to
determining the effect of magnetic field on thermal con-
ductivity.

A castrod of bismuth (14 ems. long and 1 cm. in diameter)
was warmed at one end to 100° C. and kept at zero at the
other end; the ends of the rod were soldered into large
copper blocks within the heating and cooling chambers, and

* Communicated by Prof. J. J. Thomson, F.R.8.

t+ Journ. de Phys. (2) vi. p. 379. { Compt. Rend. ev. p. 168 (1887).
§ Wied. Ann. xxxi. p. 760 (1887).

€{ See Lownds, Phil. Mag. Oct. 1901,

530 Mr. V. J. Blyth on the Influence of —

the rod was surrounded by non-conducting material, in order
that the flow of heat along it might be uniform and linear.
Three thermoelectric junctions of copper and german-silver
were attached to the rod—one at the middle point and the
other two at a distance of 1 em. from either end; the junctions
were soldered into small radial holes drilled in the red. The
poles of the electromagnet, which were 2 cms. apart, measured
5 ems. X 3 cms., and could be placed so as to embrace either
the hotter or the colder half of the rod. After the distribu-
tion of temperature in the rod had attained a steady state,
the temperatures of the three junctions were individually—
and as nearly as possible simultaneously—observed with re-
ference to a standard junction kept immersed in melting ice.
Several readings were taken periodically before application
of the field, and again several during the interval when the
field was applied (usually about 9 minutes); and this process
was repeated several times until a large number of readings
of temperatures had been obtained. From these the tempe-
rature-differences at the ends of that half of the rod subjected
to magnetization were derived, and the average of those cor-
responding to no field compared against the average of those
corresponding to the particular field applied. Various field-
strengths, from 650 to 3550 c.c.s. lines per sq. em., were
used, but in no case did the temperature-difference with the
field on differ from that with the field off by more than a
very small amount. Moreover, the want of exact concordance
among the values of the temperature-ditferences obtained
showed that these were varying by small amounts through-
out the experiments in consequence of accidental causes.
Of the apparent changes produced by application of the
field the largest was one of 0°3 C. increase in the tempera-
ture-difference at the ends of the magnetized part of the rod.
The mean of such changes observed was about 0°07 C.,
which would correspond to a diminution of conductivity of
about 1/7 per cent. Thus it appears that the effect on the
conductivity of bismuth of such fields is exceedingly small,
since, had the change amounted to $ per cent., it could have
been easily detected by this method, in spite of the slight
fluctuations of temperature which took place during the
observations. The H.M.F. in the circuit composed of the
copper wires of the thermo-junctions and the bismuth rod
between them suttered considerable alteration on the appli-
cation of the field. Had it been assumed that this was due
to a change in temperature-difference, the diminution of con-
ductivity mdicated would have been 5:6 per cent, for a field

| ny ai om

Magnetic Field on Thermal Conductivity. 531

of 3550. This may be compared with the results quoted by
van Kverdingen*. .

k=conductivity under zero field.

k= . » lield applied.
iis k
Field 3550. zr = 1058.
van Hyerdingen ...... 6000 1:058
Medues fo. .iev.asceeecce: 7800 1:057
von Httingshausen ... 9000 1052 to 1:021.

The above experiment was repeated with a bar of bismuth
obtained from Messrs. Johnson, Matthey & Co., and in this case
the von Httingshausen and Nernst effect was found to be too
small for detection. In the previous case the change in
deflexion representing the effect was 10 scale-divisions; but
although the conditions were all exactly the same in the trial
of the Johnson-Matthey bar no deflexion was observed on
applying the field.

In order to measure the temperature-difference between
two points directly by a single reading a system of thermo-
junctions of german-silver and iron was arranged, the
junctions being insulated from the rod. These were thrust
into small radial holes in the rod, and kept out of contact by
thin slips of mica. No distinct. effect of magnetic field on
the temperature-difference was detected by this method ;
moreover, it was found that the temperatures indicated by
these insulated junctions differed somewhat considerably from
those given by junctions soldered to the rod at the same
points. Therefore an arrangement in the form of a thermal
Wheatstone’s bridge was adopted, whereby it was possible,
without admitting the Nernst effect, to have the junctions
soldered to the points between which the temperature-dit-
ference was to be observed. The two pairs of arms of the
bridge (fig. 1) were kept out of electrical contact by means
of small strips of insulation inserted between the metal pieces
and the walls of the slots in the copper blocks which were
soldered to the inside of the heating and cooling chambers.
The thermo-junctions of german-silver and iron attached to
the points A and B were connected in series through the
galvanometer, whose sensitiveness was 11 divisions deflexion
per 1° C. difference of temperature. The bars were wrapped
up in felt, and the magnet set so as to embrace between its
poles one of the arms of the bridge. Various forms of bridge

* Leiden Communications, 25th March and 22nd April, 1898.

532 Mr. V. J. Blyth on the Influence of

arrangement were experimented with. In one form each
pair of arms consisted of a straight bar of the metal let into
Fig. 1.

(CE GATH

COPPER BLOCK

= all

STEAM BATH

the blocks in the heating and cooling chambers at its ends,
and having a thermo-junction at its middle point. After the
flow of heat along the bars had become steady the two
junctions were found to be at nearly the same tempera-
ture ; but when one half of one of the bars was subjected to
a transverse magnetic field, this balance was disturbed to a
greater or less extent, according to the field applied. With
this arrangement soft iron was tested under a transverse field
of 2650 c.a.s., and the change of temperature-difference was
0-3 or 0°4 scale-division; for hard steel a similar small
change of 0°5 division was obtained by application of a field
of 4800. These changes are too small to be regarded as
definite. The experiments with mild steel at higher field-
strengths are tabulated below.

Change in Tempe- _ Percentage diminu-

Magnetic Field on Thermal Conductivity. 533

After the flow of heat had attained a steady state the
reading corresponding to the temperature-difference between
the middle points of the bars was taken, and also the de-
flexions representing the actual temperatures of each middle
point with reference to a cold junction. The deflexion cor-
responding to the temperature-difference was initially small,
but when the magnet current was switched on, it increased
with comparative rapidity for 20 minutes, and thereafter
more and more gradually for 10 minutes longer, when it
became constant. When the field was removed the difference
diminished again, usually requiring from 40 to 45 minutes
to regain its steady value. This process was repeated several
times and the mean of these rises and falls for each field is
represented by each of the numbers given in the table; the
first fall and the subsequent rises and falls were less than the
first rise, doubtless on account of residual magnetism. By
means of the observations of the actual temperatures of the
middle points of the bars, it was shown that the changes in
temperature-difference were due to a rise in the temperature
at the middle point of one of the bars, and an approximately
equal lowering of the temperature at the middle point of the
other ; on the removal of the field the temperatures fell and
rose respectively, until the original small difference before
the field was applied had been approximately regained. The
changes were proved to be not in any degree due to heat
transferred from the electromagnet coils. The bar which
was not between the poles was in a stray field of about 1900.

By using this bridge method, the alteration in conductivity
of bismuth was found to be 0°3 per cent. for a field of 8500;
but this result is probably unreliable, since the length of the
bismuth bars (8 in.) was afterwards found to be too great to
justify neglecting the loss of heat by escape through ‘the felt
lagging.

The effect of a longitudinal field was measured in two ways
—hby the “ bridge method, ”” and by the method of observing
directly the quantity of heat which flows along a magnetized
and an unmagnetized bar in a given time. Preliminary
trials showed that a decrease of conductivity would be de-
tectable by the latter method, although they did not provide
data for evaluating the change numerically. Two similar
bars were set up with their ends in the copper block of the
steam-box and insulated from it. One bar passed through a
coil which was wound anti-inductively, and arranged so that
the two halves could be joined in opposition so as to produce
zero field and yet have the same heating effect as when they
were put in conjunction to generate a field,,which inthis
case amounted to 41 0.¢.s. units. To the top ends of the

534 Mr. V. J. Blyth on the Influence of

bars german-silver-iron junctions were soldered. After the
distribution of temperature had become steady, the current
flowing but generating no field, the junction readings were
taken, and then again some time after the field had been
excited. The generation of the field produced a rise of tem-
perature at the top of the magnetized bar of 2-2 per cent. in
the case of iron and 2°8 per cent. in the case of bismuth. In
the actual experiments time readings were taken of the tem-
perature at the top end of a bar whose lower end was fitted
hard into the copper block of the steam-chamber, the tempe-
rature being initially atmospheric. By drawing curves of
these readings the following results were obtained, the material
being mild steel and the field 51 c.a.s.:—

Magnet off; rise of temp. in 20 min., 144 div. | Percentage decrease of

One ss Na 20, ,,° 1388 .;.- J» conductivities; snes
” off ; 9 ” 20 ” 21) ” 5
Tr tee acu anens 1 a le

By a similar method a rod of soft iron, 6 in. long and
5/8 in. in diameter, was tested both for longitudinal and
transverse fields. But in this case thermo-junctions were
not used, the temperatures at the top end of the rod being
obtained from a mercury thermometer which rested in a
glass tube containing mercury attached to the top of the rod:
the top of the rod was tinned and amalgamated so as to be
in good thermal contact with the mercury. The longitudinal
field was supplied by a solenoid which was not anti-indue-
tively wound, but the heating of the thermometer by the

Longitudinal field; giving induction 16,000 c.a.s.

Rise of Temp. in 20 min.

Tnitial Difference. | Percentage
emperature:|ete. eee ot ee eee ele: Diminution.
Magnetism off.| Magnetism on.

1563 | (298-7 C. 26°-9 28 9-4
19:25 28-4 25:0 3-4 12:0

Rise in| 15 min.

26°6 21°6 19:4. 22 10:2
Transverse field; 7850 o.a.s.

Rise in 20 min.

13°2 32°7 32°35 "3D 1:07
14:3 32'1 31°6 9) 1:56
15°8 32°0 31:7 3 “94

= = — ad ‘ P ——

Magnetic Field on Thermal Conductivity. 535

coil, which was separated from the rod by Kieselguhr insu-
jiation 4 in. thick and a tube of ebonite, was slight; and in
all cases a correction was applied for whatever slow change
of temperature might exist during each experiment.

On account of the large demagnetizing factor in the case
of the transverse magnetization of the rod, the intensity of
magnetization would in this case be much smaller than that
produced by the longitudinal field. This may account for
the comparatively small value of the change produced by
transverse field; for Gray and Jones* have found that the
change of electrical resistance of iron is dependent on in-
tensity of magnetization rather than directly on magnetic
field.

This method was unsatisfactory on account of the difficulty
of securing that the initial conditions for the two comple-
mentary experiments should be exactly the same as to tem-
perature. It was found better to set up two similar bars
of the same material side by side with their ends fixed in
the steam-box, and take the two sets of time-readings
sunultaneously. This modification was applied in the deter-
mination of the following result for mild steel bars. The
table below contains figures taken from the curves repre-
senting the changes of temperature at the ends of the bars.

Time from Magnet on Left-Hand Bar. == Magnet on Right-Hand Bar.
instant of |
letting in |
steam. /Temp.of R.H./Temp. of L.H.) Diff. |Temp.of R.H.|Temp. of L.H. Diff.
0 15-9 15-9 0 || 169 16-9 0
20 26°3 23:95 (2:35 | 26:4 24-9 15
40 34-25 3065 |36 || 334 Si 1%
60 37°85 33:8 405 | 369 34:85 | 2:05
{0 |. 39:0 34-6 Ae | Bee) 35'8 ae
80 39°7 85°25 | 445 | 38:55 36°5 2-05
90 40°15 35°8 4:35 | 89-0 36:9 2-1
| 21

100 406 36:2 4-4 39:2 oT 1

It will be seen that after an interval of 80 minutes has
elapsed since the steam was blown into the box, the tempera-
ture-difference becomes constant. Taking as the mean values
of these constant differences 4°°4 and 2°1 we find the dimi-
nution of the rise of either bar, as compared with what the
rise would have been had there been no field applied, by

* Proc, Roy, Soc, vol. xvii. p. 208.

|
|
|

536 Influence of Maynetic Field on Thermal Conductivity.

halving the excess of the one difference over the other. More-
over, when a series of readings was taken with neither bar
in the field the rise of temperature in 80 min. of the R.H.
bar was found to exceed that of the L.H. bar by 3°25, which
is midway between 4:4 and 2:1. Thus the effect of the field
was to diminish the rise of temperature by 1°15, which cor-
responds to a diminution of the thermal conductivity of 3:1
per cent.; the field in this case was 6500 c.a.s. By repeti-
tion of the above experiment this result was fully confirmed.

The application of this method to bars of bismuth 4 in.
Jong, as in the case of the other methods, did not yield any
definite results.

For measuring the effect of longitudinal field by the bridge
method, a form of bridge was used in which the arms con-
sisted of wires each having a right-angle bend at its ends, so
that its ends could dip into mercury-cups; the arrange-
ment of the mercury-cups is shown in fig. 2. One of the

Fig. 2.

COLD
HOT

CHAMBE FP CHAMBER

arms was composed of a variable number of thin wires, the
number of which was adjusted until the temperatures of
the cups A and B were equal, as indicated by the sensitive
thermo-junctions dipping into them. The wires were all
coated with a thin layer of enamel, which broke the electrical
circuit through the bridge, thus excluding the Nernst effect
when magnetic fields were employed. By use of this
arrangement fairly good values were obtained for the con-
ductivity of the specimens tested by comparison with that of
a standard copper wire whose conductivity was assumed; and
the method proved a very convenient one for this purpose.
For the diminution of conductivity of an iron wire under a

ee ee ee ee

Theoretical Optics since 1840. 53d

longitudinal magnetic induction of 17,500 c.a.s. lines per
sq. cm., the value 10°2 per cent. was found; and this value
is in tolerable agreement with those quoted in an earlier part
of the paper as obtained by the direct method.

Summary of Results.

The change in the thermal conductivity of bismuth pro-
duced by magnetic field is very small ; Bu a transverse field
of 3550 it is considerably less than 4 per cent., and it is
scarcely measurable even in higher fields by any of the
methods used.

As tested by the bridge method, mild steel suffered a re-
duction of its conductivity of 3°3 per cent. for an increase of
transverse field of 7500, and a reduction of 2°1 per cent. for
an increase of 6700. The reduction 3:1 per cent. was ob-
served for the same material by the method of direct measure-
ment on application of a transverse field of 6500.

The effect of a longitudinal field of 51 c.G.s. on the con-
ductivity of mild steel was to diminish it by about 4 per cent.

In the case of soft iron, as tested by direct measurement,
a longitudinal field producing a magnetic induction of 16, 000
per sq. cm. diminished the conductivity by about 10°5 per
cent.; while the effect of transverse field is comparatively
small—about 1 per cent. for a field of 7850; by the bridge
method the effect of a longitudinal induction of 17,500 was
found to be a diminution of conductivity of 10:2 per cent.

I beg to express sincerest thanks to Prof. J. J. Thomson
for continual encouragement and assistance.

Cavendish Laboratory, Cambridge.

LVI. Theoretical Optics since 1340. —A Survey.
By R. T. Guazeproox, D.Sce., F.RS.*

IR GEORGE STOKES took his ee in 1841; the
first of the papers contained in his Collected Works was
read in 1842: he became Lucasian Professor in 1849.

Speaking as I do so soon after his death, it is, perhaps, not
unnatural to look back over the progress of our Science
during the sixty years for which he has been one of the most
prominent of its exponents.

To attempt such a task in any completeness would need a
fuller knowledge and an abler pen than mine; will you,
however, bear with me if I take one corner of the field
covered by his activities and attempt a brief survey of this.

* Communicated by the Physical Society, being a portion of the
Presidential Address delivered on Febr uary 13, 1903.

538 Dr. R. T. Glazebrook :

It is, perhaps, the more necessary, for I think it is not always
recognized how much of our knowledge of Optical Science
is due to Stokes. It was he who first verified with any
degree of exactness Huyghens’ construction for the refraction
of light at a uniaxial crystal ; the interpretation of Kirchhoff’s
discovery of the coincidence between the dark lines of the
solar spectrum and the bright lines of certain incandescent
solids and gases is due to him, and on this the whole of spec-
trum analysis rests; he explained the phenomena of fluor-
escence, and as an old man, some years ago, expounded in his
own unrivalled manner the origin of the Roéntgen rays and
their connexion with the kathode rays. The analysis of a
plane wave of light into its constituent parts, and the first
dynamical account of diffraction, are due to him; and his
experiments, if we accept any modification of the elastic-
solid theory of light as true, settled that Fresnel’s explanation
of the cause of refraction, rather than that of Neumann and
MacCullagh, is the right one.

In his brilliant Rede Lecture, Cornu writes :—

“The study of the properties of waves, looked at from
every aspect, is then at present the really fruitful path.

“It is that which Stokes, in his double capacity of mathe-
matician and physicist, has followed.... All bis beautiful
investigations, whether in hydrodynamics or in theoretical
or experimental optics, relate to the transformations which
waves undergo in the diverse media through which they pass.

“In the varied phenomena which he has discovered or
analysed, movement of fluids, diffraction, interference,
fluorescence, Rontgen rays, this guiding idea that I have
pointed out is ever visible,and itis this which has made the
scientific life of Sir George Stokes one harmonious whole.”

Let us consider then very briefly the progress of theoretical
optics since the days of Stokes’ first paper on the subject :
“ On the Theories of the Internal Friction of Fluids in Motion,
and of the Equilibrium and Motion of Hlastic Solids” *. The
advance in the early part of the century had been most
marked. The discovery of the principle of interference by
Young, and the brilliant work of Augustin Fresnel, who
had covered the ground with giant strides, had placed the
undulatory theory on a firm footing, but there was no con-
sistent view of the subject which would account even for the
facts then known on a rational basis.

Fresnel’s theory of double refraction was not dynamical;
he arrived at it in the first place by purely geometrical reason-

ing, based on Huyghens’ construction, and only attempted at _

* Camb. Phil. Trans. viii. (1845).

Theoretical Optics since 1840. 539

a later date to give ita mechanical basis. In this attempt he
failed. “If we reflect,” says Stokes, “‘on the state of the
subject as Fresnel found it and as he left it, the wonder is
not that he failed to give a rigorous dynamical theory, but
that a single mind was : capable of effecting so much.”

Between the days of Fresnel and Stokes great men had
worked at the subject. Navier, Poisson, and Cauchy in
France ; Neumann in Germany ; MacCullagh in Dublin ;
and George Green in Cambridge, had all contributed their
share, andl the results were somewhat confusing.

MacCullagh and Neumann, treating the ether as an elastic
solid, had obtained on certain hypotheses Fresnel’s laws for
reflexion and refraction, and his theory of double refraction.
Green, using a somewhat different method, had shown,
apparently, that the tangent law was only an approximation
to the truth, while the wave-surface could only be deduced
from the true equations of an zeolotropic elastic solid by some
forced and improbable relations between the constants.

According to all the theories, two waves in general can
traverse an elastic medium, the one travelling with velocity
V A/p, the other with velocity “B/p where A and B are
two constants. Of these the first consists of longitudinal, the
second of transverse vibrations ; and since there is no evidence
of the former wave in optics, the constant A must either
vanish or be infinite.

Neumann’s theory assumed A to vanish ; Green had shown
that for an elastic solid with free boundaries the condition of
stability demanded that A—4/3 B should be positive, and
hence he assumed A to be infinite. On this view of the ether
he was clearly right. Such was the position of the problem in
1859, the year in which the papers of Green, MacCullagh,
and Cauchy were published. Stokes’ earliest paper on the
subject, written when he was 26 years old, deals with the
properties which we must assign to the ether if we are to
explain the facts observed. To propagate transverse waves
it must behave to light motions as an elastic solid ; the con-
stancy of the length of the year, and other astronomical
results, show that it opposes no sensible resistance to the
motion of the earth and the planets, for such motions it has
the properties of a perfect fluid.

He distinguishes—the fact is well-known now, but it was a
great step then—between the two kinds of elasticity, rigidity
and resistance to compression. Bis a measure of the rigidity,
A—4B/3 of the resistance to compression. For a fluid,
then, which is practically incompressible, the ratio of A to B
may be very great, as Green requires it, while in Stokes’

540 Dr. R. T. Glazebrook :

view it is still possible that for the tiny motions involved in
the propagation of light the fluid may have rigidity.

However, be this satisfactory or not, and the difficulty is one
which occurs in every elastic-solid theory of Optics, the result
remains that an elastic-solid -theory is not consistent with
the facts. The phenomena of reflexion and refraction at the
bounding surface of two media may be due either to a change
in density or to a change in rigidity.

Green’s theory of refraction assumes the change to be one
of density, the rigidity of the eether in all isotropic media is
the same; his theory of double refraction assumes this to
arise from a variation of the rigidity in different directions
within a crystal.

These dithculties are clearly exposed in Stokes’ Report to
the British Association in 1862, in which he also shows that
MacCullagh and Neumann’s theory is impossible so long as
the potential energy of the ether when transmitting light is
assumed te be that of a strained elastic solid. If we suppose
the ether to differ from an ordinary elastic solid but to
possess what has been called rotational elasticity, in conse-
quence of which it opposes forces tending to cause molecular
twist to an extent proportional to the twist, then MacCullagh’s
form of the potential energy is obtained and his conclusions
bold. From this point of view the matter has been developed
of late years by Larmor.

The Report of 1862 deals with another matter, specially
interesting to myself, because in later years Stokes encouraged
me to pursue it.

Up to that date the experiments to verify Huyghens’
construction for a uniaxial crystal had been of the roughest
character. Stokes devised a method of testing the construc-
tion to a very high degree of accuracy and carried it into
effect for Iceland spar. The results are very briefly referred
to; they were published later, but hardly in greater detail,
at Lord Kelvin’s urgent request, in the Proceedings of the
Royal Society.

The outcome was that while for a uniaxial crystal at least
Huyghens’ construction was undoubtedly true, no theoretical
basis could be given for it.

It was left to Maxwell to carry the question a stage
further. He showed that the laws which regulate the propa-
gation of electric force in a crystal are identical with those
of light, while experiment proved that the velocity of light is
the same as that of an electric disturbance, and hence we
have the electromagnetic theory of light.

It should be noted, however, that this theory, as Maxwell

Theoretical Optics since 1840. 541

left it, is not mechanical. Hlectric displacement and mag-
netic force are vector quantities which accompany each other
ina changing electric field. They satisfy certain equations ;
and it follows from these, and the result is verified by experi-
ment, that they are propagated according to the same laws as
light. It is reasonable to suppose that the periodic dis-
turbance which constitutes light is very intimately connected
with one or other of these ; the supposition that it is identical
with Maxwell’s electric displacement leads to consequences
consistent with fact, and, indeed, in the able hands of those
who have developed the theory has been the fruitful means
of correlating many varied phenomena ; but it does not tell us
what electric displacement is, or how it is related to the
movements of the ether; neither does it enlighten us as to
the structure and mechanical properties of the ether, beyond
the simple fact that in the eether transverse waves only are
propagated, no forces can be called into play which tend to
set up a pressural wave. Maxwell himself attempted to
formulate a mechanical model of the sether, and to some
extent succeeded. Lord Kelvin, so fertile in his thoughts,
has made various suggestions, we will return to one later. To-
day the electron theory of electricity, thanks mainly to the
brilliant work of Stokes’ Cambridge colleague, J.J. Thomson,
holds the field ; but the relation of the electron to the ether
and the mechanism by which electrons produce ether waves
have yet to be discovered.

Larmor’s suggestion that the flow of ether constitutes mag-
netic force, while a twist in an ether endowed with rotational
elasticity produces electric displacement, forms perhaps the
most consistent picture of the process which we possess.

Lord Kelvin, indeed, in 1888 suggested a structure for
the eether which allows of a homogeneous mechanical account
of optical phenomena being given.

On this view the resistance to compression of the eether is
negative, if free it would collapse, but the necessary stability
is given by the supposition that it is fixed at the boundaries;
it-is a structure like a collection of soap-films stretched across
a wire framework ; if the connexion be broken the whole
collapses, so long as it remains the system can propagate
transverse waves. With such an ether there is no difficulty
in giving a consistent account of Optics, but it is difficult to
imagine that the ether has such properties. I believe, how-
ever, that Lord Kelvin now thinks that a slight modification
of his original hypothesis will lead to the same result so far
as optics are concerned, but will enable him to get over the
difficulty of postulating fixed boundaries.

Phil. Mag. 8. 6. Vol. 5. No. 29. May 1903. 20

542 Theoretical Optics since 1840,

On such an hypothesis the molecular velocity of the
ether might measure magnetic force, while electric dis-
placement would then be proportional to the curl of the
twist, or we might adopt the analogy suggested by
Heaviside (‘ Electrician,’ Jan. 23, 1891), and developed, as
I have said, by Larmor, according to which the kinetic
energy measures the magnetic force and the twist the electric
displacement.

The electromagnetic theory, though it does not rest on a
mechanical basis, has linked together optical and other phe-
nomena in a striking fashion. The advance from the days of
Green has been a great one.

And leaving now the general theory, the development of
its details has not been less striking. On all sides there
has been advance, and along most of the lines of advance
Stokes was a pioneer.

Newton’s difficulty in accepting the undulatory theory was
really solved when Young enunciated the principle of inter-
ference, but it needed Fresnel’s experiments to convince men
of its truth. It was clear, of course, that the effect at any
point due to a wave of light could be calculated by finding
the effect due to each element of the wave and summing
these; but Stokes, in his papers on diffraction (1851), was the
first to establish a correct expression for the effect produced at
a distant point by an element of the wave and to show how
these effects were to be summed.

The germ of all that has been discovered by means of
spectrum analysis is contained in his explanation of Kirchhoff’s
original experiment, often quoted by Lord Kelvin, and from
his paper on ‘‘ Fluorescence” have sprung the modern theories
of dispersion, including anomalous dispersion. On this point
the note he has added to this paper in the third volume of his
Collected Works has a special interest. Although he did not
fathom the connexion between eether and matter, and, on the
whole, the criticisms passed by later writers on his theory of
aberration are to be accepted as justified, his papers must be
studied by any one who is anxious to penetrate the mystery,
and did much to put the facts in a clear light.

My survey is, I realize, entirely inadequate ; itis but a frac-
tion even of the corner of the field I set out to examine that |
have covered, but [must stop. Ihave said enough, I hope, to
show that progress has been continuous and marked, and
in no small degree that progress has been due to the work
of Sir George Stokes.

I had intended to bring before you some more practical
questions connected with the work of my own Laboratory.

On the Numerics of the Elements. 543

These must await a more fitting opportunity ; meanwhile let
me conclude as I began, by thanking you very heartily for
placing me in this position, and assuring you of my desire to
forward your best interests.

LVII. On the Numerics of the Hlements.—Part III.
By Eymunn J. Mitts, D.Sc., FR.S*

T has been shown in previous parts + that the numerics of
the elements are of the form

n x
where p represents the number of the periodic group, n+1
the number of periods in the system, and w the integral
ordinal within a given group. So far as is known, all the
numerics of the existing elementary bodies, excepting that of
hydrogen, are included in the above equation when n=15 ;
and the range in value is from y=0 to y= 240.

It has been objected { to this method of representation that
it includes an infinite number of elements within the range
indicated. Ample precedent, however, for this is found in
the phenomena of Cumulative Resolution$. In the de-
nitration of bismuthic nitrate by water, for instance, there
are three distinct continuous stages :—

J, n Bi, O, 0 3N, O;— (n are 1)N, Ons Bip, O3n » Nante Onon+5; |

and at infinity Bil) Os oN Ona
LT: nr Big Os ° 2N, O; Tie (n = 1)N; 0;= Bion Osn ° Non +2 OF:
and at infinity Bi, O; . Nz Os.
PEL. n Bi, O, ° N, O;— (n— 1) N, C— Bion Osn é Nz (OF
and at infinity Bi, O3.

In the first stage ratios are known for n="1 and 1; in the
second, for n=2 ; in the third, for n=§, §, 4 1, anda.

Another objection has been raised to the method that it is
too easily applicable to any numeric. This objection, however,
is not so much a criticism of the mathematical method, as a
censure on the weakness of experimental processes. These,
in the most favourable cases, cannot be depended upon more
nearly than ‘02; and the mathematical method can only
follow them. So far, increasing experimental accuracy has
been attended by a closer coincidence with the theory. The

* Communicated by the Author.

+ Phil. Mag. 1884, vol. xviii. p. 895; 1886, vol. xxi. p. 151.

{ Ibid. 1902, vol. iv. p. 108. § Ibid, 1877, vol. iii. p. 492.
2-0°2

544 Dr. BE. J. Mills on the

severest comparison is where the values of # are low: here,
if the theory had been inaccurate, gross discrepancies must
have been immediately indicated *.

As has been stated in Part II., the form of the periodic
function here adopted is based primarily on a law of cooling,
followed by polymerization and reversal.

Periodicity itself would appear to necessitate an impulsive
origin for the elementary bodies. Liveing, many years ago,
attributed this property to chemical change in general.

The object of the present communication is to include the
results of the discoveries and discussions of the last sixteen
years. :

Group I.
y= 15—15('9375)*.

ae Yy. y cale.
Elie 501 Gin oe een a°94 4°14
irs terrae eel) AeQul C13
De ere ay, Melee 9°09 8°92
Borate ee ee 10°94 10°87
Ce am Ai S Rect eee 79) EO 12°01
ING Nae ee, 14:00 14°00

Group IT.

y= 30—15 (-9375)*.

a: Y. y cale.
Os ree gett [standard] = 15:94
Eg ey ak ek oe 18°98 19°14
Nevie tie sacar 116 19°86 19°82
Nao ihe ies ae 23°00 23°09
Me J eR 5 24-28 24°30
AL ieee) 27°01 27°01
SD. oe 28°20 28°10

Group III.

y=45 —15(°9375)*.

oP Yy. y cale.
PPI GMOY CR 30°96 30°94.
STU Meo an TAZ 31°98 31°82
CTSA GE MCLG 39°37 35°45
Ky) Saar HCY Led 39°02 38°92
A UE Ge SRE BELG 39°76 39°66
Carin. Pare stitute 39°90 39°99
SiG fey Mar shed 43°98 44-00

* Copper, for example, occurs in Group V. It must obviously be
entered under +=8, 4, or 5; 2. e. have the numeric 62°64, 63-41, or 64:14.
The experimental number having been now practically settled at 63-36,
there can be no doubt that «=4 is the only correct selection,

——
i

Group IV.
y =60—15(-9375)-.
Be y.
3 A799
3) 51°26
10 52°01
17 D4°97
20 D581
36 58°55
42 58°83
Group V.
y=T5—15(° ee
wv.
4 336
6 6 O1
17 69°90
26 72°20
63 74°73
Group VI.
= rar -15(° es
" 73° 96
6 CSPOT
y 81°46
18 85°25
27 87°37
36 88°59
Group VII.
y= a 15(° ce e
‘i 90° 76
6 93°68
7 95°53
22 101°34
27 102°32

Numerics of the Elements.

Group VIII.

y=120—15( uhh r,

105° 1)
107°68
L165
113°40
LEG?

118°55
EIQ‘SS

y eale,

79°14
79°82
81°61
89°31
87°37
88°93

y cale.
90°94
93°41
95°45
101°37
102°37

y cale.
105°94
107°64
biG
113°52
11701
118°53
119°d54

546

Group LX.
y=135—15¢ he
ths
i) 126° 56
10 127°28
A ulalt Pay
a's 132°58
Group X.
y= 150—15(-9375)*.
oe y.
2 136°76
4. 138°40
5 139°17
6 139°95
4 143°05
qa 149-89
Group XI.
= See ee ;
8 156° 17
Pe kelity 159°40 ?

Dr. E. J. Mills on the

Group XII.

y=180— ICSD

‘1 1663 ”

qi 170°34
il 172°48
Group XIII.

y=195—15(-9875)*

3 182: 40

4 183°61
17 190-06
28 192°65
42 194°06

Group XIV.

y=210— eg

196: 45

199°28

203°40
206°17
207°52

y cale.
126°61
127°14
127°62
132°54

y cale.
136°82
138°41
139°14

_189°32

143°09
149°89

y cale.

156:05
159°66

y cale.
165°94
170°45
172°62

y cale.
182°64
183-41
136999
192°54
194-00

y cale.
196°72
199-14
203°52
206°37
207°54

Numerics of the Elements. 5AT

Group XV.
y= 225 —15(-9375)*.

De y. y cale.
Ve hy eae aoe 225 +1 ?
Group XVI.
y= 240 —15(°9375)*.
ie y- y cale.
LCi tienen Sel ) 231°61 231°66

a re ee 28 237°64 237°d4

The Specific Values of some Numerics.

Many of the former values remain practically unchanged.
Most of the original memoirs had been consulted, and the
necessary calculations made, before the appearance (1903) of
the “‘ International Atomic Weights ’’—the values in which
are in several cases nearer than my own to my theoretical
figures. Clarke’s (1897 and 1902) well-known memoirs *
have proved of great service.

Hydrogen and Oxygen.—By a repetition of old methods,
several investigators have found that O=15°88 if H=1.
Keiser (1889), however, was the first to utilize hydro-
palladium as a source of pure hydrogen, and ina series of
very accordant experiments found O=15:95; a result not
hitherto explained away. Later on (1898), using hydrogen
from the same source, in a simpler apparatus, he obtained the
number 15°88.

Attention may be directed to some cross ratios to be found
in Clarke’s (1897) Memoir, but so far not utilized in this
connexion :—

pylos:
Peel. 0; 196713. 100 er One
= Sana yet po ON —— el fs
He Au 3Ag01 J AP Sle Sole) ee
pyold :
O . Co _ 21:367 — 58-630, O _ 15:90
Craen6ss 1 he a Oo
pp. 305, 310:
OF Gis 20230, 58456. gO 159d
i PEL oS Caan Sati 2 MRE

* Smithsonian Miscellaneous Collections, and Am. Chem. Journ, 1902.
+ Stas.

548 Dr. E. J. Mills on the
Ppsaol, 2 : |
Oy, Zn —_ 19°683) Soa 079 O'S Wa

Jn. 80312 oe”
p. 290 :
Fes yO; _ 55°008 , 29992, gy .59 0 _ 15:88
BG. ie: 1 70008
pp: L790
Al; , 3H,0__ 53°780 | 99818, 4, O 188
ia Ale D 10 “ Eo

I regard these ratios as very important, because they are
now for the first time disclosed. and could not have been
obtained intentionally. There is thus a residual uncertainty
about O: H.

As regards the methods employed, it is open to question
whether a current of gas can be dried ; at any rate, I have
not succeeded in drying a current of air. Glass globes, and
other glass apparatus, must resemble thermometer-bulbs in
undergoing progressive contraction. Hydrogen (according
to Dittmar and Henderson) decomposes sulphuric acid at the
ordinary temperature—presumably in presence of light.
Phosphoric anhydride (according to Crookes) is apt, unless
previously heated, to give up matter to hydrogen, and, one
would suppose, to other gases. Hydrogen made from metals
is likely to contain carbonic impurity (Morley). Mercury
is a nearly certain impurity in most gases; its presence
reduces the relative gravity of oxygen by about -02.
Béttger’s important observation (Chem. Centr. 1878, p. 574)
that the mixture H,: O, when expioded, always produces
some peroxide, seems to have been almost entirely over-
looked : and the same remark applies to Richardson’s dis-
covery (Proc. Chem. Soc. 1889, p. 134) that water forms
peroxide on exposure to light. A quantity of peroxide
amounting to ‘05 p.c. of the water would reduce the value

O
a by about *06.

The preparation of hydrogen by electrolysis of baryta-
water, and its subsequent occlusion by palladium, is a great
step in advance, as enabling hydrogen to be weighed instead
of measured. Scott’s use of argentic oxide, also, has pro-
bably resulted in the production of oxygen of improved

Numertes of the Elements. 549

quality. Buta new source of oxygen, in a substance capable
of progressive decomposition, is still to be desired.

It would appear to be in all cases essential to determine
the effect of light.

The numeric of oxygen has been at various times taken as
100, 1, 15°96, 15°88, and 16. At present there are two
Seales im use, viz, O—16, H=1:008; and O=15788, H=1.
When the composition of water is ultimately decided, these
ratios may undergo some change. But none of the values
proposed has any special physical meaning as a ground for
preference in practical use.

The value O=15:94, adopted in this memoir, has the
advantage of lying exactly midway between—and so, perhaps,
conciliating—the modern hydrogen and oxygen scales. It
is calculated from rigorous mathematical conditions, and
includes all known elements, excepting hydrogen ; it is, con-
sequently, interdependently related to all the elements.
There is a reason, therefore, for preferring this value ; or,
at any rate, some value similarly calculated. It may, indeed,
be said that, within the limits of experimental error, the
practical value is in fact O=15°94.

Linear periodicity is no longer admissible.

Clarke comments on his own table of numerics (1897) in
these terms :-—“In most cases even the first decimal is
uncertain ; and in some instances whole units may be in
doubt.” The determinations are, in fact, so much affected
by constant error, that their probable error is seldom worth
ealeulating. Of all constant errors, the most important
would seem due to the fact, now in course of general accept-
ance, that pure chemical substances do not interact with
each other *.

* Amongst common metals, the nnmeric of zzvc is still much too un-
certain. For samarium I have taken Bettendorff’s value ; for z2rconzum,
Bailey’s. The mean of Hardin’s, Keiser’s, and Joly & Leidié’s not too
concordant results has been accepted for palludium. Other authorities
are Meyer and Lenker, seleniwm (mean); Seubert & Kobbe, rhodium ;
Morse & Jones, cadmium; Kothner and Pellini, ted/wrwm (mean); Jones
& Brauner and Pavliéek, lanthanum (mean); Jones and Van Schele,
praseodidynmuum (mean) ; Jones, neodidymiwm ; Cleve, yiterdium ; Seubert,
osmium and rhodium ; Classen, bismuth; Mallet, gold. Erbia and terbia
remain in considerable doubt. In some cases of modern recalculation
confusion has arisen from taking former numbers—at one time announced
as “‘on the hydrogen scale (1:00),”—as being on the present hydrogen
scale (1:008).

F 550°]

LVI. On the Specific Ionization produced by the Corpuscles
given out by Radium. By J.J. HE. Duracn, 1851 Lahibi-
tion Scholar, Trinity College, Cambridge*.

a former paper} I have shown that the corpuscles in the

Lenard-ray stream make on the average 0°4{ positive
and negative ions in travelling through one cm. of air at a
pressure of one mm. of Hg, or, if we suppose that a corpuscle
creates a pair of ions at each collision with the molecules, these
corpuscles make 0:4 collision under the conditions of distance
and pressure specified above ; this number measures what we
may call the specific ionization produced by the corpuscles
and will be denoted in what follows by the symbol @ ; it must
be noted that we are dealing only with the ionization produced
in alr, 2 of course depends on the gas ionized.

Prof. Townsend § has shown that for the corpuscles || pro-
duced in air by Rontgen rays the number of ionizing
collisions reaches a constant maximum value (equal to 204)
when the velocity-of the corpuscle exceeds a certain amount
(about 10° cms. per sec.).

I have tried to show ** that the very large difference in
the values of a obtained by Townsend and myself can be
accounted for by the difference in the velocities of the cor-
puscles in the two cases, the velocity of the Lenard rays in my
experiments being about 4 10° cms. per sec.

If the difference be due to the difference in velocity, then,
according to the theory indicated, 2 must decrease as the
speed of the corpuscle increases, provided the corpuscle has
sufficient energy to produce ions at all the velocities considered.

Now the velocity of the corpuscles given out by by radium
(usually called the deflectable Becquerel rays) has been

* Communicated by Prof. J. J. Thomson, F.R.S.
~-+ Phil. Mag. ser. 6, vol. iv.

{ Starke & Austin (Drude’s Annalen, Band ix.) have recently shown
that 25 per cent. of the corpuscles in the cathode-rays are reflected on
striking the surface of an aluminium plate at perpendicular incidence,
this, introduces an uncertainty in the value 0:4 given above, as it is not
certain what becomes of the corpuscles after redexion, they being under
the influence of an electric field. If, in my former experiments, they
return to the plate kept at constant potential without producing further
ionization the number 0:4 will have to be reduced in the ratio of 4 to 3,
2. e. to 03; at present 0-4 must be regarded as the probable upper limit
of the quantity denoted by a.

- § Phil. Mag. ser. 6, vol. i.

| See a paper by the same author in ‘ Nature,’ vol. lxv. p. 415.

q Further experiments have shown this number to be from 10 to 20
per cent. too large. Townsend, Phil. Mag. ser. 6, vol. iii.

** Phil. Mag. loc. cit.

Specific Lonization produced by Corpuscles of Radium. 551

measured by Kaufmann with great accuracy * and found to
have all values between 2°36 10° and 2°83 107°, so that we
should expect « for the deflectable Becquerel rays to be less
than that for Lenard rays if the explanation offered be correct.

Townsend states in the paper first mentioned that an esti-
mate of « for radium corpuscles was made by him and found
tu be at least 13 T, a number considerably greater than 0°4.

In the experiments I am about to describe it will be shown
that the number 13 obtained by Townsend is about 76 times
too large.

The radioactive substance used In my experiments was
radium chloride obtained from the Société Centrale de pro-
duits chimiques and labelled initial activity 1000.

The radium{ was in the first experiments placed inside a
closed vessel and covered with an aluminium plate, the leak
being measured between this plate and another above it ;
the space surrounding the radium was in connexion with the
space between the plates through a small hole in order to
equalize the air-pressure in the two spaces.

With this apparatus the results of the experiments were
difficult to interpret owing to apparatus inside becoming
radioactive under the action of the ‘‘emanation” from the
radium.

The radium was then taken outside and placed about 20 cms.
away from the leaking system, so that the emanation could
not penetrate to the leaking plates, and also it was certain
that a magnetic field in the region in which the radium was
placed would not appreciably affect the current between the
plates directly.

It was found that in this position practically all the leak
was due to deflectable Becquerel rays or the corpuscles from
radium ; the leak due to the corpuscles alone was, however,
too small to be measured accurately, and the radium had to be
moved closer to the leaking system.

The final arrangement is shown in fig. 1. One gram of
radium was strewn uniformly over the bottom of a lead box
B, the top of the box was covered with a thin aluminium leaf
/ 0:0043 mm. thick in two sets of observations, and with an
aluminium plate 0:083 mm. thick in a third.

Above the radium a thick lead plate PP had a hole 2°5 ems.
in diameter drilled in the centre, this was covered on top

* Nachrichten d. K. Gesell. d. Wissen. Gottingen, 1901.

+ In these experiments his electrometer was not sufficiently sensitive
to measure the leak due to the corpuscles themselves, so that a lower
limit only could be found.

{ This substance is generally spoken of as radium, though it is really
mostly radium chloride: : 3 ;

552° Mr. J. J. E. Durack on the Specific Ionization

with a plate of aluminium L 0:083 mm. thick, and made air-
tight by screwing down a thicker plate of aluminium over it

Fig. 1.

70 ELECTROMETER

70 PUMP & MCLEOD GAUGE

70 EARTH

70 CELLS

B = Jo EARTH

and melting an elastic glue into the crevices. A ring of ebonite
RR separated the brass box CC from the lead plate. Above
the plate L and 13°5 mm. from it was placed another plate
pp; the back of this plate was of lead, which was turned so
as to form a thin rim of lead on the side nearer L; an alu-
minium plate similar to L was then placed over the rim and
fastened to it so that there was an air-space between the
aluminium and the lead ; pp was connected to a quadrant
electrometer with a rod passing through the ebonite plug H
and shielded from electrostatic effects.

The space inside CC was in communication with a pump
and McLeod gauge.

All joints between metal and ebonite and between metal
and glass were made air-tight with sealing-wax.

The plate PP was 8 cms. diameter, and the apparatus is
drawn to scale in fig. 1.

During the time the observations were being made CC and B
were kept connected to earth, and PP to one pole of a battery
of storage-cells, the other pole being to earth. By keeping
B connected to earth while P is charged to a high potential
the ions formed in the air between B and P are destroyed,
and consequently prevented from diffusing out and, may be,
finding their way to the electrometer.

It is known from the experiments of Rutherford* that an
aluminium plate 0°08 mm. thick is sufficient to absorb all the

* See Rutherford and Miss Brooks, Phil. Mag. ser, 6, vol, iv, p. 5.

produced by the Corpuseles given out by Radium, 558

so-called “a” or non-deflectable rays, and hence the con-
ductivity produced in the gas between PP and pp was due
to the deflectable rays; this was verified by preliminary
experiments on the action of a magnetic field on the rate of
leak.

It has been shown by many experimenters that a metal
plate struck by Rontgen or cathode-rays gives out negatively
charged ions ; moreover, that the rate at which these ions
are given out is greater for the heavy metals than for the
light ones, this effect is very small when Rontgen rays fall on
an aluminium plate.

For this reason the plate yp has been made as described
above ; there will be very little absorption of the Becquerel
rays by the aluminium plate on the face of pp, and conse-
quently very little tendency to give out negative ions,
practically all the absorption takes place in the lead, but this
will not cause any error in the measured leak due to the cor-
puscles themselves unless these ions are given out with
sufficient velocity to carry them back through the aluminium
plate; from the experiments of Sagnac on the secondary
ionization produced at the surface of a metal by Réntgen
rays it is probable that they would not have sufficient velocity
to do this.

The opposite surfaces of PP and pp being both of the
same metal, there should be no error due to a contact P.D.
effect.

The electrometer used in these experiments was of the
Dolezalek type, the insulation of the quadrants being greatly
improved and a gilt mica needle used instead of the paper
needle of Dolezalek. The needle was kept charged to a con-
stant potential by dipping the suspending quartz fibre into a
solution of CaCl, and connecting the needle through the fibre
to a battery *.

The ordinary formula for the sensibility of a quadrant
electrometer, the needle being kept at constant potential V3, is

ld acy er
0= ag == (Vi—V.)(V;—43V,+ V2)

where @ is the deflexion produced by a P.D. (V,—V.,) be-
tween the two pairs of quadrants, t is the torsion of the
suspending fibre per unit angular displacement, and 9; is the
coefficient of capacity of a pair of quadrants, all other con-
ductors in the neighbourhood being kept at zero potential.

* Doiezalek, Zeits. fiir Instrument. Dec. 1901,

554 Mr. J.J. E. Durack on the Specijic Ionization

If V, be kept constantly =0, and V, be small in comparison
with V3, this formula takes the usual form
we iL dq T
Now it has been shown by Hopkinson* that the apparent
capacity of a pair of quadrants (say the pair 1) when the
needle is charged to a potential V3; is equal to

dgy\" 1
q+ We cVe. « 4) lee

Suppose a quantity of electricity Q, given to the pair of
quadrants 1, the potential V, will be |

d
Vi =Q)/9u alae a V3",
and for the formula A we may write

1d ote se
0/Qi= = Vala ar (a) es V3".
Hence 6/Q, (which is the sensibility for current) has a maxi-
mum value for a certain value of V3, viz. :—
BEY AG
V3= Vout (Ht).

When high sensibility for leaks is an important factor the
needle should be charged to this potential, and even when
high sensibility is not required it is advisable to work with
the electrometer at its maximum sensibility, for then small
changes in V; make no change in 0/Q).

The value of V3; for which 6/Q, is a maximum is easily
found by measuring the capacity of a pair of quadrants and
finding for what value of V3 this capacity is equal to 29),
i. e., twice the capacity when V;=0. With my electrometer
this was the case when V3; was equal to 60 volts. The
observations from which a was to be deduced were made as
follows :—The plate PP was connected to one pole of a battery
of cells (say the positive pole), the other pole being to earth,
a small P.D. was set up initially between the two pairs of
quadrants, the insulated pair being initially negative with
respect to the earthed pair if the leak to be measured was
positive, and positive if the leak was negative; thus the needle
travelled through its zero position in taking a reading, which
was done by finding the time required for the light-spot to
pass over a certain number of divisions on the scale, these
divisions being half on one side and half on the other side of
the zero.

By reading in this way the effect of changes in capacity

* Phil. Mag. ser. 5, vol, xix.

produced by the Corpuscles given out by Radium. 555

for different deflexions (which are, however, usually very
small) is eliminated, and leaks due to faulty insulation are
minimized, these leaks helping the leak to be measured for
half the time and opposing it for the other half.

It is of great importance that the P.D. between PP and
pp should be sufficient to saturate the gas, 2. ¢., to remove the
ions as fast as they are formed.

In the first two series of observations the current was
measured for several different P.D.’s, and in the third a P.D.
was always applied which was known from the previous
observations to be sufficient to produce saturation. The
nature of the current-E.M.F. curves may be seen from the
results given in Table I. and plotted in fig. 2.

Fig. 2.

Current. |
Pressure. ED: eee ae)
Lower Plate +. | Lower Plate—. |
Ua Sl a +124 23-8
20 +15:0 —25°5
40 +158 — 25:0
60 +161 — 25:2
80 +164 — 25:0 |
100 +163 —25°1

556 Mr. J.J. E. Durack on the Specijic Ionization

The first column gives the pressure in mm., the second column
the average P.D. during the leak between PP and pp in volts,
the third column the current when PP was connected to the
positive pole of the battery, and the fourth the current when
the field was reversed.

The positive current is taken in the direction PP to pp, so
that pp receives a positive charge, the unit of current here,
as in all the tables and curves, is 10-14 amp.

It will be seen from fig. 2 that ata pressure of 19 mm. the
gas is practically saturated with a P.D. of 40 volts.

Care must be taken, not only that the E.M.F. is sufficient
to saturate the gas, but also that it is not too great, otherwise
the negative ions generated by the Becquerel rays may, as has
been shown by Townsend (loc. ct. Phil. Mag. vol. i.), themselves
generate other ions; calculation from Townsend’s numbers
shows that the effect would begin to be evident in my experi-
ments when V=45 p, where V is the P.D. in volts and p is
the pressure in mm. In all the tables V is less than 45 p.

As all the observations could not be carried out in a single
day, and the radium had to be kept dry to prevent it from
deteriorating in strength, the box B was removed at the end
of each day and kept in a drying-apparatus, stops were made
for B to fit into so that it could be replaced in the same
position on the following day, to make sure that this was so
the last readings of the previous day were repeated each
morning.

TABLE IT,
| :

| Current.

Pressure. iPs1;

Lower Plate +. | Lower Plate—.

| |
|

20°5 60 to 100 +184 | =288
157 100 +129 —23-0
12:0 + 86 —183
93 60 to 100 + 60 14-7
73 20 to 100 + 35 —12°7

The first series of observations for the determination of a
is given in Table II. and plotted in fig. 3; when these five
points were determined the box B was accidentally knocked,
and the exposed surface of the radium thereby considerably
altered, as was seen afterwards on removing the thin aluminium
leaf which covered B when the observations given in Tables II.
and III. were taken.

produced by the Corpuseles given out by Radium, 907
Fig. 3.

PRESSURE

TaBLeE III.

| Current.
Pressure. / 1250 de: 2s

Lower Plate+. | Lower Plate —.

|
| —_————— ——— — -_————

| 0-68 2 to 20 — 2°82 — 490
ahaa: | 20 to 40 = 1-34 — 5:90
| 5:26 | +1:20 — 8:34
79 | if 3°36 —10°8
10:7 / 20 to 100 +5°60 —13°5

The aealnews given in Table IV. and plotted in fig. 9,
were found with an aluminium plate 0°083 mm. thick on the

top of B. |

The lines in figs. oy 4, and 5 have all been drawn through
the centroid of the points * w hich is marked with a eross, ine

* ake Pearson ce On the Lines and Planes of Closest Fit,’ Phil. Mag.
ser. 6, vol, 11.

Phil. Mag. 8. 6. Vol. 5. No. 29. May 1903. re

D958 Mr. J. J. E. Durack on the Specific Lonization

centroid of n points, whose coordinates are 21, 22, Kc. “> Yay Yr
&c., being defined by the coordinates

Rg es
a

nM
pines aga
t Parmer

TasBLE IV.

0:50 —3°56 — 4:26

2 |
0-015 O =o OU = asl |

produced by the Corpuseles given out by Radium. 599

Figs. 3, 4, and 5 show that the relation between current
and pressure is of the form

Y= —e+mMp
when the lower plate is charged positively, and
Y= —¢—mp

when charged negatively, y, and 72 denoting the currents, p
the pressure, and m and ¢ positive constants.

slo)

PRESSURE

The interpretation of this result is very simple : we have
negatively charged corpuscles constituting the deflectable
Becquerel rays travelling from PP to pp at a rate independent
of the pressure, on their way they produce equal numbers
of positive and negative ions in the gas, the rate of production
being proportional to the pressure.

Let N, be the number of corpuscles passing per second
through L and e the charge carried by a single corpuscle,
then the current due to the corpuscles alone is —Noe.

Suppose that each corpuscle makes @ collisions in traversing
one cm. of the gas at a pressure of one mm., let p be the
pressure, @ the average distance travelled by the corpuscles in
going from PP to pp, and e the charge carried by the ions
generated in the gas.

2P2

960 Specific Ionization produced by Corpuscles of Radium.

When the lower plate is charged positively pp will collect
positive ions from the gas, and the total current will be

y= —Noe + Noe’apd.

When the field is reversed pp will collect negative ions from

the gas, and the current will be
Yo= —N ye — Noe’apd.

It has been shown by many experimenters that e/m, the
ratio of the charge to the mass, is approximately the same for
cathode-rays, Becquerel rays, the ions producing the Zeeman
effect, and the ions given off by Zn under the action of ultra-
violet light, and 1000 times greater than that for the H ion
in electrolysis. It has also been shown by J. J. Thomson *
(by direct measurement of both) that the charge carried by
the ions given out by Zn is the same as the charge on the
ions produced in air by Rontgen rays. Townsend + has
proved, by direct comparison, that the charges on the ions
produced in air by Rontgen rays, Becquerel rays, and point
discharges, and on the ions given off by Zn are all equal to
the charge carried by the H ion in electrolysis.

The same experimenter has shown (‘ Nature,’ loc. cit.) that
the ions produced in air are identical as regards mass and
charge with the ions given off by Zn under the action of
ultra-violet light.

From these facts Prof. Thomson has concluded that in all
these cases the charges carried by the negative ions are all
equal, and the mass of the carrier about 1000 times smaller
than the H atom. Hence in the equations 1 and 2 we may
put e=e’ and we have

y= —Ne(l— apd)... 2)
Y= —Noel + apd) — ~~ Saeee (2)
From which we obtain
: —Noe=3 (11 +72)
and it =)
| i .
pa\y + v2

To find the average distance travelled by the corpuscles be-
tween PP and pp we know from Becquerel’s experiments on
the velocity of the deflectable Becquerel rays, that the cor-
puscles are projected in all directions from the surface of the
radium, hence in these experiments d will lie between 13°5 mm.

(the perpendicular distance between the plates) and 14°3 mm.
and cannot be far from 14 mm.

* Phil. Mag. Dec. 1899.
+ Phil. Trans. 1899, 1900.

Condensation of the Radioactive Emanations. d61

The average values of Ne and of @ for all the observa-
tions in any series of experiments are found directly from
figs. 3, 4, and 5, being the values deduced from the position
of the centroid in the three cases.

The centroids are given by

wg 10 she EVE bupitee
= + 9:88 y= =e? y= —(0°54
yo= —19°5 Yo= — 8°55 Y= —6°8

Hence we find
Ne =4'8 III. and ep ioxo JU.
=n: = hone
=3:7 V. SSG Wel

The values of Noe obtained show that the effect of putting
an aluminium plate over B (and practically doubling the
distance travelled by the corpuscles before they reach the
place where the ionization was measured) was to reduce
the Becquerel ray current in the ratio of 4°8 to 3°7.

The tilting of the radium also reduced this current as we
should expect, for the surface exposed was thereby decreased.
This accounts for N,e being less in fig. 4 than in fig. 3.

The effect on « is hardly appreciable, for the difference
only amounts to about 4 per cent. which is inside the limit
of possible error.

From the values of 2 given above it may been that the
mean free path of the Becquerel ray corpuscles in air at
1 mm. is about 6 cms. This very large value for the mean
free path accounts for the very small absorption of the de-
flectable Becquerel rays.

In conclusion, my thanks are due to Prof. J. J. Thomson
for many suggestions given during the progress of the work.

“avendish Laboratory, Cambridge.

LIX. Condensation of the Radioactive Emanations. By
KE. RurserrorD, I.A., D.Sc., Macdonald Professor of
Physics, McGill University, Montreal, and F. Soppy, J/.A.
(Oxzon.).

[Plate XIV.]
d ha a previous paper (Phil. Mag. 1902, iv. p. 581) we have
shown that the radioactive emanation from thorium passes
in unchanged amount through a white-hot platinum tube and
through a tube cooled to the temperature of solid carbon
* Communicated by the Authors.

562 Prof. Rutherford and Mr. Soddy on

dioxide. The acquisition of a liquid-air machine by the
laboratory has enabled us to investigate the effect of lower
temperature on the emanations from both thorium and
radium. The result has been to show that both emanations
condense at the temperature of liquid air, and possess sharply
defined points of volatilization and condensation.

If either emanation is conveyed by a slow stream of
hydrogen, oxygen, or air through a metal spiral immersed
in liquid air, no trace of emanation escapes in the issuing
gas. When the liquid air is removed and the spiral plunged
into cotton-wool, several minutes elapse before any deflexion
of the electrometer-needle 1s observed, and then the condensed
emanation volatilizes as a whole, and the movement of the
electrometer-needle is very sudden, especially in the case of
radium. With a fairly large amount of radium emanation
under the conditions mentioned, a very few seconds elapse
after the first sign of movement before the electrometer-
needle indicates a deflexion of several hundred divisions of
the scale per second. It is not necessary in either case that
the emanating compound itself should be retained in the gas-
stream. After the emanation is condensed in the spiral the
thorium or radium compound may be removed and the gas-
stream sent directly into the spiral. But in the case of
thorium under these conditions the effects observed are natu-
rally small, owing to the very rapid loss of activity of the
emanation with time, which experiment showed occurs at the
same rate at the temperature of liquid air as at ordinary
temperatures. As a matter of fact, in the case of radium the
salt itself was seldom used. it was convenient to obtain the
emanation from the solution and store it mixed with air in
small gas-holders, the loss of activity during the course of a
day’s experiments being only a small part of the whole.

If the radium emanation is condensed in a glass U-tube,
the progress of the condensation can be followed by the eye
by means of the fluorescence which the radiations excite in
the glass. With a sufficientiy slow gas-stream the fluores-
cence is confined to the limb where the gas enters. If the
ends of the tube are sealed and the temperature allowed to
rise, the glow diffuses throughout the tube, and can be again
concentrated at any point to some extent by application of a
pad of cotton-wool soaked in liquid air. The U-tube can be
made to impress its own image on a photographic plate
through aluminium-foil, and the impression is uniformly
dense throughout the length of thetube. It retains its lumi-
nosity to a feeble extent after several days.

The suddenness of the volatilization-point of the condensed

Condensation of the Radioactive Emanations. 563

emanation is very remarkable considering the minuteness of
the actual amount of matter that must be involved. Arrange-
ments were made to investigate the phenomena in an accurate
quantitative manner. The method adopted was to condense
the emanations in a spiral copper tube and to employ the
latter as its own thermometer. by determining its electrical
resistance. For this purpose a constant current was maintained
through the spiral, and the fall of potential between two fixed
points on the spiral was determined by means of a Weston milli-
voltmeter. This method proved very reliable and convenient.
A great number of preliminary experiments showed that to
obtain accurate results two requirements must be satisfied.
In the first place, since the temperature measured is the average
temperature of the whole spiral, the latter must be completely
immersed in a bath of liquid kept well stirred. In the second
place, in order to be sure that the spiral was not heated locally
by the entering gas-stream, it was necessary to subject the
latter to a preliminary cooling to the desired temperature.
This was accomplished by the apparatus represented in fig. 1
(Pl. XIV.). The spiral and connecting tubes were made out
of a continuous copper tube of length 310 cms., internal dia-
meter 2 mm., and thickness of wall °32 mm. This was first
wound into an inner spiral of 16 turns of mean diameter
1°80 cm., which was soldered together into a compact
cylinder. ‘This effected the preliminary cocling of the gas-
stream. The tube was then wound back over the inner
spiral into an outer spiral of 14 turns of mean diameter
2°90 ems. The turns of the outer spiral were separated from
each other and from the inner spiral by air-spaces. The
outer spiral constituted the thermometer, and the potential-
leads were soldered on to the top and bottom and inclosed in
glass tubes. The system was supported inside a glass cylinder
closed at the bottom, of height 41 cms. and diameter 3°5 cms.,
by means of an air-tight rubber cork fitting the open end,
through which the ends of the spiral and the leads passed. A
small stirrer at the bottom of the tube was driven by a centra!
rod passing through a suitable bearing supported by the inner
spiral, and through a glass tube in the centre of the cork.
This rod was operated by an electric motor supported above
the cork. The spiral was kept from actual contact with the
glass by a sheet of mica perforated into holes, and was given
sufficient rigidity by means of an ebonite ring fitting tightly
into the space between the upper part of the inside and
outside spiral. A current was sent (tig. 2, Pl. XLV.) through
the spiral by means of leads soldered above the cork from a
storage-battery, passing through a Weston ammeter and

564 Prof. Rutherford and Mr. Soddy on

sliding-resistance. By means of the latter the current was
kept always constant at 0°900 amp. The potential-leads
were connected with a Weston millivoltmeter which registered
at ordinary temperature a deflexion of about 6 millivolts, om
60 divisions on the scale, at the temperature of liquid air
rather less than 2 millivolts. This corresponds to a resistance
at ordinary temperature of about ‘01 ohm., and it can readily
be shown that the heating effect of the current in the spiral
is negligible. No substance seems to be known which is
liquid at the ordinary temperature and remains liquid at the
temperature of condensation of the radium emanation (about
—150°). Ethyl chloride most nearly fulfils this condition,
but solidifies in the neighbourhood of —140° C. A bath of
this substance, however, proved useful in one series of mea-
surements with. the thorium emanation. The rest of the
determinations were carried out ina bath of liquefied ethylene,
This boils at —103°°5 and freezes at —169°, and gave just
the range of temperature desired in these experiments. About
70 litres of the gas, purified by fractional distillation, was ordi-
narily used. This was sent into the apparatus by the tube Aj
Pl. XIV. fig. 1, escaping by the tube carrying the stirring-
rod. The liquefied ethylene always covered the top of the
spiral to the depth of several centimetres. The apparatus
was surrounded by a tall copper cylinder well covered with
lagging which contained the liquid air. Copper was prefer-
able to glass for the purpose, for it ensured in the actual deter-
minations a more uniform supply of heat. to the apparatus.

Calibration of the Copper Thermometer.

The readings of the voltmeter described were determined
at the following temperatures : 100°, 0°, the boiling-point of
ethylene —103°°5, the freezing-point —169°, and the tem-
perature of liquid air. The ethylene employed was carefully
fractionated for this purpose. 120 litres were condensed and
the first and last 20 litres rejected, the determinations being
made with the middle fraction. The temperature of liquid
air is a variable, depending on the composition of the liquid,
but if the latter is known the temperature can be fixed with
great accuracy from the tables given by Baly. A sample
was therefore drawn off into a gas-holder from beneath the
surface of the liquid, at the time the temperature was read,
and its composition determined by analysis. These constants
were frequently redetermined throughout the course of the.
experiments and found to remain unaltered. “

Condensation of the Radioactive Lmanations. D603

The following table represents the results :—

Temperature. Resistance (ohms). Ratio.
KOOP 'C: "00947 135°1 ©
0° : ‘00701 100
— 103°°5 "00437 i 62°3
—169° "00262 al°4
—192°2 "00202 28°8

In the last column the ratio of the resistance is given, the
value at 0° being taken as 100. In Pl. XIV. fig. 3 the results
are plotted with the resistance as ordinates and the temperature
as abscissee. It will be observed that the curve is very nearly
a straight line cutting the axis, if produced, at very nearly
the absolute zero. For the particular thermometer used,
therefore, the readings of the millivoltmeter may be taken
without appreciable error to be proportional to the absolute
temperature. The instruments employed were accurately
calibrated. The accuracy of the temperature determination
by this method depends oniy on the sensitiveness of the
millivoltmeter. At the temperature at which most of the
observations were made, one division of the scale corresponded
to about 4° C., and the readings could be made to 1/10 of a
division. The determinations were therefore accurate to
within 0°°5, which was sufficient for the purpose. The great
advantage of the method is the ease and certainty with which
a continually changing temperature can be followed.

Experiments for the Radium Emanation with a steady
current of Gas.

Experiments with the radium emanation are much simpler
than for that of thorium, since the activity does not decay
appreciably over the time required for a complete series of
observations,and much larger effects can be obtained. PI. XIV.
fig. 2 represents the general arrangement of the apparatus for
the determination of the volatilization temperature of the
radium emanation ina steady current of gas. The latter (either
hydrogen or oxygen) was conveniently obtained from a set of
eight voltameters, arranged in series across the 110 volt
circuit and capable of taking a current up to 3 amperes.
The latter, measured by a Weston ammeter, furnished a
measure of the number of c. c. of gas passing per second.
This enters the apparatus at A. The radium emanation mixed
with air is stored in the gas-holder B. The exit of the
copper spiral is connected with a testing-cylinder T of the
kind previously described, in which the ionization current
through the gas, due to the rays from the emanation, is
measured by the electrometer EH. D is a drying-tube.

566 Prof. Rutherford and Mr. Soddy on
The ethylene bath was cooled by liquid air slightly below

the temperature of condensation, and a definite volume of the
emanation was sent into the apparatus from B, and conveyed
by a very slow gas-stream for'10 minutes into the spiral so
that it was condensed near the beginning of the spiral. The
current of gas to be employed is then adjusted and the tempe-
rature of the bath allowed to rise slowly. One observer took
the determinations of the temperature and the lapse of time,
the other the readings of the electrometer. The temperature
at which the electrometer-needle commenced to move was
recorded, and the rate of movement at succeeding tem-
peratures. In most of the experiments the temperature rose
at a rate of about 1°°6 to 2° per minute.

The following table gives an illustration of the results
obtained :-—
Divisions per second of

Temperature. the electrometer.
—-160° 0)
— 156° )
—154°°3 1
—153°°8 ZA
—152°5 24

The observed temperature of the first appearance of the
emanation is subject to a correction for the time taken for
the emanation to be swept into the testing-vessel after
volatilization. This depends on the volume of the spiral] and
its temperature, and on the current of gas, and can be
approximatelv calculated for each experiment. Knowing the
rate of rise of temperature in the experiment the actual
temperature at which volatilization commenced could be
deduced. In the table given above for a gas-stream of
1°38 cms. per second the application of this correction lowers
the temperature of volatilization about 0°°8 C. The following
table includes some of the corrected results for the radium
emanation. Under the column T, the temperatures at which the
emanation began to volatilize are given, under T, the tempera-
tures at which one half of the total amount had been given off.

Gas. ce. c. per second, <. Te
Hydrogen. 3454's) 525 —151°3 — 150
ey —153°7 =
Cay —153°7 —151
"99 — 152 im
1°38 — 54 see
23 —162°5 —162
Oxy gen ji He 2 tot —152°5 —151°5_
aa —152°5 Apes

“38 —1955 — 153

Condensation of the Radioactive Emanations. 567

With hydrogen streams from -25 c. c. to 1°38 c. c. per
second and for the slow stream of oxygen the results are in
good agreement and give a mean value for T, of —153°, for
T, —151°5. But a well-marked difference appears when
the stream of hydrogen is increased to 2°3 ¢.c. per second.
This corresponds to an initial velocity of 50 cms. a second
through the spiral, and 20 cms. per second after the temperature
of the bath has been obtained. The result is therefore to be
expected, for in such a rapid stream the gas is not cooled
down to the temperature of the spiral and the volatilization-
point of the emanation is in consequence apparently lower.
For the same reason the temperature observed for the oxygen
stream of only °58 c. c. a second is probably too low, for this
gas is cooled with more difficulty than hydrogen. LHven if
the temperature of the spiral is ultimately attained, a rapid
current of gas would tend to sweep out the emanation it had
volatilized in its passage, without giving it time to be
recondensed in the subsequent portions of the spiral. This
effect, for reasons to be discussed later, would also be greater
In oxygen than in hydrogen. Fur ther determinations for
the radium emanation by another distinct method are given
later in the paper.

At this stage some experiments may be mentioned that
were performed with a much larger quantity of radium
emanation to determine the amount that is volatilized at
various temperatures. In one experiment at —154°, no
escape of emanation was observed although less than
1/10000 part could have been detected. At “152° about
one half per cent. and at —150° considerably more than half
of the total amount had come off. There is no doubt that in
a bath, kept constant at the temperature of initial volati-
lization, all would volatilize if sufficient time were allowed,
but it is probable that the time required would be considerable.
There isin fact evidence that the condensed radium emanation
possesses what corresponds to a vapour-pressure in an ordinary
substance,

Experiments for the Thorium Emanation by the same Method.

The rapid loss of the activity of the thorium emanation,
which decays to half value in one minute, makes the deter-
mination of its volatilization-point a more difficult task. In
the first place too slow a gas-stream cannot be employed or
the ionization effects are too small. In the second place the
thorium compound must be retained all the time in the gas-
stream, unless the temperature of the spiral is made to rise
so rapidly that its determination becomes impracticable. The
results therefore bear a different interpretation trom those

568 Prof. Rutherford and Mr. Soddy on

given for radium, for in this case the point measured is the
temperature at which some of the thorium emanation first
escaped condensation, and not the point at which volatilization
begins of that already condensed. In place of the T-tube and

gas-holder of fig. 2 (Pl. XIV.) a highly emanating thorium
compound was placed i in series with the gas-stream, and the
temperature T observed at which the emanation first began
to make its appearance in the testing-vessel. The following
are some of the results obtained :—

Gas. ce. c. per Second. a
Hydrogen”... Vee —155° C.
1-3 — 159°
Oxygen . . “58 —155°5
55 —156°
“98 —155°°5

If these results are compared with those obtained for the
radium emanation it will be seen that the temperatures with
an equal gas-stream in the two cases are very nearly the
same. Thus, in the determinations in an oxygen stream of
58 c.c. per second, the radium emanation commenced to
volatilize at —155°, and some of the thorium emanation
escapes condensation at —155°°5 C. It was at first thought
that this result indicated that the condensation-points of the
two emanations were identical. It will be recalled that no
difference could be detected in the chemical properties of the
two emanations, both being quite unattected by the most
powerful chemical reagents. Yet it seemed improbable that
the two emanations could be materially identical on account
of the completely distinct character of their radioactive
properties. Not only are their rates of decay widely different,
being 5000 times faster in the one case than the other, but
the excited activities they give rise to are also completely
different, not only in the rate of decay, but even in the
number of changes through which they apparently pass
before their activity disappears. In the course of further
work a very distinct difference of behaviour in the con-
densation phenomena in the two cases was brought to light.
It was observed that some of the thorium emanation was
condensed at temperatures as much as 30° above the point
of complete condensation. The curve fig.5 (Pl. XIV.) is an
example of the results obtained. The maximum ordinate
taken as 100 represents the amount of emanation entering
the testing-vessel at temperatures far above the point at
which condensation commences. This amount begins to
decrease at about —120°, and becomes less than 1 per cent.

Condensation of the Radioactive Emanations. 569

of its original value at —154°. This curve was obtained in
a steady stream of oxygen of 38 ¢.c, per second. For faster
currents the curve is displaced slightly to the right.

When tested under the same conditions, the radium eman-
ation showed no such behaviour. When the solution of
radium chloride is retained in the gas-stream, the temperature
at which some of the emanation escapes condensation is only
slightly above the point before found at which the condensed
emanation commences to volatilize. Apart from the question
of the actual condensation-points themselves, there is, there-
fore, a well-marked distinction in the character of the phe-
nomena in the two cases. To investigate this difference, a
new method was devised which allowed determinations to be
made with the two emanations under comparable conditions.

Experiments by the Static Method.

The use of a steady stream of gas through the spiral in
which the emanation is condensed has many disadvantages,
some of which have been alluded to. By the use of a
mercury-pump, and by working in a partial vacuum, these
disadvantages are avoided, and the conditions of experiment
made more definite. Pl. XIV. fig. 4 represents the arrange-
ment employed.

The Geissler pump P was connected with the copper
spiral S and the thorium compound in the tube A, and
possessed a volume large in comparison with the volume of
the whole of the rest of the apparatus. The small bulb V
was first filled with hydrogen or oxygen entering at C, and
the thorium tube-spiral and connecting-tubes exhausted by
the pump to a pressure of a few millimetres of mercury.
The three-way tap was then reversed, the tap E being open
and F closed. In this way a quantity of the emanation was
swept out of A into the spiral; E was closed, and the
emanation allowed to remain in the spiral a definite time.
This period varied in different experiments from 10° to 90*.
At the expiration of this interval, the pump in which the
mercury had been lowered was put into communication with
the spiral by the tap F, which was then closed, the mercury
raised, and the emanation expelled into H and carried on to
the testing-vessel by a steady current of oxygen entering the
tube at K, and kept continuously passing throughout the
experiment. The pressures employed were deduced from
the readings of the height of the mercury in the pump-tube
when the mercury was lowered, and the relative volumes of
various parts of the apparatus. The various manipulations

570 Prof. Rutherford and Mr. Soddy on

of the taps and of the mercury-pump were all timed through-
out by a stop-watch, aud the observations with the electro-
meter were always taken at the same interval after the
commencement of the operations. In this way the decay of
activity of the emanation was the same in each experiment,
and the results obtained in different experiments comparable
with one another. One observer took charge of the manipu-
lation of the apparatus, the other recorded the lapse of time,
the temperature of the spiral at the instant the contents were
drawn into the pump by opening the tap F, and the readings
of the electrometer after the emanation had been sent into
the testing-vessel. The latter could be taken within 90
seconds from the time the emanation was removed from the
thorium in those cases where it remained in the spiral for a
period of 30 seconds. The tap F was a three-way, so that
the pump could be cut out of the circuit and experiments
in a steady stream of gas carried on without alteration of the
apparatus. ‘The amounts of the emanation that remain un-
condensed at different temperatures are shown graphically in
fig. 6, Pl. XIV. The different curves represent different
series of observations with hydrogen and oxygen respectively,
in which the time during which the emanation remained in the
spiral was in some cases 30 seconds, in others 90 seconds.
Curves A and B illustrate the difference in the condensation-
curves for hydrogen and oxygen under similar conditions.
The pressure in the spiral after the removal of the uncon-
densed emanation corresponded to 19 mm. of mercury. The
curves show that a greater proportion of the emanation is
condensed for the same temperature in hydrogen than in
oxygen. The curves C and D, which were obtained under
different conditions of pressure and amount of emanation from
curves A and B, show that a greater proportion is condensed
in 90 seconds than in 30 seconds. The proportion condensed
in a steady stream is less than in any of the experiments by
the static method. In all cases, however, condensation com-
mences at about the same temperature, viz., —120° C., and
there is no doubt that this must be taken as the real con-
densation-point of the thorium emanation, and that the
identity in the temperatures observed in the earlier experi-
ments with a steady stream must be regarded as purely
accidental.

Experiments with the Radium Emnanation.

The apparatus (fig. 4, Pl. XIV.) was slightly altered for the
determination of the volatilization-point of the radium ema-
nation. The thorium tube was replaced by a drying-tube of

Condensation of the Radioactive Hmanations. STE

calcium chloride and the bulb V filled with air mixed with the
radium emanation which was then allowed into the exhausted
spiral kept below the temperature of condensation. The
apparatus was then repeatedly exhausted by the pump, and
after each exhaustion a bulb-full of oxygen was sent into the
spiral, the temperature of the bath being allowed to rise
slowly during the exhaustion. The temperature at which the
first trace of emanation escaped and the amounts at succeeding
temperatures were noted as before. The following table is an
example of the results obtained :—
Divisions of Electrometer

Temperature. per second.
— 153°
—151° 0
—148°-5 “74
— 146°5 D3
— 143° orl
—139° 7
— 135° “08

The mean of several results gave —150° as the point at
which the emanation first began to volatilize, and this is in
good agreement with the result by the blowing method, that
is, —153°. The difference is in the expected direction, for
in the static method the mass of the gas employed is much
smaller, and any emanation that is volatilized by the rush of
heated gas in its passage through the spiral has time to be
recondensed. The temperature —150° C. may therefore be
taken with considerable confidence as being the true point at
which the radium emanation first commences to volatilize.
On the other hand, the table shows a somewhat less sudden
volatilization than in the case of the blowing method, but
this is inherent to the static method employed. The glass
spiral connecting-tube between the pump and the copper
spiral had a greater volume than the latter itself, and at each
exhaustion some of the volatilized emanation is left in this
spiral. In the case of the thorium emanation this decays
practically to zero before the next observation is taken, but
in the case of the radium emanation it does not, and is added
to the amount removed at the next exhaustion. The tem-
perature of volatilization found in these experiments has
almost exactly the value given by Ramsay and Travers for
the boiling-point of nitric oxide under atmospheric pressure
149°°-9 C. A bath of liquified nitric oxide was prepared, and
used in place of the ethylene in former experiments. [ts
boiling-point. rose steadily until about one-fitth had boiled off.
_ It then became constant at —151° C., as determined by the

72 Prof, Rutherford and Mr. Soddy on

resistance of the copper spiral, and remained so until the
latter began to be no longer completely covered. The nitric
oxide was not sufficiently pure to enable much weight to be
put on this result as a determination of temperature, for from
its behaviour it obviously must have contained a considerable
quantity of dissolved nitrogen, but it is of interest as being
a completely independent check on the thermometer at
almost the exact point of condensation, and shows that the
value ascribed to the latter cannot be far from the truth.
Such a bath of boiling liquid rising very slowly in temperature
over the exact range in which volatilization takes place,
afforded a means, however, of examining more exactly the
progress of the volatilization after the initial point was
reached. The latter occurred in this case at —155° C., a
steady current of air being maintained through the spiral. In
four minutes the temperature had increased to —153°°5, and
the amount volatilized was about four times as great as at
—153°. In the next 55 minutes the temperature had in- .
creased to 152°°3, and the whole amount practically had
volatilized, which was at least fifty times the amount at the
temperature of —153°°5. Such a result would of course
be explained by slight local inequalities in the temperature of
the spiral, but since the latter was immersed in a rapidly
boiling liquid it is difficult to believe that such could have
been the case. It seems more reasonable to attribute it to a
true vapour-pressure possessed by the condensed emanation,
although great refinement in the experimental methods would
be necessary before such a conclusion could be considered

established.

The Explanation of the Anomalous Behaviour of the Thorium
E'manations.

The results obtained are satisfactory in so far as they show
that the two emanations do not condense at the same tempera-
ture. The anomalous behaviour of the thorium emanation in
condensation, which in the first experiments seemed to indicate
that the two emanations condensed at the same temperature,
has been shown to be due to an effect, not present in the case
of the radium emanation, which depends on the nature of the
gas, the concentration of the emanation, and the time that
the latter has been left to condense, It remains to develop
a view which gives a satisfactory explanation of this be-
haviour. In the first place the actual number of particles
of emanation that are present must be almost infinitesimally
small compared with the number of particles of the gas with
which they are mixed. It is difficult to make an accurate .

Condensation of the Radioactive Emanations. 573

calculation of the number actually present, but an estimate
of the order of the number present can be deduced from the
following considerations. The radiation from the thorium
and radium emanations consists, as far as itis known, entirely
of a rays. The view has recently been put forward that these,
in the case of radium, consist of projected particles of the
same order of mass as the hydrogen atom, carrying a positive
charge, and travelling with a velocity about 1/10 the velocity
of light. Itis extremely likely that the radiations from the
two emanations are quite comparable in character, and produce
in their passage through the gas a similar number of ions.
From results deduced from experiments made in an attempt
to measure the charge carried by the @ rays there is no
doubt that each of these projected particles produces at least
10°, and possibly 10°, ions in its path before being absorbed
in the gas. For the present purpose, 10’ ions will be taken
as a probable value. The electrometer employed readily
measured currents of 10-3H.S. units per second. Taking the
charge on an ion as 6x 107! ES. units, this cdrresponds to
a production of 1:°7x10® ions per second, which would be
produced by 17 expelled “ rays’’ persecond. Hach radiating
particle cannot expel less than one ray, and may expel more,
but it is likely that the number of rays expelled by a particle
of the thorinm emanation is not greatly different from the
number expelled by a particle of the radium emanation. The
view will be developed more generally in a subsequent paper*,
that the decay of activity of a radioactive substance is caused
by the number of particles present diminishing owing to their
changing into new systems, the change being accompanied by
the expulsion of rays. From the law of the rate of decay
=I,e-“, on this view AN particles change per second
hen N are present. Therefore to produce 17 rays per
second AN cannot be greater than 17. Since in the case of
the thorium emanation A equals 1/87, it follows that N cannot
be greater than 1500. The electrometer used therefore de-
tects the presence of about 1500 particles of the thorium
emanation, and since, in the static method, the volume of the
condensing spiral was about 15 c,c., this corresponds to a
concentration of about 100 particles per c. ce. An ordinary
gas at atmospheric pressure probably contains 10° particles.
On this estimate therefore the thorium emanation could have
been detected if it possessed a partial pressure in the con-
densing spiral of 10-4 atmosphere. [tis thus not surprising
that the condensation-point of the thorium emanation is not
* Infra, p. 576,
Phil. Mag. 8. 6. Vol. 5. No. 29. May 1903. 2 ¢

574 Prof. Rutherford and Mr. Soddy on

sharply defined. It is rather a matter of remark that con-
densation can occur at all with such sparse distribution of
emanation particles in the gas, for in order for condensation
to take place the particles must first approach within each
other’s sphere of influence.

Now consider the case of the radium emanation. The rate
of decay is about 5000 times slower than that of the thorium
emanation, and consequently the actual number that must
be present to produce the same number of rays per second in
the two cases must be of the order of 5000 times greater
for the radium than for the thorium emanation. This con-
clusion involves only the assumptions that the same number
ot rays are produced by a particle of emanation in each case,
and that the rays expelled produce in the passage through
the gas the same number of ions. The number of particles
that must be present for the electrometer to detect them in
this experiment must therefore be about 5000 x 1500, 2. e. of
the order of 10’. The difference of behaviour in the two
cases is well explained in the view that jor equal electrical
effects the number of radium emanation particles must be far
larger than the number of thorium emanation particles. It
is to be expected that the probability of the particles coming
into each other’s sphere of influence will increase very rapidly
as the concentration of the particles increases, and that in
the case of the radium emanation, once the temperature of
condensation is attained all but a negligibly small proportion
of the total number of particles present will condense in a
very short time. In the case of the thorium emanation,
however, the temperature might be far below that of con-
densation, and yet a considerable proportion remain uncon-
densed for comparatively long intervals. On this view the
experimental results obtained are exactly accounted for.
A greater proportion condenses the longer the time allowed
for condensation under the same conditions. The con-
densation oceurs more rapidly in hydrogen than in oxygen,
owing to the diffusion being greater in the former gas.
For the same reason the condensation occurs faster the
lower the pressure of the gas present. Finally, when the
emanation is carried by a steady gas-stream, a less proportion
condenses than in the other cases, because the concentration
of emanation particles per cubic centimetre of gas is less
under these conditions.

Decay of Activity of the Condensed Emanation.
Some experiments were made to test whether the rate of
decay of activity of the thorium emanation was altered at the

Condensation of the Radioactive Emanations. D179

temperature of liquid air. The method employed was to pass
a slow steady stream of the thorium emanation, mixed with
hydrogen or oxygen, into the copper spiral immersed in
liquid air for a space of five minutes. The emanation was
thus condensed in the spiral. The current of gas was then
stopped, and after definite intervals, extending in successive
experiments from one to five minutes, the spiral was rapidly
removed from the liquid air, plunged into hot water, and the
emanation present swept rapidly with a current of air intoa
large testing-vessel. The results showed that the emanation
lost its activity at the same rate at the temperature of liquid
air as at ordinary temperature, ?.e. its activity fell to halt
value in about one minute. This is in agreement with results
previously noted for other active products, showing that the
rate of decay is unaffected by any physical or chemical

agency.
Summary of Results.

The results show that the thorium emanation begins to
condense at about —120°C. The rapid rate of decay of its
activity renders a determination of the point at which the
condensed emanation commences to volatilize experimentally
impracticable. But under all conditions tried some of the
emanation escapes condensation at temperatures much below
the temperature of initial condensation. In a slow stream
of gas the presence of the emanatien is first observed at about
—155° C. It is probable that —120° represents the true
temperature of volatilization and condensation, and that the
escape of emanation below this temperature is due to the
extremely small number of condensing particles Bree
The radium emanation commences to volatilize at —153° nn
in a steady stream of gas, and at —150° in a uous
atmosphere, and this latter value may be accepted with con-
siderable confidence as being the true temperature of initial
volatilization. In the case of radium there is no sensible
difference between the temperature of volatilization and of
condensation, and the whole of the emanation is condensed at
temperatures only slightly below the initial point of volatiliza-
tion. This difference of behaviour of the two emanations is
explained on the view that the number of particles of emana-
tion present for equal effects is probably many thousand times
greater in the case of radium emanation than in the case of
thorium emanation. All the radium emanation is volatilized
within a very few degrees of the initial point, the rate of
volatilization of course depending on the rate of rise of
temperature. But with a very slowly rising temperature,

976 Prof. Rutherford and Mr. Soddy

practically all of the emanation comes off very suddenly at a
temperature not much more than one degree above that at
which only 2 per cent. has volatilized. The general indication
of all the experiments, considered together, is to show that
the condensed emanation possesses a true vapour-pressure,
and that the emanation commences to volatilize slowly two
or three degrees below the temperature of rapid volatilization
even when the process occurs in a stationary atmosphere.
The emanations therefore possess the usual properties possessed
by ordinary gaseous matter, in so far as the phenomena of
volatilization and eonemea a are concerned. It was shown
in a recent paper that they also possess the property possessed
by gases of being occluded by solids under certain conditions.
These new properties, taken in conjunction with the earlier dis-
covered diffusion phenomena, characteristic of tke radioactive
emanations, leave no doubt that the latter must consist of
matter in the gaseous state.
McGill University, Montreal,
March 9, 1903.

LX. Radioactive Change. By HE. Ruraerrorp, I.A., D.Sc.,
Macdonald Professor of Physics, McGill University, and
F. Soppy, J.A. (Ozon.).

CONTENTS.

IT, The Products of Radioactive Change, and their Specitic Material
Nature.
II. The Synchronism between the Change and the Radiation.
III. The Material Nature of the Radiations.
IV. The Law of Radioactive Change.
VY. The Conservation of Radioactivity.
VI. The Relation of Radioactive Change to Chemical Change.
VII. The Energy of Radioactive Change and the Interval PEs of
the Chemical Atom.

§ 1. The Products of Radioactive Change and their
Specific Material Nature.

ib previous papers it has been shown that the radioactivity

of the elements radium, thorium, and uranium is main-
tained by the continuous production of new kinds of matter
which possess temporary activity. In some cases the new
product exhibits well-defined chemical differences from the
element producing it, and can be separated by chemical
processes. Examples of this are to be found in the removal
of thorium X from thorium and uranium X from uranium.
In other cases the new products are gaseous in character, and

* Communicated by the Authors.

on Radioactive Change. Suid

so separate themselves by the mere process of diffusion, giving
rise to the radioactive emanations which are produced by
compounds of thorium and radium. These emanations can be
condensed by cold and again volatilized ; although they do
not appear to possess positive chemical affinities, they are

frequently occluded by the substances producing them when
in the solid state, and are liberated by solution; they diffuse

rapidly into the atmosphere and through porous partitions,
and in general exhibit the behaviour of inert gases of fairly
high molecular weight. In other cases again the new matter
is itself non-volatile, but is produced by the further change of
the gaseous emanation ; ; so that the latter acts as the inter-
mediar y in the process of its separation from the radioactive
element. This is the case with the two different kinds of
excited activity produced on objects in the neighbourhood of
compounds of thorium and radium respectively, which in turn
possess well-defined and characteristic material properties.

For example, the thorium excited activity is volatilized at
a definite high temperature, and redeposited in the neigh-
-bourhood, and can be dissolved in some reagents and not in
others.

These various new bodies differ from ordinary matter,
therefore, only in one point, namely, that their quantity is far
below the limit that can be reached by the ordinary methods
of chemical and spectroscopic analysis. As an example that
this is no argument ayainst their specific material existence,
it may be mentioned that the same is true of radium itself as
it occurs in nature. No chemical or spectroscopic test is
sufficiently delicate to detect radium in pitchblende, and it is
not until the quantity present is increased many times by
concentration that the characteristic spectrum begins to make
its appearance. Mme. Curie and also Giesel have succeeded
in obtaining quite considerable quantities of pure radium
compounds by working up many tons of pitchblende, and the
results go to show that radium is in reality one of the best
defined and most characteristic of the chemical elements.
So, also, the various new bodies, whose existence has been
discovered by the aid of their radioactivity, would no doubt,
like radium, be brought within the range of the older methods
of investigation if it were possible to increase the quantity ot
material employed indefinitely.

§2. Lhe Synchronism between the Change and the Radiation.

In the present paper the nature of the changes in which
these new bodies are produced remains to be considered,
The experimental evidence that has been accumulated is now

578 Prof. Rutherford and Mr. Soddy

sufficiently complete to enable a general theory of the nature
of the process to be established with a considerable degree of
certainty and definiteness. It soon became apparent from
this evidence that a much more intimate connexion exists
between the radioactivity and the changes that maintain it
than is expressed in the idea of the production of active
matter. It will be recalled that all cases of radioactive
change that have been studied can be resolved into the
pr oduction by one substance of one other (disregarding
tor the present the expelled rays). When several changes
occur together these are not simultaneous but successive.
Thus thorium produces thorium X, the thorium X produces
the thorium emanation, and the latter produces the excited
activity. Now the radioactivity of each of these substances
can be shown to be connected, not with the change in which
it was itself produced, but with the change in which it in turn
produces the next new type. Thus after thorium X has been
separated from the thorium producing it, the radiations of the
thorium X are proportional to the amount of emanation that
it produces, and both the radioactivity and the emanating
power of thorium X decay according to the same law and at
the same rate. In the next stage the emanation goes on to
produce the excited activity. The activity of the emanation
falls to half-value in one minute, and the amount of excited
activity produced by it on the negative electrode in an
electric field falls off in like ratio. These results are fully
borne out in the case of radium. ‘The activity of the radium
emanation decays to half-value in four days, and so also does
its power of producing the excited activity.

Hence it is not possible to regard radioactivity as a
consequence of changes that have already taken place. The
rays emitted must be an accompaniment of the change of the
radiating system into the one next produced.

Non-separable activity—This point of view at once accounts
for the existence of a constant radioactivity, non-separable by
chemical processes, in each of the three radio-elements. This
non-separable activity consists of the radiations that accompany
the primary change of the radio-element itself into the first
new product that is produced. Thus in thorium about 25
per cent. of the a radiation accompanies the first change of
the thorium into thorium X. In uranium the whole of the
« radiation is non-separable and accompanies the change of
the uranium into uranium X.

Several important consequences follow from the conclusion
that the radiations accompany the change. A body that is
radioactive must 2pso facto be changing, and hence it is not

on Radioactive Change. x79

possible that any of the new types of radioactive matter—
é. g., uranium X, thorium X, the two emanations, &¢.—can
be identical with any of the known elements. For they
remain in existence only a short time, and the decay of their
radioactivity is the expression of their continuously dimin-
ishing quantity. On the other hand, since the ultimate
products of the changes cannot be radioactive, there must
always exist at least one stage in the process beyond the
range of the methods of experiment. For this reason the
ultimate products that result from the changes remain
unknown, the quantities involved being unrecognizable,
except by the methods of radioactivity. In the naturally
occurring minerals containing the radio-elements these
changes ust have been proceeding steadily over very long
periods, and, unless they succeed in escaping, the ultimate
products should have accumulated in sufficient quantity to be
detected, and therefore should appear in nature as the in-
variable companions of the radio-elements. We have already
suggested on these and other grounds that possibly helium
may be such an ultimate product, although, of course, the
suggestion is at present a purely speculative one. But a
closer study of the radioactive minerals would in all
probability afford farther evidence on this important question.

§ 3. The Material Nature of the Radiations.

The view that the ray or rays from any system are
produced at the moment the system changes has received
strong confirmation by the discovery of the electric and
magnetic deviability of the a ray. The deviation is in the
opposite sense to the @ or cathode- -ray, and the rays thus
consist of positively charged bodies projected with great
velocity (Rutherford, Phil. Mag., Feb. 1903). The latter

was shown to be of the order of 2°5 10° cms. per second. The
value of e/m, tne ratio of the charge of the carrier to its mass,
is of the order 6 10°. Now the value of e/m for the cathode-
ray is abont 10. Assuming that the value of the charge is
the same in each case, the apparent mass of the positiv e
projected particle is over 1000 times as great as for the
cathode-ray. Now e/m=10* for the hy drogen atom in the
electrolysis of water. The particle that constitutes the 2 ray
thus behaves as if its mass were of the same order as that of
the hydrogen atom. The @ rays from all the radio-elements,
and from the various radioactive bodies which they produce,
possess analogous properties, and differ only to a slight
extent in penetrating power. There are thus strong reasons

580 Prof. Rutherford and Mr. Soddy

for the belief that the « rays generally are projections and
that the mass of the particle is of the same order as that of
the hydrogen atom, and very large compared with the mass
of the projected particle which constitutes the 6 or easily
deviable ray from the same element.

With regard to the part played in radioactivity by the two
types of radiation, there can be no doubt that the a rays are
by far the more important. In all cases they represent over
99 per cent. of the energy radiated *, and although the
8 rays on account of their penetrating power and marked
photographic action have been more often studied, they are
comparatively of much less significance.

It has been shown that the non-separable activity of all
three radio-elements, the activity of the two emanations, and
the first stage of the excited activity of radium, comprise
only a rays. It is not until the processes near completion in
so far as their progress can be experimentally traced that
the 8 or cathode-ray makes its appearance f.

In light of this evidence there is every reason to suppose,
not merely that the expulsion of a charged particle accom-
panies the change, but that this expulsion actually zs the
change.

§ 4. The Law of Radioactive Change. x

The view that the radiation from an active substance
accompanies the change gives a very definite physical
meaning to the law of decay of radioactivity. In all cases
where one of the radioactive products has been separated,
and its activity examined independently of the active sub-
stance which gives rise to it, or which it in turn produces, it
has been found that the activity under all conditions inves-
tigated falls off in a geometrical progression with the time.
This is expressed by the equation

where J, is the initial ionization current due to the radiations,
I, that after the time ¢, and A is a constant. Hach ray or

* In the paper in which this is deduced (Phil. Mag. Sept. 1902,
p. 329) there is an obvious slip of calculation. The number should be
100 instead of 1000.

+ In addition to the a and 8 rays the radio-elements also give out a
third type of radiation which is extremely penetrating. Thorium as well
as radium (Rutherford, Phys. Zeit. 1902) gives out these penetrating
rays, and it has since been found that uranium possesses the same
property. These rays have not yet heen sufficiently examined to make
any discussion possible of the part they play in radioactive processes.

on Radioactive Change. « 581

projected particle will in general produce a certain definite
number of ions in its path, and the ionization current is
therefore proportional to the number of such particles projected
per second. Thus
Ne
Ns

where 7; is the number projected in unit of time for the time
t and n, the number initially.

If each changing system gives rise to one ray, the number
of systems N, ‘which remain unchanged at the time ¢ is

given by 3
N=| dt = 2e™,
;

The number N, initially present is given by putting t=0.

Ne
No = -
N
and N, == GO,

The same law holds if each changing system produces two
or any definite number of rays.
Differentiating

=—AN;,
or, the rate of change of the system at any time is always
proportional to the amount remaining unchanged.

The law of radioactive change may therefore be expressed
in the one statement—the proportional, amount of radioactive
matter that changes in unit time is a constant. When the
total amount does not vary (a condition nearly fulfilled at the
equilibrium point where the rate of supply is equal to the
rate of change) the proportion of the whole which changes
in unit time is represented by the constant A, which possesses
for each type of active matter a fixed and characteristic value.
may therefore be suitably called the “ radicactive constant.”
The complexity of the phenomena of radioactivity is due to
the existence asa general rule of several differ ent types of
matter changing at “the same time into one another, each type
possessing a different radioactive constant.

§ 5. The Conservation of Radioactivity.

The law of radioactive change that has been deduced holds
for each stage that has been examined, and therefore holds

d82 Prot. Rutherford and Mr. Soddy

for the phenomenon generally. The radioactive constant X
has been investigated “under ¥ ery widely varied conditions of
temperature, and under the influence of the most powerful
chemical and physical agencies, and no alteration of its value
has been observed. The law forms in fact the mathematical
expression of a general principle to which we have been led
as the result of our investigations as a whole. Radioactivity,
according to present knowledge, must be regarded as the
result of a process which lies wholly outside the sphere of
known controllable forces, and cannot be created, altered, or
destroyed. Like gravitation, it is proportional only to the
quantity of matter involved, and in this restricted sense it is
therefore true to speak of the principle as the conservation
of radioactivity”. Radioactivity differs of course from grayi-
tation in being a special and not necessarily a universal
property of matter, which is possessed by different kinds in
widely different degree. In the processes of radioactivity
these’ different kinds change into one another and into
inactive matter, producing corresponding changes in the

radioactivity. Thus the decay of radioactivity is to be ascribed

to the disappearance of the active matter, and the recovery
of radioactivity to its production. When the two processes
balance—a condition very nearly fulfilled in the case of the
radio-elements in a closed space—the activity remains con-
stant. But here the apparent constancy is merely the

expression of the slow rate of change of the radio-element

itself. Over sufficiently long periods its radioactivity must
also decay according to the law of radioactive change, for
otherwise it would be necessary to look upon radioactive
change as involving the creation ‘of matter. In the universe
therefore the forall radioactivity must, according to our
present knowledge, be growing less and tending to disappear.

* Apart from the considerations that follow, this nomenclature is a
convenient expression of the observed facts that the total radioactivity
(measured by the radiations peculiar to the radio-elements) is for any
given mass of radio-element a constant under all conditions investigated.
The radioactive equilibrium may be disturbed and the activity distributed
among one or more active products capable of separation from the
original element. But the sum total throughout these operations is at
all times the same.

For practical purposes the expression “ conservation,” applied to the
radioactivity of the three radio-elements, is justified by the extremely
minute proportion that can change in any interval over which it is
possible to extend actual observations! But riguily the term “ conser-
vation” applies only with reference to the radioactivity of any definite
quantity of radioactive matter, whereas in nature this quantity must be
changing spontaneously and continually growing less. 1'0 avoid possible
misunderstanding, therefore, it is necessary to use the expression only in
this restricted sense.

on Radioactive Change. 583

Hence the energy liberated in radioactive processes does not
disobey the law of the conservation of energy.

It is not implied in this view that radioactivity, considered
with reference to the quantity of matter involved, is conserved
under all conceivable conditions, or that it will not ultimately
be found possible to control the processes that give rise to it.
The principle enunciated applies of course only to our present
state of experimental knowledge, which is satisfactorily
interpreted by its aid.

The general evidence on which the principle is Naced
embraces the whole field of radioactivity. The experiments
of Becquerei and Curie have shown that the radiations from
uranium and radium respectively remain constant over long
intervals of time. Mme. Curie put forward the view that
radioactivity was a specific property of the element in
question, and the successful separation of the element radium
from pitchblende was a direct result of this method of re-
garding the property. The possibility of separating from a
radio-element an intensely active constituent, although
first sight contradictory, has afforded under closer examination
nothing but confirmation of this view. In all cases only a
part of the activity is removed, and this part is recovered
spontaneously by the radio-element in the course of time.
Mme. Curie’s original position, that radioactivity is a specific
property of the element, must be considered to be beyond
question. HEvenif it should ultimately be found that uranium
and thorium are admixtures of these elements with a small
constant proportion of new radio-elements with corre-
spondingly intense activity, the general method of regarding
the subject is quite unaffected.

In the next place, throughout the course of our investiga-
tions we have not observed a sinyle instance in which radio-
activity has been created in an element not radioactive, or
destroyed or altered in one that is, and there is no case at
present on record in which such a creation or destruction can
be considered as established. It will be shown later that
radioactive change can only be of the nature of an atomic
disintegration, and hence this result is to be expected, from
the universal experience of chemistry in failing to transform
the elements. For the same reason it is not to be expected
that the rate of radioactive change would be affected by
known physical or chemical influences. Lastly, the principle
of the conservation of radioactivity is in agreement with the
energy relations of radioactive change. These will be con-
sidered more fully in § 7, where it is shown that the energy
changes involved are of a much higher order of magnitude
than is the case in molecular change.

584 — Prof. Rutherford and Mr. Soddy

It is necessary to consider briefly some of the apparent
exceptions to this principle of the conservation of radio-
activity. In the first place it will be recalled that the
emanating power of the various compounds of thorium and

radium respectively differ widely among themselves, and are
greatly influenced by alterations of physical state. It was
recently proved (Phil. Mag. April 1903, p. 453) that these
variations are caused by alterations in the rate at which the
emanations escape into the surrounding atmosphere. The
emanation is produced at the same rate both in de-emanated
and in highly emanating thorium and radium compounds,
but is in the former stored up or occluded in the compound.
By comparing the amount stored up with the amount pro-
duced per second by the same compound dissolved, it was
found possible to put the matter to a very sharp experimental
test which completely established the law of the conservation
of radioactivity in these cases. Another exception is the
apparent destruction of the thorium excited activity deposited
on a platinum wire by ignition to a white heat. This has
recently been examined in this laboratory by Miss Gates,

and it was found that the excited activity is not destroyed,
but is volatilized at a definite temperature and redeposited in
unchanged amount on the neighbouring surfaces.

Radioactive ** Induction.” —Various workers in this subject
have explained the results they have obtained on the idea of
radioactive “induction,” in which a radioactive substance
has been attributed the power of inducing activity in bodies
mixed with it, or in its neighbourhood, which are not other-
wise radioactive. This theory was put forward by Becquerel
to explain the fact that certain precipitates (notably barium
sulphate) formed in solutions of radioactive salts are them-
selves radioactive. The explanation has been of great utility
in accounting for the numerous examples of the presence of
radioactivity in non-active elements, without the necessity of
assuming in each case the existence of a new radio-element
therein, “but our own results do not allow us to accept it.

In the great majority of instances that have been recorded
the results seem to be due simply to the mixture of active
matter with the inactive element. \n some cases the effect is
due to the presence of a small quantity of the original radio-
element, in which case the “ induced ” activity is ‘permanent.
In other c cases, one of the disintegration products, like uranium
X or thorium X, has been drag roed down by the precipitate,
producing temporary, or, as it is sometimes termed, “ false”
activity. In neither case is the original character of the
radiation at all affected. It is probable that a re-examination

es Ooh eC TO

on Radioactive Change. 585

of some of the effects that have been attributed to radioactive
induction would lead to new disintegration products of the
known radio-elements being recognized.

Other Results.—A number of cases remain for consideration,
where, by working with very large quantities of material,
there have been separated from minerals possible new radio-
elements, 7. e. substances possessing apparently permanent
radioactivity with chemical properties different from those
of the three known radio-elements. In most of these cases,
unfortunately, the real criteria that are of value, viz., the
nature of the radiations and the presence or absence of
distinctive emanations, have not been investigated. The
chemical properties are of less service, for even if a new
element were present, it is not at all necessary that it should
be in sufficient quantity to be detected by chemical or
spectroscopic analysis. Thus the radio-lead described by
Hoffmann and Strauss and by Giesel cannot be regarded as
a new element until it is shown that it has permanent activity
of a distinctive character.

In this connexion the question whether polonium (radio-
bismuth) is a new element is of great interest. The
polonium discovered by Mme. Curie is not a permanent
radioactive substance, its activity decaying slowly with the
time. On the view put forward in these papers, polonium
must be regarded as a disintegration product of one of the
radio-elements present in pitchblende. Recently, however,
Marckwald (Ber. der D. Chem. Gesel. 1902, pp. 2285 &
4239), by the electrolysis of pitchblende solutions, has ob-
tained an intensely radioactive substance very analogous to
the polonium of Curie. But he states that the activity
of his preparation does not decay with time, and this, if
confirmed, is sufficient to warrant the poeelecian that he is
not dealing with the same substance as Mme. Curie. On the
other hand, both preparations give only « rays, and in this
they are quite distinct from the other radio-elements. Marcek-
wald has succeeded in separating his substance from bismuth,
thus showing it to possess different chemical properties, and
in his latest paper states that the bismuth-free product is
indistinguishable chemically from tellurium. If the per-
manence of the radioactivity i is established, the existence of
a new radio-element must be inferred.

If elements heavier than uranium exist it is probable that
they will be radioactive. The extreme delicacy of radio-
activity as a means of chemical analysis would enable such
elements to be recognized even if present in infinitesimal
quantity. It is therefore to be expected that the number of

586 Prot. Ruthertord and Mr. Soddy

radio-elements will be augmented in the future, and that
considerably more than the three at present recognized exist

in minute quantity. In the first stage of the search for such
elements a purely chemical examination is of little service.
The main criteria are the permanence of the radiations, their
distinctive character, and the existence or absence of dis-
tinetive emanations or other disintegration products.

§ 6. The Relation of Radioactive Change to Chemical Change.

The law of radioactive change, that the rate of change is
proportional to the quantity of changing substance, is also
the law of monomolecular chemical reaction. Radioactive
change, therefore, must be of such a kind as to involve
one sy stem only, for if it were anything of the nature of a
combination, where the mutual action of two systems was
involved, the rate of change would be dependent on the

concentration, and the law would involve a volume-factor.

This is not the case. Since radioactivity is a specific
property of the element, the changing system must be the
chemical atom, and since only one system is involved in the
production of a new system and, in addition, heavy charged
particles, in radioactive change the chemical atom must
sutfer disintegration.

The radio-elements possess of all elements the heaviest
atomic weight. This is indeed their sole common chemical
eharacteristic. The disintegration of the atom and the
expulsion of heavy charged particles of the same order of
mass as the hydrogen atom leaves behind a new system
lighter than before, and possessing chemical and physical
properties quite different from those of the original element.
The disintegration process, once started, proceeds from stage
to ‘stage with definite measurable velocities in each case.
At each stage one or more @ “rays” are projected, until
the last stages are reached, when the B* ray” or electron is
expelled. ‘Tt seems advisable to possess a special name for
these now numerous atom-fragments, or new atoms, which
result trom the original atom after the ray has been expelled,
and which remain in existence only a limited time, continually
undergoing further change. Their instability is their chief
characteristic. On the one hand, it prevents the quantity
accumulating, and in consequence it is hardly likely that
they can ever be investigated by the ordinary methods. On
the other, the instability and consequent ray-expulsion
furnishes the means whereby they can be investigated. We
would therefore suggest the term metabolon for this purpose.

on Radioactive Change. 587

Thus in the following table the metabolons at present known
to result from the disintegration of the three radio-elements
have been arranged in order.

Uranium. Thorium. Radium.
Be nc x Thedien NG tadium He th tet
: Thorium Emanation. radium-Lxcited Activity I.
Thorium-Exe‘ted Netivity I. ditto II.
te ne i

2 )

The three queries represent the three unknown ultimate products.
The atoms of the radio-elements themselves form, so to speak,
the common ground between metabolons and atoms, possessing
the properties of both. Thus, although they are disintegrat-
ing, the rate is so slow that sufficient quantity can be
accumulated to be investigated chemically. Since the rate
of disintegration is probably a million times faster for radium
than it is for thorium or uranium, we have an explanation of
the excessively minute proportion of radium in the natural
minerals. Indeed, every consideration points to the con-
clusion that the radium atom is also a metabolon in the full
sense of having been formed by disintegration of one of the
other elements present in the mineral. For example, an
estimation of its “life,”’ goes to show that the latter can
hardly be more than a few thousand years (see § 7). The
point is under experimental investigation by one of us, and a
fuller discussion is reserved until later.

There is at present no evidence that a single atom or meta-
bolon ever produces more than one new kind of metabolon
at each change, and there are no means at present of finding,
for example, either how many metabolons of thorium X, or
how many projected particles, or “rays,’’ are produced from
each atom of thorium. The simplest plan therefore, since it
involves no possibility of serious error if the nature of the
convention is understood, is to assume that each atom or
metabolon produces one new metabolon or atom and one
Save:

§ 7. The Energy of Radioactive Change, and the Internal
Energy of the Chenucal Atom.

The position of the chemical atom as a very definite stage
in the complexity of matter, although not the lowest of
which it is now possible to obtain experimental knowledge,

588 Prof. Rutherford and Mr. Soddy

is brought out most clearly by a comparison of the respective
energy relations of radioactive and chemical change. It is
possible to calculate the order of the quantity of energy
radiated froma given quantity of radio-element during its
complete change, by several independent methods, the con-
clusions of which agree very well among themselves. The
most direct way is from the energy of the particle projected,
and the total number of atoms. For each atom cannot produce
less than one “ray” for each change it undergoes, and we
therefore arrive in this manner at a minimum estimate of the
total energy radiated. On the other hand, one atom of a
radio-element, if completely resolved into projected particles,
could not produce more than about 200 such particles at
most, assuming that the mass of the products is equal to
the mass of the atom. This consideration enables us to set a
maximum limit to the estimate. The a rays represent so
large a proportion of the total energy of radiation that they
alone need be considered.
Let m= mass of the projected particle,
v = the velocity,
e = charge.
Now for the « ray of radium

U=Z5 Or
PBs 13

The kinetic energy of each particle

im’? = ; —e= eto.
J.J. Thomson has shown that
e=6 10- B.S. Units=2 10-* Electromagnetic Units.

Therefore the kinetic energy of each projected particle
=10-°erg. Taking 102° as the probable number of atoms
in one gram of radium, the total energy of the rays from the
latter =10¥ ergs =2°4 107 gram-calories, on the assumption
that each atom projects one ray. Five successive stages in the
disintegration are known, and each stage corresponds to the
projection of at least one ray. It may therefore be stated that
the total energy of radiation during the disintegration of one
gram of radium cannot be less than 10° gram-calories, and
may be between 10° and 10! gram-calories. The energy
radiated does not necessarily involve the whole of the energy ~
of disintegration and may be only a small part of it. 108
gram-calories per gram may therefore be safely accepted as

on Radioactive Change. 589

the least possible estimate of the energy of radioactive change
in radium. The union of hydrogen and oxygen liberates
approximately 4 10° gram-calories per gram of water pro-
duced, and this reaction sets free more energy for a given
weight than any other chemical change known. ‘The energy
of radioactive change must therefore be at least twenty-
thousand times, and may be a million times, as great as the
energy of any molecular change.

The rate at which this store of energy is radiated, and in
consequence the life of a radio-element, can now be considered.
The order of the total quantity of energy liberated per second
in the form of rays from 1 gram of radium may be calcu-
lated from the total number of ions produced and the energy
required to produce an ion. In the solid salt a great pro-
portion of the radiation is absorbed in the material, but the
difficulty may be toa large extent avoided by determining
the number of ions produced by the radiation of the emana-
tion, and the proportionate amount of the total radiation of
radium due to the emanation. In this case most of the rays
are absorbed in producing ions from the air. It was experi-
mentally found that the maximum current due to the
emanation from | gram of radium, of activity LOOO compared
with uranium, in a large cylinder filled with air, was 1°65 10~°
electromagnetic units. Taking e=2 10-*, the number of ions
produced per second =8:2 10". ‘These ions result from the
collision of the projected particles with the gas in their path.
Townsend (Phil. Mag. 1901, vol.i.), from experiments on the
production of ions by collision, has found that the minimum
energy required to produce an ion is LO—" ergs. Taking the
activity of pure radium asa million times that of uranium,
the total energy radiated per second by the emanation from
1 gram of pure radium=8200 ergs. In radium compounds
in the solid state, this amount is about “4 of the total ener ey
of radiation, ech therefore is about

: 10" ergs per second,
310" ¢ ergs per year,
15, 000. ort am-calories per year.

This again is an Piterssstinidte. for only the energy em-
ployed in producing ions has been consider ed, and this may
be only a small fraction of the total energy of the rays.

Since the @ radiation of all the radio- plements 3 is extremely
similar in character, it appears reasonable to assume that the
Feebler radiations of thorium and uranium are due to these
elements disintegrating less rapidly than radium. The energy
radiated in jhe ses is about 10-® that from radium, and

Phil, Mag. 8. 6. Vol. 5. No. 29. May 1903. 2K

590 On Radioactive Change.

is therefore about ‘015 gram-calorie per year. Dividing this
quantity by the total energy of radiation, 2°4 10’ gram-calories,
we obtain the number 6 107! as a maximum estimate for
the proportionate amount of uranium or thorium undergoing
change per year. Hence in one gram of these elements. less —
than a milligram would change in a million years. In the
case of radium, however, the same amount must be changing
per gram per year. The “life” of the radium cannot be
in consequence more than a few thousand years on this
minimum estimate, based on the assumption that each particle
produces one ray at each change. If more are produced the
life becomes correspondingly longer, but as a maximum the
estimate can nardly be increased more than 50 times. So
that it appears certain that the radium present in a mineral
has not been in existence as long as the mineral itself, but is
being continually produced by radioactive change.

Lastly, the number of “rays” produced per second from
1 gram of a radio-element may be estimated. Since the
energy of each “ray” =10-° ergs =2°4 10- oram-calories,
6 10! rays are projected every year from 1 gram of uranium.
This is approximately 2000 per second. The @& radiation of
1 milligram of uranium in one second is probably within
the range of detection by the electrical method. The methods
of experiment are therefore almost equal to the investigation
of a single atom disintegrating, whereas not less than 104
atoms of uranium could be detected by the balance.

It has been poimted out that these estimates are concerned
with the energy of radiation, and not with the total energy
of radioactive change. The latter, in turn, can only be a
portion of the internal energy of the atom, for the internal
energy of the resulting products remains unknown. All
these considerations point to the conclusion that the
energy latent in the atom must be enormous compared
with that rendered free in ordinary chemical change.
Now the radio-elements differ in no way from the other
elements in their chemical and physical behaviour. On the
one hand they resemble chemically their inactive prototypes
in the periodic system very closely, and on the other they
possess no common chemical characteristic which could be
associated with their radioactivity. Hence there is no reason
to assume that this enormous store of energy is possessed by
the radio-elements alone. It seems probable that atomic
energy in general is of a similar, high order of magnitude,
although the absence of change prevents its existence being
manifested. “The existence of this energy accounts for the
stability of the chemical elements as well as for the con-

Removal of Voltate Potential- Difference.' oU1

servation of radtoactivity under the influence of the most
varied conditions. Jt must be taken into account in cosmical
physics, The maintenance of solar energy, for example, no
longer presents any fundamental difficulty if the internal
energy of the component elements is considered to be avail-
able, ¢.e. if processes of sub-atomic change are going on.
It is interesting to note that Sir Norman Lockyer has inter-
preted the results of his spectroscopic researches on the latter
view (Inorganic Evolution, 1900) although he regards the
temperature as the cause rather than the effect of the process.

McGill University, Montreal.

LXI. Removal of the Voltaic Potential- Difference by Heating
m Oil. By J. Brown, £28."

ik 1879, at an early stage of my investigations on voltaic

action T, it was suggested that the difference of potential
observed near the surfaces of dissimilar bodies in contact is
due to chemical action of films condensed on their surfaces
from the atmosphere or gas surrounding such bodies.

It was pointed out { that such a condition of things is
quite analogous to that of an ordinary voltaic cell divided
by a “Uae or ronan le electrolyte, e. g., copper
electrolyte | a1 the copper and zinc being
in contact and the Biiscence of potential being taken between
the two air | electrolyte surfaces. The film is therefore
probably of an electrolytic nature, thus falling in with
Faraday’s view$ that “in considering this oxidation, or
other direct action upon the METAL itself as the cause and
source of the electric current, it is of the utmost importance
to observe that the oxygen or other body must be in a
peculiar condition, namely in the state of combination and not
only so, but limited still further to such a state of combination
and in such proportions as will constitute an electrolyte.”
In 1886 I explained || the important difference between my
view and that of De La Rive, which latter included the
formation of non-conducting oxide films on the meta!
surfaces as necessary to maintain the electrification. |
showed 4 experimentally that if the surfaces of the zine and
copper plates, arranged as in Volta’s condenser, be nearly
true planes and be brought sufficiently close together to
allow their films to come in contact, but not the metals

* Communicated by the Author.

+ Phil. Mag. vii. p. 111 (1879). { Lded. p. 110.
§ Experimental Researches, 1. p. 278 ;

|| Proc. Roy. Sec, Let. p.. 295 (18 56 6). q Ibid. p. 307,

j92 Mr. J. Brown on Removal of the Voltate

themselves, a voltaic cell is produced of which the films are
the electrolyte.

In 1888 [ tried the effect of freezing the films on a Volta
condenser by subjecting it to a temper ature of —21° C. as
obtained by a mixture of ice and common salt, with indefinite
results, owing perhaps to unsuitable apparatus.

In 1900 Majorana if peewee experiments showing that
on cooling a zinc | gold couple to the temperature of ‘liquid
nir, the volta effect was reduced from ‘88 volt to 05 volt,
and rose again on the return to ordinary temperature to

75 volt. With couples of other metals similar results were
pbtained: This effect, in my opinion, corresponds with the
cessation of chemical activity at the temperature employed.

To get rid of chemical action at the surfaces of the metals
by the removal of the chemica lly acting substance, many
attempts have been made, chiefly by inclosing the couple in
a vessel exhausted to ahigh degree or surrounding it with
‘pure’? inert gases, but without success. Heating the
metals has also been frequently tried, but the oxidation or
other alteration of their surfaces at higher temperatures
intervenes, precluding any true estimation of the effect
sought to be investigated.

In order to avoid this source of error in the experiments
now to be described, 1 immersed the couple in a bath of oil
of high boiling-point.

The diagram represents in section a zinc-copper Volta
condenser with plates C, Z 11-4 centimetres in diameter,
screwed on the ends of iron rods A and B of which the lower
is fixed and the upper slides in an insulated guide-tube.
Means are provided for setting the plates parallel and at a
minute distance apart. D repr resents an enamelled iron dish,
a hole in the bottom of which provides for its being fixed
between the zine and the collar z on rod B so as to hold the
oil.

Heavy petroleum known as Price’s gas-engine oil was
used. Owing to its viscosity the plates (having nearly true
surfaces) could be only slowly separated, although ‘radial
grooves were cut in the zine to permit the more easy pene-
tration of the oil between the plates when these were being
pulled apart.

The following is the order of experiment :—The plates,
having been well cleaned with fine glass-paper, were set close
together and connected one to each pair of quadrants of the
electrometer. After momentarily connecting them together
by a wire and then separating them in the usual w ay, 1D air,

* Accad. Lincei Atti, Aug, 19th, Sept. 2nd and 16th (1900).

Potential-Difference by Heating in Ou. D9d

a deflexion of 140 was observed. Oil sufficient to cover both
plates was then poured into the bath ; and, on again con-
necting and separating the plates several times, the deflexion

averaged 110 divisions in the same direction as before. The
oil bath was then heated to about 145° C., after which the
connexion and separation gave no deflexion. The whole was
then allowed to cool and again tested, with the same result.
The “volta effect” had disappeared. Its disappearance is
apparently due to some effect of the heating since the mere
immersion in the oil did not cause it, and its absence is not
due to temperature merely, since this absence continued after
the oil had cooled.

I take it that the volta effect ceased as soon as the condensed
films were evaporated. If the disappearance of the volta
etfect had taken place immediately on immersion in the cold
oil, it might have been considered to be caused by some
conduction through the oil causing equalization of the
potentials observed on air, as happens when plates in air are
connected by a drop of water. There is, in fact, some such
conduction of a very minute kind, the oil acting as an clectro-
lyte and causing the combination to behave as a voltaic cell

594. Removal of Voltaic Potential-Liference.

of exceedingly high resistance with an electromotive force of
about *7 volt at first, falling after heating to about one-sixth
of that amount. It may thus be noted that this electromotive
force is greatest at the time when its existence is seen to have
little effect on the pcint in question. In order, however, to
finally obviate any conduction effect of this kind, the oil was
removed and the plates ¢ carefully wiped with cotton-wool till
nothing but a mere film of oi! remained on their surfaces.

In the first experiment (No. 1) the volta effect was still
absent when this had been done, but after one and a half hours,
on testing again, [ found it heal returned and deflexions of
about 30 were obtained in the same direction as in air. I
concluded that moisture from the atmosphere had found
opportunity to reach the zine surface in some quantity. In
a repetition (No. 2) of the whole experiment the same etfects
were observed up till the removal of the oil, after which
in this case, the return of the volta effect did not take place
in four days, or if at all present, it was very slightly reversed.
In this experiment the oil had been kept at a ‘high tem-
perature for several hours and probably formed a more
permanent protective film on the metallic surfaces. In a
further experiment (No. 3) in which the high temperature
Was maintained only for a short period as in No. 1, the results
again corroborated No. 1 only that the volta effect t appeared
still more quickly. In nine days after removal of the oil
(except such oil films as adhered to the plates) it had
regained almost its pristine value, the average deflexion
being then about 130.

‘At the conclusion of each of the three experiments, the
vine plate, on examination, appeared almost unaltered in
appearance—only very slightly tarnished. On the copper
there appeared to be a very thin transparent varnish-like
film. On re-cleaning the plates with glass-paper the usual
volta effect on air was observed.

To sum up, I conclude that all the effects observed fall in
satisfactorily with the condensed electrolyte-film theory as
described above. On first immersion in cold oil the films
continued to act in their usual way, as if in air, though with
a somewhat less deflexion, probably owing to a minute con-
ductivity in the oil Some reducing the difference of
potential during the slow separation of the plates after
metallic contact. When heated to above the boiling-point of
water, the films evaporated and lett nothing to effectively act
electrolytice illy on the plates. After removal of the oil
(unless a protective varnish-like film had been formed) the
moisture of the air again found access to the surface and a
difference of potential » was again observed.

——. = te

P95) *|

LXII. Notices respecting New Books.

Electrical Problems for Engineering Students. By Wiit1aM L.
Hooper, Ph.D., and Roy T. Wutis, M.S. Boston, U.S.A., and
London: Ginn & Company, 1902. Pp. vi+170.

Eas book of problems should prove very useful to teachers of

electrical engineering. Starting with simple problems on the
calculation of resistance, the authors go on to the consideration of
the magnetic circuit, dynamos, alternating currents and alternators,
induction motors, and power-transmission. Each chapter of pro-
blems is prefaced by suitable notes. In the cases which we have
~ tested, the answers are all correct. In some of the chapters, there
is a somewhat wearisome sameness about the examples. We can
confidently recommend the book as a yery suitable and useful one
for a class of engineering students.

LXIIL. intelligence and Miscellaneous Articles.
ON THE HEAT EVOLVED WHEN A LIQUID IS BROUGHT IN CON-~

TACT WITH A FINELY-DIVIDED SOLID. BY TITO MARTINI.

NEW study upon the heat evolved when a liquid is brought into
contact with a finely-divided solid recently appeared in thus
Magazine*. Mr. Parks displayed some new calorimetric results
vbtained by the moistening of silica and sand, which he explains
by supposing that the heat evolved is due to the area of surface
that is brought imto contact with the liquid, and that the heat
increases as the suriace moistened is enlarged.

In my own experiments regarding the Poulet effect, which the
author has clearly recapitulated in his paper, before deciding to
advance an explanatory hypothesis, I thought of the possibility of
the calorific phenomena being due to the surface area in contact
with the liquid; but I observed that an excessively fine powder of .
quartz produced a result very different from precipitated silica. In
fact, while the first only produced very weak thermal effeets, the
second manifested a considerable rise in temperature, whether in
contact with water or with other liquids (alcohol, ether, benzine,
&e.). Ithen thought of measuring the quantity of liquid absorbed
by the two powders, with the result that precipitated silica absorbed
a much larger quantity of liquid than that absorbed by the
powdered quartz.

In consequence of these results, it oceurred to me to use another
substance that like silica was capable of being finely divided,
and make comparisons with this new precipitate and the same
substance reduced to powder.

To this end, I used finely-powdered crystallized carbonate of
calcium and a precipitate of the same substance. Using the
method which I have already described in this Magazinet, L found
that the crystallized carbonate of calcium, moistened with acetic
ether, produced a rise of temperature of O0°26C., absorbing

*~ Phil. Mag. August 1902, p. 240.
y Phil. Mag, March 1899, p. 829, and December 1900, p. G18,

596 Intelligence and Miscellaneous Articles.

0-264 ¢.c. of liquid per gramme of powder. The moistening of the
precipitate of carbonate of calcium with the same liquid caused
a rise in temperature of 0°58 C., the powder absorbing 1:563 e.c.
of acetic ether per gramme of powder. The precipitated silica,
moistened with the same liquid, rose in temperature 31°40 C.,
absorbing 1°67 c.c. per gramme. Experimenting with benzine, I
found that the precipitate of carbonate of calcium absorbed 1°61 c.c.
per gramme of powder, rising in temperature 0°'22 C., while the
precipitated silica rose in temperature 11°21 C., absorbing 1°52 ¢.c.
per gramme. These facts would seem to prove that increase in
the area of surface brought in contact with the liquid is not a
cause sufficient to explain the marked rise in temperature resulting
from the moistening of precipitated silica, animal and vegetable
charcoal, and in the case of all those substances which I have
denominated as hygrophiles ; wishing by this appellation to indicate
the property that certain powders have of holding tenaciously a
portion of the liquid they absorb.

The union of the liquid with hygrophile substances might be,
to my mind, a physico-chemical phenomenon analogous to those
cited by van Bemmelen in his researches upon hydrates of unstable
composition, that are formed by exposing silica to more or less
humid air*, |

My own recent researches in reference to the phenomena, of
hygrophile powders placed in contact with alcoholic mixtures and
diluted acids+ seem to confirm my hypothesis. A non-hygrophile
powder, for instance, like quartz or powdered marble, well dried
and then placed in contact with an alcoholic mixture (three parts
alcohol and oue part water), will not alter in any sensible degree
the alcoholicity of the mixture; while with silica or animal charcoal,
well dried, a part of the water is subtracted from the mixture: and
silica, well dried, is capable of subtracting water trom a diluted
solution of sulphuric acid. From this it can be deduced that the
behaviour of hygrophile powders produces results that are due to
a more energetic action than a simple mechanical one, which would
be sufficient to explain the phenomena manifested in the case of
non-hygrophile powders that are moistened with liquids without,
however, tenaciously holding any portion of them. For this
reason, I hold that the heat evolved from hygrophile powders may
be produced from a decrease in the specific heat of that part of the
liquid tenaciously held by the powders; because this part of the liquid
will have lost its quality as a fluid, and assumed a state of solidity
or quasi solidity ; for this reason I compare the Pouillvt effect, in
the case of hygrophile powders, to a species of inverted solution.

T may add that if the values found by Parks are inferior to my
own and those found by Bellati, this difference is due to a
change taking place in the silica at a high temperature, as has been
noted by Bellatit in reference to the experiments of Linebarger.

Venezia, February 1903.

* Archives Néerlundaises de Sciences exvactes et naturelles, t. xv. p. 821.
Harlem, 1880.

t Attedel R. Istituto Veneto, t. 1xi. parte seconda, p. 647, giugno 1902.

{ Atte del R. Istituto Veneto, t. 1xi. parte seconda, p. 510.

ER ee ce ne a a

Phil. Mag. Ser. 6, Vol. 5, Pl. XII.

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THE

LONDON, EDINBURGH, ann DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[SIXTH SERIES.}

JUCNeE, NIOS:

LXIV. The Kinetic Theory of Gases developed from a New
Standpoint. By J. H. JEANS, M.A., Isaac Newton Student
and Fellow of Trinity College, Cambr idge”.

Introduction.

Sally ae aim of the present paper is to develop the Kinetic
Theory as far as possible from a purely mathe-

matical standpoint, namely that of abstract dynamics, and in

this way to remove certain inconsistencies from the theory.

In the orthodox treatment of the subject a gas is regarded
as a collection of similar dynamical systems: these systems
interact on one another, and the difficulties of the theory centre
largely round the question of determining the occurrence of
these interactions. The method of the present paper is to
regard the whole gas as a single dynamical system. Tollow-
ing this plan we are able to escape all the weli-known
difficulties—the assumption of a molekular-ungeordnet state,
the restriction to infinitely small molecules, &:.—and may be
able ultimately to arrive at a theory which applies to solids
and liquids as well as to gases.

§ 2. The basis upon which the orthodox treatment of the
subject rests can be shown to be neither & prior logical, nor
a posterior justified by success.

The problem of the Kinetic Theory is, virtually, to follow
the motion of a dynamical system starting from an unknown

* Communicated by the Author.

Phil. Mag. 8. 6. Vol. 5. No. 30. June 1903. 28

598 Mr. J. H. Jeans on the

configuration. To overcome the difficulty of the initial con-
figuration being unknown we are compelled to regard the
whole question as one of probability. Not knowing the
positions of individual molecules of the gas, we have to argue :
“The probability that there isa molecule of a certain kind
within a certain region has such or such a value.” The calcula-
tion of this value, in the orthodox treatment of the subject, rests
upon the “ molekular-ungeordnet ” assumption of Boltzmann.

The assumption which Boltzmann announces that he is
making is that the gas is, and always remains, in a molekular-
ungeordnet state. It does not appear that any strict definition
of a molekular-ungeordnet state has ever been attempted.
Certainly Boltzmann does not give a definition. Two ex-
amples of a geordnet state are given in the Vorlesungen*,
and these are of such a special nature that the reader feels
convinced that it is legitimate to disregard the geordnet state
altogether. The form in which Boltzmann uses the assump-
tion is somewhat different. This has been pointed out by
Burbury, who has clearly stated the assumption in its working
form, under the designation of “Assumption A ’’ +t.

The effect of this assumption is to enable us to regard
certain probabilities at any given instant as independent, and
we then assume not only that the probabilities at a later
instant are inter se independent, but also that they are
independent of the events which took place at any earlier
instant. This assumption cannot be logically reconciled with
the fact that the motion of the system is continuous in time,
?.€., that the events which occur at any instant depend on
those which occurred at a previous instant.

§ 3. The fundamental assumption, then, cannot be justified
a prior by its consistency. To show that it is not justified
a posteriort by its success, it will be necessary to examine
some of the consequences of the assumption.

The assumption being granted, it is proved that a certain
function H must continually decrease as the time progresses.
From this follows the well-known objection of the reversal
of velocitiest. Let A be a system such that the value of
H is Hy, and in the course of a small interval of time let it
change to a system B, for which H has the smaller value H,.
Then, if we reverse all the velocities in system B, we get a
second system in which the value of H is still H,;. The
motion of this system must of necessity be through the
various configurations which were passed during the change

* Vol. i. p. 20.
+ ‘ Konetic Theory of Gases,’ p. 9.
{ Boltzmann, Vorlesungen, 1. p. 42.

Kinetic Theory of Gases. 599

from A to B, and so we arrive at a system which is identical
with A except that all the velocities are reversed. Tor this
system the value of H is Ho, and this is greater than H,. How
is this to be reconciled with the theorem that H must always
decrease ?

Now this theorem of H decreasing must have been im-
plicitly contained in the equations of motion and the
fundamental assumption. ‘The H-theorem points to an
irreversible process. This irreversibility cannot have been
contained in the equations of motion, for these are essentially
reversible in time; it must therefore have been introduced
in the molekular-ungeordnet assumption. The view of the
present paper, as will appear later, is that the molekular-
ungeordnet assumption is not a true assumption at all, but
amounts to a licence to misuse the calculus of probabilities.
The orthodox view is that the decrease in H is a consequence
of supposing the gas to be in a molekular-ungeordnet state,
and hence that a gas for which H increases must be geordnet.
By the time this result is reached there seems to be less
justification than before for supposing the typical gas to be
ungeordnet : it will be seen that to every wngeordnet state
there corresponds a geordnet state, so that only one-half at
most of all possible arrangements will be ungeordnet. Also
of the two corresponding states there does not seem to be
any reason why one should be labelled wngeordnet rather than
the other : in other words it would seem to be just as likely
that our results when applied to a real gas should be false as
that they should be true. For this reason the assumption
of a molekular-ungeordnet state does not seem to be justified
hy success.

The present paper contains an outline of a kinetic theory
based upon entirely different foundations. This new theory
is free from all assumptions, and the arguments are mathe-
matical instead of physical, so that if the reasoning is sound,
inconsistencies cannot occur.

The proposed new Basis.

§ 4. A simple illustration will best explain the course of
procedure which is to be followed.

Suppose that we are concerned with a series of throws with
a die, this die being of the usual type, so that in each throw
the chances of each number from one to six being thrown
are exactly equal. Suppose that our problem is to find the
average value of the throw in an unknown series of throws.

If we consider a series of 10 throws, it can be shown that
the ‘‘ expectation ” of the average throw {in other words, the

2 2

600 Mr. J. H. Jeans on the

ae throw averaged over all possibie series of 10 throws)
is 34, but the “ expectation ” of the difference between this
and the average for any single series (in other words, the
probable error) is (about) 0°6. I£ we consider a series of
1000 throws the expectation of the average throw remains
the same, but the probable error is only (about) 0°06. If we
pass to the limit, and consider a series consisting of an
infinite number of throws, the expectation of the average
throw remains 34, but the probable error becomes zi.

$05. This suggests the definite pr oposition: ‘* The average
value of a throw in an infinite series of throws is 34.” This
proposition does not stand on the same level of absolute truth
as the proposition “2x 2=4,” but its truth is sufficient for
all practical purposes, and, moreover, it represents the highest
level of truth which is attainable in the absence of a definite
knowledge of the values of individual throws. The pro-
position (understood in its proper sense) is not refuted by
pointing out that a series such as

1 ol ad 2njy. (Geries Ay)
is a possible series, and that the average value in this series is
not 34 but unity. The reply to this criticism is that the
probability is infinitely against a series of random throws
being of the form of series A, or of any other form for
which the proposition is not true ; fora series of random
throws it is infinitely more probable that the proposition will
be true than that it will be untrue. We may conveniently
indicate that a proposition is of this type, by prefixing the
words ** It is infinitely probable that . . .”

§ 6. The propositions of the kinetic ‘theory, founded upon
the basis which is now proposed, will be of this type; they
will state infinite probabilities, and not certainties. The
uncertainty as to the positions and velocities of the individual
molecules of the gas will correspond to the uncertainty as to
the actual values of the throws in the illustrative problem of
the dice: the theoretical uncertainty in the final result will
replace the uncertainty which enters, in the usual treatment,
at the outset by assuming the gas ‘to be ungeordnet. The
assumption of an ungeordnet state, as enunciated by Boltz-
mann”, was obviously intended to exclude special cases
analogous to the special case of series A. That it does not
have this result in the form in which it is used will appear
later. But with our present understanding it is quite un-
necessary to make any assumption or limitation of this kind,
just as in our question of the dice, it was quite unnecessary

* Vorlesungen, 1. p. 20.

Kinetic Theory of Gases. 601
to begin by postulating that there should be no “ regularity ”

in the throw of the dice. A limitation of this kind could not,
in any case, add anything to the certainty of the ultimate
result. Ii may he noticed that the difficulty of giving a

precise definition of a molekulur-geordnet state of a gas ls
exactly paralleled by the difficulty which would be experienced

in attempting to define “ regularity ” in the case of the dice.

Outline of the New Theory.

§ 7. Let us now suppose that we are dealing with a great
number N of molecules inclosed in a vessel of volume QO. We
shall consider the simplest case first, and shall accordingly
suppose the molecules to be incompressible elastic spheres of
the usual type. Each molecule possesses three degrees of
freedom, those of molecule A being represented by &., Yu, Za,
the coordinates of its centre. The corresponding velocity
coordinates will be denoted by wa, va, wa. The whole gas,
regarded as a single dynamical system, will possess 3N degrees

of fr eedom, and its state will be specified by the 6N coordinates

a) Vay Was Vas Yas Kas Udy VU15 Wy, eoeee e ° ° (1)

Let us imagine a generalized space of 6N dimensions. In
this space, the system of which the coordinates are given by
(1) can be completely and uniquely represented by a single
point, namely the point of which the Cartesian coordinates
referred to 6N definite rectangular axes are given by (1).
If our gas is to be entirely inside a certain containing vessel,
we shall only need a certain portion of this space, say that

bounded by

| Se Veayi== Oh) Of Opole gen Osneb vi:
Uz= +R; Uy, = QO; Sei AA FA
| Vz= tH; Va= te Shae sy) te (2)

Tf the molecules are incompressible spheres of radius R, we
shall not need to consider the possibility of a system in which
the centres of any two molecules are within a distance smaller
than 2R. We may therefore exclude from consideration all
those portions of our generalized space which are bounded by

(@a— 4%)” + Ya Yo)’ + Ea %)=4R*, - (8)
and other seri equations, one for every possible pair of
molecules. The simplest case of all is that in which R=0;
and in this case this last limitation may be disregarded.

Taking R=0 is the same thing as supposing the diameter to
Vv nish 3 in comparison with the: mean free path.

602 Mr. J. H. Jeans on the

Any point in the space which remains will represent a
single possible configuration of the molecules of the gas.
This configuration will, in the course of the natural motion of
the gas, give place to other configurations, and these will be
represented by new points in the generalized space. The
natural motion of the gas may accordingly be represented by
the motion of a representative point in the generalized space.
Any single point will describe a “path” or “ trajectory ”
this space, and in this way the whole of the generalized space
may be mapped out into trajectories. Since the motion of
the gas is completely determined when all the coordinates (1)
are given, it follows that through any point there is one and
only one trajectory: two trajectories can never intersect.
Since the motion of the gas is dynamically reversible, it can
be seen that there will be a symmetry in the arrangement of
these trajectories. Each trajectory will have an ‘image ”
which can be obtained from it by changing the signs of the
velocity-coordinates u,v, w. So also each point has an image
obtained in a similar way. If P is any point and P’its image,
P! represents the system which is obtained by reversing the
motion of the system represented by P*.

§ 8. We are now going to start an infinite number of our
dynamical systems, so as to have systems starting from every
conceivable configuration, and try what we can discover
about their subsequent motion. Or, what comes to the same
thing, we are going to imagine the generalized space filled
with a continuous fluid, allow this fluid to move along stream-
lines which coincide with the trajectories already found, and
examine the motion of this fluid.

It is obvious that the initial distribution of density in this
fluid may be chosen in a perfectly arbitrary way: all that is
necessary 1s that every point of the generalized space shall
be occupied.

We shall find it convenient to choose that the initial distri-
bution of fluid shall be homogeneous. The special advantage

* Tf we revert to the orthodox standpoint for a moment we see that of
all the systems represented in our generalized space, some will he
ungeordnet and some not. We can imagine our generalized space
divided into wegeordnet and geordnet regions and points. If P is an
ungeordnet point, its image P’ will, according to Boltzmann ( Vorlesungen,
i. p. 43) be geordnet, although the converse is not necessarily true. Thus
fully half of our generalized space must be geordnet. The conveutional
treatment of the kinetic theory compels us to asswme, that if a trajectory
starts from an ungeordnet point, it must pass only through wngeordnet
points throughout its whole length. In view of the fact that less than
half of the space is wnyeordnet, this assumption would seem to be anything
but axiomatic.

Kinetic Theory of Gases. 603

of this choice is that the fluid remains homogeneous thr oughout
the motion. This follows at once from Liouville’s theorem *.
Not only does the density at every point of the fluid remain
constant, but the velocity at this point, being determined
solely by the coordinates of the point, will also remain
constant. We have therefore to discuss a case of hydro-
dynamical ‘steady motion.” ‘There is no flow at infinity
across the boundary of the generalized space. For at infinity
one or more of the velocity-coordinates must be infinite, so
that E the total energy must be infinite; whereas throughout
the motion of a point of the fluid E must remain constant.

Comparison with Orthodox Theory.

§ 9. Let us examine the relation between the procedure

now suggested and the usual procedure which rests upon,
the calculus of probabilities. It may, in the first place,
be remarked that a problem of probability has only a
definite meaning when a certain amount of knowledge is
given and a certain amount withheld. For instance, sup-
pose we have an urn containing a number of masses of
different weights. Ifthe weights are known, a question such
as ‘‘ What is the probability that a weight selected at random
shall weigh less than an ounce ?”’ has a definite meaning and
a definite answer: if the weights are not given, the question
is meaningless and has no answer. So also in the Kinetic
Theory, it is meaningless to talk about the “ probability ”
a system being in a specified state: the phrase only acquires
a meaning when it is understood that the system is selected
at random from a given definite series of systems in different
specified states. We shall take this given series of systems
to be the series represented by a homogeneous fluid filling
our generalized space. On this basis questions of pr obability
will have a definite answer. If we had selected a different
series of systems—represented, let us say, by a definite
heterogeneous fluid—the answer would be different: if we
neglect to specify our series of systems the problem is
meaningless, and there is no answer at all.

§ 10. Consider, for instance, the question suggested
in §2. “What is the probability, at a single definite
instant, that in the element of volume of which the coor-
dinates lie between x and #w+dxz &c., there shall be found
the centre of a molecule of which the velocities shall lie
between u and ut+du Ke. ?”

* “On the Conditions necessary for Equipartition of Energy,” Phil.

Mag. [6], iv. p. 585, equation (7); or J. W. Gibbs, ‘Elementary Prin-
ciples of Statistical Mechanics,’ Ch. I.

004 Mr. J. H. Jeans on the

With our present conventional basis of probability, we have
only to ask “ For what proportion of the systems represented
in our generalized space is the condition ‘satisfied that there
shail be a molecule such that x lies between wx and
atdz...&c., u lies between wu and w+du &c.?” Now for
a certain number of systems this condition will be satistied
by molecule A. These systems will be those for which
Yq lies between x# and x+dz; and similar conditions are
satisfied by ya, Za) Uas Vay Wa These systems together form an
element ot the generalized space

dx dy dz dudv dw\\\. ..dx,d2,... di; dy, 7

the integration being with respect to all the 6N variables
except La Ya 2a Ua Va Wa, and extending over all values except
such as are excluded by equation (3). Those systems for
which the conditions are satisfied by molecule B form an
equal and similar element, and so also for every other of the
N molecules. The probability which we require is the ratio
of the sum of these N elements to the whole volume of the
generalized space, and is therefore

N da dy dz du dv dw -, \\). » day dae... , eis
ie SOR OE ee Nee

§ 11. This is the probability when nothing at all is known
about the gas. Let us now sappose that the velocities of the
individual molecules are known, and calculate the probability
in this case. An element such as (4) will not now be con-
tributed by every molecule: there will be an element contri-
buted by each molecule of which the velocities le within the
assigned limits, and the number of these may he taken to be
N7(u, v, w)dudvdw. The element of volume is not given
by expression (4), but by

ane

dx dy dz\\\...da,dax,...dysdy,, . + . (6)

the velocity-coordinates not entering into the integration
at all. We now find instead of expression (5) a probability

N f(u, v, w) dx dy dz du dv dw auth Lda da:
\\\ eck dz, dx, dz.

§ 12. In the special case of a gas in which the radii of the
molecules are very small, the regions which are excluded by

Kinetic Theory of Gases. 605

equations (3) may be neglected, and we may write

awe

Mj ey OUr da, du, CC = {i dx, ayo C—O ae
\\\ ... dz de....= IL \\\ dx, dytdz =QO%;
\\\... da, dx, dev, al dz, dy” dz,

for we now have \\\ dz, dy,d%,.=Q, the volume of the con-
taining vessel. Hxpression (7) now becomes

atte, v, w)daudydzdudvudw. . . . . (8)

The first factor is the mean density of molecules in the
containing vessel, and the connexion between this result and
that usually obtained for a gas, whether homogeneous or not,
will be obvious.

§ 13. Let us now revert to the general result of § 11. We
found in expression (7) the probability that there should be a
molecule (which we may now agree to call A) of which the
coordinates should lie between # and x+dz, &c. Let us now
find the probability that, in addition to this, there shall be a
second molecule having ‘its six coordinates lying between 2’
and w'+dzx’, Xe. The probability that in addition to the
original condition satisfied by A, this second condition shall
be satisfied by B, can be deduced from expression (7) by
limiting the integration in the numerator to values of x lying
between z' and #’+dzx’, values of y lying between y’ and
y + dy’, and so on for zy, w, vs, wo. The probability of which
we are in search will be N/(w’, v’, w’) du’ dv’ dw’ times this
corrected probability; for this is the number of molecules
which can take the part of molecule B. The probability in
question is therefore found to be

N?f (u,v, w) f (wu, v’, w’) dx dy dz du dv dw dx’ dy’ dz’ du! dv! dw’
; \\\. CCE Cero oe ; (9)
ie .. dx, dt, dx, dita...

§ 14. In the special case in which R=O this reduces, by
the method of § 12, to

(5) fw v, w)f(u', v’, w’) dx dy dz du dv dw du'dy’ dz du’ dv! dw’.

§ 15. The probability given by expression (10) is exactly
that which would be found ina homogeneous gas, with the
help of the ‘ molekular-ungeordnet ”’ assumption. The whole
supposed point of this assumption is, however, to exclude a

(10)

606 Mr. J. H. Jeans on the

certain class of systems, whereas it has just been seen that
the result arrived at is only true upon the understanding pe
all conceivable systems—geordnet as well as ungeordne
included. It would therefore appear that the effect of aa
assumption is simply to defeat its own ends: it is brought in
ostensibly to make a certain calculation of probability
legitimate; whereas in point of fact the calculation is illegi-
timate (or at any rate cannot be shown to be legitimate). if
we adhere to the limitations of the “ ungeordnet ” assumption,
and becomes legitimate as soon as these limitations are
ignored.

The calculations which have just been given | must, In a
logically perfect kinetic theory, replace the “ molekular-
ungeordnet” assumption as the justification for treating the
possibilities of two molecules having given coordinates as
independent events. The fact that the motion of the fluid in
our generalized space is steady motion must supply the
further justification for supposing these probabilities to
remain independent throughout all time. This latter result,
it will be noticed, rests on Liouville’s theorem, and this in
turn rests upon the conservation of energy. There is no
justification for supposing probabilities to remain independent
when the gas is nota conservative system. It must be neticed
that all our results are true only with reference to our arbi-
trarily chosen basis of pr obability.

§ 16. We have seen that the “ungeordnet” assumption
leads to accurate results as regards frequency of collisions;
and hence we infer that all results which depend upon this
result and upon the dynamics of collisions will be accurate.
The results must, however, be interpreted in a special way.
Take, for instance, the H-theorem which deals with a special
law of distribution, say f. The theorem must not be taken
to prove that dH/dt is negative for all possible systems
corresponding to the given f, but that the expectation of the
value of dH/d¢ for a system selected at random from all
systems having this 7 is negatiy e, in other words that the value
of di /dt averaged over all systems having this given 7 is
negative. There is no justification for confining the theorem
to ‘‘ ungeordnet ” systems, and none for stating the preposition
to be true of individual systems: it is, so to speak, only true
on the average.

§ 17. Weare here confronted with a paradox. For each
system for which dH/dé is negative, there will be a second
system—the image of the former (§ 7)—for which dH/d¢
will have an equal but positive value. These two systems
must of course be equally included in the average, and since

Kinetic Theory of Gases. 607

the whole number of systems which are included in the
average consist of pairs of this kind, it is clear that on the
average dH/dt is zero. We are, in fact, integrating dH/d¢
through the region of our generalized space which is given
by a specified fi ; this region can be divided into two regions
such that one is the image of the other, and the values
of dH/d¢t in the two regions are equal in magnitude but
opposite in sign. The explanation of the apparent paradox
will be found in a later section (§ 32).

The Partition of the Generalized Space.

§ 18. We now discuss a number of questions concerning
the distribution of systems of various specified kinds in our
generalized space.

§ 19. The first problem which we shall discuss is concerned
with the distribution of density of gas inside the containing
vessel.

Let us consider a class of system which we shall call
class A. To define it, we imagine the vessel which contains
the gas divided into a great number n of “cells,” each of
equal volume o, so that nw =. These cells are to be denoted
by the numbers 1, 2, 3,.... Then a system of class A is
defined as one such that a; molecules have their centres
in cell 1, a, in cell 2, and in general a, in cell s, so that of

s=1
course >a,=N.
s=1

Denoting individual molecules, as before, by A, B, C.
we see that there will be a certain number of systems repre =
sented in our generalized space, such that the molecule A lies
in one specified cell, the molecule B in another, and so on
for all. It will be easily seen that all systems of this kind
vccupy a small continuous element, which we may call the
element c, and which, since there e are N molecules altogether,
forms a fraction (co/Q)® or n—N of the whole. This, if must
be noticed, is true whether we consider all systems, or only
systems in which the molecules have assigned velocities.
Obviously also it is true, if we consider systems in which the
kinetic energy has a certain assigned value.

Now if the molecules are distributed in the various cells in
such a way that there are a, in cell 1, a, in cell 2, and so on,
then all the systems represented by points inside the element
c belong to class A. There will bea number of other elements
containing only systems of class A; and these will correspond
one to each wav in which the N molecules can be distributed
into the » cells so that there shall be a, in the first, a in the

608 Mr. J. H. Jeans on the

second, and so on. The number of ways ion which this can
be done is
\N

lay |e |@3-- - |[&n

(Se

The systems of class A are therefore comprised in this
number of elements, each element being of the same size as
element c. Hence we see that the systems of class A form
a fraction 0, of the whole number of systems, where

This again is true whether we consider all possible systems
or only those systems having a given energy.

§ 20. We can evaluate @, when N is large compared with n,
and there are (in the limit) a very great number of molecules
in each of the n cells. We have, when a, is very great, the

approximate formula used by Boltzmann*

Ge ds
a= / 27a ie )

or taking the logarithm of each side
log jas =} (log 27+ 1)+(4,+$)(log a,—1);

and when a, is very great this assumes the limiting form

log |a,=a, log a,,

an equation in which the difference between the two sides is
infinite, but is vanishingly small in comparison with either
side. Hence from equation (12),

log 6, =log N—N log n—% log |as
=N (log N—log n)—Za_log a,.
Now N=*a,, and we may write N/n=ap, where a is the

mean number of molecules in each cell. Making these substi-
tutions, our equation becomes

log 0 = Xa, log a)— Za, log a,= — La, log (4).

The right-hand member of this equation is, in general, an

* Vorlesungen, i. p. 41.

Kinetic Theory of Gases. 609

infinite quantity of the order of N, and is for this reason diffi-
cult to manipulate. We accordingly introduce a new quantity

K_, defined by

Gyo ee \e
oes Nos (3) RR Siena sey

0
so that K is, in general, finite ; and we have

6, =e—Nka, sn, 4 ey LS)

§ 21. But now the different classes of systems may be
represented in a new generalized space—the subsidiary space,
as we may callit. This space is to have n—1 dimensions,
corresponding to n variables €, &... & subject to SE=N
A system of class A is represented by the point

Gi ign Says ah pee a ays ais)

which we shall call the point A.

The various classes may therefore be represented by the
intersections of n systems of paraliel lines drawn at unit
distance apart. Further, we can represent the different
systems which occurred in our original generalized space in
the subsidiary space, by placing an imaginary mass 0, at the
point A, @ at B, and so on.

We now pass to the limit and take N=«. The values of
&, &... (or what is the same thing a, a,...) will now be
infinitely great, and we accordingly take the unit of length
in our subsidiary space to be infinitely small.

We can now replace the distribution at points by a con-
tinuous volume-distribution. The distribution @, at point A
is now to be replaced by a density p spread through the
rectangular unit element of which A is the centre such that
the agoregate density in this unit element is @,. It is
obviously possible (equation 14) to take

p=
as the gener al continuous distribution, where K may be chosen
so that it is continuous, and [naeannes identical with K,z at A,
K, at B, &c. All the systems in our original space may in
this way be represented in our subsidiary space.

The number of systems of any specified type in our original
generalized space (the total being taken as unity) is there-
fore equal to the number of the same type in the subsidiary
space, and this

= = 9 = \\\---ediid&...

A, ee

o-NK

pease

610 Mr. J. H. Jeans on the
Jn particular, the number for which K (defined by equation
13) lies between K, and Ky will be

K=K,

MN) ose dB dé. ..

where the integration extends through those parts of the sub-
sidiary space for which K lies between K, and Kg.
§ 22. Now in the subsidiary space K will be found to havea

minimum value. In equation (13), let us treat i “ as a con-
a

tinuous variable, and replace it by 6. We then have

Keke 2¥a 0 g(@) = =3 4, log @,. Me cl,
Co Ns

The values of @ are limited by the condition

or what is the same thing, by
~36,=1. Jo. =e

For small variations in @, the condition that K shall be a
minimum is seen by variation of equations (17) and (18) to be

*S{14log 8,+2}88,=0, . . . . (19)

where A is an indeterminate multiplier. We must therefore
have

1+log@,.+X=0 . |. er

tor all values of s, and hence @,=constant. From equation
(18) we see that this constant value must be 6,=1. Thus
when we regard as/a, as a continuous variable the minimum
occurs when, a,=@)=...=a@,=:..=d9. . When as isqaeum
great, and only capable of integral values, the minimum
still occurs for values such that, except for infinitesimally
-mall quantities,

4 22 2 ee i
a, an ao
The minimum value of K is found to be K=O, except for
an infinitesimally small quantity: it does not, however,
follow that NK=0. The minimum value of K subject to

Kinetic Theory of Gases.' 611

dy, d, &¢c., being integral, will, however, be greater than the
unrestricted minimum for K, so that the infinitesimal value
of this former minimum will be positive.

Hence it follows that, except at one point in our subsidiary
space and points which are in its immediate neighbourhood,
e-NK js vanishingly small. The density at this point is there-
fore infinite in comparison with that elsewhere.

§ 23. There now three possibilities between which we have
to discriminate. If we draw asmall region in our subsidiary
space, inclosing the minimum value of K, the density inte-
grated throughout this small region may be either vanishingly
small or finite or infinitely great in comparison with the
integral density taken throughout the remaining space. It
will be found that the last possibility i is the true one.

To prove this, we expand K in the neighbourhood of the
minimum value K=0. We have (equation 17)
ety Ss 9
K= 2a! log ae a Betas 7)

If we put as=a,+6s, where ¢,/a, is small, we get

ae. IL ce Es
ao ly
lon. a et) ~
D pane ae tc): 2
iy Oi A OR

whence, since & ¢,=0,
s P

2. \2
7 x (<*) e e e e e e (23)
Zn s Cy

We may now suppose the small region inclosing the

minimum value of K to be bounded by K=«, where « is a
small positive quantity, and the equation ot this boundary in
rectangular coordinates will, by equation (23), be

€ a
S (4) = Unk.
s \Qo

Hence we see that (dé, d&... taken inside the region

K <x, is proportional to «”—! so long as « is small. By
differentiation, we find that the value of the integral from K
to K+dK is proportional to K™— dk so long as K is small.
Hence, except for a multiplying factor, the integral (16)
may be written in the form
PRIS
CRON RA: RMR cee
K=K,

612 Mr. J. H. Jeans on the

so long as K,, Ky, are both small. We now see that in
this case the whole value of the integral arises from the con-
tribution supplied by an infinitesimal range of values of K
near to and including the lower limit. It is obvious that the
proof can be extended so as to include all values of K whether
great or not.

§ 24. Returning to the original generalized space, the
following propositions will now be seen to be true :—

G.) All except an infinitesimally small fraction of the
whole space has a value of K which <e, where ¢ is a small
positive quantity, and this is true however small e may he.

(ii.) K is positive at every point—either finite or vanish-
ingly small—and the mean value of K averaged throughout
the whole space is vanishingly small.

Gi.) Of that part of the space for which K >K,, where
K, is some finite positive quantity, all except an infinitesimal
fraction of the whole has a value of K which < Ko+e,
where ¢ is a small positive quantity, and this is true however
small e may be.

§ 25. Let us now suppose that the edges of our cells are
so great compared with the average distance between two
molecules that we may legitimately regard the number of
molecules in each cell as infinitely great, but that at the same
time these edges are so small compared with the scale on
which the density of the gas varies, that we may regard the
density as constant over a large number of adjacent cells.
If the cells can be constructed so that these suppositions are
simultaneously possible, it will be possible to give a definition
of the density at a point in the gas which shall be logically
sound—we define the density at any point P as the number
(or mass) of molecules in the cell which contains P, divided
by the volume of this cell.

Let us denote the density at a point by p and the mean-
density of the gas by py. By hypothesis, p is appreciably
constant throughout a cell. Anintegral such as {Ve da dy dz

taken throughout a cell may accordingly be replaced by po.
The value of p/pp in the sth cell may be replaced by as/a,,
when the system is of class A (§ 19).

We now see that instead of defining K by equation (13)
we may suppose it defined by

where the summation extends throughout all the cells, and

Kinetic Theory of Gases. 613

a ; 1¢|
if we replace p by Bs ((\, dx dy dz, this becomes

BON 1 (vCard Be
=A \I(P tou(& to dy dz. SUMS Bear (25)

We have now obtained a value of K which is dependent
only on the positions of the molecules, being entirely inde-
pendent of the way in which the gas was divided up into cells.
The propositions stated in § 24 are therefore independent of
the arrangement of cells. —

§ 26. Equation (21) shows that the minimum value of K
is given when p=py everywhere ; 7. e., when the density is
constant throughout the gas. Proposition (i.) of § 24 may
therefore be taken to state that if a point be selected at
random in our generalized space, it is infinitely probable that
the corresponding system will be one for which p is constant
everywhere.

This is not difficult to understand. Selecting a point at
random in our generalized space is equivalent to placing N
molecules at random at points inside the containing vessel.
The fundamental principles of the theory of probability lead
us to expect that it will be infinitely probable that the dis-
tribution of gas will be uniform.

§ 27. We have discussed the distribution of x, y, < co-
ordinates: the distribution of uw, v, w coordinates can be
treated in the same way. Im this case, however, what is
required (for reasons which will appear later) is not a
knowledge of the partition of the whole space, but only of
that part of it for which the kinetic energy has an assigned
value E. ‘This is the part given by the equation

4m = (6, =u tok) We ie Gera (26)

Selecting a point at random from this part of our space, is
not equivalent to distributing velocities at random to the
N molecules, but is equivalent to distributing 3N velocities
(tay Vay Wa, Us, Vz, &e.) about a mean value 2H/3mN. We
shall therefore not expect the resulting distribution to be
uniform, but shall expect the velocities to be grouped about
this mean value according to the law of trial and error.

We could treat the whole question on the lines on which
the former question was treated. We should find that
instead of the old function K defined by equation (25), we
should have a function H defined by

H=|l\f log fdu GOGO. a. 4 QOPI
where 7 is a function of u,v, w such that the number of

Phil. Mag. 8. 6. Vol. 5. No. 30. June 1903. yl

614 Mr. J. H. Jeans on the

molecules of which the velocities lie between wu and u+du, &e.
is Nf(u, v, w) du dv dw. We find that H has a minimum
value for the region defined by equation (26), and we find
that the propositions of § 24 apply equally, mutatis mutandis,
to this case.

The minimum value of H and the corresponding law of
distribution can be found by the variation of equation (27),
keeping f subject to

\\\\fdu dv dw=1, . | sole. le) hor

\\) en r(u? +7 +w!) fdudvdw= 5. i) Gey

The resulting equation is
\\\ \\ (L+logf+\+ gpm’ + v’ + w") ofdudvdw=0, . (30)
where \, # are indeterminate multipliers. The solution is
1+log f+ +h em(u’ +0? +0?) =0; . 25a
or, changing 2d, w for new constants,

f= Je Cs ae oy eae ‘ oe (32)

the well-known law of Maxwell and Boltzmann.

§ 28. This law gives f=0 when wu. v, or w becomes infinite.
There is therefore the difficulty that if we divide all possible
velocities into ‘‘ cells *? in the manner of § 19, the number of
molecules in some of these cells cannot be treated as infinitely
great. The difficulty is best met by taking a definite velocity
ie such that the molecules of which the velocities do not
satisfy

we) TEN See VO>..

form an infinitesimal fraction of the whole. If the velocities
which satisfy (33) can be partitioned into cells in the manner
of § 19, so as to satisfy the conditions of § 25, there is no
further difficulty, and equation (32) gives the law for velocities
which satisfy (33). The law has no meaning for velocities
which do not satisfy (33). It is obvious, for instance, that
the law given by equation (32) does not impose any upper
limit whatever on the possible values of uw, v, and w for a
single molecule, whereas in point of fact such a limit is
definitely imposed by equation (26).

§ 29. We have investigated the law of partition of the
coordinates w, y, ¢ and of ‘the coordinates u, v, w separately.
They could have been quite easily investigated together as
follows :

Kinetic Theory of Gases. 615

Assume the number of molecules having coordinates lying
between w and x+dz,...wand u+du... &e., to be

ING, 21 Uy. wdxdy dndududw, |... (34)
and introduce a new function H defined by
H= \\\\\\ flog fde dy dzdudvdw. . . (35)

Then it will easily be seen that the propositions of § 24
apply to the region of our generalized space for which the
total energy is E, provided we replace K by H, and instead
of K=0, write H=Hp), where H, is the minimum value of
H defined by equation (35), when f is subject to the con-
ditions

\\\\\) fae WHOS CD COCHIN oo Vee es (BG)
(MW) dmeee + 2? + w?) fda dy dz dudv dw=E. . (87)

The resulting law is found to be
Fl, ¥, w, 5 yz) = Ae FmOe+Pba), | (38)

giving uniformity of density for all values of w, y, z and
Maxwell’s law of distribution of velocities in a single

e quati on.

The Normal State.

§ 30. When the 6N coordinates of the molecules of a gas are
such that H has its minimum value, or a value which differs
from this minimum by an infinitesimally small amount, the
gas will be said to be in its ‘normal state.” For gases in
states other than the normal, the difference between the
value of H for the gas and the minimum possible value cor-
responding to the same energy, may be taken to supply a
measure of the divergence of the gas from the normal state.

We now find that proposition (i.) of § 24 may be replaced
b
(iv.) All except an infinitesimally small fraction of the
whole of the generalized space represents gases which are in
their normal states.

§ 31. Let us now examine what becomes of the two
remaining propositions.

Suppose that we start the gas from a configuration about
which nothing is known except that the total energy is
(speaking physically, we have a gas of which the temperature
and pressure are known), then the representative point may
be supposed to be selected at random from that part of our
generalized space for which a energy is H. Suppose we

De ee

616 Mr. J. H. Jeans on the

try to calculate the average value of H throughout the motion
of the gas. Since nothing is known about the initial con-
figuration, nothing is known as to which trajectory the
representative point is describing. Thus, relatively to the
knowledge which we possess, and to our arbitrary basis of
probability, the representative point is at any instant equally
likely to be at any point of our generalized space for which
E has the assigned value. Hence the expectation of the
average value of H throughout the motion (lasting through
any interval we please) is exactly the same as the average
value of H throughout the whole of the region for which H
has the assigned value, and therefore is equal to the minimum
value of H throughout this region. It follows that all the
physical properties of the gas (7. e., properties which depend,
firstly, only on the statistical law of distribution, and not on
the individual molecules, and, secondly, only on tke values
integrated through an interval of time, and not on values at
any single instant, e.g., the pressure of the gas) may be
calculated on the supposition that the gas is in the normal
state throughout.

This must be the interpretation of the second theorem of
§ 24. There is a theoretical possibility of failure, for it 1s
possible (although infinitely imprebable) that the value of H
may differ from its minimum value by a finite amount through
the whole of a stream-line. This question will be continued
in a later section (§ 38).

§ 32. We now examine the third proposition of § 24. If
we consider all the points on the various stream-lines for a
given value of e, which have a value of H, say H’, different
from the minimum, we see (from the proposition analogous
to (iii.) of § 24) that only for an infinitesimal fraction of
these can H increase in either direction to a value of H which
is greater by a finite amount than H’. Thus of the points
for which H=H’, this value of H is a maximum on the par-
ticular stream-line to which it belongs, for all except an
infinitesimally small proportion of these stream-lines. Hence
if we start a gas in any configuration for which H is greater
than its minimum value, it is infinitely probable that in the
initial motion dH/dt will be zero or negative.

Here we have the solution of the apparent paradox men-
tioned in § 17. There is no real irreversibility in the motion
of the gas on the whole, but there is an apparent irreversi-

bility if we start from a point at which H is different from
its minimum value.

Kinetic Theory of Gases. 617

Recaptulation and Discussion.

§ 33. The whole of what has been proved amounts to the
following: Firstly, a gas not in the normal state tends to
approach that state; and, secondly, in examining the physical
behaviour of a gas, departures from the normal state are
insignificant, and we may legitimately proceed as if the gas
were in the normal state throughout.

These results have only been obtained for the simplest type
of gas, but it is obvious that they can be extended so as to
apply to any kind of gas. The normal state is in each case
found by assigning the minimum value to the function
analogous to the H-function already discussed—a function
which may be conveniently referred to as Boltzmann’s
minimum-function.

The whole of the physical behaviour and statistical pro-
perties of a gas can be deduced from a knowledge of the
H-function, just as the behaviour of a dynamical system can
be deduced from a knowledge of the energy-function.

Some examples of the use of this function, illustrating some
of the peculiarities which may arise, are given in the remain-
ing sections :—

EKxamples of the Minimum-theorem.

I.—freld of External Force.

§ 34. Let us suppose the molecules to move in a field ot
external force of potential y, a function of w, y, z. The
analysis is exactly similar to that of § 29, except that equation
(387) must be replaced by

(UY me + 02 + 2) + hf de dy dz du dv dw=E, .( 39)
and from this we immediately obtain the law

fa Aemimw+etu%)—y, ss (40)

l1.—Minture of Gases.

§ 35. Let the N molecules be of different kinds, aN of one
kind, BN of another, and so on. The various coordinates can
be represented in a generalized space as before. The chance
that the whole gas shall be in a specified state is the product
of the separate chances that the gas of each kind shall be in
the corresponding state, whence we find, as the correct form

for H,

H=Zal\\\\\ 4, log f,dadydzdudvdw . . (41)
Ga et

618 Mr. J. H. Jeans on the

in which f, is the law of distribution of the molecules of the
first kind, and so on. The conditions to which /,, fg... are
subject are, firstly, conditions of the form

(i 4 dudvdwdedydze=1, . ate

and similar conditions for /g, &c., and, secondly, the single
energy condition

Sa\\\\) dma(u? +0? + w?) fa du dudwdxdydz=H. . (43)
ps

The equations giving fa, 73 ... are found to be
1 + log fatrAat sum, (wu? + v7 + w*) =0,
and this gives a solution of the form
ie — A e—hm(u? +v?+w?),
p= Bee Te +e), ke) ee

The constant h is the same throughout, whence the Boyle-
Charles-Avogadro law can be deduced at once.

Iil.— Molecules of Finite Size.

§ 386. The analysis of § 27 applies without alteration to
this case, being independent of the size of the molecules. The
analysis of §§ 19-26 also applies if a correction is made for
the regions of the generalized space which are excluded by
equations (3). It will be found that this correction has no
effect on the ultimate result. 7

We also see from § 13 that the “ chance of two molecules
having assigned positions ” is independent of the velocities of
these molecules—a result which is in direct opposition to the
views put forward by Burbury*.

IV.—The Law of Eguipartition.

§ 37. The method of the present paper is in no way limited
to the simple type of molecule which has been discussed up to
the present. If each molecule has m degrees of freedom we
must suppose our generalized space to possess 2mN dimen-
sions, and we can proceed exactly as before. If EH now
denotes the energy of a single molecule, we find that no
matter what function of the 2m coordinates H may be, the
law of distribution is of the form

fe neta 8 a Saas

* ‘Kinetic Theory of Gases,’ chapters v. and vi.

;

Kinetic Theory of Gases. 619

and the law of equipartition can be deduced in the usual
way.

This proof of the law of equipartition is independent of
the special assumptions both of Maxwell and of Boltzmann.
We do not assume (as Maxwell does)

(a) That the representative point passes in turn through
every point of that part of the generalized space for which
the total energy has the assigned value.

(6) That the total time-during which the point is in any
element of this space is proportional to the size of the
element.

Neither do we assume (as Boltzmann does)

(c) That the gas is, at every instant, ‘ ‘ ungeordnet, azn Oe
more precisely, that Burbury’s ‘ Condition A” is satisfied at
every instant.

The precise assumptions upon which our proof rests are :—

(d) That at any instant that part of the total energy of
the gas which is accounted for by the intermolecular forces
forms an infinitesimal fraction of the whole; and

(e) That the conservation of energy is maintained through-
out the motion of the gas

V.—A Gas with a Mass- Velocity.

§ 38. We have seen (§ 30) that a gas is in a state different
from its normal state through only an inappreciable fraction of
the whole of the generalized space, butat the same time (§ 31)
it is possible that it may be in a state different from normal
throughout the whole of a stream-line. Jor instance, the
normal state is such that the mass-velocity of the gas is nd,

but we know that if the gas starts with a mass-velocity it

will retain this velocity throughout its motion, and will there-
fore never reach a normal state. The stream-lines for which
the gas possesses an appreciable mass-velocity form only an
inappreciable fraction of the whole, and are not w orthy of
consideration with reference to our arbitrary standard of
probability. With reference to the conditions of nature the
case is different, so that we now proceed to consider these
particular Suen fae

Let U, V, W be the components of the mass-velocity of
the gas, then the analysis of § 29 will apply, provided we
suppose f subject not only to the conditions expressed by

equations (386) and (37), but also to
(\\\\V wf der dydzdudvdw=U .°. . (46)

620 Prof. A. Battelli and Mr. L. Magri on

and two similar equations for V and W. The resulting law
is found to be

fm AeW hel (u— UP + (e—V)?+(w— W)"), <1) ee
The case of a mass-velocity of rotation may be treated in the
same way.

§ 39. We have so far dealt only with the case in which
the energy is supposed to remain constant throughout the
motion. Besides the energy there are no quantities which
are known to remain constant throughout the motion except the
six mass-velocities of rotation and translation, and, of course,
the total number of molecules in the gas. For the pur-
poses of the Kinetic Theory, we may suppose these mass-
velocities to each be zero. The solution is then given by
equation (45).

On the other hand, the values obtained for the ratio of
the specific heats show that this solution does not accord with
the facts of nature. This may be for either of two reasons.

It may be that the number of constant quantities is greater
than we have supposed, and that the knowledge of some now
unknown constant would alter our result, just as § 38 a
knowledge of the mass-velocity altered the result previously
obtained. As I have suggested elsewhere, the uniformity of
the experimental results obtained from different samples of
gas supplies an argument of overwhelming strength against
this supposition *.

Or it may be that the number of constant quantities is less
than we have supposed, through the energy of the gas not
remaining constant, a possibility which provides an escape
from the difficulties in question.

LXV. On Oscillatory Discharges.
By A. BatTEvui and L. Maenrt f.
\y Ww (Plate XV]
4 Part II. t
The Arrangement and General Course of Experiments.

30. Bee reporting the results of experiments, we
| wish to describe the whole arrangement of the
apparatus.

* “The Condition necessary for Equipartition of Energy,’ Phil. Mag.
[6] iv. p. 585, §§ 14-17.

+ Communicated by the Authors.

t Part I., this volume, ante, pp. 1-34.

Oscillatory Discharges. 621

The electrostatic machine had one electrode put to earth,
and the other electrode connected with one of the armatures
of a condenser by means of a wooden rod.

The spark- and the metal spiral calorimeters were in
series with the circuit traversed by the discharge ; after this
had passed, the condenser was put in connexion with a
ballistic galvanometer in order to measure the residual
charge.

If calorimetric determinations were not to be made, the
square or circle forming the metallic circuit was introduced in
the place of the metallic calorimeters, the spark passing in the
air. If, however, those measurements were also to be made,
three or four discharge-photographs were previously taken,
the spark-gap being next inserted in the calorimeter, and
after having once again produced discharges, simultaneous

5)
readings of the metal spiral calorimeter, of the spark-
calorimeter, and of the electrometer were taken.
After each series of these readings, the residual charge
was measured. The above readings finished, the spark-

photographs were often taken again.

Part III.
GENERAL RESULTS OF EXPERIMENTS.

31. From the single elements, as determined by the
methods above mentioned, we next calculated the final
results of our experiments, as contained in ‘Tables I.
isu

In the first six tables the results of simultaneous measure-
ments of the period of oscillation, of the amounts of heat
evolved in the various parts of the circuit, and of the dis-
charge-potential are recorded.

In Table VII. the periods of oscillation are wanting.
Tables VIII. to XI. are exclusively relative to measurements
of the periods of oscillation.

In the Tables I. to VII. we have given, in addition to
the values of the explosive distance in millimetres and those
of the discharge-potential, the mean amount of heat Q,
evolved with each discharge in the spark, and that, Qs,

evolved in the metallic circuit, and the ratio . serving to
G2

deduce the resistance of the spark from the resistance of the

622 Prof. A. Battelli and Mr. L. Magri on

metallic circuit. The last column contains the value of the
period, as given by our measurements.

At the beginning of each table the values Ly of the self-
induction of the circuit are indicated—including the con-
ductors serving for the connexions—as measured by Nernst’s
high-frequency current method; the value R’p of the re-
sistance by the metallic calorimeter, as calculated by
Rayleigh’s formula, multiplied by the value of the ratio

of the resistance of unit length of the wire of the spiral to

that of an equal length of wire stretched out ina straight line
(§ 24, Part I.). The value of the capacity C of the condenser
and the theoretical value T of the period, calculated by the
formula

a a
T = _ / LC,
| v
are also given.

The quantities Q,, Qs, and a, likewise given in the tables,
will serve for the study of the distribution of energy, to be
made in Section V.

The theoretical values of T are, on the other hand, not
very sure, owing to the uncertainty attending the value of L
corresponding to the spirals, and we are thus not able to
ascribe to them more than a relative importance.

32. The results contained in Tables VIII. to XI. are.
however, of a much higher importance. They are relative to
experiments made with circuits where the self-induction for
each period, which period, as derived from the measurements
made on the spark-photographs, could be calculated exactly
(see §§ 22 and 28, Part I.), and we wish to call attention
more especially to these. __

On the Plate (Pl. XV.) some of the photographs which
served to determine T are reproduced.

Nos. 1, 2, and 4 are reproductions of photographs relative
to Tables X., [X.¢, and XI.a, respectively. No. 3 is
relative to Table [X.5: this was obtained by producing
a discharge between platinum-iridium electrodes, all the
remaining being obtained with cadmium electrodes.

623

Oscillatory Discharges.

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Prof. A. Battelli and Mr. L. Magri on

TAB. Vaile

Circuit formed by a square of copper wire 0:08 em. in thickness and
398°6 cm. in side.

Self-induction of the square
for T, =0:00000425
27390 cm.
Idem of the connexions 1523 cm.
Capacity of Condenser 14175 cm.
Capacity of Circuit 97 cm.

2 aoe
Value of T= — VLC=0:000004254.
Experimental Value of T.

is:
Self-induction of the square
for T, =0-00000301
27329 cm.
Idem of the connexions 1523 em.
Capacity of Condenser 7178 cm.
Capacity af eee 97 cm.

| Value of T= = =* VLC=0:000003034.

eee Value of T.

0000004214 0000004204
4304 4302
4244 4177

4226 4262

4202 4279

4202 4291

4266 4240

4277 4226

4185 4209

4210 4213

4196 4252

Mean value T=0-000004235

0:000002994
3016
2979
3006
3019
2980
3036
3020

Mear. value T=0:000003006

TABLE LX.

Circuit formed by a copper-wire circle 0°452 cm. in thickness, the
diameter of the circle being 201 cm.

|
a.
| Self-induction of the circle
| for T=0-00000237
7829 cm.

Idem of the connexions 1432 em.
Cares as ee C=14175 em.

— =" yEC=0-00000240.

epee Distance 2°5 mm.
pT Value of T.

0-000002334

2348

2389
2358
2370
2371
2378
2408
| 2405

Mean value T=0'000002373

|
|
|
|

ise
Self-induction of the circle
for T=0-00000167
7824 em.
Idem of the connexions 1432 em.

|Capacity of Condenser C=7178 em.

Dat A
=> ¥ LC=0:000001707.
Explosive Distance 2°5 mm.
Experimental Value of T.

0:000001655 0:000001665
1693 1658
- 1660 1654
1648 1693
1685 1689
1692 1668
1679 1671
1677

| /
| |

Mean value TIT =0:000001672

Oscillatory Discharges.

627

TasuE IX. (cont.).

Self-induction of Circle for T=0:00000120 7810 em.
‘Self-induction of connexions 1432 cm.
Capacity of Condenser C=3568 cm.

= ze VLC=0:000001201.

Y:
Explosive Distance 2°5 mm.
Experimental Value of T.

Explosive Distance 5 mm.

Experimental Value of T.

0:000001162 0:000001199
1160 1230

1196 1224

1193 1222

1173 1222

1166 1198

1209 ile

Mean value T=0:000001195

0000001213 | 0:000001190
1205 1197)
1209 1202
1220 1221
1239 1182
1205 1210
1194 1224 |

Mean value T=0-000001207

TaBLE IX. (cont.).

TABLE X.

é.

Circuit as in Column «.
Electrodes of Platinum-Iridium.
Total Self-induction of Circuit

for T=0 00000237
9261 em.
Capacity of Condenser C=14175 cm.

i ac
T= VLC=0:00000240.

Explosive Distance 2°5 mm.
Experimental Value of T.

0000002395 0000002270
2412 2480
2369 2489
2497 2426
2454 2476
2338 | 2386
2282 | 2186

Mean value T=0:00000239

Circuit formed by small Copper
wire 0°452 cm. diameter.
Diameter of Circle 57-2 cm.
Total Self-induction of Circuit
for T=0-00000074
2993 em.
Capacity of Condenser 3568 cm.

Mes Ab,
= = VEC=0-000000684.

Explosive Distance 2 mm.

Experimental Value of T.

0:0000007431 0:0000007422 |

7263 7105
7411 7625
7565 7493
7567 1442 |
7560 7414 |

Mean value T=0-000000744

628 Prof. A. Battelli and Mr. L. Magri on

| a

TABBY

Circuits formed by Copper-Wire Spirals.

Self-induction of Large Spiral

4546000 cm

Self-induction of Small Spiral

and Connexions 57797 em.

Capacity of Condenser C=14175 em. |Capacity of Condenser C=14175 em.
5) pad
T=— VEC=0-00005317.
Explosive Distance 2 mm.
Experimental Value of T.

9 am
T= — yLC=0:000005995.
Explosive Distance 2 mm.
Experimental Value of T.

0:00005404
5374
5339
5363
D417
5434
5444
5386
5403
53035
| 5347
5296

Mean value T=0'00005376

0000006201
5993
6067
5923
6034
6093
5995
5970

Mean value T=0:000006034

TaBLE XI. (cont.)

y-
Self-induction of Small Spiral
and Connexions 57797 cm.
Capacity of Condenser C=3568 cm.

Fay waete
T= — VLC=0-:000003008.
Explosive Distance 2 mm.
Experimental Value of T.

0:000002986

3037
3011
3173 (?)
3032
3053
3011
3022

| Mean value T=0:000003024

0-:000003054
2981
2904
3039
3036
3001
3042
3021

|
|
|
|

Oscillatory Discharges. 629

Part IV. Discussion or RESULTS.

33. In order to have an adequate idea of the importance
to be ascribed to the noteworthy agreement observed between
the experimental and calculated values of the period T, it
will be necessary to give an account of the accuracy attained
in the determination of the various elements relative to
this measurement.

(a) Huperimental Determination of the Period.

It will be useful here to consider briefly what results may
be derived from the numerous photographs obtained.

First of all there is to be noted that the section of the
spark is very large when a considerable amount of elec-
tricity is discharged, as in the cases recorded in Tables L.,
Mim iva, VX. 2, [Xie X.a;and X. 8:

It next will be worthy of notice that the successive sparks
a discharge is made up of do not always pass between the
vertices of the spherical calottes forming the electrodes of
the spark-gap, but as a rule take various positions on the
electrodes, thus lengthening the explosive distance. This
phenomenon is clearly seen on many of our photographs,
where the aspect of the discharge is that of a strip, whose
width, as a rule, increases with time (fig. 2, Plate XV.).

A behaviour more regular in this respect is noted when
the sparks are longer, and when a smaller amount of elec-
tricity is being discharged. Then the section of the spark
is very small, and the variations of length of the photographic
images of the various elementary sparks are less.

Now if the spark is produced between rather volatile elec-
trodes—as, for instance, cadmium electrodes—its behaviour
is very regular, as may be seen from photograph No. 3 on
Plate XV. If the electrodes consist of platinum or platinum-
iridium, the spark as a rule shows a very irregular aspect,
as that of photograph No. 2 of the abov é-mentioned Plate,
where noticeable displacements between the single partial
sparks are to be observed, each of which, so to speak, has to
open itself a discharge-way of its own.

On this displacement of the elementary sparks may depend
the variability of the period of oscillation from one elementary
discharge to another, as observed by Trowbridge and Sabine,
as well as the fact noted by Lodge and Glazebrook that the
last period of the spark is longer than the rest, this variation
being probably due, not to the hysteresis of the air for ming

Pag Mag. 8. 6. Vol. 5. No. 30. June 1903. Doel

630 Prof. A. Battelli and Mr. L. Magri on

the insulator of the condenser, but to the great resistance
offered by the spark on its disappearing.

But it is a consequence of Stefan’s * theory also, that there
should always exist a difference between the initial and
final values of the period of the discharge. In fact,
according to this theory there is added to the undulatory
movement corresponding to Thomson’s theory another period
capable of modifying materially the period during the first
moments of the discharge.

Whatever may be the reason of the above-mentioned
displacement of tke single-spark components, it is clear that
this phenomenon affects to a great extent the accuracy
attainable in the experimental determination of the period
of oscillation. This accuracy, in fact, depends not only on the
constancy of the velocity of Pobre cs the mirror and of the
degree of precision with which this same velocity may be
measured at the moment of the photograph being taken ; but it
depends equally on the precision with which the free:
between the photographic images of two successive ele-
mentary sparks may be determined. Now, if these sparks
are being displaced on the electrodes, the epee distance
does not ‘correspond with the true one.

We, however, eliminated, at least for a great part, this
inconvenience of measurements, as, out of the numerous
photographs made for each case and for each explosive
distance, we used only those on which the images of the
sparks were well defined and regularly distributed.

In addition, as already stated, when calculating the mean
ralue of the distances between two successive elementary
sparks, the first and last sparks were always left out of the
calculation, and the effective period was derived from the
mean distance between the remaining small sparks, these
latter being always very numerous.

The value given for the experimental period was the mean
of those derived from the mean of many photographs for
each case and each explosive distance.

The agreement of these values is noteworthy. In order
to give an adequate idea of this we record in Tables VIII.
to XI. all the values used for determining the experimental

value of T for circuits with well-known asian eo

Measurements of the same value of the period made on

different days always gave perfectly concordant figures.

From this fact it may be inferred that, in the vaiues of
the period measured by us and recorded in the preceding
tables, a notable accuracy has been reached.

* Wied. Ann. xli, p. 421 (1890).

Oscillatory Discharges. 631
(b) Value adopted for Capacity of Condenser.

34. The great care bestowed on the absolute measurements
of the capacity of the condenser, and the agreement of the
value thus obtained with the one resulting from a comparison
with the sample kindly forwarded by Prof. Roiti, entitle us
to maintain that the value obtained by us is trustworthy in
all respects.

On the other hand, it might be suspected that for large
potential-differences between the armatures, as those corre-
sponding with the explosive distances of some millimetres
used by us, the charge should extend over the glass edges
not covered with tinfoil to a much higher degree than in the
case of the very slight charges used with the above-mentioned
standardizing, and that ihemee the true capacity is larger
than the one noted. Whether this is really the case, we were
not in a position to ascertain ; but it is certain that, if for
high potentials there occurs a greater diffusion of charge on
the glass, this could not augment practically the effective
capacity of the condenser, as at the moment of the spark
the electricity going on to the glass is not discharged in the
same way as that taken by the metallic armatures.

One also might object that the capacity for rapidly oscil-
lating discharges should be different, even for air-condensers,
from that given by measurements with slow charges—in fact
this objection has been raised against Hertz’s experiments.

But applying to our experiments Drude’s calculations
(Physik des Atthers, p. 459), one easily understands that no
correction is to. be made on this account in the above-
mentioned value of the capacity used in our experiments.

Moreover, as the total resistance of the circuit containing
the spark will subsequently be shown to be negligible as

compared with ene reduced formula of Thomson thus

LC
applying to this case—from the striking agreement which in
this case also exists between the ealouleted and observed
periods, it may be inferred that the value adopted for the
capacity of our condenser, obtained from determinations
made with slow charges aa low potentials, is really true
also for oscillatory theehar ges and for the potentials used
in our experiments. In addition, this agreement may be
regarded as an evidence that the dielectrical hy steresis of
the air is really negligible for the periods of the discharges
photographed by us.

2U2

632 Prof. A. Battelli and Mr. L. Magri on
(c) Value of Resistance and Self-Induction.

35. The calorimetric methods used by us afford, in our
opinion, the most satisfactory comparison between the re-
sistances offered by two different circuits to oscillatory
discharges. We therefore, having by Lord Rayleigh’s
formula calculated the resistance of some rectilinear con-
ductors, with which we have compared the resistances of our
spirals (§ 24 and following), may claim to have succeeded in
finding in absolute measure those same resistances with the
degree of approximation the calorimetric measurements will
allow of.

It might be objected that in fact Lord Rayleigh’s formula
rigorously applies to pertectly harmonic currents only, and
that the effects the damping will produce on the resistance
should be taken into account; but one easily understands
from Barton’s * formule that the correction on account of
the damping would in our case be less than 1 per cent.
Now Barton *, from a calculation recorded in Maxwell’s
Treatise, recently found (as did Lord Rayleigh) the expression
for the resistance and self-induction of a current for damped
harmonic currents as well as for those obtained by a con-
denser-discharge. In Barton’s theory the damping of the
currents is measured by a certain number fk, which, using
the notation adopted by us, is given by the equation :

and thus in our case is without any doubt always inferior
to 0°02. Now, denoting by R” and R’ the values of the
resistances of the same circuit, as calculated by Barton’s and
Rayleigh’s formule respectively, their ratio is given by

Tey icles

Rite Lt o Tigh’ aimecutet
a quantity absolutely to be neglected as being inferior to the
mean approximation the calorimetric measurements were
made with.

Moreover, Cardani’s f direct experiments made with con-
denser- discharges prove experimentally that within the limits
of error of those measurements the resistance of a rectilinear
wire may for those discharges be regarded as having really
the value assigned to it by Lord Rayleigh’s formula.

* Phil. Mag. [5] xlvii. p. 433 (1899).
+ NV. Cim. | 4] vii. p. 229 (1898).

Oscillatory Discharges. 633

36. As regards self-induction, we wish to state that
different experimenters, having measured the coefficient of the
same coil with direct currents and with alternating currents,
have found values differing little from one case to another ;
but the reversals used were always of few hundredths per
second.

Tallqvist (7. c.) more especially dealt with the influence
the method of measuring the self-induction of the circuit may
possess, comparing the experimental values of the period of
oscillation with those deduced from Thomson’s formula.
From this comparison, he argues that the true values of L
for oscillatory discharges are somewhat smaller than those
obtained experimentally by the method of direct currents as
well as by the telephone method with alternate currents.
As a rule, however, the value of L adopted for the spirals in
the researches so far carried out in oscillatory discharges
has always been either the one calculated by the formule
true for direct currents, or the one found experimentally
with those currents.

On the other hand, our self-inductions have either been
calculated directly and with the proper corrections relative
to the frequency of the discharges, or have been determined
experimentally with high-frequency currents by comparison
with already calculated self-inductions. In the case also of
the self-induction, the effect of the damping is wholly negli-
gible in our experiments, so that Rayleigh’s formule may be
used instead of those of Barton.

As regards the case of circuits of any form, the method
suggested by Stefan* for taking account of the unequal
distribution of the current in the section of a wire may not
be applied to the small-radius spirals, as for this it would be
required that the thickness of the wire be negligible as
compared with the radius of curvature of the circuit, and
that the current be distributed symmetrically around the axis
of the wire. This of course is not true for the ordinary
spirals, on account of the dissymmetry of distribution of the
currents, dissymmetry due to the action of one winding
on another. ‘This perturbing action tends to localize the
currents only on some portions of the surface of the con-
ductor ; and that this is really the case is clearly shown by
the fact, established by our experiments (see § 24), that in
the case of alternating currents a wire bent to a spiral will
oppose a much higher resistance than that corresponding
to the same wire stretched out in a straight line. As theo-
retical formule able to give us the effective self-induction of

* Wren. Ber. xev. IL a, p. 917 (1887).

634 Prof. A. Battelli and Mr. L. Magri on

a spiral for high-frequency currents are wanting, we had to
apply to the experimental method, which indeed led to
satisfactory results.

(d) Resistance of Spark.

37. Our experiments gave us also the means of deter-
mining the resistance of the spark, which nowadays forms
one of the principal problems connected with the electrical
discharge. Though it has been the object of some deter-
minations, it can not be said to be known with certainty,
and more especially it is not known how it depends on the
frequency of the oscillations.

Biernacki* tested the resistance of the spark of a con-
denser by comparing it with that of an electrolyte inserted
between the balls of a resonator identical with the oscillator
itself, but this investigation is relative only to the sparks of
Hertz’s oscillators, viz., to oscillatory discharges of high
frequency, where small quantities of electricity only are in
question.

Kaufmann +, on the other hand, found that the quantity of
heat evolved in the spark by the discharge of a battery
of Leyden-jars is connected with the resistance W of the
remaining part of the circuit by the formula

q=At

A and B being constants. Thus the resistance of the spark
is not comparable with a metallic resistance.

Moreover, he found that the heat evolved in the spark
increases with the potential-difference more rapidly than the
total energy of the discharge; that is to say, he found

approximately 7 = const., instead of BE = const. This latter
v v
result is not in accord with those derived from our ex-

periments. |

Besides, he found the quantity of heat evolved in the
spark to be larger (about doubie) between two zinc electrodes
than between two brass electrodes. We had for cadmium
and platino-iridium electrodes about the same values of Q
(see ‘table III.).

More recent and accurate measurements are those of
Cardani t, who of course determined the apparent resistance
of the spark by deriving it from the total heat evolved less

* Journ. de Phys. [3] iv. p. 474 (1895).
+ Wied. Ann. lx. p. 653 (1897).
t N. Cum. [4] x1. p. 113 (1900).

Oscillatory Discharges. 639

that evolved in the metallic part of the cireuit. According
to his experiments—as Orgler* had found by a different
method—the resistance R of the spark should be represented,
in terms of its length J, by the relation

R=A/+B,

A and B being constants. But the variations of the resist-
ance with the period of oscillation cannot be deduced from
Cardani’s experiments. This goes to show that the experiments
so far performed, as above stated, fail to give the complete
solution of the problem. But, on the other hand, it may be
maintained that, in order to take account of the spark, one
would have to write the equation for the movement of the
electricity under the form

Qu dQ IQ @2Q :
a Ge a tR (FS Vat OS det wdt=0, . (2)

differing from the one applying to the discharge in a wholly
metallic cireuit by the term wdt, repr esenting the work
accomplished in the production of the spark. If w could be
regarded as constant, the action of the spark would be per-
fectly equivalent to that of a resistance, and w would have to

=) dt. In that case the

solution of (#) would differ from that of Thomson’s equation
only by the different value of R, which then would represent
the combined resistance of the metallic circuit and the spark.
But the processes occurring in the spark are very complex,
and their nature is not known with certainty.

One might maintain with Heydweiller f that the variation
of the resistance of the spark, after being rapid at the
beginning of the discharge, would proceed slowly, so that for
oreat resistances of the circuit after a relatively short
fime a constant “ régime” would be set up. But if this were
true, w would be such a function of ¢ and R that (a) would
not be integrable ; hence this hypothesis cannot be tested by
experiment.

It thus only remained to submit to new measurements
the resistance the spark offers under various conditions ; these
we made with our apparatus, the arrangement of which
enabled the total energy spent in the spark to be measured,
and to be compared with that spent at the same time in
tne metallic part, whose resistance R’p, for oscillations of

be compvised in the coefficient of (“

* Drude’s Ann. 1. p. 159 (1900).
+ Wied. dz. xlin. p. 310 (1891).

636 Prof. A. Battelli and Mr. Ll. Magri on

the frequency measured each time, was calculated in the
manner mentioned in § 26. In the tables given above

the 8th column, containing the values of Rog where Q, is

the heat evolved in the spark and Q, that evolved in the
metallic spiral, serves to give us the mean resistance 7 of the
spark. Though these values of 7 are perhaps a little smaller
than the true ones, on account of the dispersion of heat
possibly occurring along the metallic rods of the spark-gap,
yet our experiments will allow of the conclusion that the
resistance of the spark has been in most cases smaller than
that of the metallic part, and without any doubt always inferior
to 1 ohm. The measurements completed by us would ascribe
to the mean resistance of sparks of from 1 to 5 mm. values
ranging from 0°18 to 0°96 ohm, with the reservation above
mentioned.

Another important fact may be deduced from our ex-
periments, viz., that the capacity and resistance of the
metallic part of the circuit remaining the same, the resistance

derived from the ratio Q increases very slowly as the length

Qs
of the spark increases (see Tables I. to VII.). This may be
explained, either by admitting that the main part of this
resistance lies at the passage from the electrode into the air,
or that with increase of length the section of the spark
increases in proportion.

With the arrangement adopted by us one may besides
ascertain how the resistance of the spark depends upon the
period of oscillation; and a perusal of the tables above
given shows that this resistance—the explosive distance and
capacity of condenser being the same—increases with increase
of period.

The noteworthy accord between the calculated value of
the period of oscillation and the one given by our experiments,
is an evidence of the smallness of the value of the effective
resistance of the spark; and another evidence of the accuracy
of the measurements carried out is afforded by the fairly
satisfactory agreement between the disposable energy of the
condenser and the sum of the thermic energies evolved in
the metallic circuit and in the spark.

It is almost superfluous to state that all we have said
regarding the resistance of the spark is relative to the mean
values it presents during the whole time it lasts.

Oscillatory Lischarges. 637

Part V. MEASUREMENTS OF ENERGY SPENT IN THE
DIFFERENT PARTS OF THE CIRCUIT.

38. The expression
We sO

where C is the capacity of the condenser, and V the potential
it has been charged to, gives the maximum limit of the
energy the condenser is capable of supplying on its being
discharged through any circuit.

Now when the discharge occurs, part of the energy the
condenser possesses is dissipated in the dielectric ; another
part is employed to overcome the resistance of the circuit and
of the spark; a third part is spent in splitting metallic particles
off from the electrodes, and in causing them to glow; and a last
part will finally be (radiated) sent off from it, viz., will be
spent in the production of the electrostatic and electro-
magnetic fields. It is evident that these various portions
will not all be found again under the form of thermic energy
in the discharge-circuit—comprising the spark ; and that it
will be necessary to account for the means of measuring the
single portions themselves.

Direct determinations of the energy dissipated elsewhere
than in the metallic part of the circuit and the spark have
only been made as far as the amount absorbed by the dielectric
of the condenser is concerned ; and some are relative to the
ease of alternating currents supplied by ordinary industrial
machines, as those of Rosa and Smith*, of Lombardi fF,
Arno {, and Schaufelberger §, &c. But in our ease the loss
of energy in the dielectric of the condenser may be neglected,
as we used an air-condenser.

Among the investigations performed in order to determine
the heat evolved in the spark and in the metallic part of a
discharge-circuit, we wish to mention those of Heydweiller
and Cardani, as they were made with a special view to
determine quantitatively the phenomenon.

Heydweiller’s || measurements relate only to continuous
discharges, as he inserted in the circuit resistances of several
megohms formed by solutions of cadmium iodide in amyl
alcohol.

* Phil. Mag. [5] xlvii. p. 19 (1899).

+ Lombardi, Abstracts from the Llettricista, Year 5, No. 10, Mem.
R. Ace. Sc. Torino, ser. ii. vols. xliv. & xlv.

{ Rend. Ace. Line. 1892, 1893, 1894.

§ ‘Inaugural Dissertation ’ (Faculty of Zurich), 189s.

|| Wied. Arn, xliii. p. 310 (1891).

638 Prof. A. Battelli and Mr. L. Magri on

He determined with a sort of liquid thermo-rheostat the
heat evolved in the circuit, and having also meastred in
(Si

OOM
electricity, g, the residual eleciricity, and C the capacity of
the condenser) the total work of discharge, he could deduce
by difference the work spent in the spark.

The main action of the spark would consist, according to
Heydweiller, not in its resistance, but in the work hecessary
to maintain the discharge-potential.

Cardani *, in investigating the resistance of the spark,
dealt indirectly with the distribution of energy in a circuit
of constant and small self-induction, where by varying the
capacity of the condenser the period of oscillation was also
altered between certain limits. Studying next the discharge
in rarefied gases, Cardani observed that the part of the energy
dissipated in the spark depends on the form of the discharge
and on the section of the spark itself, being much larger when
the discharge passes in the form of a luminous brush.

But both Heydweiller’s and Cardani’s measurements fail
to afford the complete solution of this part of the problem, as
those of Heydweiller apply only to continuous discharges, while
those of Cardani are not relative to the energy disposable.

For the solution of the problem it is necessary that the
determinations of the thermal energy evolved in the different
parts of the circuit should be executed simultaneously; as it is
important also that in measurements of this kind the sum
of such energies should be compared with the total energy
disposable in the discharge.

As, moreover, the arrangement of our experiments for the
determination of the period of oscillation and for measuring
the various resistances was such as to allow of the necessary
measurements being made simultaneously, we also tried to
draw some conclusions relative to the energy found in the
different parts of the discharge-cireuit, as compared with the
total disposable energy.

On this account, in addition to the above-described deter-
minations of the capacity and the heat evolved in the metallic
parts and in the spark, we had to ascertain the discharge-
potential and the value of the residual charge.

the form (where g is the initial quantity of

Electrometer.
39. In order to obtain the value of the potentiai at which
the discharge began, we availed ourselves of a Righi fF idio-

* Nuovo Cimento [3] xxxv. p. 142 (1894) ; [4] xi. p. 113 (1900).
+ Nuovo Cimento | 2\ xvi. p. 89 (1876).

Oscillatory Discharges. 639

static electrometer, this being very suitable tor an accurate
determination of high potentials. We, however, added to the
needle of this slagunenneter (made out of a thin aluminium
plate) a light electromagnetic damper, formed of a copper-
plate frame, moving in a magnetic field, and of a form quite
similar to fiat, of a ‘Despretz- Dy’ Arsonval galvanometer.

The needle and the damper were very light, their move-
ment being nearly aperiodic, so as to allow ae following the
rapid var “eivoma of the potential.

As a matter of course, the necessary precautions have been
taken in order to protect the damper and the mirror against
the electrostatic actions.

Method of securing Constancy of Potential.

40. The electrodes we used for the discharge, after various
endeavours, had the form of small cylinders 3 mm. in dia-
meter, terminated by spherical calottes. It proved very
difficult, on account of the smallness of the electrodes, to
secure a fairly constant potential of discharge for each series
of experiments. With aluminium, cadmium, iron, Kc. elec-
trodes, the alterations of the surface were so rapid, and the
delay of discharge, when the sparks passed in the interior of
the calorimeter, was so great and so variable, as to make it
impossible to ascribe to the mean deviation a reliable value.
In the case where we had to complete calorimetric measure-
ments, we hence found it very convenient to use platinum, and
still better platino-iridium electrodes, also in order to avoid
oxidation phenomena.

In order to dimimish greatly the delay of discharge, we
put in the interior of the spark-calorimeter, or at a slight
distance from the spark-gap, when the photograph was
taken, a small celluloid tube containing a little radioactive
snbstance. The action of this substance was so strong that
the successive discharge-potentials were very slightly difterent
fzom one another, and allowed of obtaining a ‘eood average
tor the value of the discharge-potential, provided the surface
of the electrodes was not too much altered.

In any case it was necessary the sparks should occur with
sufficient slowness to allow of the needle following the
variations of the potential, in order to have reliable ecalori-
meter-readings. On this account, we were not able to make
in each case the re adings the inselves simultaneously with the

calorimeter-readings, for which it was ne eessary that the
sparks should follow each other with sufficient rapidity. We
therefore made in many cases the determinations of the
discharge-potentials immediately before and atter each series

640 Prof. A. Battelli and Mr. L. Magri on

of calorimetric readings, requiring always a_ satisfactory
accord between the two sets of readings.

We next obtained the absolute value of the discharge-
potential by standardizing our electrometer with a good
absolute Kelvin balance-electrometer made especially for
potentials of the order of magnitude of those used by us.

Acccording to the potential-difference we had to measure,
the electrometer was regulated so as to give to its constant
the value 1°505 or the value 2°71.

Galvanometer for measuring the Residual Discharge.

41. But in order to know exactly the portion of energy
really intervening in the discharge, it was necessary, as
above stated, to determine aiso the value of the residual
charge.

For this purpose the condenser was charged by means of
a large double Holtz machine, the motion of which was
maintained slow and uniform by means of an _ electro-
motor. When we wished to determine the residual charge, in
order that the condenser might not be charged very quickly,
in most cases we approached a pole of the machine itself
terminated by a point to a plane electrode connected with
one of the armatures of the condenser, instead of establishing
a direct connexion with the machine, the other armature
being joined to earth.

After ascertaining in the required manner the distance
between the electrodes of the spark-gap, the ve locity of the
motor was modified so as to have sparks passing in the spark-
gap at intervals of about one or two minutes. After this
we proceeded to measurements ; that is, we set free a short
pendulum conveniently placed, as soon as the first spark had
passed in the spark-gap, so as to establish the connexion
between the condenser and one of the terminals of a ballistic
galvanometer, the other terminal being joined to earth.

In order to secure a good insulation and a complete pre-
tection of the needle from the electrostatic actions, the frame
ot the galvanometer was formed of only two layers of wire
covered with a thick guttapercha coating, and the needle
(made up of a small magnetized steel mirror) was inclosed
in a cylinder, whose lateral surface was of metallic gauze,
the bases being of brass. Readings were effected through a
narrow slit made in one of the bases.

Jn our experiments, where sparks never exceeded 5 mm.
in length, and where the resistance of the circuit was ex-
cessively small, the residual charge, being due only to the

Oscillatory Discharges. 641

amount of electricity which could not be discharged by the
spark itself, was found to be constantly negligible, 2. e.
always inferior to the hundredth part of the initial charge.

Disposable Energy and its Distribution in the
Circuit of Discharge.

42. The work done in imparting the potential V to the con-
denser of capacity C would represent the energy effectively
disposable, and should accordingly be found again in the
discharge, but for the part dissipated in the dielectric, outside
of the metallic circuit and the spark.

This dissipation of energy may reach sensible values in
condensers with solid dielectric, and, as a matter of fact, there
exists no reliable method of calculating it. In fact the methods
used for ordinary alternating currents of industrial machines
cannot be applied to the present case, and Wulf’s* method,
based upor the determination of the damping-coefficient
of the amplitude of oscillations, as derived from the residual-
charge curves, and of the theoretical decrement, as calculated
from the potential-differences corresponding to two successive
maxima, does not give results of sufficient accuracy. But
with our researches this inconvenience was reduced to a
minimum by the use of air-condensers, or at the least was
certainly of an order of magnitude inferior to the unavoidable
errors of the calorimetrical measurements.

Another portion of energy, net found again in the circuit
either, is that radiated by electromagnetic waves.

The theory of oscillatory discharge allows of this part of the
energy being calculated, as 1t affords a means of comparing
the intensity 2 of the current traversing the wires of the
discharge-circuit—supposed parallel and at the distance d
from one another—with the intensity 2’ observed in the
air-cylinder, having one of the wires as axis and half of the
distance d between the two wires as radius of:the bases. The
ratio between 2 and 2’ (see Drude, Physik d. Aethers, p. 369)
is given by

a) soda
SE bese

These calculations cannot, it is true, be applied to our
experimental arrangements; but it may still be observed
that they may give ‘account of the order of ma gnitude of the
vortion of energy dissipated. If, for instance, it be observed
that in the experiments performed by us the value of Ee,
that is the wave-length, is always superior to 600 m.; and

* Wien. Ber. cv. IL a, p. 667 (1896).

642 On Oscillatory Discharges.

that of d, though adopting as maximum distance that between
our circuits and the earth, is always smaller than 2 metres,
the preceding formula will give

“<6(45), or + <0-000066

7 > NBOO Rae 7

In the case of circuits wound into spirals, the dispersion
cannot be much different ; hence with our experiments it
may always be regarded as ‘negligible.

That the sum of the energies spent outside the metallic
circuit is negligible within the limits of accuracy reached
with our measurements of the discharge-potential and of the
heat evolved in the spark, may also be derived from the
experiments themselves. In fact, in the Tables I. to VIL.
we compared the sum Q,+Q, of the heat evolved in the

ere and in the metallic spiral, with the energy corresponding

3CV?; and from a perusal of those tables it may be
seen that nearly all the energy is found again in the form of
heat in those two portions of the circuit. On the other hand,
we wish to maintain that the uncertainty as to the true value of
V (due to the great variability of the effective length of the
spark), and the fact that the spark-calorimeter does not give
a very exact measure of all the heat evolved in the spark
itself, deprives our comparison of part of its value. In these
first researches, however, it was more interesting to study the
repartition of the energy between the spark and a metallic
part of known resistance, than the absolute value of the total
energy; and this repartition we have succeeded in ascertaining
with sufficient accuracy.

Conclusions.

43. Froma survey of these results the following conclusions
may, in our opinion, be drawn :—

1. The period of oscillation agrees, within the limits of

experimental errors, with the theoretical value, as given by
Thomson’s formula. The less satisfactory accordance observed
in the case of very short periods (about 7x 10-7) is due to
the fact that in such cases the self-induction of the cireuit
cannot be allowed for.

Z. The resistance of the spark in the case of little-damped
discharges, due to rather large amounts of electricity, as
those given by our condensers, and for explosive distances
comprised between 1 and 5 mm., is very small and always
inferior to 1 ohm. Ceteris paribus, this resistance increases
considerably less rapidly than the length of the spark. This

Re
|

On Electric Waves along Parallel Wires. 643

would suggest that either the resistance of the spark for the
most part is due to the passage from the electrodes into the
surrounding gas, or that the section of the spark augments
as 1ts length i increases.

ae The resistance of a wire bent to a spiral is for oscil-
latory discharges much higher than that shown by the same
wire when str Skalnadl out aitG a straight line.

The difference between the two values augments as the

frequency of the discharge increases and the digtanee between
the single spires decreases. Lord Rayleigh’s formula thus
does not apply to circuits bent into a spiral.

4. The sum of the calorific energies spent by the discharge
in the spark and the metallic circuit agrees fairly well with
the value of the energy of the condenser.

5. With cadmium electrodes the sparks are much more
regular than those corresponding to platinum and platino-
iridium electrodes.

6. The values of the spark-resistance and of the energy
spent in the spark itself are, in the conditions of our experi-
ments, practically identical for platino-iridium and cadmium
electrodes. \,

LXVI. On the Connexion between Speed of Propagation and
Attenuation of Ilectric Waves along Parallel Wires. By
W. B. Morroy, M.A., Professor of Naiural Phaeton
Queen’s College, Belfast*.

Ayes electric oscillations, of frequency = are guided

a
by imperfectly conducting leads, the various vectors contain
y imp y 2 )

a factor

WW age
Go Ke sin( pest B)
rn j
o alone

the propagation being 2 the positive direction of the axis
of z. ‘The course of the analysis leads, in general, to an ex-

e ry e TT e , .
pression for the complex quantity m= 4 +v« as a function

Sa Pp
of p and of the magnitude a PP where a isthe radius
p
of the wire, w the permeability, and p the resistivity of its
material.
In the present paper I start with the approximate formula
for m in the case of two parallel wires, as discussed in former

* Communicated by the Author.

644 Prof. Morton on Speed of Propagation and

papers* in this Journal, and proceed to investigate the rela-
tion between the real and imaginary parts for the limiting

. : )
cases In which ay / PP has a very small or very large value.

p
The results are shown graphically, not only for these extreme

cases. but also for intermediate values of the quantity a i

p
The plotting of the complete curve is rendered possible by the
use of Aldis’s tables+ of the functions Jo(a Vi) and J,(x /2).

In this case nt 10:
ge Zan / wept
a

The speed of the waves along the wires will be expressed as
a fraction of V, the speed of free radiation. For a measure
of the attenuation it will be found convenient to take, instead

of «, the quantity ae or Ene, where A, is the wave-length

20
in free space. For good-conducting wires A, is practically
equal to A, and our measure of attenuation is then the
logarithmic decrement of amplitude corresponding to a dis-
| Xu : ; :
tance 5— along the wires. For cases of rapid attenuation
when A, is no longer nearly equal to A, we may suppose that
the frequency is kept constant, and that the alteration in the
state of affairs is brought about by changing the properties
of the leads. 2

For two wires at distance b, we have f, if jz can he neglected,

2 = er al
PF —wa tr, : ae) ee
log- J, (wJi).a Vi
Vi ea

b Z A
log ie Vi) .a Vi
Vm Vf Date

= + ix)

and

where v is the speed of the waves along the wires.

* Phil. Mag. vol. 1. p. 605 (1900) ; i. p. 563 (1901).
+ Aldis, Proc. Roy. Soc. vol. lxvi. pp. 42, 43 (1899).

t Phil. Mag. vol. 1. p. 610, equation (12).

Attenuation of Electric Waves along Parallel Wires. 645
Write

and we have

(| ptoni ee ey

Velocity of Propagation + V.

. V
Attenuation Constant x ie

b
Using the value = = 100, I have plotted the curve showing

the connexion between & for different values of «, which
are specified by the numbers placed beside the marked
points.

Phil. Mag. 8. 6. Vol. 5. No. 30. June 1903. Ox

646 ~ Prof. Morton on the Speed of Propagation and

It is easy to find the shape of the curve at its extremes :
(1) For very large values of «, i.e. well-developed “ skin-

ee
2 V2.2. log—

E + 7) = 1 ° . s . . e e e (4)
?.e. a straight line inclined at 45° to the axes.
This part of the curve is compressed into very small seale
at the upper part of the diagram.
(2) For very small values of x, the current penetrating to the

core of the wire. Jef) )
Jy (a wane a7 Ji
(- +i€) =14 =
4 a? log —
a

We may neglect unity in comparison with the large term
which follows, and so obtain

Attenuation of Electric Waves along Parallel Wires. 647

or the curve at its lower end approximates to the form of a
rectangular hyperbola.

equation, so that we get the same curve for all distances of
the wires apart. In other words we have, in the extreme
cases, a definite attenuation (as measured by the quantity &)
associated with a given speed of propagation. The value o

an / YP which gives a particular attenuation and speed is, at
p
the upper, “skin-effect,’ part of the curve inversely as

h : ee ed
log—. In the opposite extreme region it 1s inversely as the
a ;

square root of this logarithm.
I have re-calculated the values of the speed and attenuation

”) e b -
for the same values of # (O'1, 0°2, &c.) using 3 =200 and

=300 instead of =100. The points so found are marked
on the diagram with a circle and a cross respectively. It
will be seen that, even in the middle parts, they lie close to

the curve drawn for - == i) (0)

In former papers I have shown that a variety of more com-
plicated cases of propagation along a set of parallel wires
may be replaced, as regards attenuation and retardation of
the waves, by an equivalent pair of parallel wires. It would
seem therefore to be ver y generally true that—

In systems which cause a given amount of retardation tn the
speed of the waves, the altenuation-constant, K, is proportional
to the frequency ; or, there is a constant logan mela deen ‘ement
m running distance equal to the wave-length im free space
of oscillations of the same frequency.

We can express in words the relations involved in equations
(4) and (6). The former is equivalent to

KX, V—v
Dae iwi

When the dissipation of energy in the wires ts small the

° . . . . 1 J
logarithmic decrement, on running the fraction —— of a wave-
b) wv e 2or *

length, is equal to the fractional decrease of the speed of pro-
pagation.

2X2

648 Mr. W. H. Derriman on an Oscillating

Equation (6) gives

KV 2B

(Nie
PLP
er vas

When the attenuation is rapul the attenuation-constant ap-

; 20
proaches the value x where X ts the actual wave-lenath along
the wires.
(ueen’s College, Belfast,
2nd March, 1903.

LXVIL. On an Oscillating Table for Determining Moments of
Inertia. By W. H. Derriman, B.Sc., Demonstrator in
Physics, University College, Liverpool *.

TFNHE following description of an oscillating table for
determining moments of inertia is given in the hope
that the apparatus may prove useful in the laboratory, both
for determining moments of inertia of bodies experimentalsy,
and also for illustrating some of the laws relating to moments
of inertia. )
With this apparatus the moment of inertia of a body can
be determined not only for axes which do, but also for axes
which do not pass through the centre of gravity of the
body.
If a body of moment of inertia [is suspended by a wire and
allowed to make torsional vibrations, the time of vibration, ¢,
is given by the formula

(= an

where ¢ is a constant depending on the dinensene and nature
of the material of the wire. This gives the well-known means
of determining the moment of inertia of a body about an axis
passing thr ough the centre of gravity of the body, the constant
c being determined by another experiment with a body of
known “moment. of inertia. | mes!

— The apparatus which it is the object of this paper to
describe consists of a circular wooden table TT supported
by brass rods RRR, to which the suspending wire W is

* Communicated by the Physical Society : read January 23, 1903.

os G
Table for Determining Moments of Inertia. 649

attached by a small vice V. In the diagrams: shown, fig. 1
represents a side view ‘of the table, and fig. 2a plan of the
top of the table. P is a pointer attached to the centre of the -
table, and below is a fixed pointer P’ resting on a table
beneath, In the top of the table a circular groove (fig. 2) is

eut, in which small pieces of lead LULL can slide. These
pieces of lead form together half of a cireular ring of
rectangular cross-section. In setting up the apparatus a

plumb- “line is first hung from the supporting vice V’ and the
/

pointer P’ placed immediately below. The plumb-line is
then removed and the table suspended by the wire W. The
body whose moment of inertia we require to determine is _
placed at the given position on the table and the lead weights
LLL moved round i in the groove until the centre of ovavity
of the whole is in the axis V/P’, this being ascertained by the
pointer P being exactly above P’. The table therefore
always oscillates about the same axis; and since the lead
weights are ata fixed distance from this axis, the moment of
inertia of the table remains constant. Any alteration of the
total moment of inertia is only that due to the body piace. on
the table, 3 Lk . Vin Bas

650 Messrs. K. Honda and S. Shimizu on the

If the time of vibration of the table alone is observed and
then the time of vibration of the table with a body of known
moment of inertia placed on it, the moment of inertia of the
table can be calculated. It is only necessary then, in deter-
mining the moment of inertia of a body about a given axis, to
place it on the table in such a position that the given axis
coincides with the fixed axis of vibration, and again determine
the time of vibration.

Laws connecting the moments of inertia of a body about
different axes can be easily verified with this table, e. g., the
law that “the moment of inertia of a body about any axis is
equal to its moment of inertia about a parallel axis through its
centre of gravity together with the moment of inertia of the
whole mass collected at its centre of eravity about the given
axis,” can be verified by varying the distance of the ‘hody
from the axis of vibration.

LXVITI. The Wiedemann Lifect in Ferromagnetic Substances.
By XK. Honpa and 8. Suimizu*.

[Plate XVI.]

HE Wiedemann effect in iron and nickel is so well known
that it is superfluous to enter into the details of pe
phenomenon. The experiments by G. Wiedemann+, C. G
Knottt, Prof. H. Nagaoka and one of us§, show that so
long as the longitudinal field is not strong, the direction of
tw eh in iron coincides with that of a circular field, if this
direction is right-handedly related to that of the longitudinal
field ; they Bice show that in nickel the direction of twist is
opposite to that of iron in weak fields. The direction of twist
is reversed when either the circular or the longitudinal field
changes its direction. The Wiedemann effect in nickel steels
of different percentages was recently studied by Prof. Nagaoka
and one of us, and it was found that the twist is the same as
that of iron. The effect of tension on the Wiedemann effect
in iron and nickel was examined by C. G. Knott, who found
that tension diminishes the twist in these metals.

The present paper consists of two parts; firstly, we deal
with the influence of tension on the Woademens effect in
nickel steels, and secondly, with the same effect in ferro-

* Communicated by the Authors.

7G. Wiedemann, Poge. Ann, cil. p. 571 (1858) ; evi. p. 161 (1859) ;
Electricitat, iii. p. 797.

{ Knott, Trans. Roy. Soc. Edinb, xxxi. (1), p. 195 (1882-83) ; xxxy.

(2) p. 377 (1889); xxxvi. (2) p. 485 (1891).
§ Nagaoka and Honda, Jour, Coll, Sci, xiii, p. 263 (1900). .

Wiedemann Liffect in Ferromagnetic Substances. 651

magnetic bars and the effect of torque on it. We lately
published a paper* relating to the effect of tension on the
magnetic change of length; in this we found that the mag-
netic elongation of nickel steels is largely affected by tension,
and that when the tension exceeds a certain value, the con-
traction is accompanied by magnetization. From Maxwell’s
explanation as well as that of Kirchhoff for the Wiedemann
eftect, it seems probable that the direction of twist in nickel
steels is reversed when the suspended weight exceeds the
said limit. We therefore studied this point particularly and
found that the above inference is not correct. So far as we
were aware the Wiedemann effect in cobalt had not yet been
studied, perhaps because it is difficult to obtain a specimen
in the form of a wire on account of its brittleness. It was
therefore desirable to have an experiment for the metal.
Our apparatust used in studying the change of rigidity by
magnetization was conveniently used for examining the
Wiedemann effect in ferromagnetic bars. We had two co-
balt bars, one in the cast state and the other in the annealed.
The observations showed that the twist in cobalt was just the
reverse of that of iron, as was to be expected from its change
of length by magnetization.

We tested eight different examples shown in the following
table :—

Metal. Length. | Diameter. |
cms. cm.
45 per cent. nickel steel .... 20°80 | 0:0956
her es i yee} 20:90 | 0:0516
35 per cent. nickel steel...) 20°92 | 0:0939
‘ 3 » «| 20:96 | 0-0509
Soft iron bar ...ccceeeeeeee 21:03 , 1-004
haNielcellsar. 4..4t tuseceea vice 21:00 | 1117
Cast cobalt bar .......e+s+0 21:00 1-038
Ann. cobalt bar ........<... 21:00 | 1:082
|

Our arrangement for studying the Wiedemann effect in
nickel-steel wires was the same as that used by Prof. Nagaoke
and one of us in a former experiment.

To the extremities of a nickel-steel wire 21 cms. long were

dH, e . .
brazed stout brass wires, and a light mirror was attached to

* Phil. Mag. iv. p. 358 (1902).
+) [bid eiv. p 537 (1902).

652 Messrs. K. Honda and 8. Shimizu on the

the lower brass wire. The upper wire was clamped to a
small tripod which rested on the top of a magnetizing coil
provided with hole- slot- and plane arrangement. One end
of the accumulator was connected with the tripod while the
other was led to the mercury pool placed under the suspended
wire. The wire hung vertically in the axial line of the coil,
which was 30 ems. long,and gave a field of 37°97 c.G.s. units
at the centre by passing a current of one ampere. The ver-.
tical component of the terrestrial magnetic field was com-
pensated by placing another coil in the interior of the
magnetizing coil. The twist was measured by scale and_

The preliminary experiment showed that the resistance to
the twist offered by the mereury in the pool was not neeli-
gibly small when the thick brass wire was dipped into the
mercury. The resistance was especially noticeable when the
brass wire carried a narrow rectangular piece for the purpose
of damping. Hence, in order to efface the resistance, a non-
magnetic nickel-steel wire 0°5 mm. thick and 5 ems. long was
soldered to the lower end of the brass wire and dipped into
the mercury pool. By this the damping of the torsional

Wiedemann Effect in Ferromagnetic Substances. 653

oscillation was rendered very small, especially in the case
when a weight was attached. ‘To stop the oscillation a brass
wire was fixed horizontally to the vertical wire and bent
downward, as shown in the annexed figure. Just below it a
smail mereury cup was placed; this cup was connected with
a large one by a caoutchouc tube. This large cup was placed
near the observers and could be raised or lowered by means
of a screw adjustment. The motion caused the mercury in
the small cup to be raised or lowered, so that the side wire
dipped into the mercury or hung free. When we wished to
stop the oscillation of the wire, the side wire was dipped into
the mercury in the small cup, while the reading was always
taken with the wire hanging free of the mercury.

The experiment was conducted in the following manner:—

1. The circularly magnetizing current was kept constant,
and the amount of twist due to varying the longitudinally
magnetizing current was measured.

2. The wire was then stretched by different loads and the
above processes were repeated.

3. The longitudinally magnetizing current was kept con-
stant, and the amount of twist due to varying the circularly
magnetizing current was measured.

Before each experiment care was taken to demagnetize the
wire completely either longitudinally or circularly by passing
an alternate current of gradually diminishing intensity. This
was found absolutely necessary to secure correct results.

Twist by varying the longitudinal fieldi—If the direction of
the longitudinal field is right-handedly related to that of the
circular field, nickel steel is twisted in the direction of the
latter. Asshownin PI. XVI. figs. 1 & 2, under a given circular
field, the amount of twist at first increases till it reaches a
maximum, after which it gradually diminishes. But the re-
versal of the twist is never observed, though the field exceeds
1200 c.a.s. units. The position of the maximum twist is
slightly displaced in high fields as the longitudinal current
increases. The amount of twist is oreater in 45 per cent.
nickel steel than in 35 per cent. nickel steel.

In the experiment above cited, Prof. Nagaoka and one of
us observed in some cases the reversal of the direction of
twist in 45 per cent. nickel steel ; but in the present experi-
ment we did not notice this reversal of twist.

The effect of tension—TVhe effect of tension on twist in
nickel steels is not so marked as that of tension on the mae-
netic change of length in the same metal. As seen from
figs. 3 & 4, the tension always. diminishes the amount of
twist ; the diminution is large in weak fields, and becomes

654 Messrs. K. Honda and S. Shimizu on the

eradually less as the field is increased. The diminution is
approximately proportional to the applied tension.

To test the effect of heavy loading, thin wires about $ mm.
thick were examined. Even by a ‘tension at which contrac-
tion occurs by magnetization, the direction of twist in nickel
steels is not reversed, boob the amount of the maximum
twist is reduced to about 4 or L its value corresponding to no
tension, as seen from figs. 5 & 6.

Whichever theory we adopt, whether Maxwell’s or
Kirchhoff’s, the direction of twist is principally determined
by the sign ‘of the quantity 3\—o, where A and o are respec-
tively the length- and the volume- change of the ferromag-
netics. When there is no tension acting on the wire, the
sion of 34—o must be positive, because the direction of twist
in the alloy is the same as that of iron. By applying a heavy
load the magnetization is accompanied by contraction, so that
r Is negative. Hence, in order that 3\—o should be posi-
tive, o must necessarily be negative under a heavy load ;

et is, the change of ohne by magnetization a

change its sign from positive to negative as the load is
increased.

Twist by varying the circular fieldi—In figs. 7 & 8 we
notice that under a constant longitudinal field the angle of
twist at first increases at a constant rate, but later at a
eradually diminishing rate. As the longitudinal field is in-
creased the curves approximate to right lines, a result which
is to be expected from Kirchhoft’s theory of magnetostriction.
For, according to the theory, if the circular field is small
compared with the longitudinal field, the amount of twist for
a given longitudinal field is proportional to the longitudinal
current. ‘The amount of twist is greater in 45 per cent.
nickel steel than in 35 per cent. nickel steel.

By figs. 7 & 8 we can obtain the twist under a given
longitudinal current by gradually increasing the longitudinal
field s the result so obtained, if it is compared with figs. 1 &

23 2, shows that the twist produced by the interaction ‘of. the
circular and longitudinal fields is independent of the order of
applying them.

The apparatus for studying the Wiedemann effect in ferro-
magnetic bars was that used in the experiment on the change
of tigidity by magnetization ; the longitudinal current was
led to the bar by means of mereur y contact without causing
sensible resistance. The ferromagnetic bar was soldered at
both ends to brass bars of thicker diameter, as in the former

experiment just referred to, It was fixed by means of the

Wiedemann Effect in Ferromagnetic Substances. 655

screw nut at one end of the bar in the axial line of the mag-
netizing coil, which was placed magnetic east and west. The
pivot at the other end of the bar car rying a double wheel was
lightly placed in contact with the agate cup fixed to the
Ww “en frame. The twist was Tacnenred by means of a
rotating eylinder with a reflecting mirror, a vertical seale,
and a ‘telescope. Since the W iedemann effect is an odd
function of longitudinal or circular field, it is easily distin-
euishable from neler effects such as the change of the modulus
ae elasticity, which is an even function of fhe field. Prelimi-
nary experiments showed that the circular field has no effect
upon the modulus of elasticity, perhaps because the field is
not strong enough to cause smelt changes. They also showed
thatthe friction at the pivot is not serail - - for the amount
of twist when the pivot was left free or w hen it was supported

gave almost coincident values. The direction of currents was
alee so chosen that the rotation of the mirror causes contrae-
tion of the weak spring stretching the thin copper wire.
With the arrangement a twist amounting only to 1°83 x 107?
per cm. of our specimen was easily read,

The measurement was conducted in the same order as in
the case of nickel steels. Here we noticed that a slight
residual magnetism considerably affected our results ; hence,
before each deflexion was taken demagnetization was carefully
effected.

Twist by varying the longitudinal jfield.—F ig. 9 represents
the curves of twist per cm. in an iron bar plotted against the

oO
external longitudinal field. Here c¢ is the longitudinal cur-

rent per square centimetre. The general course of the curves
is similar to that observed in the wire of the same metal.
Under a constant circular field, the angle of twist increases
at first slowly and then rapidly till it reaches a maximum in
a field of about 100 c.G.s. units; it then diminishes and
ultimately changes its direction. The field in which the
twist reaches a maximum, and alse the field of reversal, are
markedly larger in the bar than in the wire. Moreover, the
diminution ue twist in the bar, after reaching a maximum, is
comparatively slow. These discrepancies will ev idently dis-
appear if we take into account the demagnetizing force
acting in a direction opposite to that of the magnetizing
force.

The results for nickel are drawn in fig. 10; the general
features of the curves are similar to those in the wire of the
same metal. The direction of twist is opposite to that of

iron in weak fields; butin strong fields the direction does not

656 Messrs. K. Honda and S. Shimizu on the

reverse, Taking into account the demagnetizing force, the
discrepancies with regard to the field of the maximum twist
and the slow diminution can easily be reconciled.

The direction of twist in cobalt is the same as in nickel.
In east cobalt the amount of twist is rather large, as shown
infig.11. The twist increases at first slowly and then rapidly,
till i reaches a maximum; it then gradually deer eases, and
ultimately changes its direction as The field is increased.
Thus the course of the curves is just the reverse of that in
iron. The behaviour of annealed cobalt as regards the
Wiedemann effect is remarkably different from that of cast
cobalt, as shown in fig. 12. In the first place the amount of
twist is much smaller in the annealed than in the cast cobalt..
Secondly, the field in which the twist reaches its maximum
is rather large in annealed cobalt. Thirdly, the decrease of

oD
twist after reaching the maximum is very slow and its direc-

cam} v
tion does not change, though the field is pushed to 1200 ¢.a.s.
units. The results for annealed as well as for cast cobalt are
just what is to be expected from the magnetostriction of these
specimens. It is also to be observed that these cobalt bars
were made of different samples.

Twist by varying the circular field.—Fig. 13 represents the
results for soft iron; as the circular field is increased, the
twist is increased first slowly and then rapidly. As the
longitudinal field is increased the twist reaches a maximum
and then gradually diminishes ; if the field is strong enough
the twist occurs at first in the opposite direction and then in
the ordinary. Comparing the above result with those ob-
tained by varying the longitudinal field, we notice one marked
difference, that for the same circular ane longitudinal fields
the amount of twist is largely dependent on the order in
which they are applied. The twist obtained by first applying
the circular field and then the longitudinal is several times
greater than the twist obtained when the order of applying
them is reversed.

In nickel the twist is opposite to that of iron ; under a

given longitudinal field it increases nearly at a constant ee
as the longitudinal current is increased, as seen from fig.
For a given longitudinal current, the twist reaches a maximum -
and then gradually decreases as the longitudinal field is in-
creased. Here again we observe that the twist obtained by
the application of the circular field, followed by that of the
longitudinal one, is far greater than the twist obtained when
the order of application i is reversed,

Wiedemann Effect in Ferromagnetic Substances. 6097

The general feature of the twist for cobalt is similar to that
in nickel. In cast cobalt (fig. 15) the twist is increased first
slowly and then rapidly as “the circular field ix increased.
With the increase of the longitudinal field the twist reaches
a maximum and then oradually diminishes. If the field be
strong enough the twist occurs at first in the opposite direc-
tion and then in the ordinary. In annealed cobalt (fig. 16)
the twist is very small and the rate of increase is nearly con-
stant. Here also the twist obtained by first applying the
circular field and then the longitudinal is several times
ereater than the twist when the order of application is
reversed.

The effect of torque—tTo study the effect of torque, it is
convenient to keep the longitudinal field constant and to vary
the circular field; for, though the application of the longi-
tudinal field is always accompanied by the twist due to the
change of rigidity, the passage of a longitudinal current does
not cause any appreciable twist ; hence, by varying the cir-
cular field, it is not necessary to apply the correction due to
the change of rigidity. The torque was given by means of
the suspended weight, as in the exper iment on the change of
rigidity by magnetization. Keeping the longitudinal field
constant, we found that in all cases the effect of tor que is to
diminish the twist by an amount which is nearly proportional
to the torque. Figs. 17, 18, 19, & 20 show the general
feature of the decrease of twist due to torque. In soft iron
and annealed cobalt the effect is very small, but in nickel and
cast cobalt it 1 1s considerable.

In a paper* on the mutual relation between torsion and
magnetism Prof. Nagaoka and one of us have obtained from
Kirchhoff’s theory the result that for given longitudinal cur-
rent and field, the amount of twist is inversely proportional
to the square of the radius of the ferromagnetic wire. It is
interesting to notice that the comparison of the above results
in iron and nickel bars 1 em. thick, obtained by varying the
longitudinal field, with the corresponding results in wires of
these metals slveut lL mm. thick, shows the correctness of the
law of the inverse square of the radius.

In conclusion, we wish to express our best thanks to
Prof. Nagaoka for useful suggestions in the course of the
present experiment,

* Nagaoka and Honda, Jour, Coll. Sei, xiii. p. 276; Phil. Mag. iv:
p. 63 (190 2).

f 658 J

LXIX. On a General Lheory of the Method of False Position.
By Kart Pearson, /RS., University College, London*
(1) [* is Im many cases impossible, in others extremely

laborious, to fit a curve or formula to observations
by the method of least squares. I have shown in another
placef that the method of moments provides fits which are
sensibly as good as those given by the method of least squares.
But while the latter method fails to provide a solution in the
great bulk of cases, and while the former is much more
frequently successful, there still remains a class of cases in
which the unknown constants are involved in the curve or
function in such a complex manner that neither method pro-
vides the required solution. In such cases the following
generalization of the ‘* method of false position ” will be found
serviceable. Apart from practical value, however, the method
is of considerable interest as showing a quite unexpected
relationship between trial-and-error methods of fitting and
the general theory of multiple correlation.
(2) Let there be a series of observed values Y’, Y”, Y/”..

LLL

corresponding to values of another variable X’, xX" pie fs

and suppose we desire to determine the m constants a, 6, y...v

so that
Y=0(Xhay Bygyenv)) oo
shall be a curve or formula closely representing the observed
facts.
Suppose (z+ 1) reasonably close trial solutions to be made,
i.e. (n+1) false positions given to the curve, and let the cor-
responding constants be

at, es se, io Tana

O15 Pi, Vig ee e) os eae
a2) Ps, ey hs eee
Any [Ses Ying : Vis

Let the corresponding values of y, calewated from these
trial solutions, be :

/ ifid J//
J } J / J ee
Yi» AL > oe
Y2 > Y2 > 2

Yu, Yn, Yn
and let there be m such values used,

* Communicated by the Author.
+ ‘On the Systematic Fitting of Curves to Observations and Measure-
ments,’ Biometrika, vol. 1. pp. 265- 504, and vol. 11. pp. 1-25.

General Theory of the Method of False Position. 609

For brevity write :

a= on Sp =) GP. oC. Tir (11. )
where
S(y—y P= (yr — y+ (ye y+ yy)
and
es a
rx On Xtm= Se WYp—y) » +» + Ui
where

SYp—Y) (Yo —Y) = (yy “eG side gen a” bis y")
+ (yy) Yor i Netter

Let the actually observed values be, yy! yy", yo”..., and the
best values of the constants for these values :

Boy Boy Yo Rec Vi.
Then, clearly, if p and p! take any values from 1 to n,
it is merely straightforward arithmetic to discover the

numerical values of any op and7,,. Let

Y=$(X%, Boy B,, Yoo ot Vy)
be the required formula. Then, by the method of least
squares, we require to make
pee cee

a minimum by elie INOW aL ON yk

Now by “reasonably close feaal > solutions, I intend to
convey that any series of constants a), Bp, Yp,..-Vp differ by
fairly small quantities from the “ best values.” See we
shall consider the differences a —2,, By—Byy Yp— Yo.» Vp —VYo
so small, that to a first approximation their squares Ge be
neglected. The whole process may, however, be repeated
when a very close degree of approximation is required, by
taking a series of fits with small divergences from the first
approximation. We have to our degree of approximation

Y=¢(X, a+ a1, — 2%, B+B,—8. Mok Voy v+y,—yv)

dg dp , db | re)
= =y+(Ao7 +A, Fou IN cae De +... AY iy

where
A a= ap—a, Ke,
Further let us write

dd/da=ca,

Then we have to make

t= S(y- (ia ae ‘aA, te cap +... +cvA Mes

S denoting a summation of y, y, through all the possible

dp) dd kv
de® Sap —l).

660 Prof. Karl Pearson on a General
Ds 5 Yo Yo’ Yo's Yo”. .aud the corresponding # values in
Cay CB» te ays ;
This gives us the type equations :
S(ca(y,—y) ) =A aS (Ca) +A, BS(cacz) +... + AvS(cacy),
S(cg (y, —y) ) = As (ca¢3) = APS (cg?) AP esse AVS (egcr),

S(er(y,—y)) =A, (cyca) + A,8S(eveg) +... + A,vS(ev"). iv.)
We have thus » equations to find the » unknowns A.2,
A,@,...A,v, so soon as the summation terms have been found.
But, clearly,
YY = Apa Cy tApBegt+...+Apvev. . + (¥.)
Multiply by y,—y and sum :
Mp Fo Mop= Apa (caly,—y)) F APES (egy YI +--
+ApvS(er(y,—y)). + (vi)
Taking p from p=1 to p=n, we have n equations to find
the unknowns S(ca(y, —y) ),S(¢a(yo—y)) ...S(@(y.—y)) on the

left of equations (iv.) above.
Now let D=the determinant

Aja, Ave: Aw
A,a, A.P,... Agy

Nags AnP,. sc An
and suppose d,, to be the minor corresponding to the con-
stituent of this in the pth row and gth column. :

Then
1

cee h {dial —y) + daa (Y2 —Y) + Uza(Y3—y) +... + dnalyn—y) §

1 2
[S {di3(yi—y) + dopY2—y) + dg (¥s—y) +... + dnglyn —y)- + (vil
Hence © | ,
S (¢ 7) = = {dya?oy” + dyaaog* +... + dna on"

-- 2d adsaG1Col's9 + ehawe + Qa —ja dnatn—{onln= 1 f
ia w (otra. Seer -
= D? 1 S (dpa"op") ai 28 (dpadp'at pO p'lpp') i. ees? S (viil.)

p=1
the second sum 8! embracing all pairs from 1 to » of unequal
p and p :

Theory of the Method of False Position. 661
Multiplying and summing we have
m

= Bt 2 , :
S(cacg) = = bD? : Ss (dpadpgop’) -b S'(dpadp'3 $+ dp'alpg) apop' ry! } (ix.)
a

the symbol 8’ being interpreted as betore.
Lastly, solving equations (vi.) we have

pH=n
Sicaly,—y)}= i | : (dpa pp) \ ‘ 5 (sc)

If results of which (vill.)-(x.) are the types be substituted in
iv. we have » equations to find the unknowns Aga, Ad®,...Agv.

These equations did not look very hopeful ad initio. I solved
them, however, by brute force for the first three cases, or for
formule involving only one, two, and three constants, and to
my surprise the results came out with remarkable simplicity
of form—namely, the general regression equations discussed
in my memoir of 1901 (PhiJ. Trans. A. vol. 200. p.9). A
little consideration showed that the analytical process was
similar to that involved in the discussion of the theory of
multiple correlation, but there seemed to be no direct physical
reason for applying the results of the correlation theory to
the problem of false position. I therefore put equations (iv.)
and (vill.)—(x.) before Dr. L. N. G. Filon, who has so often
come to my aid in algebraical difficulties, and he has provided
me with the following general solution.

We have, using y,, to denote S(¢a”), yg3 for S(e¢,),

Xap for S(cacg), he. and who, tor S(caly,—y)), Wg for
S(ea(yo.—y)), &e. from (ix.) and (viii.) :

Hie fl”
Xca= Dp S (dpedpatp”) + 8'( (dpedp'a + dp’c Apa) Opop'"pp') }
p=

. , p=n
Xe3= oe ik (dpedppop ) + Ss ‘((dpectp' B + cp! edpB)Fpap' “pp ‘) }

e
Wt

). = Dp (4 (dpe” Oy’) + 28’( (ped ple) epairny')

hi ira
Me; = D2 AS (dpedpyop )+S’ ((dpedp' v+dp'e dpy) a pop! rpp') ;
Multiply by Asa, As®...Asv respectively and add, remem-
bering that
e€—vV
S (dpeAse) =0, or = D, according as p is not or is equal to s:
e=a
e=y mas ae
\ : Xe oc ked Vt cee :
S (Xee Ase’) a VD S (dpeapr sp). Naar (X1.)
a p=
6. Vol. 5. No. 80. June 1903. a0¥

GS. a
{|

Phil, May.

662 Prof. Karl Pearson on a General

Again from (x.)
Moy P=”

vou= PD a (dpatp?p)

es
MoyP=”

bpep=ph 8 : (dpBoprp)
p=

NiGig = mae

bov= FH 8S (qpvepr.y)
p=

Multiply again by Ase, As8,...Asv respectively and add.
We find :
S (hy-Ase) =mon0s',5. =. >
Equations (xi.) and (xii.) are true for every value of s
from 1 to n.
Now multiply equations (iv.) by Asa, As@..., Asv and add
them: we find after dividing by a common factor :
oos= Aa Jas t+ A,B Jpst Avy Syst... + A.vdos . (xiii)
where
p=n
Jes = S (dpeOprsp)/D.
p—A
There will be n such equations, if we take s=1 to s=n.
Now consider the determinant

R= be Poly VO dy eee Von
| V105 it Vio; ae Vy 0
720, ? 21s il, 7 271

MNO) Vis Tan « J |

where the 7’s are defined by equations (1i.) and (i1.) above.
Let R,, be the determinant found by striking out the first row
and column, and let py be the minor of R,, corresponding to
the constituent 7 in R,,.. Further let Ro, be the minor of R
corresponding to the constituent ros, then it may be shown
that
: t=n

S(7 pu) == Roz: . . . . . (xiv.)
t=1

Write out the equations like (xii) for s=1 to s=n, mul-
tiply them respectively by pyy, Poys---Pye and add.

Theory of the Method of False Position. 663

We have by (xiv.):

A, A, A,
= Roe: a= pr daayR,, + MF dpar By, +...+ =p, d'voe'R,, » (xv.)

since f=n
et (pu?) =0 unless s=é’, and then it =R,..
Rearranging we have :
Roe 0, Aa A fe) Av
ee ee aa ary OCG to Oe CR ye
Keo. amen 1 pee Crm)

Multiply by Aye, Aze,... Ane the equations obtained by
writing t/=1 to n respectively. We find finally :

i. {(g Fo Vare fe (Re = Ane + ey +(e!) One \ ./ +(Xvil.)

Roo 2 Root n

This is the required result, and appears to be a very remark-

able one.

(3) We notice that :

(i.) The quantities in round brackets are the well-known
partial regression-coefficients of the theory of multiple cor-
relation.

(ii.) The form of the function used is not directly involved
in (xvil.), the coefficients being solely functions of the observed
and trial solutions.

Hence, if the trial curves be given by the use of a me-
chanism which involves s degrees of freedom in its placing
and setting screws &ec., s+1 trials will give us by the method
of false position the best position and setting of the mechanism
to strike the closest curve. In this ease the actual mathe-
matical form of the function may be unknown or unknowable *.

ii.) The multipliers of the constant-differences Aye, Ave, Ke.
are absolutely the same, whatever constant we are seeking.
Hence, if they are once determined numerically, however
many constants there are in the formula, no additional trouble
is involved. For example, in fitting a circle to n arbitrary
points, the correction of its radius on the reference-circle

* For example, it is a commun practice with draughtsmen to fill ina
curve through a series of plotted points by aid of a spline bent through a
series of arbitrary points obtained by the sharp vertical edges of weights
placed on the drawing-board. Hach such edge has two degrees of free-
dom. Hence given m such weights and the spline, 2+1 trial solutions
would by the method of false position give the position for the weights
to get the best spline curve through the observations. Of course such a
process would be using a steam-hammer to crack nuts, but it will suttice
to suggest how perfectly our result is freed of mathematical function or

hypothesis.
WV 2

664 Prof. Karl Pearson on a General

radius will be given by exactly the same for mula as the cor-
rections for the coordinates of its centre.

The various uses of the formula (xvil.) can only be briefly
indicated here.

It arose from the consideration of a special physical
problem. A somewhat complex formula for astronomical
refraction had been obtained which involved for given
meteorological conditions one arbitrary constant only. How
was the value of this to be determined from the observed
values of refraction at different altitudes? The direct
application of the method of least squares was idle; the
constant was involved in far too transcendental a manner for
such a method to be of service. Accordingly two trial solu-
tions were made, and the values of o,, o1, anil ro, found; then
the correction of the constant, ¢,—e, is given by

g—e= Mn (4-6) . 22h Ga

where € and e, are the two trial values, and ¢ is taken as the
reference trial.

This corrected solution has again to be taken as a trial
solution with the better of the two trials, and thus avery close
value for the constant in question can be determined.

Clearly the only calculation involved in (xviil.) is by (ii)
and (iil.) :

ro 0, ee S (YoY) eu)
o| S(yi—y)?

Formula (xviil.) immediately led to its generalization for
two unknown constants determined by three trials, 7. e.

M9 Vol E
€,—€= Eyal Seah aot ee €,—€) : (x1x.)
and this ultimately to the complete generalization given in
(xvil.).

If n+1 trials are used to determine one constant, then it is
easy to see that the best result will be obtained by using
(xvii.) straight off.

Another service which, | think, can be performed by the
method of false position is of the following kind. It is well
known that the accuracy of both physical and astronomical
investigations can be largely influenced by temperature,
pressure, or hygrometrical conditions. What are the most
suitable conditions to carry on a particular class of observa-
tion under? Let such conditions be represented by a &, ¥.
Then make four trial sets of observations of the kind under

Theory of the Method of False Position. 665

consideration on quantities whose real values may be con-
sidered absolutely known by past experience, the values of the
physical conditions being varied for the four trials. The
method of false position “Will then give us very closely the
most suitable physical conditions for undertaking investiga-
tions of the proposed kind.

A very simple extension of these ideas ought to make the
method of considerable service to experimental psychology.
What are the psycho-physical conditions best suited to mental
judgment or to clearness of sense-perception ? Interval after
food or exercise, external temperature, pulse, &c., &e., are all
‘constants ” whose best values can be found by the ‘ method
of false position,’ and a novel field for research seems to
suggest itself here.

Lastly, turning to more mathematical conceptions, the
method appears to offer a definite systematical treatment for
the combination of the results of different series of observa-
tions on the same physical substance. For example, two
observers give a pressure-volume formula of the same form
for a gas, but with different values of the constants. It is
required to modify the constants, so that the formula may fit
most closely a new set of data, or the combined data of the
previous observations. In such cases the formule may be
used as trial solutions, and additional trial solutions be made,
if required, by very slightly varying the constants.

Another such application will occur to the astronomer,
namely, the modification of the constants on which planetary
and cometary orbits depend. Here as many observed
positions of the body may be used as the calculator can be
taxed with, and the six constants of the orbit found by trial
solutions differing slightly in their constants from the approxi-
mate or hitherto current values. I am not aware that the
method of false position has ever been used by astronomers,
but I think it possibly might be of assistance to them.

Having indicated some possible uses of the present method,
I give an illustration of its application. I limit myself to
one case in order that this paper may not be unduly extended.
I hope in some experiments about to be undertaken to give
later an example of more practical utility.

IMlustration.—Let us fit a good circle to the following five
points :

C—O. ie O) oor y =2,
pes = Youlo, ct. y= Ld.
=o Ue 1-6,

By simply plotting the points on a piece of decimal paper,

666 Prof. Karl Pearson on a General

and striking circles with a pair of compasses, the following
circles were found without difficulty to give moderately
close fits :

(e —2°2)? + (y — 0)?= (2°2)?,
(@—2°3)? + (y, +3)? = (2°4)*,
(@2—2°7)? + (yo +°8)?= (2°8)’,
(ty —2°4)? + (yg t°T)2= (2°5)2.

Here there are three constants h,, k,, and 7,, the coordinates
of the centre and the radius, to be found.
We have at once, using the first circle as a reference-circle :

Aha Se= —°3, re.
AWhk= IN —°'8, Nor b.
eae A3k= — 7, Asr="

The following are the ordinates found from the four circles:

Observed. Reference Circle. Circle I. Circle LI. | Circle ITT.

pp, |t 9 0 +886 1) -22:05805 lamp
Toe) Ics 1-844 1-717 | 1-425. | ae
pe SN Ps 2:19] 2081 | 1911 | 1-768
ee a 2220 2-049 1-696 | 1984 | 1-797
fast Tesi 1-265 1394 1680 | 1-291

The ordinates show, what was indeed the fact, that our
trials were rough, 7.¢., made without any attempt at great
exactitude ; actually they were four out of the first five
circles shinee We now form the differences of the ordinates
and have

From these we find at once by straightforward arithmetic :
og, =" 25645, -o(="19833, “og "29462) os=-olleae
and fairly easily by using Crelle’s Tables :
oy = AT 0,334, Tops lode Os 193 = 815,868, :
Tog = 01 Seas: ry ='373,191, 19 = 403,317,

Theory of the Method of False Position. 667

The coefficients in 7 of the regression equation are now
respectively :

Pol (1 —13,) — 102 ("12 — 31723) — "3 (731 a 293)

172, — 73, — 17, + 27937 97 Ce
23 31 12 23°12" 3]
2
(1 — is.) aa 1°93(1"93 =P os) —To1 ("12-7 237°31)
hii. 4 eet Oe or | : Sa SOU a Oe

oo 2 az A
ahaa ta 2Toat 27°31

¥93(1-- iy) ame 01 (731 = Ko3P 12) aa 192( 723 — 3,712) ,
- : 2 : ='318,083.
Ih SS oe 27937273)
Whence the general numerical formula for modifying the
constants of the reference-circle is:
A ¢='093,522A,€ + 602,783 A,€ + '255,849A3¢,
Putting e=h, k, 7 successively we have for the circle of
approximately closest fit :
h,=2°562, i; == —*689, fa Z Oot.
The accompanying table gives the ordinates, or differences

found from this approximate circle of closest fit, and from the
four trial circles.

Ordinates. | | Differences. |
bu dhe |
| | |
| Ob- | Closest | Closest stay oie (2nd 3rd 4th
| served. Circle. | Circle. Trial. | Trial. | Trial. | Trial.
a SS) eee —— |i eee || pemee |)
c= 0a O05 Old ! +:015 | ‘000 +386 | —°058 000
ee 15 1460 || —-040 | +:344 | 4:217 | —-075 | —:‘129
be—2...| 18 | 1908 || +108 | +391 | --281 | +111 | —-0382 |
woo.) 20) a 1-932 — 068 +°049 |, —004 | —-016 | —:273 |
fee) Wop 554579) 4-045)! |= -239 ds | +180 | —-279 |
S a t of Mean | | | y |
quare Root of Mean | . | eas ¥ ey
aquste Diferonce | |) 008. | 28 239 | 104 | “184 |
|

It will be observed that tested by the square root of mean
square of the differences, the circle obtained by this method
of false position is 3 to 4 times as good as all but one of the
trial circles. The third trial was a peculiarly lucky one, but
even here the false-position circle is more than half as good
again. The accompanying diagram gives the four trial
circles and the false-position circle. If we wanted a still
closer approximation, we should now throw out the worst of
the trial solutions, 7. e. the first, and work from the first

(

668 Mr. R. A. Lehfeldt on a Potentiometers

approximation and the remaining three trials to get a second
approximation. The diagram, however, shows that little

General Method of False Position.—Best Circle through Five Points.

billed: yen ALLA PEt ae

eer edad Bray

CPECEEESEE EEE

PEER EEE

PEEPEEEEEEEE EE EERE EEEEEE EEE
PEA ERE eee
aap AMEE
aes Seo a
7 AE oeeaepe PET PEPE
Parana

a Cee es

PSSEE EE i SCENE HE
gabe ESE SSE
|| \ Becks LE heeaya Frans |
ea hee Ree.
FEEEECE suas, SESREEEEEED
ne a BEARERS

could be gained by this extra labour, and this illustration of
the circle fully suffices to indicate the comparative ease with
which the new method may be used on a hitherto unsolved
type of problem. The labour would not have been much
greater had we required a circle (or any other three-constant
curye) through even a dozen points.

LXX. A Potentiometer for Thermocouple Measurements.
By R. A. LEAFELDT*.

OQ make a satisfactory potentiometer for thermoelectric
work, it is essential that it shall not introduce a high
resistance in the circuit of the couple and galvanometer. Most
of the potentiometers in the market, which answer well enough
for comparing voltaic cells, failin this respect. I have there-
fore devised an instrument which is shown schematically in
fiy. 1. From the positive terminal of the accumulator B
current flows to the switch K by means of which it can be

* Communicated by the Physical Society : read March 13, 1903.

for Thermocouple Measurements. 669
sent through 100 or 100 +900 or 100+ 900 +9000, in order

to get three grades of sensitiveness : it then passes throu oh 20
coils of 0-1 each, a slide-wire of a little more than 0-1 “ohm.

Fig. I.

SETI Bin See Sees Be GEE E22 5,
20 FAs Oe Ol 0

and through the adjustable resistance R back to the accumu-
lator. The fixed resistance of 100, 1000, or 10,000 ohms is
shunted by a cadmium cell C and galvanometer G, and R
adjusted till the galvanometer is balanced. The thermocouple
T with @ oalvanometer G is put across any number of the tenth-
ohm coils, and any fraction of the slide-wire. Of course two
ealvanometers, as shown in the diagram, are not necessary :
a double pole-switch puts the actual instrument into either
circuit as desired.

The voltage on the ends of one of the tenth-ohms (taken
as unit) is then 1000- 10,000- or 100,000th part of the
cadmium, 2.¢., approximately 1000, 100, or 10 microvolts,
according to the position of K.

Fig. 2 represents the actual instrument. The greatest
care has been taken to avoid accidental thermoelectromotive
forces, which are the chief trouble in using thermocouples.
‘The couple I have actually used so far is constantan copper,
which gives about 4000 microvolts between 0° and 100°.
The only metals used in the measuring circuit are copper
and manganin. All the coils are of the latter metal; the
slide-wire is of gilt manganin ; the galvanometer connexion
is made by a short bridge between the slide-wire and a similar
galvanometer wire. (These two wires are shown in the figure
by the side of the scale, though actually underneath it.)
The slider makes contact alwi ays, a separate key being used
to put the galvanometer in circuit. The potentiometer is
inclosed in a wooden case, lined with thick sheet copper and
filled with paraffin-oil to keep the temperature constant, and
the two points where the copper thermocouple leads join the
manganin measuring circuit are carefully buried deep down
in the interior of the box and near together,

670 Mr. R. A. Lehfeldt on a Potentiometer

The sliding contact is carried by a block sliding on two steel
bars: it is moved by a steel rod with clamping and fine
adjustment screws, and its position read through a lens by
means of a vernier graduated in fortieths of a millimetre.

~--o ht ~

As the wire is 100 millims. long the smallest reading is =

of the unit, which, as stated above, may be 1000, 100, or

10 microvolts; and as there are 20 tenth-ohm coils, the

smallest reading is a of the largest.

The fineness of reading is, as a matter of fact, limited by
the sensitiveness of the galvanometer used.

All the working parts are inclosed by a plate-glass lid
through which only the handles project.

Outside the potentiometer itself the apparatus used consists of
the accumulator (sometimes two or more) ; the adjustable re-
sistance R; the cadmium cell ; galvanometer—a highly sen-
sitive D’Arsonval of about 20 ohms, made by the Cambridge
Scientific Instrument Co. ; and galvanometer key. The latter
is of the usual short-circuiting reversing type, but unusually
small, made of copper, and inclosed in a box from which

for Thermocouple Measurements. 671

only the ebonite studs project, for the better avoidance of
thermoelectric effects.

To calibrate the instrument the procedure is as follows :—

(i.) The 100%, 1000, and 10,000» resistances are compared
directly with standards. To allow of this and similar opera-
tions, the heads of all the studs in the instrument carry
serews. The comparison was kindly made for me at the
National Physical Laboratory.

(ii.) Hach tenth-ohm is compared with the succeeding one
by the usual method for comparing nearly equal resistances ;
the slide-wire is compared with the first tenth-ohm in the
same way. During these operations current is led through
the coils and the voltage taken off at the same points as when
the potentiometer is ordinarily in use.

(iii.) Groups of ten tenth-ohm coils in series are compared
with a standard ohm by the method described in the follow-
ing paper.

(iv.) Further, as a check on the results, two groups of
ten tenth-ohm coilswere measured at the National Physical
Laboratory in the usual way. These measurements are of no
direct use, however, as in making them current 1s led into and
out of the coils at the points ordinarily used for taking off the

voltage ; hence the result differs from that obtained in (i11.)

by fie resistance “of the studs, which is one or two ten-
thousandths of an ohm.

(y.) The slide-wire is calibrated.

It would be a convenience in calibrating to provide an
additional terminal, connected to the point of junction of the
last tenth-ohm with the hundred-ohm coil, as this would
enable one to lead in current under the usual working con-
ditions without passing the high-resistance coil: this is
desirable when calibrating the tenth-ohms, as it is safe to use
pretty large currents through them. Otherwise I have found
the working of the instrument satisfactory.

Before measuring a thermocouple, two tests should be
made. First, the galvanometer-key should be pressed half-
way down, so that the galvanometer-circuit is broken. The
needle will probably swing a little: If it swings equally on
each side of its previous position of rest, there is no thermo-
electric effect in the galvanometer. Second, a short piece
of copper wire should be put across the thermocouple ter-
minals and the battery-cireuit broken: if then (with double-
pole switch set to the thermocouple circuit) on pressing the
galvanometer-key there is no deflexion, this shows absence of
disturbing thermoelectric eftects in the rest of the apparatus.
The measurement may then be proceeded with.

Wx oo Ge a ome

LXXI. A Resistance Comparator. By R. A. Learenpt*,
oS to sliding contacts on account of the thermo-

electric effects they tend to introduce, and irregularities
slide-wires often show when a good deal used, I have designed
this comparator without any. It consists of two coils of 99
ohms each (bc fy) connected by twenty coils of 0:1 ohm each.

NWA NX

The latter are arranged circularly, so that a switch connected
to the galvanometer may be set on any one of the intervening
studs. When the comparator is to be used in the ordinary
way, to make a simple Wheatstone’s bridge, the terminals de

* Communicated by the Physical Society : read March 13, 1903,

On a Resistance Comparator. 673

are connected by a short copper strap. When, as in the
potentiometer-coils for the measurement of which this com-
parator was designed, there is an appreciable connecting
resistance between the coils to be compared, the two-point
bridge method is used; the strap is then removed and an
adjustable resistance inserted. The ends 6g of the comparison
resistances are connected by copper straps to the cups of a
mercury commutator, and through that to a pair of large
binding screws that project outside the board carrying the
coils.

When the galvanometer switch is set on d or e each arm
is 100 ohms ; as it Ls moved round the dial the resistance is

altered by steps of ;.,, part. The galvanometer deflexions are
olnee for the two positions nearest balance and interpolation

tO 7) calculated. In this way I consider that an accuracy of

one part in 100,000 is attainable.

To calibrate the comparator the two arms are adjusted to
be as nearly equal as possible, and then compared by the use
of a pair of nearly equal resistances measured in the usual
way. Next the resistances from > to d and from e to g are
separately compared with a standard 100%, and ¢ to d and e to
7 with a standard ohm. Finally, a good box is put in parallel
with cd and ef in turn and the ratio corresponding to each

stud determined. This need only be done to <j part to ob-

tain aoou0 | in the final results.

The method of interpolating by the galvanometer has, I
think, been unduly neglected. Hven when one tries to carry
out a strictly null experiment, one is obliged, on account of
thermoelectric effects, and so on, to observe accurately minute
movements of the galvanometer needle. It therefore does
not introduce any new difficulty to read the galvanometer-
scale exactly each time, and jit may be made, as in this com-
parator, to avoid reading the position of a sliding contact on
a scale. I think therefore that there is gain of + accuracy as
well as of convenience in using the inter polation method.

The galvanometric arrangements I have adopted for this
purpose are as follows:—A plane mirror, 15 mm. diam., is
attached to the coil of the (D’Arsonval) galvanometer, A
telescope of 25 millim. aperture is placed some 600 millim. in
front, and, mounted on the telescope-tube, one of Zeiss’s trans-
parent glass scales, backed by ground-glass and illwninated
by a small incandescent lamp behind. The mirror and tele-
scope were made by Mr. Hilger: the scale is 100 millim.

long, and the graduations are ‘exceedingly ine. Altogether

the definition is so good that one can read to ,, millim., ¢. e. to

» 20 », —

674 Prof. 8. P. Langley on “Good Seeing.”

of the scale-length, with ease and certainty, although the
scale is very short. Under these circumstances, to claim one
per cent. accuracy in interpolating is well within the mark.
I should like to take this opportunity of emphasizing the
remark made some years ago by Professor Threlfall, that it
is better to attain sensitiveness in a galvanometer by having
a big mirror and first-rate optical conditions, than to push the
_ electromagnetic sensitiveness to an extreme.

The apparatus described in this and the foregoing paper
is intended for temperature measurements in an attempt at
determining the Joule-Thomson effect, and was purchased
out of a grant made for that purpose by the Royal Society,
and I am glad to express to them my thanks for the liberality

oO
which has enabled me to undertake the work.

LXXII. “ Good Seeing.” nee . P. LANGLEY *.
[Plate X VIL. |
Astrophysical Observatory, Washington,
November 12, 1902.
JVERY one who has used a telescope knows that our
atmosphere is forever in pulsating motion, and troubling
our vision of the heavenly bodies, during the most cloudless
day or night, so that observatories are put even on high
mountains to get rid of the disturbances in this atmosphere,
which tend to make the image of every object tremulous
and indefinite, and to prey ent what the astronomer terms
“ good seeing.”

[ desire to speak to the Association about a device which |
have recently essayed, for diminishing this universally known
and dreaded “ boiling ”” of the telescopic image, a difficulty
which has existed always and everywhere since telescopes
have been in use, and which has seemed so insurmountable that
L believe it has hardly ever been thought of as subject to
correction.

Hitherto it has been the endeavour of astronomers, so far
as I know, to secure a more tranquil image by keeping the
air in the telescope-tube, through which the rays pass, as quiet
as possible, and for this purpose the walls of the tube have
been made non-conducting, and extreme pains have been
taken not to set up currents in the tube. With these precau-
tions the “ seeing ” is, perhaps, a little better, but very little,

* Communicated by the Author.—A paper read before the Washington
Meeting of the American Association for the Advancement of Science,
December 30, 1902.

Prof. 8. P. Langley on “(Good Seeing.” 675

than if none were used at all, the main difficulty having been
always found insurmountable.

I have been led for some years to consider the conditions
under which this “ boiling ”’ presents itself. It is not neces-
sarily due to a high temperature of the external air, for the
most perfect definition I have ever seen of any terrestrial
object was obtained by me long since in the Harvard College
Observatory, at Cambridge, with its great equatorial telescope,
when, on the hottest day that I ever knew in a New England
summer, I directed it with a high power on the distant
“south mark,’ which I expected to find almost indistinguish-
able from the “boiling.”” I remember my extreme surprise
when, under a magnifying power of 300, | found the image
as still as the lines of an engraving. This was an extra-
ordinary exception to ordinary experience, and led me to take
an interest in the subject. I have since pursued an inquiry
to which this circumstance first directed my attention, and
I have done so at all altitudes, at one time residing on Aetna
for this purpose, noting that even on high mountains vision
was so far from being always clear that it was sometimes even
much worse than at sea-level.

I have since come to the important conclusion that while
the ordinary “ boiling” is due to all the air between us and
the sun or star through which the rays pass, the greater
portion of it is due to the air immediately near us, probably
within a few hundred yards, or even feet, from the telescope,
and this has led me to ask whether it was not possible that
some way to act upon this air could be found. Its non-
uniformity leads to deformations of the image too complex
to analyse here, which are caused not only by lateral vibra-
tions of the cone of rays, but by its elongation and contraction.

For this purpose 1 have within the last few months been
making experiments at the Smithsonian Astrophysical Ob-
servatory, first with a horizontal tube having three successive
walls with air- -spaces between, which was intended to give
the maximum security which freedom from changes of
temperature could afford. This Observatory being princi-
pally concerned with rays best studied in an image formed
by reflexion, has no large dioptric telescope, on which ac-
count these experiments have been made with a reflector. I
have no reason to suppose, however, that they will not be
equally successful with a dioptric telescope.

A large part of the “ boiling ” of the image is due to air
without the tube, but a not unimportant “part to the air
within it and, in ‘the preliminary experiments the air, kept
still in the tube by treating it with the ordinary precautions,

676 Prof. $8. P. Langley on “Good Seeing.”

was found to have little effect on the erdinary ‘ boiling ” of
the image, which so seriously prejudices the definition. An
image-forming mirror, fed by a coelostat, was placed at the
end of this triple- walled tube, which was itself sheltered by
a canvas tentand contained the stillest air of the most uniform
temperature which could be obtained. The “ boiling ” was
but little diminished merely by inclosing the beam by this
tube, which was only what had been anticipated from the
ordinary experience of all astronomers.

The device which I had determined to try was one of a
paradoxical character, for it proposed to substitute for this
still air which gave the usual troubled image, agitated air,
which it was hoped would give a still image. For the purpose
of this new experiment, the horizontal telescope, using a
reflector of 40 feet focus fed by a coelostat through the
above tube, was connected with a fan run by. an electric
motor, which was arranged to draw out the air from the
inner tube, at the same time that it forced air in at different
points in its length, so as to thus violently disturb and churn
the air along all the path of the beam from the coelostat to
the solar image.

This first experiment gratifyingly reduced the “ boiling”
and produced an incontestibly stiller image than when still
air was used. Asa further test, a series of artificial double
stars was now provided, and the concave mirror, acting both
as collimator and objective, brought the images to focus,
where they were examined by an eyepiece. With the stillest
air obtainable, the images were not sharp and only the
coarsest doubles were resolvable. Then the blower was
started and the definition immediately became sharp. Vio-
lently stirring the air in the tube, then, eliminates all, or
nearly all, the «1 boiling” of the stellar image which arises
within the tube itself when using ordinary still air. This
experiment concerned the air w ithin the horizontal tube only.

{ have next taken up the solar image formed by the mirror
in the above tube. This is clearly improved by the stirring,
but, as a supplementary impr ovement, I have wished to try
a tube something like a prolonged dew- -cap, but which is
arranged to be inclined toward the sun, so that the beam
may pass down it before being reflected by a mirror into the
horizontal tube to form the image. This inclined tube is to
be connected with the blower like the horizontal one, and
the air in both can be stirred together, but experiment has
not yet gone far enough to demonstrate whether it has, as is
hoped, any superiority commensurate with the special me-
chanical difficulties involved in the research. Again, there

Proportion of Argon in Vapour rising from Liquid Air. 677

was very marked “boiling” before starting the blower,
which largely diminished while the blower was going.

Iam not prepared to give quantitative estimates, which I
hope to furnish later; but all observers to whom I have
shown these early results have agreed, that if the “ boiling ”
was not wholly cured, what remained was but a small fraction
of that obtained with still air. I have not completed these
experiments, which | am still pursuing at the Observatory,
but they seem to me to give promise of an improvement of
universal interest to observers, which justifies the making of
this early announcement. I had hoped to have shown the
Association some photographs of the sun taken, first in the
ordinary way, and again with the churned air, but the con-
dition both of the sun and of the sky of late has prevented
my obtaining them. I can, to my regret, only give here a
photograph (Pl. XVII.) of the images of the artificial double
stars as seen through ordinary conditions, as distinguished
from those here mentioned, of artificial “ good seeing.”

LXXIII. On the Proportion of Argon in the Vapour rising
from Liquid Air. By Lord Rayuzien, O.M,, F.RS.*
iy | eee boiling-point of argon being intermediate between
those of nitrogen and oxygen, 1t may be expected that
any operations of evaporation and condensation which
increase the oxygen relatively to the nitrogen will at the
same time increase the argon relatively to the nitrogen and
diminish it relatively to the oxygen. In the experiments
about to be detailed the gas analysed was that given off from
liquid air, either freshly collected, or after standing (with
evaporation) for some time—from a day to a week. The
analyses were for oxygen and for argon, and were made upon
different, though similar, samples. Thus after an analysis
of a sample for oxygen by Hempel’s method with copper
and ammonia, 4 or 5 litres would be collected in a graduated
holder, and then the first analysis confirmed on a third
sample. In no case, except one to be specified later, was the
quantity of gas withdrawn sufficient to disturb sensibly the
composition. The liquid was held in Dewar’s vessels, but
the evolution of gas from below was always sufficient to keep
the mass well mixed.

The examination for argon was made ina large test-tube
inverted over alkali, into which the gas was fed inter-
mittently from the holder. The nitrogen was gradually
oxidized by the electric discharge from a Ruhmkortf coil in
connexion with the public supply of alternating current, the

* Communicated by the Author.

Phil. Mag. 8. 6. Vol. 5. No. 30. June 1903. 2 Z

GLOr Lord Rayleigh on the Proportion of

proportion of oxygen being maintained suitably. by additions
of oxygen or hydrogen as might be required. In the latter
case the feed should be very slow, and the electric discharge
should be near the top of the test-tube. Great care is
required to prevent the hydrogen getting into excess ; for if
this should occur, the recovery of the normal condition by
addition of oxygen is w very risky process. After sufficient
gas from the hoider, usually about 2 litres, had been
introduced, the discharge was continued until no more
nitrogen remained, as was evidenced by the cessation of
contraction and by the disappearance of the nitrogen line
from the spectrum of the discharge when the terminals were
connected with a leyden-jar. When it was certain that all
nitrogen had been removed, the residual oxygen was taken
up by ignition of a piece of phosphorus. On cooling, the
residue of argon was measured, and its amount expressed as
a percentage of the total gas taken from the holder.

The results are shown in the following table. The oxygen,
expressed as a percentage of the whole, varied from 30 to
about 98. From 48 to 90 per cent. of oxygen, the argon,
as a percentage of the whole, scarcely varied from 2-0

Percentage of | Percentage of | Argon as a percentage of
Oxygen. | Argon. | the Nitrogen and Argon.

| 30 ech ies 1-9

43 | 2°0 a9

64 | 2°0 5°6

75 | 2] 8-4

90 2°() 20°0

98 76 33°0

100 | 0-0 100°0

The experiment entered under the head of 98 per cent.
oxygen is not comparable with the others. In this case
55 litres of gas were collected as the /ast portion coming
away from a stock of liquid as it dried up. Nor was the
subsequent treatment quite parallel, for the whole of the
oxygen was first removed with copper and ammonia leaving
125 c.c. of mixed nitrogen and argon, of which again by
subsequent analysis 42 c.c. was found to be argon. The last
entry corresponding to 100 per cent. of oxygen is theoretical:
and does not represent any actual experiment.

It must be clearly understood that these results relate to
the vapour rising from the liquid, and not to the composition
of the liquid itself. So far as the oxvgen content is concerned,

Argon in the Vapour rising from Liquid Air. 679

the comparison may be made by means of Mr. Baly’s
observations (Phil. Mag. xlix. p. 517, 1900). It will appear,
for example, that when the vapour contains 30 per cent. of
oxygen, the liquid will contain about 60 per cent., and that
when the vapour contains 90 per cent. the liquid will be of
95 or 96 per cent. At every stage the liquid will be the
stronger in the less volatile constituents ; ; so that the
proportion of argon to nitrogen, or to nitrogen + argon,
will be higher in the liquid than in the vapour.

The constancy of the proportion of argon to the whole
over a considerable range may be explained to a certain
extent, for it will appear that the proportion must rise to
a maximum and thence decrease to zero. To understand
this, we must remember that “liquid air”? is something of a
misnomer. In the usual process the whole of the air
concerned is not condensed, but only a part ; and the part
that is condensed is of course not a sample of the whole. As
compared with the atmosphere the liquid contains the less
volatile ingredients in increased proportion, and the part not
condensed and rejected contains the more volatile ingredients
in increased proportion. The vapour coming away from the.
liquid.as first collected has the same composition as the gas
rejected in the process of condensation. At the beginning
of our table, a point, however, which it would be difficult to
reach in actual experiment, we should have an oxygen
content much below 20 per cent., a ratio of argon to nitrogen
+argon below 1 per cent., and in all probability a ratio of
argon to the whole also below 1 per cent.

The object which I had in view was principally to obtain
information as to the most advantageous procedure for the
preparation of argon. So many laboratories are now provided
with apparatus for liquifying air, that it will usually be
convenient to start in this way if a sufficient advantage can
be gained. The above results show clearly that the advantage
that may be gained is great. Something depends upon the
procedure to be adopted for eliminating the nitrogen. Upon
a moderate scale and where there is a supply of alternating
current, the method of oxidation, as in the analyses, is
probably the most convenient. In. this case it may be an
advantage to retain the oxygen. If the oxygen content be
about 60 per cent., as in the third experiment, the proportion
is about sufficient to oxidize the nitrogen. We may compare
this with the mixture of atmospheric air and oxygen which
behaves in the same manner. In the latter case the proportion
of argon would be reduced from 2:0 per cent. to about ‘4 per
cent., so that the advantage of using the liquid air amounts

to about jive times. In the arrangement that I deseribed for
OMY (Oem
ad 44d he

680 Hon. R. J. Strutt on Radioactivity

oxidizing nitrogen upon a large scale * the mixed gases were
absorbed at the rate of 20 litres per hour.

In the alternative method the nitrogen is absorbed by
magnesium or preferably by calcium formed in situ by heating
a mixture of lime and magnesium as proposed by Maquenne f.
In this case it is necessary first to remove the oxygen; but
oxygen is so much more easily dealt with than nitrogen that
its presence, even in large proportion, is scarcely an objection.
On this view, and on the supposition that liquid air is
available in large quantities, it is advantageous to allow the eva-
poration to proceed to great lengths. A 20 per cent. mixture
of argon and nitrogen (experiment 5) is easily obtained.
Prof. Dewar has shown me a note of an experiment executed in
1899, in which a mixture of argon and nitrogen was obtained
containing 25 per cent. of the former. In the 6th experiment
38 per cent. was reached, and there is no theoretical limit,

P.S.—I see that Sir W. Ramsay (Proc. Roy. Soc.
March 1903) alludes to an experiment in which the argon
content was doubled by starting from liquid air.

LXXIV. Radioactivity of Ordinary Materials. By the Hon.
R. J. Strurr, Fellow of Trinity College, Cambridget.

TZ is now well recognized that the air in any ordinary

vessel possesses the power of conducting electricity,
under electromotive forces insufficient to produce luminous
discharge, although only to a very slight extent. It has
been usual to refer to this eftect as the “ spontaneous ioniza-
tion” of the air. This name suggests that the conductivity
is in some way an essential property of the air, just as the
electrical conductivity of metals is inseparably connected with
the nature of those bodies.

Mr. C, T. R. Wilson, however, has found (Proc. Roy. Soe.
vol. lxix. p. 277) that when other gases are substituted for
air, the relative ionizations are in nearly the same ratio as
those which I observed (Phil. Trans. 1901, p. 507) for the
same gases under the action of Becquerel radiation. Further,
Mr. J. Patterson has found (Proc. Camb. Phil. Soe. xii. p. 44)

* Chem. Soc. Journ. Ixxi. p. 181 (1897); Scientific Papers, vol. iv. p. 270.

+ Iemployed this method successfully im a lecture before the Royal
Institution in April 1895 (Scientific Papers, vol. iv. p. 188). In a
subsequent use of it I experienced a disagreeable explosion, presumably on
account of the lime being insufficiently freed from combined water.

t+ Communicated by the Author. Part of the above was published in
‘Nature,’ Feb. 19, 1903. It appeared afterwards that some of the results
had been anticipated by Prof. MacLennan and also by Prof. Rutherford
and Mr. Cook, in papers read before the American Physical Society in
Dec. 1902, although no account of their experiments had then appeared in

print. Ihave thought it best to confine myself to the description of my
own results, so as to give an independent view of the subject.

of Ordinary Materials. 681

that, when a large vessel is used, the amount of ionization is
not proportional to the pressure, but tends towards a limit,
when further increase of pressure no longer affects it. This
is exactly the behaviour that might be expected if the effect
was due to a feeble radioactivity of the walls of the vessel,
the radiation being easily absorbed by the air. I have re-
cently carried out a series of experiments, with a view to
decide whether the nature of the walls of the vessel had any
influence on the rate of discharge of a charged body inside it.
The figure represents the
experimental arrangement
adopted. ais a charged wire
in the axis of the cylindrical
vessel b. The walls of b
could be lined with any de-
sired material by inserting a
cylinder ce composed of it.
This could be done by re-
moving the glass plate d at
the end, which was cemented
on. The vessel could be
exhausted through the stop-
cock f if desired. e was
a drying-bulb containing
phosphoric anhydride. The
wire a_ passed air-tight
through the brass cap g,
cemented on to the neck h
of b; h was made of lead-
glass, on account of the

of this kind of ee The
cap g carried a ‘brass strip
k carrying a gold leaf l,
The whole was surrounded
by a vessel m as shown. n
was an iron wire attached to
a platinum wireo. This iron
wire could be brought into
contact with & by means of
an external magnet in order
to charge the system. m
could be exhausted through
the stopcock p, and dried
by means of the phosphoric
anhydride contained in 9.
The position of the gold leaf was read by a microscope with
micrometer eyepiece focussed upon it,

682 Hon. R. J. Strutt on Radioactivity

Before making an experiment the insulation, which is all
important, was tested. m was permanently exhausted, and
the stopcock p closed. 6 was also exhausted, for the time,
and a charge given to the brass strip &, so that the leat /
diverged. An interval of one hour was allowed in order that
any absorption of the charge by the glass insulation # should
have time to take place. After that it was found that
there was no measurable movement of the leaf over the scale-
divisions in two or three hours; 4 of a division would have
been visible.

When the vacuum test of insulation had been made, dry
air was admitted into the vessel b. It was assumed that the
glass insulation, which was satisfactory in a vacuum, re-
mained so when air which had been dried by passage
through phosphoric anhydride was admitted in contact with
it. As soon as the air was admitted into b, a leakage of
electricity from the wire a was observed.

The amount of this leakage, in scale-divisions per hour,
with various materials surrounding the charged wire, is given
below.

Pinkoily ees. exer he nail none le ee a3
Witte; another Sample 220 ic-......225-e see 2°3
Glass, coated with phosphoric acid ...... 1°3
Silver, chemically deposited on glass 1°6
TRVING BR arth, sn et eon ace tee 1-2
head a3 wie, eco: I tA et, Cog. Z2
Coppers clean) Wea ean ca b..4. 0 ne eee 2°3
Ditto, thoroughly oxidized .................. 1
Platinum (various samples)...... 2°0, 279 nore
JEN CG UG 0 OUUD LT tpg te ots UMS rare feu “4

It appears, then, that there are very marked differences in
the rate of leak when different materials constitute the walls
of the vessel. There can, therefore, be little doubt that the
greater part, if not the whole, of the observed ionization of
air is not spontaneous at all, but due to Becquerel rays from
the vessel.

It is, I think, interesting to find that the phenomena of
radioactivity, which have hitherto been regarded as rare and
exceptional, are really everywhere present. ‘The rate of leak
with various pieces of tinfoil from the same stock was always
the same, as nearly as the experiments could show. But, as
may be seen in the table, a piece from another stock gave a
different amount of leakage. The same holds good for plati-
num, one specimen tried being twice as active as another

of Ordinary Materials. | 683

It was found that ignition did not affect the pene tee of
a given sample of platinum.

In order to compare the activity of the substances men:
tioned above with that of uranium salts, a. small.crystal of
uranium nitrate measuring 12 x 4 mm. was cemented to the
inside of the cylinder. The rate of leak due to it was found
_to be thirteen times that due to the most active SRO gue of
platinum. The area of the uranium nitrate was.only 54,
part of that of the platinum, so that its activity for an equal
area would be no less than 3000 times greater.

It is possible that the radioactivity “of or dinary materials
may be due to traces of the more active substances. This
would explain the varying activities of different samples of
the same material. Only an infinitesimal proportion of ra-
dium would be required. Radium is at least 100,000 times
more active than uranium, and uranium 3000 times more

active than the most active common material that I have.
experimented with. So that one part of radium in three
hundred million would suffice to account for the observed |

effects.

Becquerel rays emitted by the various substances, This can
be done, in the case of powerful radiators like uranium or
radium, either by examining the deflexion in a magnetic
field, or by observing the amount of absorption by solid or
gaseous. media. In the case of very feeble radiators it would
be quite impracticable to attempt the magnetic experiment,
while the absorption by solids can scarcely be examined,
‘since the solid absorbent would give off radiation of its own
comparable in amount with that due to the original radiating
substance. We are reduced, then, to examining the absorb-
tion by air*.

In order to compare various radiations in this way we have
only to examine the variation of leak with pressure. In the
case of the more absorbable radiations less pressure will be
required to make the current sensibly independent of a
further increase of pressure, or, what is the same thing, to
absorb practically all the radiation.

In the experiments the apparatus used was similar to that

* It may be remarked that in all probability some part of the observed
ionization of air may be due to radioactivity of the surrounding air in
the other parts of the vessel. But it is not apparent how this can be
experimentally distinguished from the ionization due to the walls. In
all probability this ionization due to surrounding air is small], since it is
scarcely possible to understand otherwise how ‘the ionization for large
pressures could be sensibly independent of pressure,

It was evidently important to compare the quality of the

684 Radtoactivity of Ordinary Materials.

described above, except that the current was taken between
coaxial cylinders, diameters 2°7 and 9°8 cms. respectively.
The outer cylinder was provided with ends of the same
material as the walls, so that the air between the walls was
not exposed to the radiation of any other substance than that
which it was desired to examine. Experiments were made
with walls of zinc and of two samples of tinfoil of different
activities.
The results are tabulated below.

Zine. More active tinfoil. Less active tinfoil.

Pressure (inches). Leak. | Pressure (inches). Leak. Pressure (inches). Leak.
2 . “OF . .

—_—_—— —-

66 95 7 9 "26

10-7 16 30 18 9°8 pe |
168 20 5°41 34 14:4 19
21°8 2°7 10°6 6:0 20°2 25
24-7 2°6 166 55 245 2°6
29:0 2°6 23° 1 6:0 30:1 23
30°71 2°8 29'8 6:2 386 2'3
38°6 32 39°2 55

These measurements are less accurate than might be wished
as they were made under somewhat unfavourable conditions,
at the Royal Institution. The vibration from the machinery
running in the basement made it impossible to take exact
readings*.

It is clear, however, that the current due to radiation from
the zine walls does not reach a limit within the range of
pressure experimented upon. With the more active tinfoil
the limit is reached at about 10 inches pressure, while
with the other specimen of tinfoil 20 inches are required
before the current reaches its full value. We may infer that
the radiation from different samples of the same material
varies, not only in quantity, but in quality also.

It was desired to compare the radiation from tin and zine
with that from uranium nitrate. Some small fragments of
the latter were cemented at intervais over the surface of the
cylinders, and the rate of leak taken for various pressures.
It was found that the leak began first to diminish con-
siderably at 20 inches pressure, although, owing to the
presence of a small proportion of penetrating rays in uranium
salts, the limit was not very definite. It appears that the
a radiation from uranium has about the same penetrating
power as the radiation from the second specimen of tinfoil.

* This remark does not apply to the measurements with the firat
apparatus, which were much more accurate.

Secondary Radiation from Gases subject to X-Rays. 685

Prof. Rutherford’s experiments * show that the & radiation
of thorium and radium differ somewhat from that of uranium,
being more penetrating. In all probability the radiations
from the tinfoil, and perhaps from the zine also, are of the
same general nature as the a@ radiations from uranium,
thorium, and radium, though differing somewhat in quality.

LXXV. Secondary Radiation from Gases subject to X-Rays.
By Coarues G. Barkua, M.Sc. (Vict.), B.A. (Cantab.),
King’s College, Cambridge; Oliver Lodge Fellow, University
College, Liverpoolt.

ADIATION from air through which X-radiation was

passing was first noticed by Réntgen {, through the

effect produced on a photographic plate which was screened
from the direct radiation.

Sagnac§, who studied secondary radiation from metals
subject to X-rays, also obtained a much smaller effect from
air, and concluded it was more easily absorbed than the
primary radiation producing it. The following is an account
of a more complete investigation of the subject of secondary
radiation from gases subject to Réntgen rays.

An X-ray bulb and exciting induction-coil were placed
inside a large wooden box which was completely covered
with thick sheet lead. A small rectangular aperture in
the side of the box near the bulb permitted the radiation to
pass in a definitely bounded beam through air or any other
gas outside the box.

In the first experiments no attempt was made to inclose
the air through which the radiation was directed, so that

* Phil. Mag. July 1902, p. 11. Every one must recognize the merit
of Prof. Rutherford’s most valuable experiments on the absorption of
Becquerel rays by air. But I must confess I cannot follow the reasoning
by which he seeks to deduce from them the coefficient of absorption. His
calculation starts on the assumption that if I be the intensity of radia-
tion close to an infinite radioactive surface, the intensity at a distance x
is [e—At, where A is the coefficient of absorption. No doubt if the radia-
tion were emitted wholly in a direction normal to the surface this would
be so. But, as a matter of fact, an element of area of the surface emits
much of its radiation in an oblique direction. This obliquely emitted
radiation has to pass through a greater thickness of air before it has
reached the distance « from the infinite radioactive plane. Thus the re-
lation between intensity and distance becomes greatly complicated. It
is impossible to calculate it without knowing the relation between the
intensity of radiation from an element of area, and the angle between that
element and the direction of propagation.

+ Communicated by Prof. L. R. Wilberforce.

t Annal. Phys. Chem. Ixiv. 1, pp. 18-87 (1898).

§ Comptes Rendus, exxvi. pp. 521-528 (1898).

686. Mr. C. G. Barkla on Secondary

after passing through another rectangular aperture in a lead
screen placed several centimetres from the side of the box
and parallel to it, the X-rays were not intercepted by any
solid body for a considerable distance—about two metres—
but passed.merely through air.

_To detect the secondary radiation, a special form of electro-
scope was used. It consisted of a case (as shown in fig. 1),

Hig. 1
a

with four sides of stout brass. One end G was of glass, and
at the opposite end a face of any desired material and thick-
ness could be placed. As in C. T. R. Wilson’s* experiments
on Spontaneous Ionization, the gold-leaf and brass plate to
which it was attached were suspended i in this case by a bead
of sulphur S, which was fixed to the lower end of a vertical
brass rod R. This passed axially through a cylindrical brass

neck N, whose lower end was movable along grooves in a
* Roy. Soc. Proe, vol, xviii. pp. 151-161 (1901).

Radiation from Gases subject to X-Rays. 687

direction perpendicular to the two ends, and from. which it
was separated by an ebonite plug P. Connexion could be
made between this rod and the insulated plate and gold-leaf
by means of a light spring K which was attached to the red,
and which when. set in vibration made contact with the
insulated portion of the electroscope. The capacity of this
was exceedingly small in the later experiments, the brass
plate being replaced by a straight piece of copper wire to
which was Seared a narrow strip sat gold-leaf. The deflexion
of the gold-leaf was observed through & microscope with
graduated eyepiece, which was fixed just outside a small
glass window M in one side of the case.

When the rod was connected to one terminal of a battery,
while the other terminal was earth-connected, the insulated
plate and gold-leaf could be charged by means of the contact-
maker, which made momentary connexion .between the rod
and plate, leaving the plate and gold-leaf charged and
insulated.

When this was the case, a leak of electricity from the plate
and gold-leaf was only possible by the sulphur support or
through the air in the electroscope. It was shown that the
leak by the support was negligible by first discharging the
electroscope completely, and then charging the cylindrical
supporting rod to a high potential, by connecting to one
terminal of a battery the other terminal of which was earthed,
and then leaving the apparatus for a number of hours. The
amount by which the leaf and plate charged was (the amount
of leak through the support) —(the amount of leak through the
air). ‘The latter was very small, as the potential of the plate
and gold-leaf was little different from that of the case, which
was earth-connected, There was no perceptible change in
the position of the gold-leaf.

When the rod was kept at a higher potential than the
insulated portion, and this again was at a considerably higher
potential than the earthed case, the leak through the gas was
not negligible, and the amount by which the ‘leaf and plate
charged was

Bifount of leak through the support) — (amount of leak
through the air) =a.
When, on the other hand, the leaf and plate were charged toa
higher potential than the suppor ting rod the loss of cha arge by
the former was
(amount of leak through the support) + (amount of leak
through the air) =8.
When the potential of the leafand plate was the same in each

688 Mr. C. G. Barkla on Secondary

case, the leak through the air was of course the same ; and
when the difference of potential between the supporting rod and
the gold-leaf and plate was the same, the leak by the support
was also the same.

The potentials of the rod, plate and gold-leaf, and the case
may in the two experiments be written 2n, n, 0, and 0, n, 0
respectively.

The leak by the support was thus $(2+), and the leak
through the air 4(@—2).

The support leak, however, in the following experiments
was to the leaf and plate trom the supporting rod, and was
excessively small as the potential of the leaf and plate was
not allowed to sink much below that of the supporting rod.

Any leak then must have been due to the conductivity of
the air in the electroscope. In its steady normal state, when
the potential was high enough to produce a saturation
current, this measured the spontaneous ionization of the air.
Anything more than this must have been due either to the
introduction of ions from outside, or to the formation of ions
in the inclosed air itself by radiation from outside.

In the preliminary experiments made upon air which was
not inclosed, care was taken that the beam of X-rays emerg-
ing from the second screen did not fall upon any solid in the
neighbourhood. It was shown by putting screens much
nearer and measuring the secondary radiation from these
that the secondary radiation from the wall (distant 2 metres),
upon which the beam fell, was inappreciable. The electro-
scope was placed well out of the direct beam (through the
two rectangular apertures in the box and screen) with a thin
paper face parallel to the near bounding-plane of the beam.
The electroscope-case, box, and screens were earthed.

The rate of motion of the gold-leaf was noted when the
induction-coil was not working, so that this measured the
spontaneous ionization of the air. When the bulb was worked
the leaf fell much more rapidly.

The aperture A (fig. 2) in the box was then covered with
lead, and the effect on the electroscope was again normal,
showing that the rapid fall was not due to direct radiation
through the lead covering of the box inclosing the bulb and
induction-coil and through the second opening B to the paper
face of the electroscope. ‘The effect was therefore caused
by radiation proceeding through A.

When B was covered with lead the motion of the gold-
leaf was again normal, so that the fall was not due to direct
radiation from A through the lead of the screen.

The electroscope being out of the direct beam, the leak was
due indirectly to radiation passing through A and B,

Radiation from Gases subject to X-Rays. 689

When the length of the aperture B was kept constant and
the width altered, the rate of motion of the gold-leaf was

EARTH

approximately proportional to the width of the slit and there-
fore to the breadth of the beam. This proved that the effect
was not due to secondary radiation from the edges of the
lead round B, for when the slit was very narrow, doubling
its width added littie to the length of the edge, while the
motion of the gold-leaf was twice as rapid.

The same thing was also proved by screening the paper
face of the electroscope from direct radiation from B by a
sheet of lead, which was so arranged as to intercept very
little radiation proceeding from the air through which the
primary beam passed.

When the paper face was covered with a sheet of lead, the
electroscope was perfectly screened,

It was at first (when very thin paper was used for the face
of the electroscope) doubtful whether some of the ions formed
in the air by the primary radiation were not pulled through
pores in the paper into the electroscope. The paper was
moistened with acidulated water, so that it could be kept
perfectly at zero-potential with the other parts of the case,
and hence so that there was no electric field outside due
to the charge on the plate and gold-leaf. There was thus
no electric field drawing the ions into the electroscope. The

690 - Mr. C. G. Barkla on Secondary

moisture, however, affected the normal fall of the gold-leaf* ;
but the ‘ereat increase produced in the rate of motion by
what appeared to be a secondary radiation was not materially
affected.

A very fon leaf of aluminium was put over the paper
face and was connected to earth with the brass case, and it
was found tha the ionization produced inside was not appre-
ciably reduced.

It was therefore evident that the ionization inside “was
produced by a radiation proceeding from the gas which

was subjected to primary X-radiation, or that there was
still a diffusion of ions through the paper and aluminium
leaf.

An aluminium plate was then placed on the side of the
primary beam opposite to the face of the electroscope but
outside the beam. This was connected first to the positive, then
to the negative terminal of a battery of 100 cells, whose other
terminal in each case was earthed. As the electroscope-face
was at zero-potential, there was in each case an electric field
of about 40 volts per centimetre across the beam in opposite
directions in the two cases. The ions which would discharge
the electroscope were in one case attracted away from the
electroscope to the plate, and in the other case attracted to
the face of the electroscope. But it was found that there was
no appreciabie difference between the two leaks in the two
cases, showing :—

(I y That there was not a diffusion of ions through the paper

and aluminium face; and

(2) That the radiation which came from the gas was not

in any way the result of recombination of the i ions, for
the ions were withdrawn before they had sufficient
time to recombine.

The ionization of the air in the electroscope was therefore
the result of radiation from the gas upon which primary

radiation fell, and this secondary radiation was independent
of the subsequent behaviour of the ions in the primary
beam.

The absorbability of the secondary radiation was then in-
vestigated. To ascertain the order of magnitude of this
absorption, the electroscope was placed with aluminium and
paper face just outside the primary beam. When this face

was covered with lead no ionization was detected. The rate
of ionization was measured when there was no_protect-
ing plate and when the face was covered with a sheet of

* Probably due to a radioactive substance in the water.

Radiation from Gases subject to X-Rays. 691

aluminium °012 cm. thick. The difference showed the amount
of secondary radiation previously absorbed by the air in the
electroscope now absorbed by thealuminium. The secondary
beam was, however, in this case not directed, so that the
effective thickness of the plate was greater than °012 cm.
With one bulb the absorption amounted to 47 per cent. of the
initial intensity—taking the amount of ionization in the
electroscope as proportional to the intensity of the radiation
passing through—while the absorption of the directed primary
beam (in this case falling perpendicularly on the absorbing
plate) was 30 per cent. Thus the absorption was of the same
order of magnitude as that of the primary beam.

To test this more accurately, the electroscope was placed
several centimetres away from the primary beam, and received
the secondary radiation which passed through rectangular
apertures in two parallel lead plates. All the rays entering the
electroscope through the second aperture passed through the
first, so that the effective thickness of a protecting plate was
very little greater than the actual thickness. As the beam
was more perfectly directed in successive experiments, the
proportional absorption by similar plates of aluminium of the
direct and secondary beams was found to come closer and
closer into agreement. The absorption-coefficients for the
primary and secondary radiations cannot differ by more than
10 per cent. of their value, for the radiations experimented
upon. I conclude that the penetrability of the primary and
secondary rays is practically the same.

In order to investigate the subject more fully—more par-
ticularly to ascertain what the intensity and the penetrability
of the secondary radiation were dependent upon—different
gases were used in place of the air through which the primary
_ beam was directed. As the gas had to be inclosed, it was of
course necessary to guard against secondary effects from the
containing chamber reaching the electroscope. The shielding
from this secondary radiation made it impossible to expose
the electroscope to radiation from a large quantity of gas,
and made it necessary to place the electroscope some little
distance from the gas the radiation from which was being
studied. The effects were thus considerably diminished.
A metal box 14 ems. x 10 cms. x 10 cms. was constructed with
inlet and outlet tubes for the gases, and with two parchment
windows, one at the end and the other at the side. In some
experiments the former was of thin aluminium (‘011 em.).
This was for the admission of primary radiation from the bulb.
The secondary radiation passing through the side window
was studied.

692 Mr. C. G. Barkla on Secondary

The arrangement was then as follows:—

A bulb and induction-coil were placed inside a lead-covered
box M (fig. 3) in one side of which was a rectangular aper-
ture A through which a beam of Rontgen rays passed.
Immediately outside this aperture were lead shutters §,, so

EARTH

that the width could be varied as desired. Two large lead
shutters S, were placed at a distance of 17 cms. from this
aperture and parallel to the side of the box, so that the width
of a second aperture B was adjustable.

The gas chamber described above was placed with its end
window immediately behind the second screen, with its end
face against the two shutters and in such a position that a
beam of X-rays passed through the parchment window and
the opposite end of the box while the sides were perfectly
protected. The electroscope L, which was placed with its thin
face opposite and parallel to the side window F, was protected
by lead from radiation which might otherwise have entered
it through its other faces. The thin face was protected from
radiation from all directions except through the window of
the gas chamber.

The primary beam did not fall upon this window, so that
no primary radiation was received by the electroscope.

Again, the two sources of secondary radiation from solids

Radiation from Gases subject to X-Rays. 693

were the thin window through which the primary beam
entered the box, and the end C through which it left. To
protect against any effect from these, a leaden screen S; with
rectangular aperture D was placed at a distance of 5 cms.
from the side window F,, and with the aperture opposite this
window. In that position no rays from the end window, or
from that portion of the opposite end of the chamber which

was subjected to the primary rays, passed through the side
window and through the aperture in the screen, so that the
electroscope, which was placed immediately behind this screen,
did not receive any secondary radiation from solids.

But it was obvious that it would receive tertiary radiation
from at least one source. To properly guard against this
would have necessitated a considerable diminution in the
energy of secondary radiation from the gas which it was
desired to measure. Instead of this, then, the tertiary radia-
tion falling on the thin face of the electroscope was made
as small as possible, and was afterwards proved to be
negligible.

This tertiary radiation arose from the secondary rays from
the first window EH falling on the side window F of the gas
chamber and on leaden screens surrounding the thin face of
the electroscope, also from the secondary rays from the other
end of the gas chamber falling on the side window and leaden
screens.

To ascertain the magnitude of this effect, experiments
were made with air. In the first case the parchment side
window # was removed and placed immediately in front of
the thin face of the electroscope, so that no secondary radia-
tion fell upon it; also the leaden screens protecting the thin
face from other radiations were placed a considerable dis-
tance from the electroscope so that the tertiary radiation
received by this must have been excessively minute. In
the other case these were brought as near as possible and
the parchment window was placed in its normal position
in the gas chamber, so that it was a source of tertiary
radiation.

In the first case the electroscope measured the ionization
arising from the secondary radiation from the air and from
the very weak tertiary radiation from the leaden screens. In
the other case the ionization arose from the secondary radiation
from the gas and a maximum tertiary radiation from screens and
windows. The difference between the intensities of the total
radiation received in the two cases was too small to be
observed.

Phil. Mog. 8. 6. Vol. 5. No. 30. June 1903. 3A

694 Mr. C. G. Barkla on Secondary

The conclusion was therefore that the tertiary radiation
from solids was negligible, so that the ionization measured. by
the electroscope was produced by secondary radiation from
the gas inclosed in the gas chamber.

As the intensity of the primary radiation was not constant
throughout the experiments, a second similar electroscope Z
was placed behind a leaden screen with a small hole X in it
opposite the thin face of this electroscope, and primary radia-
tion from the aperture A in the large box containing the
induction-coil and bulb passed through this small hole into
the electroscope. The rate of motion ‘of the gold-leaf was a
measure of the rate of ionization produced | in air by the
primary radiation, or for rays of the same kind it was a
measure of the intensity of primary radiation. The total
deflexions in a given time were then used to standardize the
intensity of primary radiation.

The two charging-rods of the electroscopes were connected

to one terminal of a battery Y whose other terminal was
earthed. Momentary contact was made with the insulated
portions by means ot the contact-makers and the gold-leaves
were deflected. Both electroscope-cases were earth-connected
so that a definite deflexion corresponded to a definite potential
of the gold-leaves. The deflexions were read by the micro-
scopes N and P. Readings were taken at intervals for
several hours in order to measure the constant fall due to
spontaneous ionization of the air in the electroscopes. The
induction-coil was then worked for thirty or, in some cases,
twenty seconds, during each whole minute for another period
—usually an hour. Readings were taken at intervais and a
constant proportionality between the deflexions of the gold-
leaves was found. The electroscope subjected to primary
radiation was then used to standardize the intensity of the
radiation proceeding from the bulb.

When another gas was experimented upon, everything
remained in position as before. A gas generator G was con-
nected to an inlet tube which was at the top or bottom of the
gas chamber according as the gas was lighter or heavier
than the gas which it was replacing. An outlet tube T con-
ducted the gas from the opposite end of the chamber. The
insulated portions of the electroscopes were recharged and
the same experiments repeated when the gas to be experi-
meuted upon filled the box. The deflexions of the standardiz-
ing electroscope in a given time did not vary much, but those
of the other electroscope varied considerably with the gases
used, as the following table shows :—

Radiation from Gases subject to X-Rays. 695

Duration Deflexion of Deflexion of
of Standardizing Secondary
Experiment. Electroscope. Electroscope.
Pei ha ea ek TITY 16°85 6°2
Hydrogen . 32 min. 16°5 Jo
Hydrogen . 54 min. 17-5 0)
Pai, keeeloo Min. 18°35 6°39

Tt should, however, be remembered that when different gases
occupy the | DOX, equally intense primary radiations entering
the box are only equally intense at the end of the box by
which they enter, and that the gases of higher absorption-
coefficient are really subjected to less intense radiation than
those which are more transparent. A correction must there-
fore be made for this loss of intensity due to absorption by
the gas contained in the chamber. Taking the path of the
middle primary and secondary rays as approximately giving
the average distance travelled in the chamber, the correction
necessary was that due to transmission through about 10 cms.
of gas.

The absorption by the different gases was approximately
as follows ft :—

Flee Eis sins fe a) Want eahelw) per Cent.

iivdrogen) s\n). eecgtaen 0)

Sei pcrcied Hydrogen aTAS
2

Carhon Dioxide’ +); 4):
Sw pau Dioxide.) 4): aye

The following table gives the relative intensities of ionization
of the air in the electroscope produced by the radiation from
different gases subjected to equally intense primary radiation.
Corrections have been made for spontaneous ionization and
for absorption of radiation in the gas chamber.

Assuming the penetrability of the radiations from the
different gases to be approximately the same—(justified
later)—the second column gives the relative intensity of
secondary radiation from the gases subjected to similar and
equally intense primary radiation from the bulb. The effect
from air has been taken as unity, the possible percentage error

in the case of hydrogen being very great.

* Experiments were made on spontaneous ionization and any stray effect
reaching the electroscope. Corrections have been made for these in the
above table.

t+ Rutherford, Phil. Mag. [5] vol. xliii, no, 263, pp. 241-255, April 1897.

3A2

696 Mr. C. G. Barkla on Secondary
Rel. Intensity Density Relative

Gas. of of Ionization
Sec. Radiation. Gas. of Gas *,
aie ae ere eyiere ee IE i i
Hydrogen | aes erica 7 ‘O7 "33
Sulphuretted Hydrogen ce OTS 1:18 6
Warbon-Dioxde 2) 4 ui a 40 15a 1-4
pulphur Dioxide yt peel 2°19 64

From these results there is obviously a proportionality be-
tween the intensity of secondary radiation and the density of
the gas, while there is no obvious connexion with the rate
of ionization.

It should be noted that the discrepancy in the case of
hydrogen can be accounted for by the presence of a small
quantity of air or other impurity in the gas chamber. As
the gas was introduced by simply displacing the gas previously
occupying the box, this impurity was undoubtedly present.
The same consideration would bring the other gases into even
closer agreement.

During the course of these experiments, the changes in the
density of the gases experimented upon due to variations in
atmospheric pressure and temperature between the observa-
tions were insignificant.

To examine the absorption of the radiation from different
gases, plates of aluminium of thickness ‘0105 cm. were placed
before the side window of the gas chamber. The intensity
of ionization produced by the radiation which passed through
the aluminium was compared with that produced when no
plates intercepted the secondary radiation. Experiments
were made with the radiation from hydrogen and from
sulphuretted hydrogen, and the differences due to absorption
of the secondary radiation in the two cases amounted to
36 per cent. and 37°5 per cent. of the normal ionization.
This was much smaller than the possible error, and in later
experiments with air and carbon dioxide no ditference in the
penetrability of the rays was found.

The experimental results may be stated as follows :—

(1) All gases subject to X-rays are a source of secondary

radiation.

(2) The absorbability of the secondary radiation is (within

the limits of possible error—about 10 per cent.) the
sume as that of the primary radiation producing it.

* J.J. Thomson, Cambridge Phil. Soc. Proce. x. pp. 10-14 (1898).

Radiation from Gases subject to X-Rays. 697

(3) Fora given primary radiation the intensity of secondary
radiation is proportional to the density of the gas from
which it proceeds—the temperature and pressure being
practically constant.

(4) The secondary radiation is not due to recombination of
the ions.

Sagnac concluded from his experiments that the secondary
rays from air are more easily absorbed than the primary rays,
but his paper does not give an idea of the amount by which
they differ. As the secondary radiation is relatively weak, a
beam of considerable cross-section must be studied, so that
the rays do not pass normally through the absorbing plate.
In the experiments described above, the plates of aluminium
placed in the path of the secondary beam produced greater
proportional diminution of the resultant ionization than was
produced on the ionization caused by the primary, when this
beam was intercepted by similar plates. The difference,
however, was small, and not more than might be accounted
for by the greater thickness through which most of the rays
had to pass by striking the plate obliquely.

The fact of the ionization produced in the electroscope by
the radiation from different gases being so accurately pro-
portional to the density of the gas from which it proceeds is
significant in this connexion, for the ionization depends upon
the intensity of the radiation and upon its nature. The
difference in the absorbability of the radiations is easily
proved insufficient to account for the difference in intensity
of ionization ; also it is extremely improbable that differences
in the intensity together with differences of the absorbability
would produce so accurate a law. It is much more probable
that differing intensities of secondary radiation alone account
for the differing intensities of ionization, and that the secondary
radiation has the same penetrability from whatever gas it pro-
ceeds. ‘This again leads to the probability that the secondary
radiations from different gases are of the same nature as the
primary rather than that the primary is similarly transformed
by the different gases.

As the primary and secondary radiations only differ appre-
ciably in intensity, we may reasonably conclude that the
radiation proceeding from gases subject to X-rays is due to
scattering of the primary radiation.

As this scattering is proportional to the mass of the atom,
we may conclude that the number of scattering particles
is proportional to the atomic weight. This gives further

698 Specific Lonization produced by Corpuscles of Radium.

support to the theory that the atoms of different sub-
stances are different systems of similar corpuscles, the
number of which in the atom is proportional to its atomic
weight.
In conclusion I wish to thank Profs. J. J. Thomson and
Wilberforce for their advice and interest in this work.
University College, eu

LXXVI. ‘gee Lonization pr bane Be Concuein of Radium.

To the Editors of the Philosophical Magazine.
GENTLEMEN,
; A R. DURACK has given an account (Phil. Mag. May

1903) of some experiments on the specific ionization
produced by corpuscles given out by radium, from which he
concludes that the number which I obtained for the same
quantity was too large. The specific ionization produced by
the corpuscles is the number of ions that a single corpuscle
will generate in going through a centimetre of gas at a
millimetre pressure.

From the experiments which I have made with ultra-
violet light I have shown that negative ions, when moving
with a sufficiently high velocity, produce others by collisions
with molecules of the gas. The number of ions produced by
a single ion increases as the force is increased, and reaches a
maximum when the force is above a certain value depending
on the pressure. ‘The voltage in these experiments was com-
paratively low, as it seldom exceeded 300 volts. For air at
a millimetre pressure the maximum number of ions which a
single ion generates is 15.

I also made some experiments with radium which led me
to conclude that each of the corpuscles which are given out
generates at least 13 ions per centimetre in air at a milli-
metre pressure.

Mr. Durack finds from his experiments that this number
ought to be *4, and he attributes the difference between his
result and the result which I obtained with ultra-violet light
to the very high velocity of the corpuscles given out by
radium, the velocity of these corpuscles being lar ge compared
with the velocity corresponding to a fall of potential of
300 volts.

According to this theory the probability that new ions
should be produced by a collision would diminish when the
velocity is increased above a certain value.

Mr. Durack states that the result of my experiments is
wrong as it does not agree with his number °4.

The Electrical Conductivity of Atmospheric Air. 699

It is easy, however, to explain the discrepancy between
these results, if the theory which Mr. Durack has proposed
is the true explanation of the difference between his experi-
ments with radium and my experiments with ultra-violet
light. The velocity of the corpuscles will depend on the
thickness of the aluminium between the radium and the gas
which is examined. In my experiments the aluminium
through which the radiation had to pass was much thicker
than that used by Mr. Durack, so that the corpuscles which
passed through the gas must have been travelling with a
diminished velocity, and consequently they would each pro-
duce a larger number of ions per centimetre in the gas through
which they pass.

If we accept this theory we might expect to obtain any
value less than 15 for the specific “ionization by varying the
thickness of the aluminium through which the radiation has
to pass.

Yours very truly,
JOHN S. TOWNSEND.

LXXVIL. Cae Pee ioneae on the Electr wn C 5 of
Atmospheric Air. By J.C. McLennan and E. F. Burton,

University of Toronto*.

I. Introduction.
1. a paper by H. Geitel t reference is made to a gradual

increase observed in the conductivity of a mass of atmo-
spheric air after being confined in an air-tight chamber. This
effect was found to require from four to five days to reach its
maximum value, and was observed in localities where no
thorium compounds or other known radioactive substances
existed.

In a subsequent investigation Elster and Geitel t found that
the air which had been confined for some time in closed caves
or house-cellars possessed an abnormally high conductivity.
This phenomenon, together with the observed increase in con-
ductivity mentioned above, they concluded, could not be due to
the presence of dust or water-vapour. They traced it rather, in
both cases, te the existence of some undetermined radioactiy ity
in the confining walls.

More recently these physicists discovered that atmospheric
air possessed the property of exciting induced radioactivity in

* Communicated by Prof. J. J. Thomson. Read before the meeting
of the American Physical Society in Washington, Dec. 31st, 1902.

+ Phys. Zeit. ii. pp. 116-119 (1900).
\ Phys. Zeit, ii. pp. 560-565 (1901).

700 Messrs. McLennan and Burton on the

bodies exposed under negative electrification. This pbenome-
non of induced or excited radioactivity had been previously
observed by Rutherford in bodies exposed to air drawn from
the neighbourhood of thorium compounds, and had been
connected by him very directly with an emanation which
these salts emit. This emanation he found possessed the
property not only of exciting radioactivity in all solid sub-
stances in its neighbourhood, but also of ionizing any gas
with which it was In contact.

Since tees air has been shown by Hlster and
Geitel*, C; T. RK. Wilson+, and others to be continually
ionized ‘by some agent, and since it has also been shown to
possess the property of exciting radioactivity, one is forced to
conciude there is present in the air an emanation possessing
properties similar to that emitted by thorium compounds.

Hitherto the source of such an emanation has not been de-
termined, but, as the phenomena of induced radioactivity and
spontaneous ionization universally characterize atmospheric
air, it seems evident, since thorium ‘compounds are but sparsely
distributed in nature, that sources other than these must
exist.

Recailing the experiments of Elster and Geitel, it seems
probable that the earth’s surface, and possibly too the materials
used in the construction of their apparatus, are sources of
this emanation. As but little evidence existed in favour of
this conclusion, the writers recently made a series of observa-
tions upon atmospheric air confined in air-tight vessels of
different metals. The result of the iny estigation showed that
the conductivity of the inclosed air depended very largely
upon the material of which the receiver was made, and the
effects observed would seem to indicate that all metals, in
varying degree, are the sources of a marked though feeble
radioactive emanation.

2. Apparatus.

In these observations the air whose conductivity was to be
measured was confined in a cylinder, 125 ems. in length and
25 cms. in diameter, similar to that shown in fig. 1. In the
first experiment it was made of sheet-iron coated with zine,
and in the later experiments linings of various metals were
inserted in order to examine their effect upon the conductivity
of the inclosed air. The bottom and cover were removable,
and, when in position, were made air-tight by means of
cement. Into a flanged opening in the cover was fitted an

* Loe. cit.

+ Proc. Roy. Soc. March 1901.

Electrical Conductivity of Atmospheric Air. 701

ebonite plug about 5 cms. in diameter, a brass tube B was
passed through this, and into it a second ebonite plug was
! tightly fitted. This second plug
g. 1. earried a brass rod C, which
extended almost to the bottom
of the cylinder. The brass
tube B, which was earthed
throughout the measurements,
served as a guard-ring, and
prevented any leak from the
vessel to the rod C across the
ebonite plugs.

The conductivity was mea-
sured by placing the cylinder
upon an insulated platform,
charging it by means of a set of
small storage-cells to a poten-
tial of 165 volts, which sufficed
for the saturation current, and
observing the rise in potential
of the electrode D, which was
joined to a quadrant electro-
meter in the usual manner. The sensibility of the electrometer
was such as to produce a deflexion of 1000 mms. on a scale
at one metre distance for a potential-difference of one volt
between the quadrants.

3. Conductivity Measurements.— Time Effect.

Before inclosing air for examination the cylinder was
placed in an open window in the laboratory, with the ends
removed and the air allowed to blow through it for some
time. The top and bottom were then replaced, cemented in
position, and the cylinder connected with the electrometer as
quickly as possible.

Measurements on the conductivity were made at intervals
of a few minutes at first, and it was invariably found that a
rapid decrease in the ionization took place until a minimum
value was reached. The conductivity then slowly increased
and approached a limiting value in :the course of two or
three days.

In repeated tests carried out in this manner with the zine
cylinder it was found that, while the initial conductivity

varied from day to day, nents was always observed a rapid
decrease to a constant minimum, followed by a gradual rise
to a constant limiting value.

A typical set of values for the conductivity of air confined

702 Messrs. McLennan and Burton on the

in the zinc cylinder at atmospheric pressure are given in
column 3 of Table I., the currents being expressed in arbi-
trary units, and the times being taken from the closing of
the cylinder.

TABLE I.

| mes Current : Arbitrary Scale.

Pressure, 501:0 cms. Pressure, 74'2 ems.

Column 1. Column 2. Column 3. |
10 mins. 30°0 Al
1b de 9°3
3 | 17-5 | 62
S0tn 13°2 au)
1:0 hour 120 _-
125. As 52S
JO seas, 9-9 —
| Le Teos Wee 69 5
| POO 2 8:0 49
4:00 ,, 66 48
BOG) ae 76 ==
6:00) ee 5:0
10:00) <2: 58
22:00 ,, 19-2 —
25:00) i, 6:0
2900. + 6:0
aa U0 se. 22:0 =
34:00 ,, oe 6:3
4400 ,, 24-0 —
A500" = 6:5

Coron

i t t
JF Co ee LTS: DLA Aa DO DES,
44 orrrTe

The ionization curve for these values (fig. 2) shows that
the minimum current, 4°8, was reached in about four hours
after the air was inclosed. After about eighteen hours the

Electrical Conductivity of Atmospheric Air. 703

curve indicates that the conductivity was tending towards a
limiting value, which the reading taken after forty-four hours
showed to be about 6°5.

As a variation in the experiments, a series of tests were
made in air confined in a receiver at high pressures. The
cylinder in this case was of heavy rolled iron coated with
zinc, and was of the same dimensions as that used in the first
measurements.

The results of observations on the conductivity of air con-
fined at a pressure of about seven atmospheres are given in
column 2, Table [., the scale used being the same as before.
The curve representing these values is shown in fig. 3, and
exhibits the same characteristics as that for the lower pressure.

Crrrrent
[S

N
= ae
J 6 9g

FEN CARE. Ae Ee ee ale SS 56 SI #5 at
tiours

“We have again the rapid decrease to a minimum followed
by a gradual rise tending towards a limiting value. The
minimum conductivity in this case was about 6°6, and was
reached in about four hours after the required pressure in
the cylinder had been obtained. The time occupied in pump-
ing the air was about one hour.

In seeking for an explanation of the curves shown in
figs. 2 and 3, their two-fold origin, as indicated by the dotted
lines, is at once suggested, the conductivity in the initial
stage being due to an agent subject to rapid decay, and that
in the second to one whose power shows a gradual increase.

The first of these dotted curves is similar to that given by
Rutherford * for the conductivity of the air in a chamber

* Rutherford, Phil. Mag. Jan. 1900, p. 6.

704 Messrs. McLennan and Burton on the

which had been cut off from a second containing thorium
oxide, after the two had been in communication for some time,
while the second is similar to that given by him for the
increase in the conductivity of the air in one chamber when
placed in communication with another containing thorium
oxide.

It will thus be seen that the first portion of the curves in
figs. 2 and 3 can be explained upon the supposition that a
radioactive emanation, probably having its origin in the
earth’s surface, was introduced into the cylinder with the
air, the decay of this emanation being the cause of the decrease
in the conductivity, and the second portion upon the sup-
position that a radioactive emanation is given off by the walls
of the containing vessel. On this view the limiting value to
which the conductivity curves tend would represent a con-
dition of equilibrium, where the rate of decay of the emanation
was equal to the rate at which it was produced.

As both the low and the high pressure cylinders were made
of the same material and were of the same size, one would
expect the same amount of the emanation to be present in
both when the steady state was reached. With an easily
absorbed radiation from this emanation, we should obtain a
limiting conductivity independent of the pressure. Baty
since a very great difference was found in the limiting con-
ductivities at the two pressures, it would’ appear that the
radiation possesses considerable power of penetration and is
not easily absorbed.

The difference in the initial conductivities given in columns
2 and 3, Table T., may also be readily explained by the differ-
ence in the air-pressures. The time required to fill the high-
pressure cylinder, and the decay taking place during that
time in the emanation introduced with the air, preclude a
comparison of the amounts of active emanation present in
each cylinder when the first observations upon their con-
ductivities were made ; but, if the amount in the high-pressure
cylinder were equal to or greater than that in the low-
pressure cylinder, the difference in the initial conductivities
is explained, while, if it were less, the greater density of the
air in the high-pressure cylinder, and the consequent greater
absorption, would still account for the higher conductivity.

4. LEffect of Different Metals.

To ascertain whether the conductivity of the inclosed air
was affected by a change in the metal composing the walls of
the receiver, 1inings of tin and lead were in turn fitted into
the zine cy linder used in the first experiment.

Electrical Conductivity of Atmospheric Air. 705

Tests of the conductivity were made both with and without
the tin and lead linings. Before each test the cylinder was
well aired and sealed in the manner already described. As
soon as the air was inclosed, measurements on the conductivity
were begun and continued at stated intervals as before.

TasieE II.
Current: Arbitrary Scale.
Time.
| Zine akine | Lead.
10 minutes 13-0 | 13-0 15-4 |
15 - 8:3 11-0 —
es 0) a | DA 76 | 13°4
45 i 53 a | 12-1
1:0 hours 30 i nlp L535)
liga oer 4°85 Ge 108
ZO) as | | We) | 115
ZED tales | ae | ae | —
OM 23, | 5-0 | | 11:8
EOE oo DO | | 11-9
9-0) “s 1250
20r | asa | 79 | — |
SO 6:0 | 8:0 | =

SL OLNuIR

The values obtained for the conductivity with each of the
metals are given in Table II., and curves representing these
values are shown in fig. 4.

706 Messrs. McLennan and Burton on the

The curves for the different metals, it will be seen, have
the same characteristics. In each there is a rapid drop to a
minimum and a gradual rise towards an ultimate limiting
value. It is interesting to note that a considerable difference
was found in the minimum conductivities for the three metals
and that the final limiting values also varied.

The decay of an emanation introduced into the cylinder with
the air would again account for the first portion of the curves,
a radioactive emanation from the inetallic walls would explain
the existence of the second portion, while the differences in
the minimum and limiting values may be considered to have
their origin in variations in the rate at which the emanation
is given off by the different metals.

In this connexion it will be noted that the limiting values
of the conductivities range according to the atomic weights
of the metals, lead having the highest, tin the next, and zine

the lowest.

). Lffect of Variations in Pressure.

In order to investigate the relation between the con-
ductivity of air and the pressure at which it was confined,
the heavy cylinder was filled to a pressure of about seven
atmospheres, and allowed to stand for some days until its con-
ductivity assumed a constant value.

TABLE IIT.

Pressure Current : Pressure | Current: |

in cms. Arbitrary Scale. | in ems. Arbitrary Scale.
501-0 23:5 1 69'3 58
481-0 | 22-7 | 62:0 5-4
420°0 | 21-2 | 53°U 4°77
384-0 | 20°3 | 44:2 | 4-2
2720 | 15°8 35°0 il 3°5
2270 14:1 22-4 2-7
1760 tery 18-2 2-2
125-0 3 14:0 | 18
| 74:2 6°5 4:4 lt

The air was then allowed to escape gradually, and the
pressure reduced from 501:0 cms. to 4°4 cms of mercury, the
conductivity being measured at these and at various inter-
mediate pressures. The results are given in Table III., and
the conductivity curve in fig. 5.

The ionization curve so nearly approaches a straight line

that we may almost conclude, in view of the wide range of

Electrical Conductivity of Atmospheric Arr. 707

the pressures examined, that the conductivity was proportional
to the pressure. This result is what we should expect to obtain

Fig. 5.

|
ath

7 |

FRESSUPE 1 Cms

with an emanation maintained at a constant strength and
emitting a radiation of a penetrating nature.

6. Penetrating Rays from External Sources.

While the effects described up to the present may be
explained by supposing the ionization to be caused by a radio-
active emanation sent off from the metals, it has been found
that part of the conductivity cannot be accounted for in this
way, but must be attributed to an active agent external to the
recelver.

The heavy cylinder referred to above was filled with air to
a pressure of about 400 ems. of mercury and allowed to stand
until its conductivity had become steady. It was then placed
in an insulated galvanized iron tank, 150 ems. in height and
75 cms. in diameter, which was gradually filled with water
so as to surround the cylinder with a layer 25 cms. in thick-
ness. The initial conductivity before the water was admitted
was 21'1. As the water rose the conductivity decreased and
fell to 13°3 when the tank had been filled. The values for
the conductivity during the experiment are given in Table LV...
and they show that the loss was almost directly proportional
to the rise of the water. The total fall in conductivity, it will
be seen, was about 37 per cent.

708 Notices respecting New Books.
TaBLe IV.

Depth in ems | Current :
He “* | Arbitrary Scale.

15-0 205
60:0 18:0
77-0 | 17:0
97-0 14:5
110-0 | 13°75
120°0 13°3

The experiment was repeated with the cylinder placed in a
tank 50 ems. in diameter. This tank permitted the cylinder
to be surrounded by a layer of water 12°5 cms. in thickness,
and it was found when the water was poured in that the con-
ductivity fell off 17:5 per cent.

From these results it is evident that the ordinary air of a —
room is traversed by an exceedingly penetrating radiation,
such as that which Rutherford* has shown to be emitted by
thorium, radium, and the excited radioactivity produced by
thorium and radium.

In order, therefore, to reach definite conclusions regarding
the extent and true character of the effect of various metals
upon the conductivity of the air which they inelose, it will
be necessary to entirely cut off the inclosing vessel from the
action of this external radiation, and the writers have not yet
carried their experiments to this point.

Physical Laboratory,

University of Toronto.

LXXVIII. Noteces respecting New Books.

Text-Book of Electrochemistry. By SVANTE ARRHENIUS, Professor
at the Uniwersity of Stockholm. Translated by Joun McCRag,
Ph.D. London: Longmans, Green, & Co., 1902. Pp. xii+
344,

Pp the English edition of this text-book by one of the leading

authorities on electrochemistry, we find much to praise and not a
little to blame. We shall probably best discharge our duties towards
the author and the translator by stating that no one interested in
the subject can afford to ignore the book, written as it is by one
whose name will ever remain associated with the epoch-making
theory of ionization.

Having said so much, we think that both the translator’s and the
reader’s interests will be best served if we draw attention to some of

* Rutherford, ‘ Nature,’ vol. lxvi. p. 318 (1902).

Notices respecting New Books. 709

the blemishes which disfigure the book, and which could easily be
removed in a future edition, a demand for which is certain to arise.

In the introductory chapter on “ Fundamental Physical and
Chemical Conceptions ” the treatment of electrical units is extremely
slovenly. It isa pity that the translator has not adopted the terms
“resistance,” “resistivity,” ‘“ conductance” and ‘“ conductivity ”
in the meanings now generally attached to them, and prefers to
use “ specific resistance” etc. On p. 5d, it is stated that “the term
‘ potential difference ’ is frequently used in place of electromotive
force ’—a statement which, alas! is only too true, but true by reason
of the very general ignorance which refuses to recognize the essential
difference between the two terms. An exceptionally bad example
of negligence is to be found on p. 6, where we come across the
following two statements: ‘The difference of the potentials at two
points is called the potential difference or electromotive force, and
is that force which tends to make the electricity pass from one point
to the other”; and lower down, “the potential corresponds, in a
certain sense, to work” (the italics in both cases are ours). Such
crude and, to a learner, extremely confusing statements might be
excused in a popular exposition of a difficult subject; in a serious
scientific text-book they are intolerable. On p. 11, the horse-power
is stated to be equivalent to 75 kilogramme-metres per sec.; this
is true of the Continental, but not of the British horse-power, which
is about 1:36 per cent. larger. On p. 124, the E.M.F, of the Clark
cell is wrongly given as 1°438 volts at 15°. On p. 114, the author
adopts the method commonly followed by advocates of the dissociation
theory, and boldly states that the very smallest E.M.F. is sufficient
to produce chemical decomposition. ‘‘ This fact,” it is added, ‘‘ was
proved by Buff with ewrrents so small that it was only after months
that a cubic centimetre of explosive mixture was obtained.” There
is here clearly a confusion of E.M.F. and current. We are not
aware of any perfectly trustworthy experiments which have shown
that any E.M.F., however small, is capable of evolving an explosive
mixture of hydrogen and oxygen from acidulated water. It is the
fashion, with many electrochemists, entirely to neglect considera-
tions of energy in dealing with this matter.

We have taken up so much space in pointing out some of the
more important errors in the book, that its excellences must be but
briefly referred to. Where the author is on more purely chemical
eround his exposition is admirably clear and to the point. An
immense number of references are given to original sources of infor-
mation, and there is a useful index at the end of the book.

Meteorologische Optik. Von J. M. Pernter, Professor an der K. K.
Universitat und Director der K. K. Centralanstalt fiir Meteorologie
und Erdmagnetismus. Mit zablreichen Textfiguren. I.
Abschnitt. Wien und Leipzig: Wilhelm Braumiiller. 1902.
Pp. 55-212.

Some time ago we had occasion to review briefly the first part of

this excellent and comprehensive treatise by Professor Pernter,

Phil. Mag. 8. 6. Vol. 5. No. 30. June 1908. 3B

710 Notices respecting New Books.

who is well known as an authority on meteorology. The present
section of the work is concerned with those phenomena which are
attributable to the gaseous constituents of the atmosphere, and which
are brought about by refraction and total reflection. These pheno-
mena are dealt with under three heads, corresponding to the three
chapters of the present section of the work. ‘To the first class are
referred the effects produced by the normal distribution of density
in the atmosphere—-i. ¢., by a uniform decrease of density in an
upward direction. The second class comprises phenomena which
result from irregular density distributions, and the third relates to
effects in which more or less rapid fluctuations in the density of
the various layers take place. ‘The discussion of the various -
problems presented by such abnormal phenomena is a very
thorough one, and the volume should prove interesting to the
general reader, as it contains a large number of vivid accounts
by eye-witnesses of the phenomena dealt with, and is well
illustrated.

Physico-Chemical Tables. For the use of Analysts, Physicists,
Chemical Manufacturers, and Scientific Chemists. By Joun
CastTeLL-Hvans, 2°..C., F.C.S., Superintendent of the Chemical
Laboratories and Lecturer on Inorganic Chemistry and Metallurgy
at the Finsbury Technical College. Vol. 1. Chemical Engineering
and Physical Chemistry. London: Charles Grifin & Company,
Limited. 1502. Pp. xxxii+548.

Gruat credit is due to Mr. Castell-Evans for the extraordinary

amount of labour which the compilation of the present volume,

the first half of the complete work, must have cost him. One
cannot but admire his courage in persevering in his formidable task,
in spite of, as he informs us in the preface, the warning given him

by a friend that he was making himself “a hewer of wood and a

drawer of water for other people.” But if so, it is now only fair

to add that probably the ‘‘ other people” feel deeply grateful.
The volume is divided into three parts. Parti I. contains various
mathematical formule and tables: it may be suggested that
physicists would probably welcome, in addition to the tables given,
tables of exponentials and the hyperbolic functions, which are so
frequently useful. Part II. contains tables relating to mechanics

(gravitation, elasticity, &c.). Part I1I., which occupies by far the

largest portion of the book, deals with physics and physical

chemistry : thermometry, expansion coefficients, calorimetry,
densities, barometry, thermal constants and volumes of gases,
vapour-densities, fusion, vaporisation, vapour wressures (we regret
to notice the term “vapour tension”), boiling- points, and latent
heats of vapours.

We hope that the book will find the recognition it deserves
among all those whose scientific work would be much lightened by
the use of such tables.

F 711 |

INDEX ro VOL, V."°-433.

—»—_

ABBOTT (G.) ; on the cellular mag-
nesian limestone of Durham, 387.

Absorption, on the effect of, on the
resolving-power of prism trains,
399.

Air, on the ratio of the specific heats
for, 226; on radioactivity excited
in, at the foot of waterfalls, 419 ;
on the charge on the ions pro-
duced in, by Roéntgen rays, 429;
on the proportion of argon in the
vapour rising from liquid, 677 ;
on the electrical conductivity of
atmospheric, 699.

Aluminium anode, theory of the,
301.

Ami (Dr. H. M.) on the Saint-
Lawrence - Champlain - Appala-
chian fault, 174.

Animal thermostat, 198.

Anode, theory of the aluminium,
301.

Argon, on the proportion of, in the
vapour rising from liquid air,
677.

Atomic weights, on the relationship
between the spectra of elements
and the squares of their, 203.

Attenuation of electric waves, on
the, along wires, 643.

Ball (Dr. J.) on the Semna cataract,
O84,

Barkla (C. G.) on secondary radiation
from gases subject to X-rays, 685.

Battelli (Prof. A.) on oscillatory dis-
charges, 1, 620.

Bismuth, on the thermomagnetic
sroperties of crystalline, 141.

Blyth (V. J.) on the influence of
magnetic field on thermal con-
ductivity, 529.

“ Boiling,” on, 674.

Boiling-points, freezing-points, and
solubilities, on the connexion
between, 405,

}

Boltzmann’s theorem, on, 134, 597%

Bonney (Prof. T.: G.)- on. ne
valleys in relation to glaciers, 172;
on the magnetite mines near Cogne,
387.

Books, new :—Lanner’s Naturlehre,
170; Annuaire du Bureau des
Longitudes, 290; Compte Rendu
du deuxiéme Congrés International
des Mathématiciens, 290; Boltz-
mann’s Lecons sur la Théorie des
Gaz, 291; Drude’s Theory of
Optics, 292; The Meteorology of
the Ben Nevis Observatories, 379 ;
de Lépinay’s Franges d’Inter-
férence et leurs Applications Métro-
logiques, 382; Carvallo’s L’Elec-
tricité Déduite de l’Expérience et
Ramenée au Principe des Travaux
Virtuels, 382; Bauer’s United
States Magnetic Declination Tables
and Isogonic Charts for 1902, 382;
Naegamvalla’s Report on the
Total Solar Eclipse of Jan. 1898,
490; von Waltenhofen’s Die
Internationalen Absoluten Masze,
491; Raoult’s Cryoscopie, 492 ;
Bericht tiber die Internationale
Experten-Conferenz fur Wetter-
schiessen in Graz, 492; Hooper
and Wells’s Electrical Problems
for Engineering Students, 5965 ;
Arrhenius’s Text-Book of Electro-
chemistry, 708; Pernter’s Meteoro-
logische Optik, 709; Castell-
Kyans’s Physico-Chemical Tables,
710.

Brace (Prof. D. B.) on a sensitive-
strip spectropolariscope, 161.

Brown (J.) on removal of the voltaic
potential-difference by heating in
oil, 491.

3urbury (S. H.) on the conditions
necessary for equipartition of
energy, 154.

a a
=f 9 pnd
~~

712

Burton (E. F.) on the electrical con-
ductivity of atmospheric air, 699.
Callaway (Dr. C.) on the plutonic
complex of Central Anglesey, 172.

Callendar (Prof, H.L.) onthe thermo-
dynamical correction of the gas-
thermometer, 48.

Campbell (G. A.) on loaded lines in
telephonic transmission, 313.

Capacities, on the measurement of
small, 493.

Capillary electrometer, on a portable,
598.

Carslaw (Prof. H. 8.) on the use of
contour integration in the problem
of diffraction by a wedge, 374.

Chant (C. A.) on the variation of
potential along a wire transmitting
electric waves, 331.

Chapman (H. W.) on the problem
of Columbus, 458.

Charge carried by a gaseous ion, on
the, 546; on the ions produced in
air by Rontgen rays, 429.

Chemical energy and light, on the
connexion between, 208.

Clinton (W.C.) on the measurement
of small capacities and inductances,
493,

Cobalt, on the Wiedemann effect in,
650.

Columbus, on the problem of, 458.

Condensation, on the thickness of
the liquid film formed by, at the
surface of a solid, 517; of the
radioactiveemanations, on the, 561.

Condenser, on a graphical method of
determining the nature of the
oscillatory discharge from a, 155.

Conductivity, on the, produced in
gases by the aid of ultra-violet
light, 389; on the influence of
magnetic field on thermal, 529;
of atmospheric air, on the, 699.

Contour integration, on the use of, in
the problem of diffraction by a
wedge, 374.

Convection, on the magnetic effect
of electrical, 34.

Coomaraswamy (A. K.) on the Point-
de-Galle group, 174; on the Tiree
marble, 388.

Dawkins (Prof. W. B.) on the red
sandstone rocks of Peel, 170; on
the rocks under the glacial drift in
the Isle of Man, 171,

IN DEX.

Derriman (W. H.) on an oscillating
table for determining moments of
inertia, 648,

Dichroism, on magnetic, 486.

Diffraction, on the use of contour
integration in the problem of, by
a wedge, 374,

Discharges, on oscillatory, 1, 620;
graphical method of determining
the nature of, 155.

Dissociation, on the theory of elec-
trolytic, 279.

Disturbance, on the spectrum of an
irregular, 258, 344,

Durack (J. J. E.) on the specific
ionization produced by the cor-

puscles given out by radium,
590.
Ege, on the spin of an, 458.

Electric conductivity of atmospheric
air, on the, 699.

convection, on the magnetic
effect of, 34.

— deviation of the easily absorbed

rays from radium, on the, 177.

waves, on the connexion be-
tween, and chemicai energy, Xc.,
208 ; on the variation of potential
along a wire transmitting, 331 ;
on the speed of propagation and
attenuation of, along wires, 643.

Electricity, on the charge of, carried
by a gaseous ion, 546,

Electrolytic dissociation,
theory of, 279.

Electrometer, on a portable capillary,
398.

Elements, on the numerics of the,
543.

Energy, on the conditions necessary
for equipartition of, 134; dis-
tribution of, in the spectrum, 288 ;
on the law of equipartion of, 618.

Epochs in vibrating systems, on the
special, 511.

False position, on a general theory
of the method of, 658.

Ferromagnetic substances, on the
Wiedemann effect in, 650.

Films, on the thickness of liquid,
formed by condensation at the
surface of a solid, 517; on the
action of, in voltaic cells, 591.

Fleming (Prof. J. A.) on the
measurement of small capacities
and inductances, 493,

on the

INDEX,

Flett (Dr. J. S.) on ash from the
eruption of St. Vincent, 171.

Fortnightly tide, on the theory of
the, 136.

Fourier’s theorem, applications of,
to the analysis of irreguiar curves,
238.

Free vibrations of systems affected
with small rotatory terms, 293.
Freezing-points, boiling-points, and
solubilities, on the connexion
between, 405.
Garwood (Prof. E. J.) on the origin

of hanging valleys, 173.

Gaseous ion, on the charge of elec-
tricity carried by a, 346.

Gases, on reversed lines in the
spectra of, 153, 524; on the con-
ductivity produced in, by ultra-
violet light, 389; on the kinetic
theory of, 597; on secondary
radiation from, subject to X-rays,
685.

Gas-thermometer, on the thermo-
dynamical correction of the, 48.
Geological Society, proceedings of

the, 170, 384.

Glazebrook (Dr. R. T.), theoretical
optics since 1840, 537.

“ Good Seeing,” on, 674.

H lines of the solar spectrum, on the
constitution of the, 524.

Heat, on the influence of radiation
on the transmission of, 243; on
the, evolved on contact of liquid
with finely-divided solid, 595.

Hitchcock (F. L.) on vector differ-
entials, 187.

Hodgkins gold medal, award of, 176.
Honda (K.) on the Wiedemann effect
in ferromagnetic substances, 650.

Hydrogen, on the spectra of, 153.

Hysteresis loss in iron, on the effect
of temperature on the, 117.

Inductances, on the measurement of
small, 495.

Inertia, on an oscillating table for
determining moments of, 648.

Inglis (J. K. H.) on the theory of
the aluminium anode, 301.

Integration, on the use of countour,
in the problem of diffraction by a
wedge, 374.

Tonization produced by the corpuscles
given out by radium, on the
specific, 550, 698,

713

Ions, on the charge carried by
gaseous, 346; on the charge on
the, produced in air by Rontgen
rays, 429.

Tron, on the effect of temperature on
the hysteresis loss in, 117.

Jeans (J. H.) on the kinetic theory
of gases, 597.

K lines of the solar spectrum, on the
constitution of the, 524.

Kelvin (Lord), animal thermostat,
198. .
Kinetic theory of gases, on the,

597.

Landolt-Bornstein, | Physikalisch -
chemischen Tabellen, 176.

Langley (Prof. 8S. P.) on “good
seeing,” 674.

Lehfeldt (R. A.) on a potentiometer
for thermocouple measurements,
668; on a resistance comparator,
672.

Light, on the connexion between,
and chemical energy &c., 208; on
screens transparent only to ultra-
violet, 257; resolution of, into
undulations of flat wavelets applied
to the investigation of optical
phenomena, 264; on the con-
ductivity produced in gases by
ultra-violet, 389.

Liquid, on the vibrations of a rect-
angular sheet of rotating, 297; on
the heat evolved on contact of
a, with a finely divided solid,
595.

Liquid film formed by condensation
at the surface of a solid, on the
thickness of the, 517.

Loaded lines in telephonic trans-
mission, on, 3158.

Lownds (Dr. L.) on the thermo-
magnetic properties of crystalline
bismuth, 141.

MacAlister (D. A.) on tin and tour-
maline, 386.

McLennan (Prof. J. C.) on induced
radioactivity excited in air at the
foot of waterfalls, 419; on the
electrical conductivity of atmo-
spheric air, 699.

Magnetic deviation of the easily
absorbed rays from radium, on the,
Gos

— dichroism, on, 487.

—- double refraction, on, 486,

714

Magnetic effect of electrical convec-

. tion, on the, 34.

field, on the influence of, on
thermal conductivity, 529.

—— solutions, on new magneto-optic
phenomena exhibited by, 486.

Magneto-optic phenomena, on new,
486,

Magri (L.) on oscillatory discharges,
1, 620.

Majorana (Dr. Q.) on new magneto-
optic phenomena exhibited by
magnetic solutions, 486.

Makower (W.) on the ratio of the
specific heats for air and steam,
226.

Marchant (Dr. E. W.) on a-graphi-
cal method of determining the
nature of the oscillatory discharge

_ from a condenser, 155.

Martini (T.) on the heat evolved
when a liquid is brought in con-
tact with a finely-divided solid,
595.

Matter, on the effect of light on the

roperties of, 215.

Mills (Dr. E. J.) on the numerics of
the elements, 545.

Morton (Prof. W. B.) on the con-
nexion between speed of propaga-
tion and attenuation of electric
waves along parallel wires, 645.

Networks, on the theory of conduct-
ing’, 489.

Nickel, on the Wiedemann effect in,
650.

Numerics of the elements, on the,
543.

Optical phenomena, on the resolution
of light into undulations of flat
wavelets as applied to the investi-

- gation of, 264; new magneto-,
A86.

Optics, survey of theoretical, since

- 1840, 537.

Oscillating -table for determining
moments of inertia, on an, 648.
Oscillatory discharges, on, 1, 620;
graphical method of determining

the nature of, 155.

Oxygen lines in the solar spectrum,
on, 524.

Parks (Dr. G. J.) on the thickness
of the liquid film formed by con-
densation at the surface of a solid,

517,

INDEX.

Pearson (Prof. K.) on a general
theory of the method of false posi-
tion, 658. .

Peck (J. W.) on the special epochs
in vibrating systems, 511.

Pender (Dr. H.) on the magnetic
effect of electrical convection, 54.
Periodic system, on the position of

radium in the, 476.

Photography, on the use of screens
transparent only to ultra-violet
light in spectrum, 257.

Potential, on the variation of, along
a wire transmitting electric waves,
Bel.

Potential-difference, on the removal
of the voltaic, by heating in oil,
591.

Potentiometer for thermocouple mea-
surements, on a, 668.

Precht (J.) on the position of radium
in the periodic system, 476.

Preston (H.) on a new boring at
Caythorpe, 384.

Prism-trains, on the effect of absorp-
tion on the resolving-power of,
B00.

Problem of Columbus, on the, 458.

Radiation, on the influence of, on
the transmission of heat, 245; on
secondary, from gases subject to
X-rays, 685.

Radioactive change, on, 576.

emanations, on the condensa-
tion of the, 561.

Radioactivity, on excited, and the
method of its transmission, 95; on
induced, excited in air at the foot
of waterfalls, 419; on the, of ura-
nium, 441 ; of radium and thorium,
445; remarks on, 481,561; onthe
nature of, 576; on the, of ordinary
materials, 680.

Radium, on the transmission of the
radioactivity of, 95; on the mag-
netic and electric deviation of the
easily absorbed rays from, 177 ; on
the radioactivity of, 445, 56] ; on
the position of, in the periodic
system, 476; on the specific ioni-
zation produced by the corpuscles
given out by, 550, 698.

Rayleigh (Lord) on the theory of
the fortnightly tide, 136; on the
spectrum of an irregular distur-
bance, 238; on the free yibrations

INDEX.

of systems affected with small
rotatory terms, 293; on the vibra-
tions of a rectangular sheet of
rotating liquid, 297 ; on the pro-
portion of argon in the vapour
rising from liquid air, 677

Resistance comparator, on A 672.

Resolving-power of prism-trains, on
the effect of absorption on the,
359.

Reversed lines in the spectra of
gases, on, 155, 524.

Reynolds (Prof, S. H.) on Jurassic

- strata cut through by the S. Wales
direct line, 175.

RoGntgen rays, on the charge on the
ions produced in air by, 429.

Runge (C.) on the position of radium
in the periodic system, 476.

Rutherford (Prof. EK.) on excited
radioactivity and the method of
its transmission, 95; on the mag-
netic and electric deviation of the
easily absorbed rays from radium,
177; on the radioactivity of ura-
nium, 441 ; on the radioactivity of
radium and thorium, 445 ; remarks
on radioactivity, 481; on conden-

_ sation of the radioactive emana-
tions, 561; on radioactive change,
576.

Schuster (Prof. A.) on the influence

_of radiation on the transmission of
heat, 245; on the spectrum of an
uregular disturbance, 344.

Screens respect only to ultra-
violet light, on, 257.

Shimizu (S.) on the Wiedemann
effect in ferromagnetic substances,
650.

Smith (S. W. J.) ona portable capil-
lary electrometer, 398.

Soddy (F.) on the radioactivity of
uranium, 441; on the radioactivity
of radium and thorium, 445 ; on
condensation of the radioactive
emanations. 561; on radioactive
change, 576.

Solar spectrum, on the constitution
of the H and K lines of the,
524.

Solid, on the thickness of a liquid
film formed on a, by condensation,
5i7; on the heat evolved on con-
tact of a liquid with a finely-
divided, 595.

715

Solubilities, on the connexion be-
tween freezing-points, boiling-
points, and, 405.

Solutions, on new magneto - optic
phenomena exhibited by magnetic,
486.

Specific heats, on the ratio of the,
for air and steam, 226.

Spectra of hydrogen, on the, and
reversed lines in the spectra of
vases, 153, 254; on the relation-
ship between the, of elements and
the squares of their atomic weights,
203.

Spectropolariscope, on a sensitive-
strip, 161.

Spectrum of an irregular disturbance,
on the, 238, 344; on the, of radium,
476; on the constitution of the H
and K lines of the solar, 524.

Spectrum photography, on the use of

screens transparent only to ultra-
violet light in, 257.

Spin of an ege, on the, 458.

Steam, on the ratio of the specific
heats for, 223.

Stephens (Ff. J.) on the geology of
the North-West Provinces, 385.
Stokes’ (Sir G. G.) work in optics,

remarks on, 237.

Stoney (Dr. G. J.) on the resolution
of light into uniform undulations
of flat wavelets applied to the
investigation of optical phen:
mena, 264,

Strutt (Hon. R. J.) on the radio-
activity of ordinary materials, 680.

Taylor (Dr. W. W.) on the theory
of the aluminium anode, 301.

Telephonic transmission, on loaded

lines in, 315.
Telescopie vision, on, 674.
Temperature, ou the effect of, on the
hysteresis loss in iron, 117.
Thermal conductivity, on the in-
fluence of magnetic field on, 529.
Thermocouple measurements, on a
potentiometer for, 668,
Thermoelectric properties of crystal-
line bismuth, on the, 141.
Thermometer, on the thermody-
namical correction of the gas-, 48.
Thermostat, animal, 198.
Thomson (Prof. J. af ) on the charge
of electricity carried by a gaseous
ion, d46.

716

Thorium, on the transmission of the
radioactivity of, 95; on the radio-
activity of, 445, 561.

Tide, on the theory of the fortnightly,
136.

Townsend (Prof. J.8.) on the con-
ductivity produced in gases by the
aid of ultra-violet light, 389; on
the specific ionization produced by
corpuscles given out by radium,
698.

Trowbridge (Prof. J.) on the spectra
of hydrogen and reversed lines in
the spectra of gases, 153, 524; on
the gaseous constitution of the H
and K lines of the solar spectrum,
524.

Tungsten alloy, on the effect of
temperature on the hysteresis loss
aimee | 17,

Vaughan (A.) on Jurassic strata cut
through by the S. Wales direct
line, 175.

Vector differentials, on, 187.

Vibrating systems, on the special
epochs in, 511.

Vibrations, on the free, of systems
affected with small rotatory terms,
295; on the, of a rectangular sheet
of rotating liquid, 297.

Ultra-violet light, on screens trans-
parent only to, 257; on the con-
ductivity produced in gases by,
389.

Uranium, on the radioactivity of,
44],

Voltaic potential-difference, on the
removal of the, by heating in oil,
591.

Wadsworth (F. L. O.) on the effect
of absorption on the resolving-
power of prism-trains, 355.

Waterfalls, on induced radioactivity
excited in air at the foot of,
419.

INDEX.

Watts (Dr. W. M.) on the relation-
ship between the spectra of some
elements and the squares of their
atomic weights, 203.

Waves, electrical, on the connexion
between, and chemical energy &c.,
208; on the variation of potential
along a wire transmitting, 331;
on the propagation and attenuation
of, along wires, 643.

Wedge, on the use of contour inte-
eration in the problem of dittrac-
tion by a, 374.

Whetham (W. C. D.) on the theory
of electrolytic dissociation, 279.
Whitaker (W.) on well-sections in

Suffolk, 386.

Wiedemann effect in ferromagnetic
substances, on the, 650.

Wilberforce (Prof. L. R.) on an ele-
mentary treatment of conducting
networks, 489.

Wilderman (Dr. M.) on the con-
nexion between the energy of
electrical waves or of light and
chemical energy &c., 208; on the
connexion between freezing-points,
boiling-points, and solubilities, 405. -

Wills (R. L.) on the effect of tempe-
rature on the hysteresis loss in
iron, 117. .

Wilson (H. A.) on the charge on the
ions produced in air by Rontgen
rays, 429.

Wires, on the variation of potential
along, transmitting electric waves,
331; on the speed of propagation
and attenuation of electric waves
along, 643.

Wood (Prof. R. W.) on screens trans-
parent only to ultra-violet light,
257.

X-rays, on secondary radiation from
gases subject to, 685.

Zero, estimation of the absolute, 55.

END OF THE FIFTH VOLUME.

Printed by Taytor and Francis, Red Lion Court, Fleet Street.

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