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THE
LONDON, EDINBURGH, aynp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
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CONTENTS OF VOL. XIV.
(FIFTH SERIES).
NUMBER LXXXV.—JULY 1882.
Dr. E. J. Mills’s Researches on Melting-point ............
Mr. C. V. Boys on Measurement of Curvature and Refractive
ererememenlelaels ete hey oe Cosa. ee bases « pelo miad
Professors Ayrton and Perry’s Experiments on the Faure
Ag SEGED COL ANICISSG Rie ae eae aR SFE
Professors Ayrton and Perry on a Simplified Dispersion-
MDC gi RAs c tN as dls Gs Be 8 4ichs g)~ HAG eS sew ee
MM. Warburg and v. Babo on the Connexion between Vis-
cosity and Density in Fluids, especially Gaseous Fluids
Mr. F. D. Brown’s Notes on Thermometry. (Plate Il.) ....
Notices respecting New Books :—
Geological and Natural-History Survey of Canada, Di-
Mecrons Heporb tor lO 9280 re, § asd. be, sodas
Dr. Geikie’s Geological Sketches at Home and Abroad. .
Proceedings of the Geological Society :—
Prof. J. W. Judd on the Relations ofthe Hocene and
Oligocene Strata in the Hampshire Basin ..... bial a
Science and Metaphysic, by Wyndham R. Dunstan, Vice-
President of the Aristotelian Society, Demonstrator of Che-
mistry in the Laboratories of the Pharmaceutical Society . .
On the Depression of the Zero-point in Mercurial Thermome-
SpSnSPEDY aE MEMO ratbst a SMe sposonenle sisarted ete whee Soe
On the Oscillations of the Plane of Polarization produced by
the Discharge of a Battery: Simultaneity of the Electrical
and Optical Phenomena, by D. Bichat and R. Blondlot
NUMBER LXXXVI—AUGUST.
M. A. F. Sundell on Absolute Systems of Physical Units....
Major Allan Cunningham on Moseley’s Theory of Steady Flow
Mr. T. C. Mendenhall on the Influence of Time on the Change
in the Resistance of the Carbon Disk of Edison’s Tasimeter
45
81
110
115
iv CONTENTS OF VOL. XIV.— FIFTH SERIES.
Mr. W. J. Lewis’s Crystallographic Notes. (Plate IIL.)......
Prof. R. Clausius on the Dimensions of a Unit of Magnetism
in the Electrostatic System of Measures ..............
_ M. 4H. Brongersma on Double Refraction, produced by Elec-
trical Influence,in Glass and Bisulphide of Carbon. (Plate IV.
HS. OG=h.) oo. wees cee hte tne se ie ee
Notices respecting New Books :—
(i) Mathematical Papers by William Kingdon Clifford ;
(11) Mathematical Fragments, being Facsimiles of his
unfinished Papers relating to the Theory of Graphs,
by the late W. K. Clifford ...........2)seeeen
Mr. T. Muir’s Treatise on the Theory of Determinants,
with graduated sets of Exercises for use in Colleges
and Schools’ 224.) wa... 2c as | one ees
Proceedings of the Geological Society :—
Mr. H. J. Johnston-Lavis on the Comparative Specific
Gravities of Molten and Solidified Vesuvian Lavas ..
Mr. G. Attwood on the Geology of Costa Rica ........
Mr. 8. V. Wood on the Newer Pliocene Period in England
Don M. F. de Castro on the Discovery of Triassic Fossils
in the Sierra de Gador, Province of Almeria, Spain ..
Prof. C. Lapworth on the Girvan Succession.—Part I.
Stratigraphical 4... 060.600 V 6 +s noe
Mr. E. Wilson on the Rhetics of Nottinghamshire ..
Dr. F. Schmidt on the Silurian and Cambrian Strata of
the Baltic Provinces of Russia..........0). sss ee
Mr. T. F. Jamieson on the Cause of the Depression and
Re-elevation of the Land during the Glacial Period . .
On some Explosive Alloys of Zinc and the Platinum Metals,
byH. Sainte-Claire Deville and H. Debray..............
On the Reaction-current of the Electric Arc, by M. Jamin, with
the assistance of M. G. Maneuvrier ...............+..
On the Motion of a Spherical Atom in an Ideal Gas, by
G.Litbeck oi. ts ee es 1
NUMBER LXXXVII.—SEPTEMBER.
MM. Elster and Geitel on the Electricity of Flame. (Plate IV.
ies -4) 2 ee ee
Lord Rayleigh on the Equilibrium of Liquid Conducting
Masses charged with Electricity ..-............5seseue
Lord Rayleigh on an Instrument capable of Measuring the
Intensity of Aerial Vibrations ......|. ...5).2. 52 aeeeee
Dr. C. R. A. Wright on the Determination of Chemical Affinity
in terms of Electromotive Force.—Part VI. ............
Mr. W. Baily on an Integrating Anemometer. (Plate V.) .
Rey. O. Fisher on the Effect upon the Ocean-tides of a
Liquid Substratum beneath the Harth’s Crust............
Page
119
124
127
135
140
141
141
142
146
147
. 149
150
151
“152
154
157
161
213
CONTENTS OF VOL. XIV.—FIFTH SERIES. Wi
1y
Mr. J. J. Thomson on the Dimensions of a Magnetic Pole in
the Electrostatic System of Units. .................... 225
Mr. F. J. Smith on a new Form of Magnetic Torsion-balance
REMMI TPUHE VOICED © och tenn: sicfe-cie seis «Gs weed «6 2 a8 aorerd 227
Notices respecting New Books:—
Dr. G. Lunge’s Treatise on the Distillation of Coal-Tar
nee ATM OMIACALAQUOL = 8.4 sca 'ece: 3, or ohet asain 6-b o areres 228
Mr. F. E. Hulme’s Worked Examination Questions in
iBiane Geometrical: Drawing 2 0 cee ee ee eee 230
On the Duration of the Perception of Light in Direct and In-
airccimvsion, by Aug. Charpentier... 0.0.0.4. c02a ce 230
On an Air-Thermometer whose Indications are independent of
the Barometric Pressure, by Albert A. Michelson ........ 233
On a Property of the Isentropic Curve for a Perfect Gas
as drawn upon the Thermodynamic Surface of Pressure,
Volume, and Temperature, by Francis HE. Nipher ........ 233
On the Influence of the Quantity of Gas dissolved in a Liquid
upon its Surface-tension, by 8S. Wroblewski ............ 236
On the Structure and Movement of Glaciers, by M. F.-A. Forel. 238
NUMBER LXXXVIII.—OCTOBER.
Mr. R. H. M. Bosanquet’s Notes on Practical Electricity .... 241
Prof. G. Wiedemann on the Methods employed for determin-
SOLE Ce, OTT as ge re a Pc 258
Mr. L. Fletcher’s Crystallographic Notes ................ 276
Mr. E. Vansittart Neale on the Tails of Comets............ 292
Mr. Silas W. Holman on a Simple Method for Calibrating Ther-
22 PENGUINS) Sign eee CCRT DER Di: ee eae ee nee 294
On Boltzmann’s Theorem on the average Distribution of
Energy in a System of Material Points ................ 299
Mr. W. Le Conte Stevens’s Notes on Physiological Optics .. 312
Notices respecting New Books :—
Mr. Latimer Clarke’s Treatise on the Transit Instrument
as applied to the Determination of Time .......... 319
Geology of Wisconsin. Survey of 1873-79. Vol. III... 319
Dr. J. H. W.Stuckenberg’s Life of Immanuel Kant.... 322
On the Conservation of Solar Energy, by Pliny Earle Chase, .
[Lilie DEA se eyo re eae MNS Sn Oe oe EE OER 322
On the Appearances of the Electric Arc in the Vapour of Bisul-
phide of Carbon, by M. Jamin, with the assistance of M. G.
IIE ACHIMIIEL: , 1) (i .psis 5 Pa ee late a ach ee Ea 324
On the Electric Resistance of Glass at Low Temperatures, by
Gis BOWSsereall, ©. occa.5/ 5 <5 oo Garr eile ee Metelg Ge ae Ee hore 325
On the Surface-tension of some Liquids in contact with Car-
hontesAcid, by S-.W roblewski'.. .. salen dees 327
vi CONTENTS OF VOL. XIV.—FIFTH SERIES.
NUMBER LXXXIX.—NOVEMBER.
Page
Lord Rayleigh’s Comparison of Methods for the Determination
of Resistances in Absolute Measure .........-2++ee00> 329
Messrs. C. F. Cross and E. J. Bevan on the Correlation of the
Chemistry of the Carbon Compounds a the Phenomena of
Mite of. y.2 as 59 acs 22 v9ieie 9 Oot» wie 346
Dr. O. J. Lodge on the Dimensions of a "Ngee Pole in the
Electrostatic System of Units ...........--eeee-seeees 357
Dr. Eugen Goldstein on the Electric Diacharag in Rarefied
GARBER of oc es ne ss sian 001d a op = + eben 366
Mr. Ernest H. Cook on Carbon Dioxide as a Constituent of
the Atmosphere... ... 504+ ee0s0-*> ng) nn 387
Mr. E. B. Sargant on the Dimensions of the Magneti¢ Pole in
Hilectrostatic Measure -.. ....: «4+ <s,5 +029 <.000iheeee 395
N otices respecting New Books :—
Mr. J. B. Stallo’s Concepts and Theories of Modern
PRYSICE oo ew ow on oleh 0 05 0.5mm nes! 9 ge 396
On Dr. C. W. Siemens’s new Theory of the Sun, by M. Faye .. 400
On the Connexion between the Gas-density and Stratum-
interval in Geissler Tubes, by Dr. E. Goldstein.......... 402
On the Elasticity of Rarefied Gases, by E. H. Amagat...... 403
On the Influence of Temperature upon the Spectra of Metal-
loids, by M. D. van Monckhoven...........-...s seen 406
On a Thermoscopic Method for the Determination of the Ohm,
by G. Lippmann :. «6... 6050-5. ses ss- «oe 407
NUMBER XC.—DECEMBER.
Mr. G. H. Darwin on Variations in the Vertical due to Elas-
ticity of the Harth’s Surface... ........ ../.5/2)) eee 409
Rey. 8S. Haughton’s New Views of Mr. George H. Darwin’s
Theory of the Evolution of the Earth-Moon System, con-
sidered as to its bearing on the question of the Duration of
Geological Time 00)... 5.00000... 027 2 rr 427
Prof. H. Helmholtz on Systems of Absolute Measures for
Electric and Magnetic Quantities .................... 430
Messrs. J. Trowbridge and C. B. Penrose on the Thomson
Dr. E. Goldstein on the Reflection of Electrical Rays ...... 449
Dr. E. Goldstein on the Influence of the Shape of the Kathode
on the Distribution of the Phosphorescent Light in Geissler’s
Pabes . 5 o5a.5 icles. tale. 1 fe sk PAD. 455
Notices respecting New Books :—
J.B. Chalmers’s Graphical Determination of Forces in
Engineering Structaires..... 2. o0250..05 4) ee 472
CONTENTS OF VOL. XIV.—FIFTH SERIES. vil
: Page
J. HE. Steggall’s Questions in Pure Mathematics proposed :
at the B.A. and B.Sc. Pass and Honours Examinations
of the University of London, with complete Solutions. 476
iroiard. Morris's Geological Chart 2.20... 0. ccc eee eet 476
Proceedings of the Geological Society :—
Prof. T. G. Bonney on the Hornblendic and other Schists
of the Lizard District, with some Additional Notes on
SRMCR SE EDEM DING MA 5 te opt naer spa opely hecerelniny art nle wi oe 477
On Mr. C. W. Siemens’s New Theory of the Sun, by M. G. A.
RE oo ooh ee Pe SS le ales Sind Rain p cel Oe ae 478
Reply to M. Faye’s Objections to Mr. Siemens’s Theory of the
PeIeeOMbIVE INV 2) SICINCTIS Ns 6) - . G2si de elc, woe oye) o ro v's oie eee wre 480
_ On a Property of the Coefficient of Absorption, by Eilhard
OSES ETLPILIY “G5! GUNG caren Oca OM re er 483
ERRATA.
dy? &
Page 217, line 10, for a put a
— 221, line 4, for cos (20-+28) put sin (20 +28).
— 222, line 4, for cos’ 6 put cos” 26.
— 223, line 80, for 7 read fy bis.
B
PLATES.
I. Illustrative of Mr. C. Vernon Boys’s Paper on Measurement of
Curvature and Refractive Index.
II. Illustrative of Mr. F. D. Brown’s Notes on Thermometry.
III. Illustrative of Mr. W. J. Lewis’s Crystallographic Notes.
IV. Illustrative of MM. Elster and Geitel’s Paper on the Electricity of
Flame, and M. H. Brongersma’s on Double Refraction, produced
by Electrical Influence, in Glass and Bisulphide of Carbon.
V. Illustrative of Mr. W. Baily’s Paper on an Integrating Anemo-
meter.
VI. Illustrative of Mr. L. Fletcher’s Crystallographic Notes,
VII. Illustrative of Dr. E. Goldstein’s Papers on the Reflection of Elee-
trical Rays, and on the Influence of the Shape of the Kathode
on the Distribution of the Phosphorescent Light in Geissler’s
Tubes.
THE
LONDON, EDINBURGH, ayn DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
J UL ¥ 1882.
I. Researches on Melting-point. By Hpmuxp J, Mitts, D.Se.,
F.RS., “ Young” Professor of Technical Chemistry in
Anderson’s College Glasgow™.
i we desire to ascertain the purity of a chemical substance
—in other words, to establish its species—two lines of
investigation are open to us. We may (1) by analytical
means determine the composition, or (2) measure by physical
methods some natural property of the body. Both modes of
research require that what is determined—whether composi-
tion or natural property—shall be constant over a fair range
of genetic condition. Both modes also involve a considerable
amount of inference ; but, of the two, far less is demanded by
the methods of physical science, which are, as a rule, distin-
guished by their greater certainty because of their experi-
mental directness. To the property of melting, these charac-
teristics are preeminently applicable.
The accurate ascertainment of melting-point, in terms: of
the air-thermometer, supplies us with physical constants of
considerable importance. While the readings of the mercurial
thermometer are subject to grave correction—its zero, in
particular, being never stationary,—it is most unlikely that the
melting-point of a substance will vary in any ordinary interval
of time, under any common change of pressure, or with trans-
ition to a distant latitude. Actuated chiefly by these consi-
derations, I undertook the researches of which an account is
comprised in the following sections.
* Communicated by the Author.
Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882, B
2 Dr. E. J. Mills’s Researches on Melting-point.
A. Benzol Derivatives.
1. Dinitrobenzol.—The benzol from which specimens A and
C were prepared had been purified by myself, first by frac-
tional distillation, then by fractional distillation after treatment
with bromine, and, lastly, by freezing and pressure. The
preparation of the dinitro-compound was effected with the aid
of hydric sulphate. The crude product was washed with water,
alkaline water, and water successively, and then submitted to
a process of purification repeatedly adopted in these experi-
ments.
[The process in question consists in crystallization from
distinct successive solvents, followed each time by pressure. It is
well known that small quantities of impurity are prone to cling
to substances with much tenacity; but the observation has most
frequently been made in connexion with some single solvent.
One can readily conceive that the tenacity with which a given
trace of a foreign body is held may, under such circumstances,
be in effect constant. If, however, we now transfer the mix-
ture to a new solvent, then, we may fairly presume, the trace
will be in a condition of altered adhesiveness, and may be
much more readily separable. It is of course not easy to
decide whether this result is always attained, or whether the
later solvent makes any impression at all; but it will probably
be granted that the method of multiple successive solvents is
in general expedient to adopt.
After each crystallization the crystals were in all cases sub-
mitted to powerful pressure between folds of carefully cleansed
linen or, occasionally, of silk tissue. The surface-tension of
the dissolved impurities appears to be for the most part consi-
derable; and this, aided by mechanical compression, greatly
economizes the time required in preparing a pure substance.
The pressed crystals were next reduced to a very fine powder,
and dried for eleven days over oil of vitriol in the dark. Care
was taken never to make determinations with substances pre-
viously melted; for it not unfrequently happens that a second
melting takes place at an appreciably different temperature. |
Specimens A and C were crystallized twice from naphtha,
and thrice &c. (A; &e., C3 &e.) from purified aleohol. Spe-
cimen B was given me by Mr. C. E. Groves, who had prepared
it from thrice frozen and pressed benzol. It was crystallized
once from water, once from naphtha, once &e. (B, &e.) from
pure alcohol. The results are contained in Table I.
Dinitrobenzol melts with some sharpness after a decided
pasty stage. It strongly resists pulverization—a character
more especially observable in specimen B.
Dr. HE. J. Mills’s Researches on Melting-point. 3
TABLE I.
Aesoh Age: 17 BE | Bie Sol Ox 1: [t-Cb.
= od a ee
° lo ° ansth o ° °
89°86 | 89-71 | 89-79 89-75 | 89-64 | 89-73 | 89-67
75| 71| 82! 78| 71
=r
os)
fen
oi
=
=r
oO
=I
en
a
home |
on
e
Ns
“1D 1S.
CO OD 4
es S|
(=)
Rapa ror a
fet pe Fe
1-1
IO
aor at
hy O or
83| -71| 74) 72]... 65 | 39
in | |
Wena eas: ye 89-76 89°78 | 89°73 | 89°75 | 89°68 | 89°71 | 89°67
Probable error ...| 012) 7010 -010 -008; ‘007; -008} -010
Thermometer ...! 2 2 | pri | eee 3 2 2
2. Dichlorobenzol.—FYor this specimen I was indebted to
Dr. Hugo Miiller, who prepared it by his well-known process
of chlorination, which consists in treating hydrogenated bodies
with chlorine in presence of iodine. It was crystallized twice
from naphtha, and four times &c. (A, &c.) from alcohol.
Dichlorobenzol melts very suddenly.
TABLE II.
AC AA IE ie) Aco Ag | Ay. A
o oO o ° °
5261 | 52-72 152-66 | 52-74 (52-74 52-74 | 52-83
6 | .i2|. wl) | a2) 6
TEL AO 714. PGS 695 4-72. |. 75
71). 67) 74| 69| 74) 66) 25
C7 Ba Rt Ss EY OM acer oiler ch bie yl ka f=
TU tee pe ee ae te | a
| 74! -75| 76] 69) 69| 64] -73
Fiat fae PR Es SERS MOM MO A Sapa rl ame |
S/S Faro sir 9 in vai ial RR (ie 75
a} 5 ai | 69 “ES WE] 73
69| 77) -68| 69} 76) 7 ac
siesta a -e
[ At 2) 741 69) 74) 72) 75
| Ef wei og ae, be 161 Ve | Te
Mra 22 cc. 5. 52°72 | 52°73 | 52-73 | 52-70 | 52-73 | 52-73 | 52-74 |
Probable error .... 008 ‘005, 6) 004; -004, -006) -006;
Thermometer ... 3 | 3 | 3 SS) Seed WEG: rte
t
4 Dr. H. J. Mills’s Researches on Melting-point.
benzol (permanently reddened by bromine) for a short time
nearly to boiling, washing and rectifying the product. The
benzol thus purified was used in preparing benzol by Couper’s
process*; and from this product, on distillation, a residue of
dibromobenzol was obtained. This was crystallized once from
spirit, twice from naphtha, and thrice from spirit ; at the last
crystallization the substance was only partly dissolved; and the
crystals obtained from the solution were alone examined.
C was prepared from the monobromobenzol above referred to.
The product of Couper’s process always contains a little dibro-
mobenzol, which cannot be removed in the ordinary way.
This was allowed to remain. Traces of another solid impurity
were precipitated by exposure to sunlight for some weeks in
presence of solid potassic hydrate, followed by filtration and
distillation. Finally the purified monobromobenzol was mixed
with bromine in the proportion C,H; Br: Brg, and left for
some weeks in the laboratory, during which it was once heated
in the water-bath. The product was washed with aqueous
caustic soda, some unaltered monobromobenzol removed by
partial distillation with water, and the remainder crystallized
once from alcohol, once from naphtha, and once from alcohol
in presence of charcoal (C;): successive fractions (C, &e.)
from alcohol were then taken. C,, was obtained from a hot
liquid which had deposited about half its contents, which I
have named Cgg.
Dibromobenzol melts nearly as sharply as dichlorobenzol.
It is hardly possible to trace a pasty stage.
TABLE ITI.
]
87:03 87-07 86°99 | 87-08 | 87-01 | 87-05 | 87:01 87-06
a
|
|
|
|
|
| Thermometer... 2 4 Z 2 2 2 Ph be 2
87:03 | 87-03 | 87-12 | 87-08 | 87-03 | 87-04 86-99 | 87-10 | 87-02
86-97 | 87-12 | | | / | .
87:03 | 87-09 | | |
igs. no 87-00 | 87-04 | 87-05 | 87-06 | 87-04 87-08. 87-01 | 87-06 | 87-04.
Probable error, ‘010 -007 ‘O11) -012) -007 -007 004 -006 # -008
») . »)
* Ann. Chim. Phys. {3} lii. p. 309.
:
ee Ee a
© | 0. iis) 20 ° © ° |o |_o °
87°08 87:05 87:10 | 86°97 | 87-06 87-10 bi 87°06 87°10
8 06 |
86°87 87-03 | 87-12 | 86-97 | 87-03 | 87-10 | 87-01 | 87-03 | 86-94
| 86°97 87-05 | 86:99 | 87°16 | 87-03 87-10 87-01 86-98 | 87-07
87-00 | 87-01 | 87°10 | 87-13 | 87-11 87-05 | 87-01 | 87-09 | 87-07
86-97 | 86°96 87-07 | 86-99 87-01 87-07 87-01 87-06 | 87-07
86:95 | 87-01 | 86-97 | 87-08 | 87-01 87-04 86-96 87-06 | 87-05
| 87-03 | 87-01. | 87-12 | 87-13 | 86-98 | 87-06 87-01 | 87-06 | 87-05
| 87-03 87-05 | 86:99 | 87-05 | 87-11 87-15 86-99 | 87-06 | 87-02
87-08 | 87°10 | 87-02 | 87-05 87-03 87-07 87-04 87-11 | 87-02
86-99 | 87°10 | 87-01 87-13 86:99 | 87-03 | 87-02
Dr. H. J. Mills’s Researches on Melting-point. 5
4, Dinitrobromobenzol.—Benzol purified by bromine distil-
lation, and freezing, was brominated by the Couper process,
and freed from dibromobenzol by heating to the boiling-point
with a mixture of Nordhausen and common oil of vitriol ;
this treatment was followed by washing and distillation.
Sample A was prepared from the above bromobenzol by
Kekulée’s method*. The crude product amounted to 148 per
cent., theory requiring 157 per cent.: it contained a small
quantity of an oily body. This was crystallized twice from
naphtha and five times &ec. (A; &e.) from alcohol.
The crystals of dinitrobromobenzol are, as observed by
Kekulé, remarkably large and well defined. They powder
harshly, like rosin. The concentrated alcoholic solution emits
sound as it crystallizes.
Dinitrobromobenzol melts with considerable sharpness.
TABLE LY.
Pies lis Ate |). Acs. | he:
|
i |
| 70-58 |70-54 | 70-56 | 70°68 | 70-67 |70-68 70°56
53| SL | 64) 35] 54! -71| “59
| 50] 65] 61) -35| -64| 55] -58
53] 49| 64] 55] -67| -71| 53
48| 51) 56] -57| -54| 5B] -56
IMEC RIT OS ies ose ts 70°55 70-57 70°62 | 70-61 | 70°62 | 70-62 70°59
Probable error ...| ‘010 -010} -010) -009) -009' +010; -015
Thermometer ...| 2 2 2 2 2 2 3
i
5. Nitrodibromobenzol.—Sample A, from (D) dibromobenzol
(q.v.) which had been crystallized once from alcohol, once
from naphtha, and once from alcohol. 25 grm. of substance
were gently heated with 250 cub. cent. of “fuming nitric
acid,’’ and allowed to cool during arather longer period. The
product, purified by means of water and ammonia, contained a
little oily impurity, and weighed 28°5 grm. (=114 per cent.,
theory requiring 119-1 per cent.): it was crystallized twice
from naphtha, and thrice &c. (A; &e.) from alcohol.
* Ann. Chem, Pharm, Cxxxvii, p. 167.
6 Dr. E. J. Mills’s Researches on Melting-point.
B was prepared from another portion of (D) dibromobenzol.
25 grm. were gently heated for two hours with 250 cub. cent.
nitrate as before, and allowed to cool during twenty-one
hours. The pressed product, which had at first contained an
oily body, weighed 17 grm. (=68 per cent.): it was erystal-
lized twice from naphtha, and thrice &c. (B; &c.) from alcohol.
The melting-point of nitrodibromobenzol is satisfactorily
sharp.
A,. | A. | Ay | By. a
OU I Ai LK. i —
° °o °
98-49 |93-43 | 93-46 | 83-46 |8349 83:50 8332
AG 49 4 4) :
| 53 | -48 | 9) 52 49
| 47 | 46] 51] 46| 44] 50] 44
55 | 54) 48| 43] 34] 45| 47
| -47 | -46 ote 46 | 49 52 49
| 55 | -483| -43| -44| 46] 48) “BB
58 | 48| ‘Sl| 39] 57 | 82) “57
| +58] °54 | “49 49} ‘52 50 49
| -47| 54] 49] 46] 52] 3O| -41
| 49] -48| 46] 52] 52] 60) 52
| 53] +51] -49| -44] 41] 5O!] 52
55} -SL| -49| 46] 49) -b2 | 49
en 83:51 | 83-49 | 83-48 | 83-46 | 83-49 | 83-51 | 83-50
Probable error .... °006) ‘007 °005) ‘006, -008) 006 -008
Thermometer ... 2 | 2 | 2 2 | 2 | 3 | 2
B. Aniline Derivatives.
1. Monochloraniline—Sample A was prepared from chlori-
nated acetanilide*, free from toluol. It was purified by solu-
tion in aqueous hydric chloride, evaporating thrice to dryness
after filtration, precipitating with ammonia, and distilling in
a current of steam. The product was crystallized twice from
naphtha, and thrice &c. (A; &c.) from alcohol.
B was prepared more directly from aniline by the following
method:—Half a pound of aniline, purified by cohobation for
several hours with one sixteenth of its weight of mercuric
chloride, was mixed with a pound of glacial acetate,and chlo-
rine led slowly over its surface. Considerable heat was evolved.
When this sign of action ceased to be manifested the mixture
was allowed to cool, and the now solid product heated with
water and caustic soda: the oily layer thus formed was with-
drawn, and cohobated for a few hours with alcoholic potash.
Water was next added to this solution and its residue; and the
* For the details of the methods of obtaining aniline derivatives from
acetanilide see Proc. Roy. Soc, x. p. 589, and Phil, Mag. 1875, xlix. p. 21.
oe se
_ ‘
Dr. H. J. Mills’s Researches on Melting-point. 7
united amines thereby precipitated were separated by appro-
priate treatment with aqueous hydric chloride*. B was
erystallized twice from naphtha, and thrice &c. (B; &.) from
alcohol.
The chlorination of acetanilide yields but little dichlorani-
line; the chlorination of the acetate still less.
Monochloraniline produces great cold when dissolved in
alcohol. On the application of heat to its powder, it melts with
great sharpness. ;
TaBsLe VI.
J
ie)
I
(or)
fer)
(=r)
I
~J
eS Bee
=]
(op)
(Jt)
[op
Je)
y
—
(Sy
Go
Wfean...........- 69:69 | 69-69 | 69:68 | 69:69 | 69:66 | 69-67 | 69:69 | 69°65 69-54
Probable error.| -010) -008! :007) -009| -007| 008} -006) -007/. -010
Thermometer. .| 2 2 2 2 2 2 2 2 3
2. Trichloraniline.—A. was obtained by chlorinating a solu-
tion of aniline in glacial acetate, as described under Mono-
chloraniline. The product was melted under aqueous potash,
twice distilled in a current of steam, and crystallized twice
from naphtha and thrice &c. (A; &e.) from alcohol.
The chlorination of acetanilide suspended in water yields
little or no trichloraniline.
Lesimple} describes a moditication of trichloraniline which
he prepared from nitrotrichlorobenzol by reduction. It has,
he states, a very unpleasant and persistent smell, and melts at
96°5. On these two points my derivative differs from his:
it has a faint but not unpleasant odour, and melts at about 77°.
In all the other reactions and characters mentioned by Lesimple
the two bodies exhibit a complete agreement. Beilstein (who,
* Loe, cit. + Ann, Chem, Pharm, ¢xxxyii, pp. 126, 127,
8 Dr. E. J. Mills’s Researches on Melting-point.
subsequently to myself, published an account of the deriva-
tive having the lower melting-point) confirms my determina-
tion. The substance with which I have dealt seems, then,
to be isomeric with Lesimple’s. Trichloraniline yields a non-
electric powder, which, in consequence of the woolliness of
this body, is rather difficult to obtain. The powder cakes
somewhat on drying. The melting-point is exceedingly sharp,
TaBue VII.
‘06 08 05 03 “10 06 | 77:02 02
Reyes... 77-05 |'77-06 | 77-06 | 77-05 |77-08 | 77-04 | 77-04 |'77-03
Probable error ...| °005) ‘004; ‘003 -005| -004 ‘003) -006) +004
Thermometer ...| 2 2 2 2 2 2 2 3
3. Monobromaniline.—In order to prepare this substance,
the best commercial aniline was heated to 100° for three
hours with =), part of mercuric bromide, which gave rise to
the formation of a trace of rosaniline. The liquid was for the
most part distilled off, cohobated for twelve hours with an
equal weight of glacial acetate, and then distilled to 130°.
The residue, after treatment with hot water, and pressure, was
powdered finely, and rapidly stirred in-a large bulk of water ;
into this, 1°75 part of bromine was ‘gradually introduced.
The brominated acetanilides thus produced were decomposed
with alcoholic potash, and the resulting bromanilines separated
by treatment with aqueous hydric chloride. The principal
product was dibromaniline.
Specimens A and B were obtained by partially attacking
with alcoholic potash the mixed bromacetanilides; the un-
attacked residue yielded no more on renewing the treatment.
They were crystallized several times from naphtha and spirit.
The remainders of A and B were further crystallized thrice
from spirit (AB). The mother-liquids of these preparations
Dr. E. J. Mills’s Researches on Melting-point. 9
were united, and their bromaniline crystallized four times from
naphtha and nine times from alcohol, in the presence, during
the last two operations, of animal charcoal (C). Q was ob-
tained by directly treating aniline with bromine. It was
purified by crystallization—once from naphtha and thrice from
alcohol with the aid of animal charcoal (Q,;), also once more
from alcohol (Q,).
Monobromaniline may be dried over oil of vitriol; but I
have preferred to use calcic chloride.
The melting-point of bromaniline is very sharp; A B
proved exceptionally sudden in this respect.
TaBLE VIII.
° ;_o ° ° °
61-76 | 61-82 | 61°65 61-93 | 61-94
| 78 | 82! 78| -86| ‘81! ‘851 -78 |
‘74| 911 76/1 -76| |
89 | 80 | 89] -88| -97
| -68| -90! -97
91 | 71) -85| -75| 84; 72) -83 |
80 | 2| -78| -85| -81
JAeTe:| 226 | 78.1 esi ore) es
87 | 84) 76) 78] 84] 88) “83
'87| -78| -76| -76| -76| -79| -81 |
84/ 89| 74) 82] 84] -79| 81]
78 | -84| -74| -84] 92] -88/1 -78
BE | oh 78| -76| 84] -85| -88
a eRe eee eee) |
ee 61:83 | 61-81 | 61-78 | 61-80 | 61-79 | 61-84 | 6186 |
Probable error.... -008) -010) 006 006) -014) -011) -013
Thermometer | eee 4 4 | 2 Dee eae
4, Dibromaniline [see Monobromaniline|—The substance
was dissolved in water containing one tenth vol. of common
aqueous hydric chloride, the solution filtered cold, and mixed
with sufficient ammonia.
Specimens A and B were obtained by the partial action of
alcoholic potash on bromacetanilides. A was crystallized
four times from naphtha and five times from alcohol; B three
times from naphtha, once from spirit, twice from alcohol.
C was similarly obtained ; it was separated in an evaporation
for monobromaniline, having been held in solution by the
hydrochloride of that body: this sample was crystallized three
times from naphtha and three times from alcohol, and animal
charcoal was used. F and G were a result of the further
action of alcoholic potash on bromacetanilides. EF was sepa-
10 Dr. E. J. Mills’s Researches on Melting-point.
rated like C ; it was crystallized three times from naphtha,
four times from alcohol, and animal charcoal was used. G was
treated on five successive occasions with a quantity, insufficient
to dissolve it, of the dilute aqueous hydric chloride already
named ; the cold filtered solution was precipitated with am-
monia. Of the successive precipitates (G,, G2, G3, Gy, Gs),
G,, Gs, and G; were used for the determination of melting-
point; G, and G3; were crystallized twice from naphtha and
thrice from alcohol, animal charcoal being present at the last
operation; G; was crystallized twice from naphtha, and twice
from alcohol in presence of animal charcoal.
The hydrochloric solution of dibromaniline already men-
tioned sometimes shows supersaturation.
bf
SS
2
G,. | G.
———_—_
)
| .
|
'
78-79 | 78-92
e “85
85 79
° / ° ° Oo ° °o
7891 78:88 | 7874 7882 | 78:84 | 7868
78 77 71 ‘71 87 92 | -90 85
91/ 69| -85| -71| 71 84 |
78 83 ‘90 90 “81 84 | “74 85
91 (ih 82 ‘87 Bo) tal bec | 92 79
78 91 qd “20, | -wBlo pe | 82 92
MiGan. 3.75: eerste 78°87 | 78:82 | 78-82 |'78-81 |'78°'78 | 78-80 | 78-82 | 78:84
| Probable error...| ‘010 012) +013) -015; -010) 014 O11; -012
| Thermometer | Rat ye Pane 2 ee | 2 | ae eae 4
;
'
5. Tribromaniline [see Monobromaniline|.—Sample A
was prepared from brominated phenylacetamide by distilling
the crude product of the action of alcoholic potash thereon
from strong aqueous hydric chloride, and adding water to the
distillate.
Z was precipitated by water from some strongly hydro-
chloric washings, and crystallized four times from naphtha,
four times from alcohol. B was crystallized from a hot mix-
ture of ordinary aqueous hydric chloride diluted with two vols.
of water, and washed with the same liquid diluted with six
vols. of water. It was crystallized twice from naphtha and
twice from alcohol, animal charcoal being present. Q was
prepared by directly acting with bromine on aniline dissolved
Dr. H. J. Mills’s Researches on Melting-point. 11
in a large volume of dilute sulphuric acid. It is the charac-
teristic product of the reaction; but a little bromaniline is also
formed, with traces perhaps of dibromaniline. It was purified
by extraction with aqueous hydric chloride diluted with nine
yols. of water, by distillation, and by crystallization from spirit
with the aid of animal charcoal. Q, was crystallized thrice
from spirit, Q, four times. In the preparation of tribromani-
line, whether from aniline directly or from phenylacetamide,
the product is accompanied with a considerable amount of a
black substance, non-volatile, and insoluble even in boiling
spirit, which evolves much hydric bromide on distillation, and
then carbonizes.
The determinations headed A, Z, and B were made with a
thermometer protected by two glass cylinders; in the other
cases the thermometer was bare.
The exact observation of the melting-point of tribromaniline
is very difficult, inasmuch as the substance becomes transpa-
rent only at the edges of a bead which is for the most part
dim and pasty.
TABLE X.
A. Z. B. Q.. Q. |
° ° ° ° fe) | fe}
116-42 | 116-07 | 11605 | 116-20 | 116-14 | 11631
26 12 “21 “31 ‘17 “31
28 “26 24. 23 28 24
17 32 21 ole 22 24.
31 18 19 | 26 30 26
23 23 16 | 31 22, 19
27 23 13 "26 19 11
23 34 19 28 22 31
28 23 13 “31 36 ol |
26 12 21 23 36 26 |
See Sian ae eroniel | Meaeceae 28 33 29 |
SOUR thal Ieee rte taal (OME EAE 28 28 | 24 |
ROPE fakes Poth see « “ol 36 |
Sea lar secsas Oe fh. cemmnes | “31 30
Bost gn Wer tsdeas, Irakabonse | 28 “39 |
a ee eee eee ee raat tess al Sey
IME Canie 5.855. 5 .edeeies 116-27 | 116:21 | 116-17 | 116-27 | 116-27 | 116-26 |
Probable error ... 013 018 ‘O11 ‘008 ‘013 | ‘011
Thermometer ... 2 2 2 2 2 3
C. Toluol Derivatives.
1. Nitrotoluol.—Nitrotoluol was prepared from coal-tar
toluol, which had been purified by agitation with oil of vitriol
and potash successively, and by distillation. According to
Beilstein’s recommendation, hydric nitrate of spec. gray.
1-48 was dropped into toluol; a stream of air was kept passing
through the flask, and a stream of water round it. Through
12 Dr. E. J. Mills’s Researches on Melting-point.
the washed mixture of liquid and solid nitrotoluol with toluol
thus obtained, a current of steam was passed, to remove toluol
first ; then a mixture of the two nitrotoluols came over ; and
from this the solid was almost completely extracted by solidi-
fication in a freezing-mixture and filtering out suddenly by
atmospheric pressure. For the success of this operation,
distillation in a current of steam is essential.
Sample A was purified by melting with a little Nordhausen,
washing with water, and crystallizing from spirit: the mother-
liquids were evaporated for deposits, d,, d,, dz. The results
were :—
d,. a. d,.
51-45 51:18 51-22
51:11 50°83 (thermometer 2) | Hach result
51:12 (recrystallized) is a mean.
41:13-51°52 (sublimed)
It is clear that neither crystallization from spirit (even after
Nordhausen) nor sublimation gives a satisfactory result.
Sample B was purified like A, twice crystallized from spirit,
once from pure high-boiling-point (132°) naphtha, twice from
spirit, once from spirit of wine.
Sample C was similarly purified: four successive extracts
(x) were taken in a mixture of 1 spirit, 2 water. Therm. 2.
The mean results were:—
£4.
Ly. de a “
44°5 44°-9 43°°8 507
This shows that the method of extracts is also a failure,
2, Lo, 23 Were united as C,; ©, was set aside as C,; C, was
twice crystallized from naphtha, once from spirit of wine.
Four similar extracts were then made, united, crystallized
from naphtha, C, added, and the mixture was again crystal-
lized, once from naphtha, once from spirit of wine: this pro-
duct is termed C,.
Sample D was thrice crystallized from naphtha, once from
spirit of wine; twice, thrice, and four times from spirit of wine.
Part of the crude substance of D had not been distilled. The
fractions are marked D,, D;, &c., according to the times of
crystallization.
M was prepared by dropping purified toluol into twice its
bulk of nitrous or “fuming ”’ nitrate of spec. gray. 1°48; 50 cub.
cent. of toluol were added to 100 cub. cent. nitrate in each
operation, which lasted 1:6 hour. It was crystallized twice
from naphtha and thrice from alcohol,
Dr. E. J. Mills’s Researches on Melting-point. 13
TABLE XI.
@. | Ca Ce | D, D;. | Ds De B
—_ —_———— | —_—_—_S ES | eee
|_o e) ° |_o ba | _o lo Pe)
| (51-43 | 51-39 | 51-22 |51-22 51-27 51-34 | 51°34 | 51:31
: | 29°) 38) 87) 82 | -10) 39’) 30} 84
40; 46) 30! -85| 10, -l7| -24/] -29
| 81). 37 |. 40| :25 |. 35| 32) -39| -34
-29 | ee tr da SEs EOE eee OSE ok
) BP eps ace |otcBTe ly n-3o- le CUT 34 184
eo} pee een) ee 19 39 34
Aa het 2 (ec 4Sa le OD [era |e 82.) oe eae
PS 6-32 be 2\ 85 1 8971) 2971-80 | 1G
=o i
| 27 eae red eae ee ee eee 31 |
| Mean ......... _seee| 51°82 | 51-38 | 51-80 | 51-27 | 51-27 [51-35 | 51-34 | 51-30
| Probable error...) O11) -013} ‘017; 016 016 ‘016 010! -010
| Thermometer Schiele ed Ye |= 2 alo etal
2. Dinitrotoluol.—tl have investigated the melting-point of
this substance as prepared (1) directly from toluol, (2) from
liquid nitrotoluol (“ metanitrotoluol’’), (3) solid nitrotoluol
when the active masses are relatively small, and (4) solid
nitrotoluol when the active masses are relatively large.
[Case I.] Dinitrotoluol was prepared from coal-tar toluol,
which had been purified by agitation with oil of vitriol and
potash successively, and distillation: a mixture of oil of vitriol
with hydric nitrate was used. The product was pressed to
free it from oily matter, and crystallized from spirit. The por-
tions that fell successively in the act of crystallization were
called A, B, C, D, and many experiments were made with
them; but the results were not very accordant. The four
samples were fractionally crystallized from spirit: the first
deposits being called A,, By, &c.; the second, Ag, By, &e.
Fractions of F (an old preparation) were also employed.
Melting-points having been taken, C,, Fy, and F; were
found to coincide, and mixed together. Four successive
fractions of the mixture were taken; and after some further
fractionation,
@), Dy [EECp.b, (POs, FEC):
yielded a;
A;, By, (F:);, [CPSF.C,)4]o, [F3F4C,)s 1, [(FsF.Ci)s Jy
yielded b;
As, Bo, Co, (Fie, [CPsFsCi)o]i yielded ¢;
D yielded d.
, a ae ae
ek hs ey)
14 Dr. E. J. Mills’s Researches on Melting-point.
The following results were then obtained :—
TABLE XII,
a, a. b, bB 1 a b. G. G. a,
oO o) (o]
69-23 | 69-12 | 69:22 | 69:20 | 69-13 | 69:23 | 69-15 | 69-29 | 69°38
23} 20} +19] +20 a 20 | +20] -31| 25
09 | 23} -22} +20) -16| +28} -42) -16| -40
33| -20| 22! -20| -18| -25| -29| 09] -99
14] 23] -09| -25| -21/ -25|] -34] 91] -38
6 | 19) Pes. 12! 10] -12| 29} -31) -98
IRI Bs SG We Si 23; 16] 12] -15| 06] 33
es Bee 23| -29| -251 26! 06! -33
ero Mae te 23 | 24} -201 +34! -31] +38
ES sal ee. eee 27) 211] ......| 29 | =OReee
men Ree 2 80 fi | 16] 2... | G4) ae
Sees | ei) Sar en, 29 | -40
ee ie) de ho ils lan ‘31
Hieber ne SOs 20) fee he Teed iG le Biecte | So ‘24
Mean ..........-. 69:18 | 69-18 | 69-19 | 69-21 | 69-18 | 69-21 | 69-28 | 69:23 | 69-30
Probable error. 025] -013} -015| -007/ 010} ‘012; -016 -017| -016
Thermometer...| 3 3 3 3 3 2 2 3 2
[Case II.] The mixture of nitrotoluols obtained by nitra-
ting coal-tar toluol was cooled to —17°, and the solid modifi-
cation (which separated in crystals) removed by sudden appli-
cation of the filter-pump and subsequent fractional distillation.
The product boiled at 219°-223°. 6:5 cub. cent. of substance
dissolved completely in 20 cub. cent. nitrous nitrate, with
TABLE XIII,
| I Ey,
en Midian bitriiM ish
68°99 69:24
69:15 19
12 *O2 |
23 24 .
20 “1 |
26 mils:
23 | 21 :
20 ‘16
15 16
293 ‘00
26 “71
23 19
“15 03
15 ‘08
18 3
Mieari: «foschctkoscanseeecee 69:18 69°16
Probable error ...........-..- ‘012 “014
Thermometer ............00. 2 2
Dr. E. J. Mills’s Researches on Melting-point. ° 15
slight evolution of heat; after four hours’ contact, 150 cub.
~ cent. water were added. ‘The precipitate, which was solid on
the following morning, was washed with warm aqueous sodic
carbonate, and then weighed about 8:5 grm., or 112°5 per
cent., the theoretical yield being 132°9 per cent. I will call
this specimen J dinitrotoluol. It was crystallized four times
from naphtha and three times from spirit. (See Table XIII.)
[Case III.] The whole of the remainder of D nitrotoluol
(p. 12) was treated with nitrous hydric nitrate in the cold ;
2°5 grm. of the nitrotoluol being dissolved in 39 grm. of the
nitrate, with which it remained in contact 24 hours. The
powder was very electric. I will call this specimen L. It
was crystallized four times from naphtha and thrice from
spirit.
The following numbers were obtained with Therm. 2:—
Tasie XIIT a.
Meant ets Ra Las: 69°17
Probable error ...........0.5- ‘010
Thermometer ....c.c.2ee000e 2
[Case [V.] When rather larger quantities are taken, though
the same proportions between the reagents and time of action
_be observed, a different result is obtained. Thus Y was pre-
pared from 4°5 grm. M mononitrotoluol; the crude product
(122 per cent.) was purified by warming with weak aqueous
potash containing ammonia, and was crystallized twice from
naphtha, eight times from alcohol. Zwas made from 20°5 grm.
of a new stock of solid mononitrotoluol (which had been dis-
tilled in steam, frozen, pressed, and crystallized twice from
naphtha and four times from alcohol); the crude product
(120 per cent.) was crystallized twice from naphtha, and eight
tonine times (Zs, Z,) from alcohol. Both samples had a faint
yellowish tinge.
16 Dr. E. J. Mille's Researches on Melting-point.
TABLE XIV.
5 |
| vg Tare | Zi,
oS PRC nT ee
| ) De, | | °
6954 | 6960 | 6948
57 60 46
54 | YI a
62 | 63 | 1
‘BT ‘7 38
Shia fio. ok “1
57 art ‘51
57 ‘BT 2] 56
51 65 56
bl 63 “62
51 | “60 59 |
59 ‘oT 59 |
| Mean .......ss.00 6956 =| | 6959 || | 6952
| Probable error ... 007 =| 006 | 01S |
Thermometer ... 2 2 | 2
3. Trinitrotoluol—A. Some crude coal-tar dinitrotoluol
was heated with about five times its weight of “fuming”
nitrate for more than thirty hours, but not so as to cause ebul-
lition of the liquid. It had lost about 15 per cent. of its
weight, but, as shown by its melting-point, had not been con-
verted into trinitrotoluol.—B was lost in the process of crys-
tallization.—C. The deposit from the nitric mother-liquid of
the preparation fused at about 59°7. The substance itself
fused at about 80°8 when crystallized nine times from spirit;
and then, when kept a few days, its melting-point rose to about
181°°8. A small residue from the entire preparation, crystal-
lized thrice from spirit, thrice from naphtha, and thrice from
spirit of wine, fused at 182°8 nearly. This body is soluble in
naphtha, insoluble in cold and very sparingly soluble in hot
spirit, insoluble in water or aqueous ammonia. Quantitative
experiment seems to indicate that it is a compound of dinitro-
toluol with trinitrotoluol. In appearance it closely resembles
trinitrotoluol. Subsequent attempts to prepare it, both directly
and in the nascent way, did not succeed.—D. The result of
A was confirmed.
I. A specimen of coal-tar trinitrotoluol about 3 years old,
yellow at the top; the melting-point of the lower and colour-
less part was taken. (This result will be noticed separately.)
The remainder from this first determination (part being yel-
low) was crystallized twice from naphtha and once from spirit
of wine. The results are given under the first E column; the
Probable error.
Thermometer... 2
Dr. . J. Miils’s Researches on Melting-point. 17
result of a further crystallization from spirit under the second
E column; and so on.
TABLE XV.
Talc Sy ve pe ae i PAA is oa Hl a pr oP ct oP
° fe) ° O° fo) fe) ° fe)
78°88 | 78°86 |78°89 | 78°78 |7 vo 78: 79 |\7 8: 83 | 78°76 |78°88 || 78:87
. . 1 . . .
we esses covccs
2 3 3 3 2 2 2 2
2 | O11} -010; -O11; -009; -018} -012) -013) -010
F. Coal-tar toluol boiling at 109°:5-112°:0 was purified
with oil of vitriol in the cold; it then boiled at 110°-113°.
Hqual volumes (300 cub. cent.) of nitrate (sp. gr. 1°48) and
this substance were mixed, the latter being run in gradually.
51 cub. cent. of toluol were recovered by distillation ; hence
benzol was absent. The product was washed, added to 300
cub. cent. “ fuming ” nitrate (sp. gr. 1°5) ; washed, added to
4 vols. “fuming’”’ nitrate (the latter), left 24 hours, and
1 vol. Nordhausen poured in—this being done in two opera-
tions, on account of the violent action in the cold. The yield
was 190°7 per cent.; theory, 246°7 per cent. Half of the
yield was crystallized from naphtha and spirit, and termed F,.
The other half was boiled for 6x6 hours with “fuming”
nitrate, and termed F,; the product was very dark, contained
scarcely any acid bodies, and showed little loss when weighed,
The fusion-points of F, and F, are the same.
___ K. Prepared from liquid coal-tar nitrotoluol which had
been twice distilled, cooled to —17°, filtered, again distilled
(under 224°); when cooled as mentioned, only a trace of crys-
tals was deposited. 19 cub. cent. of this liquid, 150 cub. cent.
“fuming”’ nitrate, 100 cub. cent. Nordhausen, yielded 31°5
grm. trinitrotoluol, = 142°6 per cent., theory requiring 165-7
per cent. The product was crystallized four times from
Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882. C
78°84 |78:81 | 78:86 | 78°87 | 78°88 |'78°82 | 78:84 | 78-78 | 78-82 || 78-88
18 Dr. E. J. Mills’s Researches on Melting-point.
naphtha, five times from spirit; its fusion-point then agreed
with that of F, and F;.
Such trinitrotoluol is found with great ease, an hour’s
ebullition with a mixture of equal volumes of oil of vitriol and
common nitrate sufficing to produce it. Now the presence of
oil of vitriol is a great hindrance to making ordinary tri-
nitrotoluol*.
M. M nitrotoluol was treated with Nordhausen and nitrous
nitrate, and yielded 157-1 per cent. of product. The melting-
point of this preparation having been found not quite regular,
the substance was again treated with the nitrating-mixture,
and crystallized twice from naphtha, and thrice (M,), four
times (M,), &. (&c.) from spirit.
The crystalline form of this modification of trinitrotoluol is
distinct from that of F, or K,, being much more prismatic and
less platy.
A small preparation (L) of trinitrotoluol made from L dini-
trotoluol (itself made from D nitrotoluol) was treated like M,
and the melting-point also determined before complete nitra-
tion had been effected. This point was 78°-91+°008, after
one crystallization from naphtha and two from spirit; and the
prismatic character of the crystals was apparent; but the
amount of substance was too little to go on with.
TABLE XVI.
M, M, | M.. M, M;
oO | fe} O° fe}
80-49 80°53 | 80°50 80°58 80°55
56 47 53 52
52 58 "DD 47 5D
49 42 5D 50 ‘47
52 D6 50 53 60
46 42 ‘47 53 DS
49 5d “58 50 “BD
49 53 “DD 50 "bb
54 50 50 47 52
| 54 48 D3 53 58
49 61 ‘61 53 58
49 58 “61 5D BD
52 “42 53 53 60
54 42 | 50 53 58
Mea. 5. sc0sessese 80°49 80°51 80°53 80°52 80°55
Probable error ... ‘008 012 “008 “005 ‘006
Thermometer ... 2 2 2 2 2
* Zeit. Chem. xiii. p. 539.
Dr. E. J. Mills’s Researches on Melting-point. 19
Thus it is evident that trinitrotoluol prepared from the solid
modification of nitrotoluol is distinct both in form and melting-
point from the others ; it is also more difficult in making.
It deserves to be mentioned that the melting-point of trini-
trotoluol appears to undergo a slight change under certain
conditions. Thus, a perfectly colourless specimen three years
old melted at 78°-76—the number of observations being 13,
and the probable error 0°012. A few grammes of the
specimen F,, after exposure to light, with frequent agitation,
for 13 days, during which it became mustard-yellow on
the surfaces, melted at 78°78; the number of observations
being 14, and the probable error 0°013. This result was
obtained after two crystallizations from naphtha and two from
spirit, when the substance had become brilliantly white.
D. Toluidine Derivatives.
Toluidine.—The modification examined is solid at the ordi-
nary temperature, and obtainable by the reduction of mono-
nitrotoluol.
Sample H was purchased from Messrs. Hopkin and Wil-
liams. It was purified by conversion into oxalate, which salt
was thrice extracted by ether and then decomposed by potash,
distillation in a current of steam, and crystallization thrice
from naphtha and four times &c. (H, &c.) from alcohol.
S was given me by Mr. Spiller. It was pressed and erys-
tallized twice from naphtha and four to five times (S,;) from
alcohol.
G was purchased from Dr. Schuchardt, of Gorlitz. It was
pressed, and crystallized twice from naphtha and three to four
times from alcohol (Gz-).
The above were ascertained to be all different preparations.
The melting-point of toluidine is difficult to observe. The
substance remains for some time in the pasty stage, and then
conducts heat very badly ; from this cause the melting-point
may easily be overestimated. On the other hand, when the
solid substance is plunged into a bath which is hotter than the
real melting-point, it melts with great readiness and sharp-
ness. Good numbers can only be obtained with finely-pow-
dered material ; the capillary tubes must be introduced into
the bath at 4° or 5° below the melting-point; and the mercury
in the thermometer must rise very slowly towards the last.
20 Dr. E. J. Mills’s Researches on Melting-point.
TABLE XVII.
| SS |
Gi: 63 | -76| -73| 69 $5 | 67
oe +7 | 62 “81 82 79 ‘76
Eee ee ) 42°77 | 42°71 | 42°73 | 42°76 42°78 | 42-79 | 42°76 42°77 42°81
Probable error.| ‘012} -011) O11) -009| 010) -009| -O11) 013 -012
Thermometer..., 2 2 2 + | 2 2 | 2 3 | 3
KE. Phenol Derivatives.
1. a Mononitrophenol.—By « mononitrophenol I mean the
more volatile mononitrophenol of the two produced by treating
phenol with water and nitrate according to Fritsche’s method
(Journ. prak. Chem. \xxy. p. 257). The crude stock was
several times distilled.
A was crystallized from water and dried over oil of vitriol
(as the rest were): it had been exposed to light (A,); it was
further and continuously exposed to light (A,). B, was a
partial precipitate from spirit by water, dried in the shade ;
the mother-liquid gave with more water a precipitate which
turned brown when dried like B,, and then melted about 0°°6
below B,. C, was made like B,, except that scarcely any
thing was left in the mother-liquid. E wasa total precipitate
from a sodic salt which contained, as a mean of two experi-
ments, 14°28 per cent. of sodium (theoretically 14°31): it was
dried in the shade. D was twice crystallized, probably from
weak spirit, and dried in shade twenty days, 7. e. very much
longer than either of the others.
The powder of a mononitrophenol has a tendency to cake |
together on keeping. |
Dr. H. J. Mills’s Researches on Melting-point. 21
Taste XVIII.
fe)
44-31 44-29 44-29 44:29 44-28 44°31
29 “DA 2 "25 3l
24 24 18 25 “31 23
33 18 10 22, 28 17
24. 32 29 27 ‘28 25
29 26 29 27 23 39
BYE 29 29 30 28 31
33 32 21 22 “31
24 21 -29 27 Bil
33 32 29 25 28
Bet 5 21 29 A se 28
Wiesraleerssdscencs 44-30 44:97 44:25 44:95 44-28 44-98
Probable error ... ‘009 010 012 005 005 ‘O17
Thermometer ... 2 3 3 2 3 3
2. 8B Mononitrophenol.—B mononitrophenol is the less vola-
tile mononitrophenol of the two produced by Fritsche’s process
(Journ. prak. Chem. Ixxv. p. 257). The crude stock was con-
yerted into sodic salt, washed with aqueous sodic hydrate, dis-
solved in water,and precipitated by hydric chloride: a sodic salt
prepared from this contained 14°17 instead of 14°31 per cent.
of sodium, the preparation being effected with but very little
loss.
A, was crystallized thrice from naphtha and once from
water ; A, was the same, twice crystallized from water; B,,
B,, B; were all crystallized together thrice from naphtha,
in one quantity; and this was crystallized thrice from water.
All the specimens were dried over oil of vitriol in the dark for
-about two months.
8 mononitrophenol becomes pale dirty yellow on exposure to
light for a day, especially if a part of it has been melted. As
the coloured product probably melts below the temperature
at which the uncoloured substance does; and as a broad gas-
flame must tend somewhat to produce the sane effect as day-
light, the long stage of incipient fusion and the uncertainty
of the limit are accounted for.
22 Dr. E. J. Mills’s Researches on Melting-point.
TABLE XIX.
A, A, B, B,. | B, |
O° ° Oo
111:29 | 111-50 | 111:37 | 111-53 | 11146
2 “60 1 7,
8D 53 >it 32 40
40 50 “41 3 40
38 53 4] 39 47
45 50 48 46 51
40 27 4376 41 51
3l 42 2511 4] 51
26 42 58 dH 49
24 45 46 On 38
ae le | 51 2 “31
e303), US eee *32
Wears cette 111-34 | 111-45 | 111-46 | 111-41 111°43
Probable error ... 014 017 ‘016 012 014
Thermometer ... 3 2 3 3
3. « Dinitrophenol.—« dinitrophenol appears to have been
first observed by Armstrong, who, however, did not obtain it
in a state of purity ; the exacter definition of the substance is
due to Hiibner and Schneider (Zeit. Chem. xiv. p. 524). In
preparing it, I followed the method recommended by the last-
named chemists, depending more especially on the insolubility
of the baric derivative in boiling spirit of 90 per cent. When
the baric derivative was dissolved in water and treated with
aqueous hydric chloride, the hydric salt was precipitated: this
was afterwards dissolved and crystallized.
a dinitrophenol has an extremely pale yellow colour when
crystallized from naphtha or spirit ; the powder has a deeper
shade; and the solution imparts a dark-orange tint to a tissue
on which it has been dried.
A, B, C, D, E were distinct preparations. A and B had
been crystallized thrice from naphtha and thrice from spirit ;
C had been crystallized from water, aqueous potassic chloride,
and twice from spirit; D had been made from a baric salt
twice extracted with spirit, after which it was crystallized
once from naphtha and four times from spirit*; E was formed
by uniting the remainders of A, B, and C, extracting the barie
salt thrice with alcohol, and crystallizing the resulting a dini-
trophenol once from naphtha and once from spirit.
* The hot alcoholic solution was poured off from a red, quite insoluble
foréign substance.
ae
Dr. EH. J. Mills’s Researches on Melting-point. 23
a dinitrophenol melts sharply, the pasty stage being short.
According to Hiibner and Schneider its melting-point is 63—64°.
TABLE XX.
A. A. B. B. C. D. K.
Oo (2) Oo ie} (2) (e} fe}
61-89 | 61°79 | 61-85 |61°82 | 61-78 | 61:82 | 61-79
“80 ‘79 i nelle | “79 85 74
Wighiay Wes = eomreee 61:79 | 61-82 | 61-79 | 61:76 | 61-75 | 61-79 | 61:77
Probable error ...| °013} -010) -006; -009} -007) :009} -007
Thermometer ...| 4 2 2 4 2 2 4
4. B Dinitrophenol.—Z. The crude compound was pre-
pared by Griiner’s method, from crystalline phenol. A con-
siderable amount of its baric salt was crystallized repeatedly
from a large volume of water, and the cooled and filtered
mother-liquid precipitated with hydric chloride.
Z. was the tenth precipitate; it was crystallized thrice from
water.
Zz was the eleventh precipitate ; it was crystallized once
from water.
Z,, was the twelfth precipitate; it was crystallized once from
water.
Preliminary determinations of melting-point were made
with the nine preceding fractions ; but the numbers were not
sufficiently satisfactory to warrant proceeding with purification.
Y was made by Dr. Armstrong from trinitrophenol, by way
of amido-dinitrophenol; it was crystallized thrice from water.
T. For this also I am indebted to Dr. Armstrong: he had
prepared it by acting with ordinary hydric nitrate on phenol.
It was crystallized once from naphtha, once from alcohol, and
four times from water.
4
24 Dr. E. J. Mills’s Researches on Melting-point.
In determining the melting-points of Z,, Z;, and Y, the
thermometers were protected by two glass cylinders ; in the
other three cases the cylinders were not used.
Crystallization, powdering, desiccation, and filling of eapil-
lary tubes had to be effected either in total darkness or ina
deep shade. £ dinitrophenol is very nearly white; but by
two hours’ exposure to a somewhat gloomy atmosphere it
becomes deep turmeric yellow.
8 dinitrophenol melts with moderate sharpness.
TABLE XXI.
Diy. Ze. Y. T, Ze. Ze,
fe} ° ° ° fe) (9)
11660 | 11163 | 111-46 | 111-57 | 111-66 | 1131-65
* . . 4
60 63 “57 57 6 ‘DD
“46 49 63 49 61 “65
52 58 68 “60 61 58
55 63 *82 57 64 DS
63 60 60 “60 80 63
46 58 “49 “57 61 60
43 68 457f 52 66 58
52 52 ‘60 "BA 53 53
63 55 57 D4 66 65
1 ey es a 111:54 | 111°59 | 111°60 | 111°56 | 111-64 | 111-59
Probable error ... 015 012 “020 ‘007 014 ‘010
Thermometer ... 2 2 2 2 2 3
5. Trinitrophenol—Sample A was a commercial specimen.
It was crystallized twice from water, once from alcohol, and
again from water.
Z was prepared from dinitrophenol made by Griiner’s pro-
cess (v. supra); the material employed was very pure, having
been precipitated from a 12th (Z,) cold aqueous extract of
the crude basic salt. This was evaporated to dryness on the
water-bath with a very large excess of hydric nitrate, and crys-
tallized once from naphtha, once from ethylic alcohol, and
twice from water.
O was made from phenol, containing minute amounts of the
two modifications of dinitruphenol, by evaporation, as with Z.
It was crystallized thrice from water, once from alcohol, and
a first (O,), second (O,), and third (O;) time from water.
M was similarly prepared from sodic « nitrophenate (B
under « nitrophenol), and was crystallized thrice from water.
F was derived from sodic 8 nitrophenate (the analysis is
J
‘Ad
‘t
Mean
Dr. E. J. Mills’s Researches on Melting-point. 25
given under 8 mononitrophenol); it was crystallized once from
water, once from alcvhol, and again from water.
N was prepared from some e (Hiibner’s) dinitrophenol, for
which I am indebted to Prof. Armstrong. This was purified
by Hiibner’s two processes, and can have contained at most
mere traces of its isomer. The trinitro-compound was crys-
tallized thrice from water.
Trinitrophenol is a nearly white substance when in crystals;
if very finely divided by any means, it appears a pale yellow.
The powdered crystals, if exposed for two hours to indirect
light on a dull morning, acquire a deep mustard-yellow colour.
The crystals of the substance termed N were almost perfectly
white.
The melting-point of trinitrophenol is, on the whole, not
difficult to observe.
TABLE XXII.
A. Zee Oa 0. (ah Ole Mao BY gee
120-97 {121-00 09 ‘11 06 16 {120-98 hace
— | $< ———— | —_ _
Thermometer... 2 2 2 2 2 2 2 2
F. Naphthalin Derivatives.
Naphthalin.—Commercial pure naphthalin, which had been
twice sublimed, was digested for a few hours with strong oil
of vitriol in the water-bath. After washing with water, it was
distilled from caustic soda in a current of steam. The first
portion of the distillate is termed A, the second B. These
portions were crystallized twice from naphtha and thrice (A;
&c.) from alcoho]. Before naphthalin melts it exhibits a de-
cided pasty stage; yet the melting-point is sufficiently sharp.
The powdered substance is highly electric.
° fo) o fe} fe) ° fe) te}
121-11 |120-95 {121-04 [121-14 [121-03 120-99 |121-20 |121-20 [121-09
06 {120-92 O07 {121-11 |120-98 |121-:13 {121-17 |120°98 |120-89
O08 {121-03 “Ol {120-97 |120:98 16 {120-98 |121-09 |121-09
‘11 {120-95 15 |121-714 {121-08 18 {121-14 "12 |120°94
703 |121-06 18 |120:97 00 “10 09 12 121-11
706 {121-00 12 {121-06 08 16 “O1 15 |121-11
03. {120-98 23 “14 06 “19 “12 12 /121-14
06 {121-20 09 09 “14 07 04 12 120-94
24 (121-00 12 ‘09 ‘ll 19 14 15 {120-99
sce eee 121-07 {121-01 |121-11 |121-08 |121-05 |121-:13 |121-09 |121:12 |121-04
Probable error. 014 016 7013 013 ‘O11 “013 016 “012
9
018
3
26 Dr. E. J. Mills’s Researches on Melting-point.
TaBLeE XXIII.
°o ° ° oO
80-06 | 80:03 | 80-01 | 80:03 |80-05 80:05 |80-06
7998| -06| -06| 08} 05| 08 | -14
80-01! -08| 091 -00| -05| 05 | -09
7995 | -00| 06] -08! -05| 02 | 09
8003 | 00] -09| -08| 05) 08 | -09
30061! -00.| -06| -08| -07| -05.| -09
30-09 | -08| 12) -08| -07| 08 | -03
80-06 | -06| -12/ -11| -05| -08 | -09
80-03} -11| -06| -11| -07| -05 | -09
7998 | -03| -09| -06| -07| -05 | -09
30-06 | -11| -06| o6| 07| 10] tl
8003! vo! -o1/ 08! -07| -05 | 03
Mente 80:03 | 80:05 | 80:07 | 80:07 |80-06 30-06 | 80-08
Probable error ...| ‘008, 008} -007) 006] 002, 004} -006
Thermometer ..| 2 | 2 | 2/2 | 2 | @ | 2 |
Nitronaphthalin.—A was a sample which had been in my
collection for some years, and the details of its preparation are
unknown. It was distilled in steam, and crystallized twice
from naphtha and thrice &. (A; &.) from alcohol.
B was a similar sample from the same source. It was
purified and fractionated exactly in the same way as A.
Nitronaphthalin becomes sensibly yellowed by continued
exposure to light. It melts with considerable sharpness.
TABLE XXIV.
56-17 |5616 156-17 | 56-21 56-15 | 56-24 |56-17 | 5610
+15 | 24) gt eee
VEG STI sce a cscs: ses 56°19 | 56°18 | 56:18 | 56:18 | 56-16 56:19 | 56°14 | 56°11
Probable error ...} 004) -006} -007| -006 009) O07) ‘006 -010
Thermometer ...) 2 2 2 2 2 2 2D ees
Dr. H. J. Mills’s Researches on Melting-point. 27
TasLe XXV.
Summary of Results.
k After :
Substance, | Weight | Preble | poggendon| set a
5 correction. ;
Toluidine .............+- 49-765 004 42-700 42-890
Nitrophenol (@)......... 44-270 003 44-205 44-392
Witrotoluol <.....:..... 51:305 005 51:239 | 51-407
Dichlorobenzol ......... 52-723 ‘002 52°657 52°821
Nitronaphthalin ...... 56°175 002 56°110 56°261
Dinitrophenol (¢)...... 61-778 003 61-714 61-843
Monobromaniline ...... 61-806 “003 61:°742 61:871
Dinitrotoluol (a) ...... 69-211 “004 69-154 69-252
_ Chie (eres 69:571 “O04 69-514 69-610
Monochloraniline ...... 69-667 003 69-610 69°706
Dinitrobromobenzol...| 70-598 “004 70°542 70°634
Trichloraniline......... 77-052 ‘001 77-004 77-068
Dibromaniline ......... 78821 004 78776 78°833
Trinitrotoluol ......... 78-841 004 78°796 78853
Naphthalin ..:...... .. 80-061 002 80-018 80:070
Trinitrotoluol (M) ...| 80°524 003 80-481 80:532
Nitrodibromobenzol...| 83°:490 “002 83-452 83-492
Dibromobenzol ......... 87:037 “002 87:007 87:035
Dinitrobenzol ......... 89-718 ‘003 89-693 89:712
Nitrophenol ........... 111-413 006 111-448 111-455
Dinitrophenol ......... 111-579 “004 111-614 111-621
Tribromaniline......... 116-247 ‘005 116-298 116°319
TrinitrophenoL......... 121-082 005 121-151 121-194
Discussion.
The determinations of melting-point which have been
recorded in the preceding tables, and the results of which are
summarized in Table XXV., show a very small probable
error in connexion with their weighted means. The probable
error of a weighted mean has ranged from 0°-001 to 0°:006,
its average value being less than 0°:004. So far, then, as
regards the actual process of ascertaining melting-point, con-
siderable accuracy has doubtless been attained.
The preliminary operation of calibrating the thermometers
was so conducted as not to have introduced material error, as
indeed is obvious from a comparison of the results obtained
with different thermometers on melting the same substance*.
Regnault was of opinion that the height of the barometer
cannot be ascertained with a less error than about 0-1 millim.
Such an error would correspond to about 0°:0037 on 100°;
and the error would be still less on the mean, as in the present
case, of several readings. The small errors in the determina-
tion of the exposure-corrections could not sensibly affect the
* See, for instance, Table VIL.
28 Dr. E. J. Mills’s Researches on Melting-point.
final results. It is to comparison with the air-thermometer
that we have to look for any important source of error. All
observers who have made an extended range of such compari-
sons have found noteworthy errors, though they have in no
case stated probable error. The probable error of the result
of my own comparisons of thermometer 2 with the air-ther-
mometer is 0°-085 for a single set of comparisons, or 0°-085
—/33=0° 015 for the results of the thirty-three sets. This
number is the measure of probable error of the equation em-
ployed in the final reductions. Compounding, then, the mean
probable error of the melting-point (-004) with that of the
comparison (‘015) with the air-thermometer, we may consider
the melting-points in Table XXYV. ascertained, in terms of
the air-thermometer, with a probable error of
o/ (004)? + (015)? =0°015.
The relation of the chemical symbol to the physical proper-
ties of a substance is a matter of such great interest that I have
sought for it in melting-point, although other investigators of
the general subject, working with less definite data, have not
arrived at very encouraging results.
It is very easy to show that, in some cases, there is a very
simple connexion between the formula and the melting-point
of a substance in the centigrade scale. Thus, dichlorobenzol,
bromaniline, and trinitrotoluol forma group in which melting-
point =¢x numerical value of formula.
Substance. Formula. Melting-point. p-
Dichlorobenzol . C,H,Cl, =147 52°821 *35933
Bromaniline . . C,H, BrN =172 61°742 “39971
Trinitrotoluol . C,H; N;0O,=227 80°532 35477
In the first of these two instances the values of ¢ are almost
exactly the same ; in the last, however, the limits of probable
error are exceeded, though a close approximation is very
evident.
The following comparison furnishes another practical iden-
tity :-—
Melting-point. Melting-point.
Trinitrotoluol ._78°853 — Dinitrotoluol . 69-252=9-601
Trinitrophenol. 121-194 — Dinitrophenol. 111:621=9-573
In the next instance there is an approximation:—
Melting-point. Melting-point.
Dinitrotoluol . 69:252 — Nitrotoluol . 51-407=17°845
Dinitrophenol. 61°843 — Nitrophenol, 44:392=17-451
Dr. E. J. Mills’s Researches on Melting-point. 29
Such illustrations may be of service in enabling us to detect,
with more or less probability, the parallelism of chemical
series, and to enable us to decide whether a function—nitra-
tion, for example—has or has not the same value in different
parts of a series. Other groups in which a similar but less
intimate relation prevails, might be adduced from the list ;
and a glance at Table XXV. will show that, on the whole,
melting-point and formula grow together. It may not im-
probably prove to be the case that, when the whole subject of
melting-point has been successfully investigated, this simple
relation is the limiting condition of the real law. The data,
however, hitherto adduced are far from adequate to a discus-
sion of numerical relations among melting-points: for such an
object it would be a fruitless task to examine them further.
Some negative results of this investigation are worthy of
attention. Thus e and 6 nitrophenol have the same additive
formula, and yet differ by 67°-063 in their melting-point. It
is clear then, as already well known, that melting-point may,
in cases of isomerism, be related to something else than for-
mula. The melting-point of naphthalin is actually lowered in
the first stage of nitration. Considerations such as these may
perhaps serve as suggestions for future work.
An accurate method of determining melting-point places it
within our power to detect far more delicate shades of isomeric
differences than have hitherto been regarded as possible.
Thus strong presumptive evidence has been adduced (p. 14)
that dinitrotoluol, when prepared directly from toluol or from
liquid (meta-) nitrotoluol, or from solid (para-) nitrotoluol by
gentle nitration, melts at 69°-252; but that when paranitro-
toluol is energeticaly nitrated, the product melts at 69°610.
There are consequently two modifications of dinitrotoluol ob-
tainable very directly from toluol—the melting-point of these
substances differing by 0°-358, a quantity far beyond the
range of error of the method. In like manner, it can be
shown that two parallel modifications of trinitrotoluol exist—
one of which melts at 78°-853, the other at 80°-532 *.
[| For a complete account of the thermometers referred to in
this memoir the reader is referred to the Transactions of thé
Royal Society of Edinburgh, 1881, p. 567; for the method of
determining melting-point, to the Proceedings of the Royal
Society, vol. xxxiii. p. 203.]
* Compare Phil. Mag. 1875, 1. p. 17.
[ 30 ]
II. Measurement of Curvature and Refractive Index. By
C. Vernon Boys, A.R.S.IL, Demonstrator of Physics at
the Normal School of Science, South Kensington*.
[Plate I.]
F the methods best known for measuring the curvature
of surfaces, that depending on the spherometer is both
accurate and convenient in the case of surfaces of sufficient
diameter and where the curvature is not too small. The
reflection-test, depending on the observation with a telescope
of two images projected ona scale, is certainly not convenient,
nor is it capable of giving very accurate results. While
endeavouring to find some more satisfactory way of exa-
mining the curvature of the surfaces of lenses that would be
both accurate and simple, I discovered the method which I
am about to describe. Though, from its great simplicity, I
can hardly expect it to be new to every one, yet I have never
heard of its being employed, nor do those to whom I have
shown it remember to have seen it before. Therefore, even if
it should be shown that this method is not new, it is certainly
so little known that I think it worthy of attention.
The centre-of-curvature test known as Foucault’s test,
which is used to examine the figure of the mirrors of re-
flecting telescopes, gives, perhaps, the most delicate means of
examining form that exists. By its means the expansion by
heat of a portion of the surface produced by touching it with
the finger is rendered evident, as an apparent mountain
standing out of the glass, which takes from five to fifteen
minutes to disappear ; and the warm air leaving a hand held
between the centre of curvature and the surface has the
appearance of flames of fire. In each of these cases no other
system of observation could show in so striking and conspi-
cuous a manner effects depending on so slight a cause.
The examination at the centre of curvature is carried out in
this way:—The mirror is placed in a convenient support so
that its surface is vertical; and in front of it is placed a lamp
with an opaque chimney, through which some pin-holes have
been made. If one of these holes is near the centre of cur-
vature, the light leaving it and reflected by the surface is
brought to a focus on the other side of the centre. This focus
is then found; and the lamp is moved till the focus is as near
the chimney as will allow of its observation. A piece of thin
sheet metal, with a straight edge, is then placed so that it
may be moved to or from the mirror or laterally. Now,
if the edge of this is sufficiently on one side to let the light
* Communicated by the Author.
Measurement of Curvature and Refractive Index. 31
pass the focus, an eye immediately behind the focus will see
the mirror filled with light; but if it is gradually moved
across while the eye still watches the mirror, the illumination
of the latter will appear to die away in the same direction as,
or in the opposite direction to, the movement of the edge, or
uniformly, according as the edge is between the mirror and
the focus, or between the eye and the focus, or at the focus.
By this means, and by this means only, can the different
radii of curvature of the successive zones of a parabolic
mirror whose radius of curvature is twenty times its diameter
be accurately measured. The close contact between the para-
bola and the circle is due to the fact that it is one of the third
order. I think it worth mentioning that the formula given
by Dr. Draper in the ‘ Smithsonian Contributions to Know-
ledge,’ vol. xiv. (1865), for testing the true parabolic form,
gives only half the deviation from the sphere, as was pointed
out by a correspondent of the ‘ English Mechanic’ who signs
himself “ Orderic Vital,’ and was confirmed by Mr. H. H.
Liveing and myself*. I have gone thus fully into the Fou-
cault test, as my method involves the same general principle,
viz. making the rays return along the path whence they
came.
Before considering the general case applicable to any kind
of lens, I think it best first to show the simplicity of the
method in a particular and common case—that of a thin equi-
convex lens. Tix an ordinary spectacle-lens in a clip, with its
principal plane vertical ; in front of it place a card with a small
hole in it; and illuminate the hole with a candle-flame. It
will be found that, when the lens is at a certain distance from
the card, there is an inverted image of the hole formed on the
card. When this is the case, the light leaving the hole and
meeting the front surface of the lens is refracted and meets
the back surface normally: most of the light passes through;
but a small portion is reflected back along the path whence it
came, and is sufficient to produce an image easily visible in
the day. This distance of the card from the lens, which is the
apparent radius of curvature of the back surface seen through
the front surface, is throughout this paper called 7 The true
focal length F of the same lens may be observed in the usual
way; but it is more conveniently found by fixing a plane sur-
face of glass behind the lens, when it will be found that
another image may be produced when the lens is about twice
as far from the card as it was before. Since an image is pro-
duced, the light must have returned along the path whence it
came, and must therefore have struck the plane surface nor-
* English Mechanic, vol. xxxi. pp. 89, 184, 207.
32 Mr. C. V. Boys on Measurement of
mally—that is, have left the lens and returned to it as a
parallel beam; therefore the card is at the principal focus.
For a plane glass surface a piece of plate glass blacked at the
back, or the surface of a prism may be used. The observations
of the distances F and / can be easily and accurately made ;
then the radius of curvature may be found from the formula
as I shall presently show.
Before doing so, however, I think if well to describe the
most accurate method of observing the distances F and f. The
card with the pin-hole is convenient; but it is difficult to find
the place with great accuracy where the focus is most sharply
defined, and to measure the distance when found. All diffi-
culty is completely avoided by the following plan:—Take a
piece of thin sheet metal, of the size and shape shown in
Pl. I. fig. 1, and fix in front of it, in the position shown by
the dotted line, a small reflecting-prism, so that, when a small
bright flame is placed on one side of the prism, a beam of
light leaves the slit in the plate. Replace the card by this
plate and prism, and move the lens till the aerial image of the
slit is formed in the corner, close by the edge of the prism.
To examine the position of the image with greater precision,
an ordinary positive eyepiece will be found convenient. When
the image and the slit are equally distant from the lens, there
will be no relative movement on moving the eye ; if there is
relative movement, the distance between the lens and the plate
must be increased or diminished according as the plate or the
image appears to move with the eye. When the distance has
been properly adjusted, it is easily measured by resting a scale
on the continuation of the lower edge of the slit, and moving
it till it touches the surface of the lens. The position of the
edge of the prism or of the slit may then be read with great
accuracy; and it will be found that, on repeating the obser-
vations several times, a discrepancy more than a tenth of a
millimetre between any of the measures need not occur.
Instead of observing the position with an eyepiece, the
Foucault plan may be adopted. Place the eye immediately
behind the edge of the prism, so that all the light forming the
image enters the eye. Move the prism laterally towards the
image, which of course moves to meet it, and observe whether
the light which fills the lens dies away uniformly, or whether
it seems to retreat from one edge of the lens. If the retreat
is in the same direction as the movement of the prism-plate,
the distance is too small; if in the opposite direction, too
Curvature and Refractive Index. 33
great. Hither of these systems will give accurate results ; I
prefer the first, as tiring the eye less and being, especially with
small lenses, the more accurate.
A conyenient support for the lens is made by boring a hole,
with a less diameter than the lens, in a piece of thin parallel-
sided wood. The lens may be slipped under two clips, so as
to rest against the edge of the hole on one side of the wood.
On the other side a piece of plate glass, blacked at the back,
is cemented or held in a similar way by clips. If this piece
of wood is fixed vertically on a horizontal slide, it may be
moved away from the prism-plate, and the distances 7 and F
determined in a few minutes. Fig. 2 is a horizontal section
of the arrangement when the principal focus F is being deter-
mined. The dotted line shows the position for 7. By
If instead of a lens a single surface only is to be measured,
there is of course no difficulty in the case of a concave sur-
face ; but a convex surface may have its curvature determined
in the following way:—Arrange the prism-plate and flame as
before. Ata distance in front of the prism-plate more than
its focal length fix a converging iens, preferably achromatic.
Observe the position of the aerial image on the other side of the
lens, and make it coincident with the edge of a plate of metal, m.
The positions must be so adjusted that the distance of m from
the lens is greater than the radius of curvature of the given
surface. Now place this surface between the metal plate and
the lens, and move it till an image is formed accurately by
the side of the prism. Then the light impinging on the convex
surface has been reflected back along the path whence it came,
and has therefore struck that surface normally; therefore the
place m, where those rays would have met had they not been
intercepted, is the centre of curvature of the convex surface.
Its radius of curvature can therefore be measured by suitably-
formed callipers. Fig. 3 is a horizontal section of the
arrangement.
Kf
I have stated above that R=p5 _in the case of a thin equi-
convex lens. This must now be proved, and the more general
case of any kind of lens treated next. First, consider that
the jens is so thin that any normal to either surface cuts each
at points appreciably equally distant from the axis. Since the
image which is produced is partly formed of rays which are near
the axis, these rays meet the axis at angles so small that the
tangent, the sine, and the arc are convertible terms. If the lens
is large and not of very long focus, this will not be true of rays
from near the edge of the lens; but as these rays are not
necessary for the image, the central ones alone may be
Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882. D
34 Mr. C. V. Boys on Measurement of
employed, and by them the curvature of the whole surface, if
spherical, determined.
On the front surface take any point p, and through it draw
a radius mR of the back surface. Join p with f, the apparent
centre of curvature of the back as seen through the front sur-
face. Draw also through p a radius ab of the front surface
and a line de parallel to the axis. Then the angles mpd, dpb,
ape are equal to one another. Call these angles @. The
angle apf=x angle mpb=p20; therefore the angle cpf=
u20—0. But the angle epR=8@;
R R+
Fai ex or pane
By the property of equiconvex lenses, poet L;
RR un sg
oF = OF and R = F-f 5
or, in a thin equiconvex lens, the radius is equal to the
product divided by the difference of the principal focal length
and the apparent radius of the back as seen through the front
surface.
It might be expected that, as this formula has been deduced
from a specially simple case, a more complicated one would
be necessary if the two sides of the lens were not equally
curved, or if one surface were plane or concave. But such is
not the case ; the same formula applies in every possible case
though, as will be shown, experimental difficulty occurs in the
case of a diverging meniscus.
The proof of the formula in the case of a thin lens which is
not equiconvex is similar to that already given. Make the
same construction as before, and let Ry, Ry be the centres of
the surfaces 1 and 2, and 7, the apparent centre of 1 seen
through 2.. Also let R.=nR,. Call each of the angles mpd
cpR,, 9; then the angles dpR, and ape will each equal nO.
As the angle apj;=y x angle mpR,= (1 +7)0, .*. angle epfj=
w(1+n)@—né. But angle cpR,\=@;
sealed eee
Ry i
Substitute R. for n, and it will be found that
2
_ Ri( A+R)
ne OR ES 2
Curvature and Refractive Index. 35
A similar proof will show that
Ro(fot+ Ri)
SS eS
i Fo( Ry + Re) @)
By the property of lenses,
<2 el
aay des Wa Leona erat a CS)
where F is the principal focal length.
By combining (1) and (38),
1
hoe Solaagl ald BA
Bo , ol se eas ne (4)
By combining (2) and (3),
tad Pee ee ih Ey 5
Rep Pav ae iO)
By combining (1) and (2),
1 sf sted Siaeea |
sp 6
R, R, Ji Je
Tt is not a little surprising that, whatever the refractive
index of the material of the glass, or the curvature of the front
surface, the curvature of the back surface can always be ob-
tained ‘from an expression in which both apparently are
omitted. They are both of course involved in each observa-
tion, F and /, which accounts for the possibility of their being
eliminated.
Tt is interesting to follow the changes which occur between
the two extreme limits of form—a double convex and a double
concave lens. Take a double conyex lens, and suppose one of
the surfaces to be gradually pushed in; when it has become
plane we have the first particular case—a plano-convex lens.
Call the flat surface 1 and the convex surface 2 ; then, by (4),
gran
“. Ai=F, or the apparent centre of curvature of the flat sur-
face seen through the round surface is at the principal focus.
By (5),
_ since F= — ; «. R,=y/fo, or the apparent radius of 2 is less
than the true radius in the ratio of yw to 1.
If the pushing-in process is continued, the surface 1 will
become concave. Four observations can then be made—F,
Ji; fz, and R, ; therefore R, may be found by either of the
D2
36 Mr. C. V. Boys on Measurement of
equations (5) or (6). As the surface 1 becomes more con-
cave, its apparent centre on the other side of the lens will
retreat to an infinite distance ; and then the concave side will
appear flat when viewed through the convex surface. This is
the case when R,= —F, as may be shown by making 7, = in
(4), or as is obvious from a diagram. When R, becomes less
than this, 7; becomes an imaginary point on the other side of
the lens, such that, if rays were sent so as to converge upon
it, they would return as though they had come from it. _ Its
position could be determined experimentally by the method
given for a convex surface on p. 33; but as the true radius
can be determined directly, there is no necessity to find this
imaginary apparent radius.
Let the concavity of surface 1 increase ; the next particular
case is that of a watch-glass, where R,=—R,. Then F be-
comes infinite, and the two points 7, and R, become coinci-
dent. When the surface 1 becomes still more concave, F
becomes negative and virtual, and R, and /, pass one another.
The experimental determination now becomes more difficult;
for neither can F or f, be observed directly; but still the
equations (5) and (6) hold. They may each be found by the
method for a convex surface, which is less convenient than
the direct method.
If the concavity of the surface 1 continues to increase,
another limit will be reached, at which /, becomes infinite.
This is obviously the case when R,=—F; that is, when the
focal length has been so shortened by the increasing concavity
as to be equal to the radius of the convex surface. When
this is the case, the surface 1 seen through 2 appears plane.
When the concavity passes this limit, 7, becomes negative and
imaginary, and the experimental difficulty is still further
increased, for R,; only can be directly observed ; but still the
equations (4), (5), and (6) are true. No further increase in
the concavity of 1 will produce any new conditions. Now,
the curvature of 1 remaining constant, let 2 become flatter ;
when it has become plane, there is no occasion to observe F’, f,,
or f, to determine the form of the surfaces. When 2 becomes
concave also, the curvature of each surface can be directly
measured; and all difficulty is removed. Every possible case
has now been considered ; and though the equations are always
true, experimental difficulty only occurs in the two classes of
diverging meniscus.
If a parallel beam of light falls on the lens, it will be
refracted at the front surface, partly reflected from the back,
and again refracted at the back surface, and be brought to a
focus at a distance from the lens equal to half the apparent
radius.
Curvature and Refractive Index. 37
As the light, in its passage to and from the apparent centre
ji, is twice refracted by 2 and once reflected by 1, it would
seem at first sight that the value of 7, might be obtained by
combining in the usual way the expression for twice the focal
length of an equiconyvex lens with surfaces having the same
curyature as 2 and the radius of 1 ; thus
gee . 1
Pia a: Bey
But this operation, depending on a false assumption, leads to
an erroneous result. It makes gi a , instead of
R R p—1R, +R,
1? ___ The error arises in this way:—When a double
p—1R, +R,
convex lens is employed, either to bring or to hurry light to
a focus, the bending-powers of the two surfaces depend on the
angles they make with the ray in the lens. Now, if one of
these angles is great, the other must be small; so that, as a
combination, they have the same focus-shortening power, how-
ever the light falls on them. But when a ray passing from
and returning to the apparent centre 7 strikes the front sur-
face, that surface makes an angle with the ray in the lens
which is greater than the mean in the ordinary way; there-
fore the surface produces a greater diverting effect; and hence
the distance 7 is less than it would be if the supposition made
were correct.
All that has been shown at present is only true when the
thickness of the lens is inappreciable. When this is not the
case, rays, whether from the principal focus F or from an
apparent centre 7, will not cut the two surfaces at points
equidistant from the axis. First, consider the case of an
equiconyex lens. Let fig. 5 represent a portion of a thick
equiconvex lens. As before, since the central rays are
sufficient to give an image, arcs, sines, and tangents may be
considered identical, On one surface take any point p.
Through it draw a radius pR, and the line pbe parallel to the
axis. Nowa ray of light parallel to the axis, meeting the
surface in the point p with an angle of incidence equal to @,
will be refracted so that the angle dpe is equal to os therefore
the angle bpd= pas Therefore the line pd continued will
~ meet the axis in a point a such that
R
ja ee Me ac 1)
But this ray is diverted at the point d, and bent down so as to
38 Mr. 0. V. Boys on Measurement of
meet the axis at the principal focus F. It is required to find
the length dF, or, shortly, F—that is, the distance of the
principle focus from the surface.- Since the line pa has cut
the front surface at a point d nearer the axis than p, the in-
clination of the normal, bs, at d will be less than 6, and will
equal m@ if
a—t
mee Tee ie (2)
t being the thickness of the lens. Now the angle pds = the
angle dbp +the angle bpd =A(m +=") ; therefore the angle
bdF = w0( m+ = *), and the angle
gd B= pO m+ "= *) — m= 61 mp—1). «eee
Since the lines dF and da leave the same point d with different
inclinations, they will meet the axis at distances which are
inversely as these angles. Therefore
T < ae =pl+m;
be
therefore
pa—t (AE 2)
Tw itm) > eR
by (1) and (2). This is the distance of the principal focus
from the surface of the lens.
The distance ef of the apparent centre from the surface may
be found in a similar way. The normal at e makes an angle
nO less than 0, such that
R—t
= F By . . . ° . . . . (5)
The angle pet=(n+1)6; the angle cef=p(n+1)0; and the
angle kef=@[u(n+1)—n]. Therefore
of 1 ; RR-t
ae ia =>, andi.
Boe w(n+1)—n’ gna (u—1)(R—t)+uR (6)
This is the distance of the apparent centre from the surface.
By (6),
pa R+f(R—0
J(2R—-t) *
Substitute this value of w in (4); on simplifying, it will be
— ee —
Curvature and Refractive Index. 39
found that
zo ope g ee EP Bene.
R fo t*)=F > Eg anety, hatte iC2)
from which R may be found if F, 7, and ¢ are given. If ¢ is
made equal to 0, equation (7) gives
Rape, or —/.
The first result is the same as that already found for a thin
lens ; while the value —/ seems to have no physical meaning.
If the thick lens is not equiconvex, there are five observa-
tions possible—the distances of the two apparent centres from
the surfaces, the distances of the two principle foci from the
surfaces, and the thickness ; but there are only three things
to be determined—the two real radii and the refractive index:
therefore the equations for R,, R,, and ~ must be capable of
solution. The following are the expressions which may be
found by a similar treatment of fig. 5 to that already employed
in the case of the equiconvex lens, if it be remembered that
all the angles made by surface 1 are Re times those made by
surface 2 at the same distance from the axis. They are
ie Bip _
ae alge gaRnoese
1 7u( Ry + R,—2) +0 F(R, + Rt) +0?
R,-t R,—t
at R,—7)—(B,—2y 7?
The first two of these equations give
PF, e—-RiG@—l),
FL p—Rt(u¢—1)’
and the second two give
Pe R,+fAi Ri-t Ri +fe Rowe
Ay _ R, —6) 2( Ry ~~ R,—t)
By these » may be eliminated. The solution for R, and R,
I haye not obtained ; but Ido not think there is any difficulty.
The following application to the case of liquids of the prin-
ciple of making the rays return along the path whence they
came, forms a neat though impracticable method of deter-
mining their refractive index when greater than V 2 :—Re-
place the cross-wires of a telescope by a prism-plate, as already
described, but in which the slit is longer and adjustable. Fix
opposite the object-glass a piece of parallel-sided plate-glass,
with its plane at right angles to the optical axis. The cor-
1u(B, + By—)— (at)
and p=
40 On Measurement of Curvature and Refractive Index.
rectness of this adjustment may obviously be determined at
the eyepiece. Let the glass plate form the bottom of a trough
in which the liquid may be placed, and let there be under this
a dish containing mercury. Now, there is a certain inclination
of the telescope at which the beam from the illuminated slit,
rendered parallel by the object-glass, is refracted at the free
surface of the liquid, and again at the surfaces of the glass
plate, so as to leave the latter vertically; then, striking the
mercury, it returns along the path whence it came, and may
be viewed by the eyepiece. Under these conditions the beam
of light on either side of the prism is at right angles to the
opposite side; therefore they make equal angles with the
adjacent sides, and the prism is at minimum deviation.
Calling the inclination of the telescope 0, we have sinOd=p i he ;
therefore w= V2(1+cos@). The telescope may be first in-
clined on one side and then on the other, and half the angle
moved over taken as 6. I have found it utterly impossible to
get the sodium-line to keep still for a moment, or to be even
fairly defined, as every movement in the neighbourhood pro-
duces a tremor on the surface of the liquids, which, in the
Science Schools at Kensington at any rate, is so continuous
as to make it impossible to observe with accuracy. I should
have said that the top of the prism must be covered in with a
glass plate, to prevent the evaporation and consequent super-
ficial cooling of the liquid forming the prism, which causes
strize in the liquid, spoiling definition even more than the con-
tinuous tremor.
Helmholtz and others have shown that, during accommoda-
tion of the eye for near objects, the cornea does not change
in curvature, the front surface of the lens becomes more
curved and advances, and the back surface does not appreciably
change. The proof given is that the images of a light pro-
duced by reflection from ihe cornea and from the back
surface of the lens do not change, while that produced by
the front surface of the lens advances and becomes smaller.
Now it would appear at first sight that these observations
prove a flattening of the back surface of the lens during
accommodation ; for if it did not change in curvature, the
rays of light passing twice through the more curved front
surface would sooner come to a focus; but since they do
not apparently sooner come to a focus, it would seem that a
flattening of the back surface must have occurred to counteract
the shortening influence of the more curved front surface. In
the case of ordinary lenses this would be so; but it so happens
that in the crystalline lens the focus by reflection is formed
Experiments on the Faure Accumulator. 41
within it, and so the more curved front surface magnifies the
smaller image, which therefore appears unchanged.
While on the subject of reflection in lenses, I think it worth
while to mention that convex lenses silvered at the back make
excellent and easily constructed concave mirrors. Since both
surfaces conduce to bring light to a focus, flatter curves may
be used than are necessary for a plain concave reflector of the
same focal length; also, since the two surfaces are not parallel,
false images are not produced ; so that the advantage of glass
silyered at the back remains, without the usual disadvantage.
A spectacle-lens of about five inches focal length, silvered at
the back and mounted, forms an eye-glass (I mean a glass for
examining the eye) which every one who works in metal should
possess. I have found by its means specks of metal, thrown
from the lathe, which were utterly invisible by other means,
but which were nevertheless exceedingly painful.
Ill. ELeperiments on the Faure Accumulator.
By Professors W. H. Ayrton and JoHN PERRY*.
ANS made, at the request of the Faure Accumulator
Company, a series of experiments on some of their
cells, we have thought that a short account of some of the
results obtained may not be uninteresting to the members of
the Physical Society.
The object of the experiments was to ascertain, first, the
efficiency of a cell—that is, the ratio of the energy given out
by it to the energy put into it; secondly, the storing-power of
a cell; and, lastly, whether or not there was a deterioration in
its working-powers. To measure the energy put into any
electric circuit, we have merely, of course, to take time-
readings of the current flowing through the circuit, as well as
the difference of potentials between its two extremities. The
current in ampéres multiplied by the electromotive force in
volts and by 44°25, gives the number of foot-pounds per
minute that is being put into that part of the circuit as elec-
tric energy. For measuring the current we have used through-
out our ammeters (short for ampeére-meters), and for measuring
electromotive force our voltmeters, the latter being employed
of course in a shunt circuit.
Of the total electric energy put into the circuit, and which
is measured, in foot-pounds per minute, by 44:25 AV, a por-
tion will be employed simply in heating the circuit, and the
* Communicated by the Physical Society, having been read at the
Meeting on February 25, 1882,
42 Professors Ayrton and Perry’s Experiments
remainder may be utilized in producing useful work. For
example, ifa time-curve be drawn for 44:25 AV when charging
a Faure accumulator, the area of the curve will measure the
total energy put into the accumulator in foot-pounds ; but
of this some portion has been wasted in heating the cell, due
to the charging having been more rapid than was absolutely
necessary. It was, of course, of considerable importance in
our experiments to ascertain what portion of the energy put
into the cell was really thus wasted; and to measure this the
following experiments were made.
Occasionally the main current was stopped, the shunt cur-
rent through the voltmeter being left completed. The reading
now on the voltmeter gives the difference of potentials pro-
duced by the cell itself, whereas the previous reading was the
combined difference of potentials produced by the cell and the
dynamo-machine charging it. Jf now a new time-curve be
drawn in which the ordinates represent the product of
44:25 AV’, where V’ is the electromotive force of the cell
measured on the circuit being broken, and A is the mean
value of the current flowing just before breaking and just after
closing the circuit, the area of the new curve will represent
that portion of the energy put into the cell which is usefully
employed in chemical decomposition. The difference between
the areas of these two curves represents, then, the amount of
energy wasted in heating the cell in foot-pounds.
Again, on discharging the cell, experiments of a similar
nature have to be made. The product 44:25 AV represents
the number of foot-pounds of work per minute the cell is pro-
ducing in the external circuit, V being the difference of poten-
tials between the two poles of the cell while it is discharging;
but, in addition, there is a certain amount of energy which is
being expended in heating the cell itself during discharge.
This, as before, may be ascertained by breaking the main
circuit, leaving the shunt-voltmeter circuit completed. The
reading on the voltmeter V’ now indicates the real electro-
motive force of the accumulator during discharge; whereas the
previous reading, obtained just before breaking the circuit,
represents merely the fraction of the total electromotive force
employed in sending the current through the external resist-
ance. Ifa time-curve be drawn with its ordinates propor-
tional to 44:25 AV’, where A is the mean value of the current
just before breaking and just after closing the circuit, its area
will represent the total number of foot-pounds of energy per
minute being given out by the cell; and the difference between
the areas of the last two curves will represent the number of
foot-pounds of energy employed in heating the cell itself. It
EE
on the Faure Accumulator. 43
is to be noticed that during charging V’ is less than V, whereas
on discharging V’ is greater than V.
An examination of thirty-five sheets of time-curves, which
we have drawn from the experiments we made, shows that, in
charging, the curve for AV rises at first; and as it rises
more rapidly than that for AV’, this means an increase in the
resistance of the accumulator.
E.M.F. x Current.
As the charging continues, the two curves for AV and AY’
approach one another, showing that the internal resistance of
the accumulator diminishesagain. On the other hand, at the
end of a long discharge the curve for AV falls more rapidly
than that for AV’, due to an increase in the internal resistance.
Now our experiments show a great constancy in the electro-
motive force of a Faure cell, and that the falling-off in dis-
charging which occurs during a very rapid discharge, or at
the end of a long discharge, is due more to an increase in the
internal resistance of the accumulator than to a diminution in
the electromotive force, which our methods of experimenting
above described enable us to separate and measure inde-
pendently. But, whether discharging rapidly or whether
discharging slowly, there is a most curious resuscitating-
power in the cell, which, if disregarded, will cause totally erro-
neous underestimates to be made of the efficiency of the cell.
This resuscitating-power is more marked for rapid discharges
than for slower ones. In the case, for example, of an ex-
tremely rapid discharge, we found that when the flow had
become apparently so feeble that the cell appeared totally dis-
charged, leaving the poles of the cells insulated caused three
times as much electric energy to be given out all together in
the second discharge as had been given out in the first. And
even when several days are taken to discharge the cell—and
we may mention that we have had continuous observations
made day and night for several days in certain cases—this
44 Experiments on the Faure Accumulator.
resuscitating-power is wonderfully marked. An insulation of
a few hours will cause the energy given off per minute on
redischarging to be eight to ten times as great as it was before
insulation. Indeed on one occasion, after a cell had apparently
nearly discharged itself, it was left shortcircuited with a thick
wire for half an hour, then insulated all night, when the num-
ber of foot-pounds of work per minute given off at the com-
mencement of the discharge the following morning was found
to be ten times as great as it was on the previous evening, and
a greater amount of energy was actually taken from it in the
second discharge than in the first. This phenomenon gives
the Faure accumulators a great value for tramcar propul-
sion, since, as is well known, it is just on starting after stop-
ping that the strain on the horses is so great.
Lifficiency—To determine the efficiency of cells we com-
mence with them empty, or at least as empty as many hours’
shortcircuiting with a thick wire could make them. We
then measured the total amount of energy put in and the
total amount subsequently given out, and we found that, for
charges up to a million foot-pounds put into the cell and dis-
charged with an average current of 17 ampéres, the loss in
charging and discharging combined may not exceed 18 per
cent. Indeed, for very slow discharges the loss in charging
and discharging combined in some of our experiments has been
as low as 10 per cent.
Storing-power.—lIt is a little difficult to measure the maxi-
mum storing-capacity of the cell at the same time that mea-
surements are made of its efficiency, because in the latter case
we must take care that we do not put in more electric energy
than the cell can hold; on the other hand, if precautions are
taken to avoid overcharging, it is a little difficult to ensure that
the full charge has been put in. We have therefore separated
our experiments for measuring the efficiency from those em-
ployed to ascertain the storing-power.
Let us take a single example of the storing-capacity. A
certain cell containing 81 lb. of lead and red lead was charged
and then discharged, the discharge lasting eighteen hours—
six hours on three successive days; and it was found that the
total discharge represented an amount of electric energy ex-
ceeding 1,440,000 foot-pounds of work. This is equivalent to
one horse-power for three quarters of an hour, or 18,000 foot-
pounds of work stored per pound weight of lead and red lead.
The curve shows graphically the results of the discharge.
Horizontal distances represent time in minutes, and vertical
distances foot-pounds per minute of energy given out by the
cell, and the area of the curve therefore the total work given
On a Simplified Dispersion-Photometer. 45
out. On the second day we made it give out energy more
rapidly than the first, and on the third more rapidly than on
1000
Foot-pounds per minute.
500
Time in hours.
the second, this being done of course by diminishing the total
resistance in circuit, During the last day we were discharging
with a current of about 25 amperes. And this cell, like the
others, showed, on being insulated after having been apparently
totally discharged, that there was still a large charge stored up;
hence the numbers given above for the capacity are probably
under the total value.
Deterioration.—As to deterioration, two months constant
charging and discharging of the two accumulators under test
showed no signs of deterioration.
_ LV. A Simplijied Dispersion-P hotometer.
By Professors W. E. Ayrton and JoHN PERRY*.
T will be in the recollection of the Members that in 1879
we described to the Society a dispersion-photometer
which enabled measurements to be made of the intensity of
the strongest electric light in a small room and for the rays
coming from the electric light at any angle—two essentials
which appeared to us necessary in an electric-light photometer.
The principle of this photometer consisted in our use of a con-
cave lens to weaken the strength of the light, so as to make
the illumination of a screen comparable with the illumination
ofa standard candle, instead of keeping the lamp a distance of
* Communicated by the Physical Society, having been read at the
Meeting on February 25, 1882.
46 Professors Ayrton and Perry on a
50 or 100 feet away, which was the plan in use until that time.
We exhibit now five successive forms of the instrument, which
illustrate the history of its development to the present time.
1. The first of these is very nearly the same as that described
in our former paper, with the exception that we discarded the
use of a long screw (shown in our original figure) for adjusting
the position of the lens—as we found that a very easy adjust-
ment might be effected with the fingers, the tension of the
bellows part making an automatic clutch which fixed the lens-
slide in any position.
2. The second specimen is on the same principle, only that
telescope-tubes are used instead of a wooden frame and a bel-
lows. Instead of the lens part alone tilting when the elevated
or depressed light has to be examined, the candle-box is here
made to tilt also, the candle being supported in gimbals so that
it may remain vertical for every angle of elevation.
3. The third specimen is on pretty much the same principle;
but as we found a difficulty in comparing two illuminated
disks whose centres were some distance apart, we arranged in
front of these disks two mirrors, which enable us to make the
comparison between two illuminated semicircles having the —
same diameter. The difficulty of adjusting the lens and
making a comparison of the illuminations, and reading the
scale, without moving one’s head, in all these early instru-
ments led us to the
4th form, which is probably familiar to the Members, as it
was exhibited at Paris and largely used there for measure-
ments. In this the candle-box and the lens-box are placed
end to end, the lens is fixed in a wooden piston which moves
in its hollow square box, which is lined with velvet; and the
lens shows its position by a pointer moving over the scale |
outside. The pointer projects from the inside of the wooden
cylinder at any point of a long slot, whose sides are made of
india-rubber tubing, so that no extraneous light can reach the
illuminated screen. A little handle working a rack and pinion
enables the lens to be placed inany position. Through a hole
at the side the two screens can be viewed reflected in two
mirrors, inclined to one another in the space between the
candle-box and the lens-cylinder; and the illuminated papers
are viewed as two semicircles having a common diameter. In
front of this hole we have slides of red and green glass ; so that,
as our custom has always been, we make two measurements—
one a comparison of the ruby-red light of the lamp examined
with the red light of the candle, and another of the green
lights. This instrument differed from the earlier forms in not
requiring any calculation to be made of the strength of the
OQ
Simplified Dispersion-Photometer. 47
light; that is, the reading of the pointer was not merely a
reading of its distance from the screen, but it was a reading in
standard candles of the power of the light. Three such scales
were placed on the instrument; and there were three certain
distances at which the lamp had to be placed for examination.
The tilting-arrangement was of course different from that of
the earlier forms.
As the instrument had by this time (the end of last year)
come into a rather extensive practical use, we had opportu-
nities of seeing that, as an instrument to be used by unscien-
tific persons, it was not yet in a perfect condition, in spite of
the many changes that had been made in its construction.
The most important difficulty was due to the fact that a slight
lateral change in the position of the observer’s eye caused the
apparent illumination of the screens to vary. Being aware of
this fact ourselves, we maintained a certain fixed position of
the eye when making observations; but the instrument could
not at once be used by persons not accustomed to make deli-
cate experiments.
5. The fifth form, which we now present to the Society,
is the outcome of our labours on this subject. We have all
along seen the disadvantage of using the Bouguer’s two-
screen method, since, when lights are examined that have
passed through tissue or tracing-paper, a very slight change
in the position of the observer’s eye makes a very great differ-
ence in the apparent illumination, whereas, using Rumford’s
method, when a sheet of white blotting-paper is employed as
a screen very considerable changes in the. position of the eye
produce no change in the apparent illumination—a result,
however, which is not attainable when ordinary drawing-paper
is used as the screen. If, however, Rumford’s method is to
be used to measure the rays coming at different angles from
an electric light, a mirror must be employed to reflect them
successively onto the same screen; and if used in the ordinary
way, the angle of incidence of the rays on the mirror will be
different in different cases. Now the difficulty that always
met us arose from the inequality of the reflecting-power of an
ordinary mirror for rays falling on it at different angles of
incidence. We have, however, completely overcome this dif-
ficulty in an extremely simple way, by causing the mirror to
turn about a horizontal axis inclined at 45° to its plane, and
the whole photometer to turn about a vertical axis. With this
arrangement the angle of incidence, and consequently the
proportional absorption, is the same whatever be the inclina-
tion of the rays coming from the lamp to the mirror; and,
further, the angle being 45°, the amount of rotation of the
48 Professors Ayrton and Perry on a
mirror about its horizontal axis necessary to enable measure-
ments to be made of rays coming at any angle, after measure-
ments have been made of the horizontal beam, is exactly equal
to the inclination of the beam in question. i
Using Rumford’s method in this latest form of our photo-
meter, we are to a great extent independent of the presence of
other sources of illumination of the screen, so that the appa-
ratus need not be enclosed in a box. At the same time, how-
ever, the sensibility of the test is much increased by placing
a shade to prevent the electric light shining directly onto the
screen. On this screen of blotting-paper, B, is thrown the
shadow of a black rod, A, placed in front of it, by a candle in
the candle-holder, D.
=
Vee
Now it is well known that if an electric light is also allowed
to illuminate this screen, and to throw a second shadow of the
rod A on the paper, and if the candle is adjusted at such a
distance that the two shadows are of equal intensity, the
strength of the light is to that of the candle in the ratio of the
squares of their distances from their respective shadows. But
instead of allowing the strong light to pass directly to the
screen, we cause it to pass through the concave lens in the
sliding wooden frame C. A pointer on this slide tells the
distance of the lens from the screen. As you are all aware,
the weakening of light-intensity produced by the lens enables
us to leave our electric lamp within a few feet of the instru-
ment. We have experimentally found that there is no appre-
ciable loss of light in passing through the lens. The candle
slides on the bar J; and its distance from its shadow is shown
by a pointer on a scale. If is the focal length of the lens,
D the distance of the electric light from the paper-screen, d
Simplified Dispersion-Photometer. 49
the distance of the centre of the lens from the screen, and c that
of the candle when the shadows show equal illumination, then,
if L is the strength of the examined source of light in standard
candles, :
eis = {ira poa)}
L= 51 D+ ae
Ce i
For our own use we prefer to employ the formula; but as all
the common instruments which have hitherto been manufac-
tured have lenses whose focal length is 4 inches, we have pre-
pared a table, a copy of which is sent out along with each
instrument, in which the value of L is given “for various
values of D, d, and c. Using this table, it is necessar y to
have the lamp. at either 60, 120, or 300 inches from the screen;
the candle is either at 10, 14: 14, or 20 inches from the screen;
and the table is made out for ever y half inch of the lens-scale.
But inasmuch as we find that the improved arrangement of
the mirror already referred to constitutes perhaps the most
useful part of the instrument, and as the use of this improve-
ment involves many alterations of D, the manufacturer pro-
poses in future not to furnish any table of values of L unless
specially asked for.
H is the plane silvered-glass mirror which makes the angle
of 45° with the axis of the lens, and with the axis about which
the mirror itself is free to revolve. As already explained, a
ray of light reflected from the mirror and passing through the
centre of the lens must, for any position of the mirror, have
an angle of incidence of 45°, and so must experience the same
amount of absorption, from whatever direction it may have
come to the mirror. Further, .this angle being 45°, a fixed
pointer marks on the graduated circle G, which moves with
the mirror, the angle which any ray we may be examining
makes with the horizontal.
In this instrument we find that from 380 to 34 per cent. of
the incident light at 45° is absorbed, whether this light is of
ruby-red or sional-preen colour ; so that we have the easy
practical rule for all cases—add one half to the measured
intensity of light reflected.
We need not here refer to the fact that, when investigating
the efficiency of an electric lamp, we always measure the
horse-power given electrically to the lamp simultaneously
with the photometric measurement.
The lamp is suspended in such a way that it can readily be
Phil. Mag. 8. 5. Vol. 14. No. 85. July 1882. aD
or
50 On a Simplified Dispersion-Photometer.
placed at any elevation. The frame of the tripod-stand is first
levelled. A pin at F, directly underneath the ceutre of the
mirror, passes through the base of the photometer and fits into
a hole in the top of the tripod-stand. The photometer, by
turning round this pin, can, without producing any change in
the distance of the centre of the mirror from the lamp, and
therefore without changing the distance from the screen to
the lamp, receive the small horizontal motion necessary for
the adjustment of a new inclination of the rays coming
from the electric light, without any alteration of the distance
of the centre of the mirror fromthe lamp. The divided circle
is clamped with the index at 0°; the lamp is lowered or raised
till the illuminated disk formed by the reflected light, passing
afterwards through the jens, is in the middle of the paper
screen. A little sliding shutter with a fine hole in its centre,
seen in the figure, enables a very exact adjustment to be made;
but in practice we find that we get sufficient accuracy without
the use of the shutter. We now measure the distance from
lamp to centre of mirror in inches. Equalizing the intensities
of the two shadows by adjusting the lens-slide when looking
at them through red or green glass, we now note the lens- and
candle-readings ; and we repeat these operations, changing
from red to green and green to red about five times in a minute,
The lamp is now raised or lowered and fixed in any position ;
a few seconds suffice to turn the mirror so that it sends its
centre ray exactly through the centre of the lens. The dis-
tance from screen to mirror in this instrument being 22 inches,
if 6 is the distance from centre of mirror to vertical from lamp,
Connexion between Viscosity and Density in Fluids. 51
and if @ is the angle of elevation, then
D=22+6sec @.
Using this value of D in the formula above, and adding one
half to the strength of the light to make up for absorption,
the true intensity of the light in standard candles can be
ascertained. We find in practice that, if an electric light is
moderately steady, ten measurements may be made, with some
confidence in their accuracy, in two minutes ; and the light
may be measured in ten different positions, from an angle of
depression of 60° to an angle of elevation of 60°, 100 observa-
tions being taken, in less than half an hour.
We may mention one very important result we have been
led to by the systematic employment of a photometer which
can be used close to the electric light ; and that is the large
amount of absorption that occurs on certain days when the
rays from strong electric lights, and especially the green rays,
pass through the air which appears to the eye perfectly clear.
At first we were inclined to think the higher results for the
candle-power of a lamp obtained with our dispersion-photo-'
meter than those obtained with an ordinary distance-photo-
meter were due to some error in our photometer itself; but
we have since ascertained that this is due to the absorption of
the air—because we find that, if simultaneous measurements
are made with ordinary Rumford’s photometers, each without
lens or mirror, placed at different distances from the lamp in
the same azimuth and in the same horizontal plane, the nearer
one gives, as a rule, the highest readings ; and the difference
is the greater the stronger the light, and is greater if the light
be examined at each photometer with green glass.
V. On the Connexion between Viscosity and Density in Fluids,
especially Gaseous Fluids. By EH. Warsure and L. v.
Bazo*.
“en laws according to which the elasticity and viscosity of
a body are connected with its density are of great sim-
plicity in the case of gaseous bodies. The elasticity of these,
a. e. the reciprocal of their compressibility, is given, according
to Boyle and Mariotte’s law, by the pressure, and is propor-
tional to the density; the viscosity, measured by the coefficient
of friction, is, according to Maxwell’s law, independent of the
density.
It is known that the first of these laws, that which refers to
* Translated from the Sttzwngsberichte der K. Preuss. Akademie der
Wissenschaften zu Berlin, May 4, 1882, pp. 509-514.
KR?
ad
52 MM. Warburg and vy. Babo on the Connexion
elasticity, holds only approximately, and even that only at
moderate degrees of density; at higher densities, according
to the investigations of Natterer, Andrews, Cailletet, and
others, the connexion between elasticity and density is not
even approximately given by Boyle’s law, but is apparently
more complicated. It can, however, according to van der
Waals*, be explained from the kinetic theory of gases, if the
volume of the molecules and the attraction between them be
taken into account.
Corresponding investigations in relation to the viscosity of
gases have hitherto been carried out only so far as Kundt and
one of ust have studied the deviations of Maxwell’s law at
very slight densities. For higher degrees of density the con-
nexion between viscosity and density has not yet been inves-
tigated. Tor the solution of this problem (treated in the pre-
sent paper for one substance, viz. carbonic acid) the corre-
sponding values at constant temperatures of the coefticient of
friction, the density, and, for many reasons, the pressure must
be determined.
We employ as the measure of the pressure the inverse
value of the volume of a mass of nitrogen at constant tempe-
rature of the apartment, the volume of that mass at the pres-
sure of one atmosphere being put =1. ‘To measure the pres-
sure according to this definition a nitrogen-manometer was
employed, which was always attached to the principal appa-
ratus, and permitted pressures between 30 and 120 atmo-
spheres to be evaluated.
The density of the substance heated above the critical tem-
perature we determined by a volumetric measurement of the
carbonic acid, which at each transition from a greater toa
less density was liberated from our apparatus, the volume of
which was known to us; the density of the mass in the appa-
ratus after the conclusion ofa series of experiments we calcu-
lated from the pressure, which then amounted to about 30
atmospheres, by Clausius’s formulat, which at so small a
pressure is sufficiently accordant with the observations. At
the temperature 32°°6 our experiments comprise the interval
of densities between 0-1 and 0°8.
For the determination of the friction-coefficient we em-
ployed the method of flow through capillary tubes. The
capillary, placed vertical, ended below in a measuring-tube
which dipped in mercury, above in a space A, which could
from time to time be shut off from the rest of the space by a
cock, and in which a diminution of pressure could then be
* Dissertation: Leyden, 1873. — + Berlin Monatsberichte, 1875, p.160.
{ Wiedemann’s Amalen, ix. p. 348.
|
between Viscosity and Density in Fluids. 53
produced by discharging carbonic acid. After the mercury
had been thereby raised in the measuring-tube, the spaces A
and B were again put into communication. From the time
occupied by the mercury in the measuring-tube in descend-
ing from one mark to another, the coefficient of friction was
calculated by means of the constants of the apparatus.
Three capillaries were employed, from 6 to 7 centim. in
length, and of which the radii amounted to 0:005162, 0:003601,
and 0:002847 centim. The validity of Poiseuille’s law was
controlled ; but an equation cannot be deduced from the expe-
riments.
The results obtained are contained in the following Table,
in which ¢ denotes the temperature measured by the air-ther-
mometer, s and w the density and the friction-coefficient in
the gramme-centimetre-second system, and p the pressure in
the measure above-mentioned; 2 is the air-content of the sub-
stance, in parts of a volume, as given by analysis. The den-
sity of the liquid carbonic acid is taken from Andreef’s expe-
riments*.
t =32°°6. ¢ =40°'3.
| A\=0:00074. A=0-00085.
Ss. p. pehOX Dp. pe. 10°.
0:800 107°3 677
0-730 88:5 574 1146 580
0-660 80:7 493 101°6 499
0:590 78:2 414 94:9 426
0:520 776 351 91:7 366
0:450 77-2 304 89:2 316
0:380 766 270 868 275
0-310 74-6 239 82°7 243
0:240 69-9 213 799 218
0:170 60:3 188 64:3 196
0-100 431 | =n 45:3 180
¢ =25°-1
4=0:00044
P- s pe. 108
105 0-896 800
95 0-875 | 741
85 0:858 703
"5 0:27 ~ | 665 |
70 0809 628
* Annalen der Chemie und Pharmacie, 1859, ex. p. 1,
54 MM. Warburg and v. Babo on the Conneaion
%
| Viscosity of liquid carbonic acid under the pressure of
| its saturated vapour.
A=0°0018.
t | 8 pw. 10%
oO
5 / 0-922 925
10 | 0:895 852
15 0-864 784
20 0°827 712
25 0-783 625
| 7: Nia tables a Pee 555 539
9 50 700 Density.
The figure gives a graphic representation of the results—
namely, the isotherms* of viscosity and tension, the latter in
dotted lines, noted according to the Table.
Andreef’s values of the pressure t exceed ours but little—
at 32°6, on an average, about one atmosphere. This may
arise from the air-content of the carbonic acid being in
Andreef’s experiments somewhat less than in ours. The
values of p calculated by Clausius’s formula, however, are not
inconsiderably higher than those observed by us; the differ-
ences increase with the density, and reach the value of 10-12
atmospheres. On account of the agreement of our results
* We thus name lines the abscissee of which are proportional to the
densities, and the ordinates to the friction-coefticients and pressures respec-
tively.
+ Pogg. Ann, Erg. Bd. v. p. 79
—|> 2
between Viscosity and Density in Fluids. > 5S
with those of Andreef, found by a quite different method, it is
not likely that the differences are due to errors of observation.
Respecting the viscosity, especially its connexion with the
density, the results are as follows:
I. Above the critical temperature, Gaseous Carbonic Acid.
1. To the maximum of compressibility (=) , 2. e. to the
s
| ds
ef ore d : i
minimum of elasticity (s A) , given by observation corresponds
no minimum of viscosity, which much rather increases in a
constantly increasing ratio with increasing density.
Pp
ds ds”
At the density 0-1, about 500 times the normal, the
Daiiciont of friction exceeds the normal (0:000165 for 40°-3)
by only about 9 per cent. of the latter.
3. At the temperatures 32°°6 and 40°-3 the substance shows,
at equal density, slightly different values of w, very different
values of p. According to this the viscosity appears to be
much more simply connected with the density than with the
pressure.
4, The influence of the temperature upon the viscosity, at
constant density, is so small that it cannot be inferred with
perfect certainty from observations embracing a temperature-
interval of only 8°. Since, however, the isotherm for 40°3
runs entirely above that corresponding to 32°°6, the viscosity
appears to increase slowly with the temperature when the
pressure is constant.
Il. Liquid Carbonic Acid.
5. Liquid carbonic acid showed far less viscosity than any
other liquid hitherto examined. The friction-coefficient of
water, for example, at 15° is 14:6 times that of liquid carbonic
acid under the pressure of its saturated vapour. Hvyen the
appearance of liquid carbonic acid enclosed in a glass tube
which is shaken excites the supposition that this substance
possesses very little viscosity.
6. The viscosity of liquid carbonic acid at the temperature
of 25°-1 increases with the density. By further extending
this investigation, and especially to other liquids also, we pur-
pose to ascertain the influence of temperature upon the visco-
sity of liquids at constant density—that is, the specific influ-
ence of temperature.
7. At densities in the vicinity of 0°$ the isotherm correspond-
are always positive. )
=
1of 7
.
56 On the Connexion between Viscosity and Density in Fluids.
ing to 25°1 runs below both that corresponding to 32°°6 and
those corresponding to 15° and 20°. From this follows that
carbonic acid of such density, heated from 15° upward, must
show a minimum of viscosity between 20° and 326.
Poisson* has given a theory of liquid-friction which starts
from the representation that, with respect to a system of
simultaneous impacts, a liquid behaves, at the first moment
after the expiration of them, like an isotropic solid body.
Hence we can speak of the constants of instantaneous elas-
ticity of a liquid. For the coefficient of friction in Poisson’s
theory we get the expression
p— KT.
where K is the coefficient of instantaneous rigidityt, and Ta
quantity of time which Maxwell has named the modulus of the
relaxation-period. For an ideal gas, Maxwell findst K=p,
and hence T, at constant temperature, proportional to the mean
length of path.
In a first approximation let us assume that T still has this
property when the volume of the molecules and the attraction
between them is taken into account; then we get for wa
theoretical expression in which K alone remains unknown—
namely
K s bus
p= mop @(1- 5");
where for the temperature to which yp refers, wy and sy denote
the values of yw and s for the pressure P of one atmosphere.
A is the normal density of carbonic acid, and 6 van der Waal’s
constant, namely four times the molecular volume, the yolume
of the substance at 0° and the pressure of one atmosphere
being taken as the unit of volume. The equation holds so
long as s<2b—that is, for carbonic acid, approximately as
long as s<0°4.
According to this equation, the occupation of space by the
molecules produces a diminution of friction with increasing
density, and consequently the opposite deviation from Max-
well’s law to that produced by the attraction between the
molecules. From the same equation, according to our expe-
riments, for carbonic acid of density 0°38 at 32°°6, K comes
to 7-2 kilograms upon the square millimetre—that is, about
3h 5 of its amount for glass, and somewhat more than for
tallow$.
* Journal de V Ecole Polytechnique, 1831, t. xiii. p. 139,
T In Kirchhoff’s notation (Vorlesungen, p. 400).
{ Phil. Mag. [4] xxxy, p. 211 (1868).
§ Pogg. Ann. exxxyi. p. 295 (1869).
es al
VI. Notes on Thermometry. By F. D. Brown, B.Sce.,
Demonstrator of Chemistry at the University Museum, Oxford*.
[Plate IT.]
Sore years ago, when I determined to try and find out
something about the attractive forces which the atoms
and molecules seem to possess, by studying the effects of heat
upon chemical substances and upon mixtures of such sub-
_ stances, I was led to the conviction that, if the work which I
proposed to do was to be of any permanent use, I should be
obliged to take many and minute precautions regarding the
-measurement of temperatures—a measurement which, owing
to the peculiarities of mercurial and other thermometers, is so
liable to error. In order to learn how best to use my thermo-
meters, and how to refer their readings to a satisfactory
standard, I made a considerable number of experiments. At
the time when these experiments were made I imagined that
the subject of thermometry, although presenting many diffi-
culties to my mind, had been thoroughly worked out by
others, and therefore that a printed record of my observations
would be generally deemed to be of little utility. The recent
publication of a paper by Dr. H. J. Mills (Hdin. Roy. Soe.
Trans. 1880), of one by Professors T. H. Thorpe and Riicker
(Phil. Mag. [5] xii. p. 1), and more especially of a report by
M. Pernet (Mém. et Travaux du Bur. inter. des poids et mes.
i. 1881, pp. 1-52), has led me to change my opinion, and to
think that there still remain many points connected with
thermometers about which not only I, but others also, would
be glad to have more certain information. Acting upon this
belief, I have put together in the following pages some of the
results of my experiments.
The Mercurial Thermometer as a Standard.
I was soon convinced that any attempt to express tempera-
tures in degrees of an ideal absolute thermometer, or even to
refer them correctly to the readings of an air-thermometer,
would involve a most extensive and wearisome investigation,
which would postpone indefinitely the work I wished to do.
To avoid this substitution of the means for the end, I decided
to construct a mercurial thermometer and to use it as a stan-
dard, keeping it until such time as the progress of our know-
ledge should render its comparison with the air-thermometer
a matter of less difficulty.
As a mercurial thermometer is very liable to be broken, I
first wanted to know whether this instrument fulfilled the
primary condition of a true standard, of being capable of
* Communicated by the Physical Society.
58 Mr. F. D. Brown’s Wotes on Thermometry.
reproduction when lost or destroyed. With this end in view,
I made two thermometers at different times, and wholly
independently one of the other, and compared their readings,
To those who may wish at any time to construct a mercurial
- thermometer without the elaborate appliances ordinarily em-
ployed, but in which absolute confidence may be placed, the
following details may be of interest:—
A capillary tube of medium bore, about 800 millimetres
long, free from all flaws, and having as uniform a section as
possible, is provided with a millimetre-scale of 600 divisions.
The etching of this scale is a matter of great consequence : it
very frequently happens that the divisions on glass tubes are
not of exactly equal length, but that, owing to some defect in
the dividing-engine or some movement of the tube while un-
dergoing the process of division, some of the divisions are so
much longer or shorter than the rest as seriously to interfere
with the subsequent process of calibration. yen when all
the lines are equidistant, they are often so thick, and present
so irregular an outline when viewed through a telescope, that
it is impossible to fix upon any particular point as that repre-
sented by the dividing-line. The tubes I employed were
selected and divided with special care by Mr. Casella, the
lines being perfectly straight, less than 0-4 millim. in thickness,
and in all cases equidistant.
As a glass tube, however carefully selected, is never of
uniform bore, it is necessary to ascertain the relative capacities
of the several divisions of the tube, or, in other words, to
“calibrate ’’ it. As is well known, this is easily done by
placing a thread of mercury in successive positions along the
tube and observing its length, the mean capacity of the diyi-
sions occupied by the thread being, of course, inversely pro-
portional to that length. In this way, and by adopting the
plan of correcting the position of the thread suggested by
Dr. Mills in the paper above referred to, which plan he had
been kind enough previously to communicate to me privately,
a table is readily constructed showing the volume of the tube
from the line marked 0 to any line marked x, and also the
value of the succeeding division. The only difficulty connected
with this process is the accurate measurement of the length of
the thread of mercury in its several positions. It is true that
this may easily be done witha dividing-engine or some similar
instrument, such as a cathetometer provided with a micrometer
eyepiece and placed horizontally. As, however, reliable instru-
ments of this class are exceedingly costly, I designed a small
piece of apparatus for the purpose, which has proved so con-
yenient and useful that I venture to describe it here,
Mr. F. D. Brown’s Notes on Thermometry. 59
A mahogany board, B B (PI. I. fig. 1), about 18 inches long
and 4 inches wide, is provided with a groove, G G, of the shape
shown in the section (fig. 1a); a piece of gun-metal, about
5 inches long and + inch thick, slides in this groove with some
little difficulty—the friction, which is produced by the spring
jf; being necessary to retain the plate rigidly in any given
position. The plate, D, is provided with a slot, e e, and a milli-
metre-scale, 8 §, the dividing lines of which must, like those of
the tube to be calibrated, be very fine and truly equidistant. The
piece of gun-metal, EH, which is provided with a vernier, carries
the reading-microscope, M, and can be moved along SS by
means of the rack and pinion p; the movement is rendered
smooth and free from lateral displacement by the spring c, which
causes the ends of HK to remain always in contact with the
straight edge of the slot. The thermometer-tube is fixed with
suitable screws under the path of the microscope, so that the
length of a thread of mercury can be easily measured by
placing the microscope so that its cross wire coincides first
with one end of the thread and then with the other, and noting
on the scale the distance between the two positions.
The millimetres of the brass scale and those of the tube, if
marked off by different makers, will often differ a little in
length ; hence it is generally more satisfactory to obtain from
the glass scale the number of whole divisions occupied by the
thread, and to measure the terminal fractions only by the
microscope.
Since the line on the outside of the tube is nearer the eye
than the thread of mercury inside the tube, it is clear that
when the microscope is adjusted to view the end of the thread,
and is then moved along until the cross wire coincides with
the nearest line, this last will be out of focus, and either the
whole microscope must be raised up or the distance between
the object-glass and eyepiece altered. Now, unless the in-
strument be constructed with great solidity, and much care
be taken to fit accurately all the moving parts, this adjustment
will probably alter the position of the optical axis, and so
render the measurements inaccurate. To avoid this diffi-
culty, I added a half-lens, L, fitted in the ordinary way on
a brass tube sliding on the end of the microscope. This
lens of course brings the focus of half the field nearer the
object-glass ; so that, by properly adjusting it, the divisions
are seen through the half-lens at the same time that the
mereury is observed through the unprotected part of the
object-glass. In this way all disturbance of the microscope
is avoided throughout the calibration, which is thus carried
out with much greater comfort and accuracy.
oo See
60 Mr. F. D. Brown’s Notes on Thermometry.
Two tubes were calibrated with this apparatus, and tables
of their volumes from the first division compiled ; they were
then furnished with bulbs, filled with mercury, and sealed
up in such a manner that they formed thermometers capable .
of indicating temperatures between 0° and 150° C. The
fixed points of the two thermometers having been determined .
with the precautions indicated below, tables showing the
temperatures corresponding to the readings of the scale were
made in the usual manner; the two instruments were then
compared together, either in a large tank of water which was
kept well stirred, or in the steam-apparatus which I de-
scribed to the Physical Society at the time when these expe-
riments were made. Before a series of readings were taken,
both thermometers were heated for at least half an hour in
steam, while their zero-points were observed after the series
was completed. The numbers given in the following table
show that the two thermometers gave practically identical
readings. It would seem, therefore, that the mercurial ther-
mometer, when carefully made and systematically heated, does
really possess that valuable property of a standard, of being |
capable of exact reproduction. |
| | |
Reading of AS, Reading of BS,
Corresponding | Corresponding
corrected for | corrected for value of AS, value of BS, | Difference.
index-error. | index-error. in degrees. in degrees.
58°55 | 70°64 14:30 14-29 —01
134:33 | 150-11 33°69 33°71 +02
179°69 | 197°20 45:29 45°30 +01
321-97 | 345°96 81°88 81°88 00
23°42 33°74 5°28 5°28 ‘00
26°33 36°85 6:03 6-04 +01
30:07 40°63 6-99 6:97 _"
33°76 44:57 794 7-93 —01
43°32 54:70 10°40 10-40 ‘00
47-98 | 59°60 11:59 11:59 00
69°42 82°13 17-09 17:09 ‘00
91°61 / 105°52 22°78 22°79 +01
Determination of the Zero-point.
In most books on physics it is stated that, in order to
obtain the zero-point of a thermometer, the instrument should
be placed in a vessel filled with broken ice and provided with
holes at the bottom, through which the water formed by the
melting of the ice may escape. In order to learn whether
this method is the best possible, the following experiments
were made:—A number of tin pots, about 7 inches high and
4 inches in diameter, were obtained, and holes made in the
bottoms of two or three of them. A large block of ice was
Mr. F. D. Brown’s Notes on Thermometry. 61
broken up into small fragments, which were well mixed up,
so as to render the whole perfectly uniform in character.
One of the tin pots, which we will call A, was filled with
some of this ice, which had been washed in a funnel with
ordinary water; A was then filled up with water, so as to
form a mixture in which the ice largely predominated. <A
second tin, B, was filled with some more of the ice, which
had been washed with ordinary water in the same way; B,
however, had holes at the bottom, and the water formed by the
fusion of the ice thus drained away. A third tin, C, contained
some of the same ice, which had been washed in a funnel with
distilled water, and then mixed with distilled water in the
same way as in A the ice was mixed with ordinary water.
In a fourth tin, D, which was provided with holes, some ice
was placed which had been washed with distilled water.
Finally a quantity of distilled water was artificially frozen,
the ice broken up into small pieces, washed, and mixed with
distilled water in a fifth tin, H. A thermometer with a long
narrow bulb, and with a stem divided into millimetres, was
carefully inserted into each tin in succession, and readings
taken with a cathetometer. About 17 millim. of the scale
were equivalent to one degree Centigrade. In A the readings
soon became constant at 1°00 ; in B the readings varied con-
siderably for about half an hour, but finally became constant
at 1°12; in C the thermometer became rapidly constant at
1°16 ; in D the readings became constant after a short time
at 1°06 ; in H the readings did not vary after the first four
or five minutes, remaining at 0°64.
At the end of these observations, which occupied nearly two
hours, the thermometer was replaced in A, where the mercury
rapidly assumed the same position as before, viz. 1°00. Seeing
that, with the exception of H, the greatest difference in the
readings does not amount to 0°01 C., we may fairly draw the
following conclusions:—First, that a constant temperature is
more rapidly and certainly obtained with a mixture of ice and
- water than with ice alone; secondly, that the temperature
thus obtained is really that of melting ice ; thirdly, that it is
preferable to wash and mix the ice with distilled water,
ordinary water tending to lower the temperature, though to an
insignificant extent.
With the view of seeing whether different varieties of ice
gave the same results, two specimens of block ice and one of
the rough thin ice collected in winter near London were
obtained, while two cylinders of distilled-water ice were arti-
ficially produced. These were all broken up separately into
small pieces, washed with distilled water, and then mixed with
62 Mr. F. D. Brown’s Notes on Thermometry.
the same in five tins, A, B,C, D,E. The thermometer placed
in these tins marked 1°30, 1°34, 19:26, 19°30, and 1°27 re-
spectively (these numbers are not comparable with the former,
as the experiments were made a month or so later, when the
zero of the thermometer had altered its position). These ex-
periments showed that distilled-water ice gave the same results
as ordinary ice, and that the melting-point of different speci-
mens of ice, when mixed with distilled water, was the same
within 0°:005 C. The exceptionally low reading obtained with
the tin E in the first series of experiments was probably due
to the fact that the ice, having been made by means of a
freezing-mixture, was not at its maximum temperature.
In subsequent determinations of the zero of thermometers
I have always used ordinary block ice, washed and mixed with
sufficient distilled water just to fill up the spaces between the
pieces, and haye not allowed the water to drain away. These
results are in accord with those obtained by M. Pernet.
Zero-movements, and Substitution of the Determination of the
Steam-point for that of the Zero-point.
In considering the well-worn question of the zero-move-
ments of thermometers, it is important to distinguish between
its practical and theoretical aspects. Tlomake a study of zero-
moyements from an abstract point of view, to find out equa-
tions expressing these movements under different cireum-
stances and with different thermometers, to learn that when a
certain thermometer has been subjected to a certain series of
temperatures at certain intervals of time its indications on
next changing its temperature will be affected with a certain
index-error, may possibly be of some utility, but it does not aid
us much in the endeayour to free the readings of thermometers
from the errors with which they are surrounded. When once
we have acquired the information that a thermometer sub-
jected only to those changes of temperature which are due to
the weather exhibits a gradual rise of zero, that the rise thus
taking place in a given time diminishes as the age of the ther-
mometer increases, but differs for different thermometers, when
we also know that a thermometer subjected to a high tempe-
rature after a considerable period of rest exhibits a decrease in
its zero-reading, dependent on the thermometer itself and also
on its previous history,—we know all, or nearly all, that we
can put to practical use.
Thus, for example, the thermometer attached to my standard
barometer was verified at Kew Observatory when it was first
supplied to me, some four or five years ago. Since then I
have from time to time observed its reading in melting ice,
Mr. F. D. Brown’s Notes on Thermometry. 63
and have modified accordingly the correction to be applied to it.
Now, no observations of other thermometers—no curves or
equations representing their zero-movements—could be of any
assistance to me in this matter. I knew that the zero would
probabiy rise, and that the amount of the rise would not be
the same in my case as in that of others, and that, therefore,
I must obtain the index-error experimentally. I ‘also knew
that if I boiled the thermometer I should cause irregular
changes in the position of the zero; and as there was no
necessity for the operation, I avoided boiling it. But if by
mischance it had fallen in boiling water, no equations repre-
senting the zero-movements of other thermometers would have
told me exactly what had happened to mine ; I should simply
have been obliged to observe its index-error more frequently
than before the accident happened.
The question which seems to me to be of the greatest impor-
tance with regard to zero-movements is, how we can best
reduce the trouble which they cause us. In the case of all
meteorological and clinical thermometers, where the changes of
temperature are small, as in the above case, it is evident that all
we can or need do is to protect the instrument from unnecessary
changes of temperature. When, on the contrary, our observa-
tions extend over wide ranges of temperature, the difficulties
increase considerably. Suppose, for example, that I want to
use a thermometer to indicate accurately a series of tempe-
ratures between 70° and 90°, It is obvious that if I observe the
index-error beforehand, and apply the correction thus obtained
to my readings, I shall not be doing right ; for the very heating
of the thermometer to 70°-90° will have altered the index-
error. But if, on the other hand, I first heat the thermometer
to 100°, then ascertain its index-error, then make my experi-
ments with it, and finally observe its reading i in ice a second
time, I shall be tolerably certain, if the index-error is the same
at the end as at the beginning of the experiment, that no
yariation has occurred during the observations.
In most laboratories, however, the frequent determination of
the zero-point of a thermometer involves a considerable expen-
diture of labour : ice has to be purchased, broken up into small
pieces, washed, and placed in a suitable vessel. All this
requires no little time, and has, moreover, to be repeated at
every determination, since the broken ice melts away in the
interval. On the other hand, the apparatus for the observation
of the steam-point is always in readiness; if, therefore, no
ereater error arises when the index-error is determined before
and after the experiments by means of the steam-point, a great
saving of time will be effected, without any corresponding loss
of accuracy.
64 Mr. F. D. Brown’s Notes on Thermometry.
When the temperatures to which the thermometer is to be
exposed are greater than 100°, the instrument should be heated
for some time to the highest probable temperature before the
steam-point is observed for the first time. In this way the
lowering of the zero which takes place when a thermometer is
heated from 100° to some higher temperature, to which it has
not been exposed for some time previously, is effected first of
all, and does not take place during the experiments, as it
otherwise would.
The only objection which can be raised to this method is
that, when some at least of the temperatures to be measured
are below 100°, it is possible that the steam-point, which is
lowered by the first heating in steam, rises again during the
experiments (that is, when the thermometer is at a lower
temperature), and then, by the second heating in steam, is
again brought to the same position as at first. In this way
the observations in steam, although concordant, would not
give the true index-correction to be applied to the readings.
That the error which thus arises is of no importance is, I
think, rendered probable by the following considerations :—
The gradual rise of the zero of a thermometer receives its
most natural explanation when it is supposed that the glass
bulb, after having been heated and somewhat quickly cooled,
is in a state of strain which causes it to have a larger capacity
than it would have if no such strain existed. As time goes
on, and more especially as the thermometer is subjected to
small fluctuations of temperature, the particles of the glass
gradually yield to the forces which are acting upon them, and
take up new and more suitable positions. These molecular
movements result in a gradual diminution of the capacity of
the bulb, and consequently in a rise of the zero. Now it is
evident that, if a certain state of strain is set up when a ther-
mometer is cooled from 100° to 0°, when it is cooled from 100°
to some intermediate temperature ¢ the strain set up will be
less considerable; there will therefore be a greater tendency
for the zero to rise when the thermometer is placed in melting
ice than when it is subjected to the temperature ¢ Conse-
quently, if it be found that, when a thermometer after being
heated in steam is placed in ice, no change of the zero takes
place for three or four hours afterwards, we may legitimately
conclude that, if the thermometer were maintained for the
same time at the temperature ¢, no movement of the zero would
occur. I have frequently kept recently-heated thermometers
in melting ice for several hours, renewing the ice when neces-
sary; and I have always observed, with all of my instruments,
that no change took place for the first three hours, and that
Mr. F. D. Brown’s Notes on Thermometry. 65
during the next two or three hours the rise was extremely
small. It follows, therefore, that if in any series of observa-
tions lasting more than three hours the thermometer be heated
in steam at the end of every third hour, there will be no un-
certainty as to the position of the zero; that if the experiments
be carried on continuously for six hours, a slight rise of the
zero may occur during the last part of the time, but that this
rise will not amount to more than one or two hundredths of a
degree.
Correction for the Exposed Portion of the Thread.
When a thermometer is only partially immersed in the
medium of which the temperature is to be observed, the
readings become subject to an error which arises from the
fact that a part of the thread of mercury, together with the
corresponding portion of the stem, are at a temperature
different from that of the bulb and immersed portion of the
stem. ‘The correction, C, usually applied in this case is given
by the formula
Ci Ea) N so iene ont: Tirade au eae)
where T=the reading of the thermometer,
t=the temperature of the exposed portion,
N=the number of exposed divisions of the stem which
are filled with mercury,
m=the apparent expansion of mercury in glass.
This formula is founded on the assumption that the error in
the reading has no other cause than the comparatively unex-
panded condition of a portion of the thread and stem.
The apparent expansion of mercury in glass, as obtained
from Regnault’s experiments, is about ‘0001545; but it differs,
of course, for different specimens of glass. When this number
is employed in the above formula, the values of C obtained are
generally believed to be too large ; indeed a little reflection
will convince us that this must be the case whenever the tem-
perature of the exposed portion is merely measured by placing
another thermometer with its bulb halfway upit. This second
thermometer evidently measures the temperature of the
ascending stream of warm air around the stem ; if the stem
of the chief thermometer were subjected to the heating
influence of this stream, and to no other, its temperature
would be rightly given by the subsidiary thermometer ; but
the thermal conduction along the thread of mercury and along
the glass stem must necessarily raise the lower part of the
Phil, Mag. 8. 5. Vol. 14. No. 85. July 1882. F
66 Mr. F, D. Brown’s Notes on Thermometry.
exposed stem to a temperature higher than that indicated by
the subsidiary thermometer. The value of (T—?) therefore is
too great, and consequently also that of C.
In order to meet this difficulty, Dr. Mills, instead of endea-
youring to give to ([—t) its proper value, has made a large
number of experiments with different thermometers with a
view to assign a more satisfactory value to m, and has thus
been led to draw the following conclusions:—The value
0001545 of the coefficient m is invariably too great. This
coefficient varies with the thermometer employed, and also
with the number of divisions of the thread exposed ; so that,
instead of assigning one definite value to m for each thermo-
meter, we must give it a value
m=a+ BN,
where a and 6 must be determined for each thermometer.
Professors Thorpe and Riicker, on the other hand, while
admitting that the value m=:0001545 may be generally too
large, maintain that it is sufficient to replace it by some other
single number, and that the employment of the varying coeffi-
cients a+6N is unnecessary; they support this opinion by
showing that in Dr. Mills’s own experiments the alterations in
the value of C, caused by the introduction of the term BN, do
not amount to more than one or two hundredths of a degree,
and are therefore insignificant. Dr. Mills, replying to this,
states that the change in the correction C brought about by
the term BN often amounts to so many hundredths of a degree
that it cannot be neglected.
Now it is clear that by merely placing a second thermometer
halfway up the exposed thread, only the roughest idea is ob-
tained of the real temperature of the thread. Suppose, for
example, that T=100°, and that ¢ is taken at 15°, being sub-
ject to an error of 5°: the value of (T—#), which is 85, will
be subject to an error of 5°, or about 6 per cent. What,
therefore, can be the use of attempting to determine the coefti-
cient 8, of which the value would appear ordinarily to be about
Sigs when so great a source of error is left unprovided
or!
In all experiments in which I have had occasion to use
mercurial thermometers, I have endeavoured to avoid any cor-
rection for the exposed thread, by making the apparatus and
thermometers employed of such relative dimensions that the
whole thread and bulb, except the topmost division, are at the
same temperature. When this is impossible, and when the
experiments require such extreme accuracy, it seems to me that
the first thing to be done is to surround the exposed portion of
gi
Mr. F. D. Brown’s Notes on Thermometry. 67
the thread with a current of running water, and so, while pre-
serving it from the uncertain effects of conduction, radiation,
&e., to render possible the observation of its exact temper ature.
The yalue of (T—?) being thus correctly measured, that of m
is found to be constant for all values of N, and to "differ but
little from 0°001545. It varies, however, with different ther-
mometers.
The following ‘exper iments show most distinctly the truth
of this statement:—
One of the standard thermometers mentioned in the first
section of this communication was partially surrounded by a
glass tube, a b (fig. 2), about an inch in diameter; this tube was
closed atthe bottom with a piece of good cork, about 8 millim.
thick, through which the stem of the thermometer passed. The '
upper end of the tube ab was fitted with a cork, in which were |
four holes—one for the stem of the chief thermometer, a second -
for a thermometer to indicate the temperature of the water
contained in the tube, while through the two others passed the
tubes by means of which the current of water was maintained.
The thermometer thus furnished was fixed vertically in the
ordinary apparatus, A, for determining the 100°-point of
thermometers. The open end of A was closed with a thin
disk of brass, with a small central hole, through which the
thermometer passed. One degree was equal to about four
divisions of the millimetre-scale of the thermometer, the
readings of which were observed with a cathetometer, and the
fractions of a division measured with that instrument. It was
found that the readings of the thermometer under these con-
ditions were correct to ‘02 of a millimetre, or ‘005 of a degree.
The numbers given below are the means of three readings,
which, however, were nearly always identical. The thermo-
meter in the water was graduated to fifths of a degree, and had
been compared with the standard.
The chief thermometer was first heated in the steam for an
hour, with two or three inches of the thread above the cork;
it was then pushed down until the quicksilver was only just
visible above the cork, and the reading noted; it was then
pulled up again, and readings taken in various positions, as
given in the following table; finally the thermometer was
again pushed down as far as possible, and the reading taken,
when it was found to be the same as before, showing that no
change in the 100°-point had supervened during the experi-
ment. Of several series of observations made in this manner,
the one contained in the following table will suffice, since
they all led to precisely the same result.
Z
68 Mr. F. D. Brown’s Notes on Thermometry.
Reading of Standard when wholly immersed =393-42.
Barometric pressure, corrected and reduced, =760°1.
Corresponding temperature of steam =100°-00.
Number of
divisions sur- ;
rounded by | Temperature peed a f | Value of O Value * iy
cold water of water. = , =393°42—T. |
and occupied : (T—Z)N
by mercury.
fe)
317 13:0 38901 4-41 0001599
277°5 12:3 389-54 3°88 0001594
221 12:0 390°30 3:12 0001604
173 1271 390°94 2:48 ‘0001631
130 12:1 39158 1:84 0001610
79 121 392°30 1:12 0001612
An inspection of the above table is sufficient to convince us
that the value of m is constant, and equal to the apparent ex-
pansion of mercury in the glass of which the thermometer was
made ; the numbers would probably have agreed even more
closely, were it not that it is impossible to arrange the appa-
ratus so that the cold portion of the thermometer-stem follows
directly upon the hot portion. There must always be an
interval occupied by the cork, the temperature of which
is uncertain. It should be remarked that there is no indication
whatever of the value of m increasing when that of N increases.
Precisely the same results were obtained with the second
standard thermometer, as is shown by the following table:—
Reading of Standard BS, when wholly immersed, = 419-21.
Barometric pressure, corrected and reduced, =760°5. Fs
Corresponding temperature of steam =100°-02.
Number of
divisions sur- :
rounded by | Temperature Cintas a Value of O, Value of m,
cold water of water. ean | =419:21—T, = Cc 2
and occupied aS (T—2)N
by mercury.
302 12-0 415-18 4-08 0001535
237 11:9 415-96 3°25 0001556
174 12:0 416-84 2:37 0001548
127 12:0 41747 1-74 0001557
od
F
Mr. F. D. Brown’s Notes on Thermometry. 69
the error of observation, and shows no tendency to increase
when N increases. It may be noted that with both the above
thermometers the mean value of m is greater than ‘0001545,
the value usually assigned to it, but that it differs from that
number by so little that the error committed by substituting
the one for the other in the calculation of the correction C will
rarely amount to more than 0°02 C.
The above experiments were made at 100°, because this is
the only temperature which can be maintained absolutely
constant for an hour without the use of a quantity of compli-
cated apparatus ; and it is evident that the slightest variation
in the temperature would entirely spoil the series of observa-
tions. At higher temperatures the sources of error which
beset the readings of thermometers increase so rapidly that
the exact value of the coefficient m becomes of less and less
importance as the temperature rises, notwithstanding the
fact that the correction C increases in amount. Since there
is no reason whatever to suppose that any different results
would be obtained at such higher temperatures, I thought
it unnecessary to make any further experiments, more espe-
cially as those given above yielded precisely those numbers
which the ordinary laws of expansion predicted.
There is another point connected with thermometry, to
which I devoted attention some years ago. It has been
suggested that when a thermometer is placed in a vapour at
maximum tension, as in the ordinary chemical process of dis-
tillation, it does not truly indicate the temperature of the
vapour. This suggestion owes its origin to the fact that drops
are seen to accumulate and drop off the end of the thermometer.
Jt has been supposed that this condensation of the vapour ona
surface which should be as hot itself, is due to the molecular
attraction of the glass for the vapour. If this be the case, the
heat evolved by the vapour during liquefaction on the thermo-
meter-bulb would raise the temperature of the latter. The
thermometer would thus indicate a higher temperature than
that of the mass of the vapour. The experiments which I
made upon this subject, like those instituted by others, were
inconclusive. I possess, however, an apparatus which seems
to me eminently suited to answer the question satisfactorily.
li is at present being employed for other purposes; but
I trust that, when it is at liberty, I shall be able to put it to
this not unimportant use.
[500 94
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Geological and Natural-History Survey of Canada. By AuFrep R.
C. Setwyy, LL.D., F.RS., Director. Report of Progress for
1879-80. Montreal: Dawson Brothers, 1881.
(THE Geological Survey of Canada, under the direction of
Dr. Selwyn, appears to make steady progress. This volume
refers mainly to the work of the Geological Corps during the
season 1879-80, which embraced further explorations in parts
of the North-west Territor 'y (the Souris-River Coalfield), Hudson’s-
Bay basin, Quebec, New Brunswick, Nova Scotia, and the
Magdalene Islands, as well as the results of the survey in
1879 by Dr. G. M. Dawson of a portion of the northern part of
British Columbia, and of the Peace-River country, which will be
found to embody the best and most reliable information on this
vast and interesting region.
The other Reports comprise many valuable details bearing on
the physical features, geological structure, climatal conditions,
soils, and economical minerals of the different provinces explored,
ot which that on Hudson’s Bay by Dr. Bell (in continuation of
the survey of the two previous years) is very interesting; for
perhaps comparatively few people have any adequate conception of
the extent of this great Canadian sea, which is the central basin of
the drainage of North America. Geologically this basin, excluding
the Winnipeg division (the rocks of which range from the Lau-
rentian to the Tertiary), lies within the great Laurentian area of
the Dominion; resting upon these, the Cambro-Silurian rocks
form an irregular border along the south-western side of the bay ;
while to the south and west of James’ Bay these latter are over-
lain by Devonian rocks, which occupy a considerable area. The
chains of islands which fringe the east coast to the northward of
Cape Jones, and also the mainland near Richmond Gulf, are com-
posed of bedded volcanic and unaltered sedimentary rocks, which
may be of Lower-Cambrian age; on the western side the quartzites
and other rocks, rather largely developed, probably belong to the
Cambrian system. The Reporter considers that few of the varied
and numerous resources of Hudson’s Bay are at all developed, that
the fur-trade and oil are the principal; but that the most important
of the undeveloped resources are the soil, timber, and minerals, and
that the latter may become in future the greatest of the resources
of the shores of Hudson’s Bay. The concluding part contains a
very suggestive paper (with a map) on the northern limits of the
principal Forest-trees of Canada. In the Report of British
Columbia, Dr. Dawson also gives an account of the distribution
of the more important forest-trees of that province.
_ The geological structure of Northern New Brunswick and
Eastern Nova Scotia is fully described in the respective Reports.
The Lignite Tertiary formation in the Souris valley (North-west
Territory) is reported on by Dr. Selwyn, with appendices on the
nature of the strata and their plant-remains by Dr. G. M. and
Notices respecting New Books. cal
Principal Dawson. In the western prairie-region the true Car-
boniferous system is not the coal-bearing formation; and although
lignites and coals are known at several different stages of the Cre-
taceous rocks, it is in the representative of the Fort-Union rocks
of the U.-S. geologists that the most extensive and numerous beds
of lignite of the Souris-River region occur, and constitute the
nearest available supply for the province of Manitoba. ‘“ The
flora of the Great Lignite Tertiary series of the North-west,
though undoubtedly similar to the Miocene of Europe, really
characterizes the beds which in the West constitute the transition
from the Cretaceous to the Tertiary, and which form one great
continuous series, probably on the horizon of the Eocene of
Europe, though with local differences which are liable to be
mistaken for differences of age” (p. 55 A.) 5
With regard to the origin of certain granites, Dr. Selwyn (p.°),
in describmg the granites along Maine and New-Hampshire
boundaries, says that there is absolutely no proof that these later
granites are “intrusive,” as so designated by Sir W. Logan, but
that, like those in Australia and Nova Scotia, all the phenomena
connected with them may be more readily explained and under-
stood if we regard them as completely metamorphosed portions of
the strata which now surround them; whereas in regions where
the granite is older than the adjacent strata similar contact-lines
may be seen, but without any change in the mineralogical cha-
racter of the latter such as occurs when the crystalline rock is the
youngest (p. 6).
Although the subjects of these Reports are locally important,
they will doubtless be of interest to those who may wish to
become acquainted with the physical conditions, geological structure,
and economical resources of the Dominion of Canada.
Geological Sketches at Home and Abroad. By A. Gurxtz, LL.D.,
F._RAS., Director-General of the Geological Surveys of the United
Kingdom. With Illustrations. London: Macmillan and Co.
1882.
Tuis work consists of a series of essays previously published in
various journals during the last twenty years. Most of them relate
to certain districts im this country, Europe, and America, where the
_ striking geological phenomena here recorded were observed by the
author. Among the more important subjects noticed in these
papers are those having more or less reference to Denudation,
Glacial action, Volcanic phenomena, and Rock-weathering. An
Erosionist of the advanced school, but by no means inclined to do
battle under the extreme “ quietest” banners of some of its cham-
pions, Dr. Geikie has been led in his wanderings to look at scenery
with peculiar interest; and thus, in the essay on the Old Glaciers
of Norway and Scotland, it is shown that the Norwegian and Scot-
tsh Highlands seem to be but parts of one long tableland of ero-
sion composed of older and chiefly metamorphic rocks, while the
fjords and valleys of the one country and the lochs and glens of the
other owe their excavation to the great process of denudation
72 Notices respecting New Books.
which has brought the land to its present form. The various
forms of rock-weathering are discussed as derived from the study
of tombstones (Essay viii.); and the effects of modern atmospheric
action, conjoined with the bedding and jointing of rocks, are shown
in the isolated pillar of Old Red Sandstone, 600 feet high, standing
out from the mainland of which it once formed a part, and known
as the “ Old Man of Hoy” (No. I.).
The power of rain- and river-action is fully shown in the deep
gorges excavated through the basalt and other rocks of the
Auvergne and Haute-Loire of Central France (No. V.); but great
as has been the efficiency of superficial erosion on the development
of the terrestrial surface of Europe, the author considers that the
fundamental laws of denudation can nowhere be better learnt than
in the western region of the Rocky Mountains, the evolution of the
mountain-forms of the Uintah range, the high plateaux of Utah,
and the great basin of the Colorado, where “the proofs of enor-
mous superficial waste rise to such a gigantic scale as wholly to
baffle every observer who has yet attempted to describe them”
». 229).
: In the essays on the Volcanoes of Central France (No. V.), the
Yellowstone Geysers (No. X.), and the Lava-fields of North-west
Europe (No. XI.), are many interesting and suggestive remarks on
volcanic phenomena. The study of the former seemed to throw
light on the character and aspect of the Carboniferous volcanos of
Central Scotland (p. 102). Again, there were features of former
voleanic action on which the phenomena of modern volcanos ap-—
peared to afford but little light; “in particular, the vast number of
fissures which in Britain had been filled with basalt and now formed
the well-known and abundant ‘ dykes,’ appeared hardly to connect
themselves with any known phase of volcanism” (p. 276). This
has been accounted for by the emission of vast floods of lava,
‘massive eruptions,” without the formation of cones or craters—a
view advocated by Richthofen more than twelve years ago,—and
that our modern volcanos, Vesuvius and Htna, present us by no
means with the grandest type of volcanic action. Dr. Geikie, after
his visit to the lava-fields of the Pacific slope, was enabled to rea-
lize the conditions of volcanism described by Richthofen, and thus
assist in solving a difficulty he had long felt in accounting for the
extent of the dykes and other protrusions of basalt, ‘* which can be
traced over an area of probably not less than 100,000 square miles
in Britain’; for they occur from Yorkshire to Orkney, and from
Donegal to the mouth of the Tay” (p. 276), which was only part
of the far more extensive region that included the Farée Islands
and Iceland. ;
These stupendous outpourings of lava in the west of Scotland, like
those on the plains of Idaho, are considered to be due to the fissure
or “ massive” type of eruption; and that the basaltic plateaux of
Abyssinia and the “Deccan traps” of India probably mark the
sites of some of the great fissure-eruptions which haye produced the
laya-fields of the Old World (p. 285).
ee oe ee a ee ae ee ae ee ee
Geological Society. 73
Although Dr. Geikie advocates the fissure-eruption theory in
explanation of certain volcanic phenomena, it must be remembered
that Mr. Scrope, in his energetic review of the Natural History
of Volcanic Rocks, strongly opposed Richthofen’s twofold division
of voleanic rocks into ‘massive eruptions” and the products of
«¢ voleanos proper,” and remarked :—“Itis utterly impossible to find
in the writings of its advocates or in nature any intelligible distine-
tion between volcanic rocks that have issued from fissures, so as to
form ‘massive’ or ‘elongated’ or ‘ dome-shaped’ mountains, and
rocks produced by eruptions from ‘ volcanos proper’ ” (Geol. Mag.
vol. vi. p. 512).
The last three chapters include lectures on the Scottish school of
_ geology, Geographical evolution, and on the Geological influences
which have affected the course of British history.
These well-written essays, now collected and revised, fully con-
vey in a clear and pleasant manner the vivid impressions made on
the author during his geologic wanderings, and are replete with
scientific facts, occasionally interspersed with notes and illustra-
tions of the striking features of the scenery or of historic and
legendary interest.
VILL. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from Vol. xiii. p. 375.]
April 26, 1852.—J. W. Hulke, Esq., F.R.S., President,
in the Chair.
|e following communications were read :—
1. “On Fossil Chilostomatous Bryozoa from Mount Gambier,
South Australia.” By Arthur W. Waters, Esq., F.L.S., F.G.S.
2. “Thamniscus: Permian, Carboniferous, and Silurian.” By
George W. Shrubsole, Esq, F.G.S.
3. ‘On the Occurrence of a New Species of Phyllopora in the
Permian Limestones.” By George W. Shrubsole, Esq., F.G.S.
4. “On the Relations of the Eocene and Oligocene Strata in the
Hampshire Basin.” By Prof. John W. Judd, F.R.S., Sec.G.S.
The section at Whitecliff Bay, in the Isle of Wight, affords us
the means of determining the true order of succession of nearly
2000 feet of Tertiary strata, and is therefore employed as a standard
to which to refer the strata seen in sections where the order of
succession is not so clear. The author supported the views of Prof.
Prestwich as to the limits of the Bracklesham series, as opposed to
the opinions expressed on the subject by the Rey. O. Fisher. He
pointed out the confusion which has arisen from the correlation of
certain strata in the Hampshire basin with the barren Lower and
Upper Bagshots of the London area, in which fossils are so rare as
to render their geological age somewhat doubtful. To the Lower
Bagshot some authors have referred 660 feet of the strata seen at
74 Geological Society.
Alum Bay; while other authors have restricted that name to about
73 feet of the same section. The age of the Upper Bagshot of the
London basin is admitted by all authors to be very doubtful. The
only way to avoid the confusion unavoidable from using the same
names for strata the correlation of which was so hypothetical, was
to employ local names for both sets of beds. He proposed to refer
to the freshwater sands below the Bracklesham and Bournemouth
strata, containing a distinctive flora, as “the Studland beds,” and
the sends above the Barton clay by the old name of ‘“ the Headon-
Hill Sands.”
Above these sands are a series of clays only about 40 feet thick
at Whitecliff Bay, but much thicker at Headon Hill and Hordwell
Cliff. These sands and clays form the Headon group; they consist
of freshwater strata with bands of limestone and lignite, but in-
cluding numerous inconstant intercalations of layers containing
marine shells, for the most part much dwarfed. The age of the
Headon group, as shown by the fossils which it contains, is that of
“the zone of Cerithiuwm concavum” of continental authors.
The brackish-water Headon group is succeeded at Whitecliff Bay
by nearly 100 feet of purely marine strata. These marine beds,
which had been shown to rest on an eroded surface of the Headon
beds, contain the remarkable fauna which had been recognized by
many British and foreign geologists as that of the Lower Oligocene.
Similar strata with the same fossils are found in the New Forest,
at Lyndhurst, Brockenhurst, Roydon, and other points, and there
also attain a considerable thickness. It was pointed out that this
marine series is quite distinct from the Headon, or zone of Cerithium
concavum, with which it had been confounded.
The author had been very severely criticised for the views which
he had put forward in a former paper as to the manner in which
the Brockenhurst series is represented in the section at the west
end of the Isle of Wight. There was much difficulty in these
variable estuarine beds in correlating the beds seen in Colwell Bay
with those exposed in the cliffs of Headon Hill. With several pre-
vious authors on the subject, he maintained that the great series of
sandstones and limestones forming Warden Point and How Ledge
are continuous with those exposed in the face of Headon Hill, and,
consequently, that the marine beds of Colwell Bay overlying these
limestone series are younger than the brackish-water bands interstra-
tified with the Heddon beds of Headon Hill. His critics, however,
insisted that these two beds agreed with one another in such a
manner that they must be regarded as parts of the same bed, sepa-
rated by denudation. In opposition to this view it was pointed out
that the Colwell-Bay bed is of the most inconstant character, and
long before reaching Headon Hill is seen to be on the point of thin-
ning out and disappearing altogether. -
In conclusion, the author pointed out that his own interpretation
of the succession and correlation of the strata in the Hampshire
basin brings them into complete harmony with that which is main-
tained by the great majority of continental geologists, while that of
his critics appeared hopelessly irreconcilable with their views.
ore
IX. Intelligence and Miscellaneous Articles.
SCIENCE AND METAPHYSIC.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
wit you allow me space to say a few words upon some points
which are raised and discussed in your review of Prof. Max
Miiller’s translation of Kant’s ‘Critique of Pure Reason.’ The first
question of importance, namely that of the meaning of metaphysic
and its relation to science, is an extremely interesting one, and, as
it seems to me, well worthy of discussion from a scientific stand-
point. One side of the question is put forward in your review;
and it is the other side which I wish briefly to state here, with the
object of eliciting discussion.
Metaphysic, as now understood, and Science are not words which
are opposed as regards meaning. The subject-matter of science
and of metaphysic are distinct: they run in different, yet closely
connected channels. And perhaps here, at the outset, 1 may be
permitted to remark that, in any sense in which the word meta-
physic is or has been held, it is inadmissible to instance Auguste
Comte as a metaphysician, even if his own reiterated state-
ments upon the question did not forbid. Any one who has
read the Philosophie Positive will know how Comte never lets an
opportunity pass without ridiculing both metaphysic and metaphy-
sician, in the old sense of the words. He regarded the metaphy-
sical method of looking at things as a stage through which the
human mind has to pass before it reaches the final stage, which he
called the positive or scientific. In fact, one of the main objects of
his great work was to free science from metaphysic as he under-
stood it. When Comte censured as useless the study of the fixed
stars with the object of discovering their chemical composition, he
was arguing upon grounds that were of the most commonplace and
superficial kind, and could not by any means be shown to be even
remotely connected with metaphysic. Jam unable to agree, except
in a very limited sense, with Prof. Max Miiller in thinking that there
is any connexion between the philosophical systems of Kant and
Comte. Metaphysic, until quite recent times, has been mainly an
attempt to discover the supposed hidden causes of phenomena; a
mode of inquiry which had its systematic origin in Aristotle, and was
extended and formulated by the Schoolmen. In science the same
tendency was manifest. Abstract entities were assumed as origina-
ting causes; and it is only recently that science has given up the
search for these causes as futile, and sought to show how phenomena
take place instead of why they take place. Here was a change of
method in science; and what I wish to emphasize is that a similar
change has occurred in metaphysic. Metaphysic has adopted
the new method. While formerly the metaphysician endeavoured
to discover what the facts of nature were in their hidden essence,
he now seeks to find out what these facts are known as or appear
76 Intelligence and Miscellaneous Articles.
to be ; in fact his whole purpose is to arrive at a complete analysis
of the contents of the mind. The constant question in metaphysice
is, What do we mean by such words as Time, Space, Cause, Neces-
sity, Power, and other facts which are taken as ultimates by Science?
Tt does not aim at discovering the cause of these facts, but simply
at studying their relations. The introduction of this method is
mainly due to Kant; and it is on this account that his claim to so
high a place in the history of philosophy rests, although his method
still retained a large admixture of the old conception. This new
method of philosophizing without the assumption of entities, which
we may call the New Metaphysic, will be understood by reference
to such works as Mr. Shadworth Hodgson’s ‘ Philosophy of Reflec-
tion,’ or M. Renouvier’s Essais de Critique Générale. What may be
the merits of the systems propounded in these books, taken as a
whole, Ido not here discuss; but of the former of them, at least, it —
may be said that there is no conclusion touching scientific questions
which Science, as such, would hesitate to indorse.
Yours truly,
WrypHam R. Dunstan.
ON THE DEPRESSION OF THE ZERO-POINT IN MERCURIAL
THERMOMETERS. BY J.-M. CRAFTS.
It is well known that a thermometer which has remained for a
long time at the ordinary temperature presents when it is heated a
depression of its zero-point. ‘The amount of the depression depends
on the temperature to which the thermometer is raised; and
M. Pernet has demonstrated that the depressions are proportional
to the squares of the temperatures when it is heated from 0° to
about 100°. For higher temperatures Mr. Mills has found a very
different course. He does not indicate all the details which
would be necessary to enable one to usefully criticise his data;
and I will confine myself to saying that the numbers he gives
resemble those obtained with thermometers which have not under-
gone a suitable preparation, and that the method of experimenting
which I desire to present to the appreciation of the Academy
leads to very different results.
Before measuring the depressions produced by a reheating, it is
necessary to make sure of two things :—(1) that the starting-
point is the zero raised to the maximum ; (2) that the phenomenon
one wishes to observe is not masked by the permanent elevation of
the zero, which may take place at the same time as the depression.
I have ascertained that this last effect is invariably produced when
one heats even for a few minutes a thermometer which has not
been previously heated for a long time to a temperature near that
of the experiment. This movement can be effectually suppressed by
preliminary processes of heating which will be described further on ;
and each series of depressions and reelevations must be repeated, in
order to make sure that no permanent displacement of the zero has
taken place. Let us suppose this preparation completed: the ther-
Intelligence and Miscellaneous Articles. Cw
mometer has been heated to the highest degree of temperature
employed in the experiments, 355° for instance ; the position of
the zero has been observed, the thermometer submitted to any
series of operations ; and, on heating again to 355°, the original
position of the zero has been recovered ; it remains to raise this
depressed zero to its highest position. A thermometer can be kept
indefinitely at the ordinary temperature, or even be heated for
several weeks to 100°, without producing the total reelevation of
the zero; and the study in detail of the means which facilitate that
movement has revealed new facts of some importance in regard to
the theoretic views considered in some preceding communications.
I will briefly repeat the explanation which seems to account
best for all the movements of the fixed points of a thermometer.
The glass, softened during the process of blowing, retains inde-
finitely, at the ordinary temperature, a residual separation of its
particles, similar to that observed in an exaggerated degree in
Rupert’s drops. On such glass being heated, greater mobility is
imparted to its particles, and the normal shrinking is induced (the
disappearance of the abnormal expansion); and this action of heat
is the more pronounced the more nearly the temperature is
approached which produced the original separation. When a
thermometer is in operation, the shrinkage causes a permanent
raising of the zero-point, which may reach the considerable figure of
26°. It is evident that if a separation of the same kind, although
inferior in amplitude, can be produced at will, can be made to
persist for an indefinite time at the ordinary temperature, and to
disappear by heating, this manner of understanding the phe-
nomenon will be notably confirmed. Experiment realizes this
prevision. In fact it is sufficient to know the true depression of
the zero produced by boiling the mercury in a thermometer to
ascertain that it persists indefinitely at the ordinary temperature.
The depression is about 2° for French glass containing oxide of
lead, the reelevation at the end of the first six months is from
0°-4 to 0°°5; the subsequent elevation during from five to ten
years rarely exceeds 0°'5; and after ten years the zero remains
stationary, leaving half of the depression subsisting, of which
the total removal, equalling an additional degree, can be effected
by suitable means. This conclusion has been confirmed by numerous
experiments on the depressions produced at different temperatures.
It is especially by heating to very high temperatures that de-
pressions are produced which donot disappear. This phenomenon
resembles that of the permanent expansion of a body when the
limit of its elasticity has been passed.
The total reelevation after a depression of the zero, is accom-
plished more rapidly at high temperatures. Let us compare the
periods of time when the intervals of temperature remain nearly
equal. Five thermometers, after being heated for 24 hours to
306°, were kept at 218° until the position of the zero had become
constant ; for which four days were required. Afterwards the
zero depressed at 218° was reelevated by heating for 18 days to
100°. It requires from six months to two years for the total
~ = aie
78 Intelligence and Miscellaneous Articles. a
reeleyation of the zero depressed at 100° when the thermometer is-
left at the ordinary temperature. The termination of the reele-
vation being the limit of the abatement of a movement, it is
evident that it cannot be stated with exact precision; and it is
especially by comparing the course at its different phases for each
interval that one gets an exact idea of the variation of rapidity of
the reelevation according to the temperature at which one works.
When the intervals are smaller the reelevation is still more rapid :
thus, from 0°8 to 0°9 of the total reelevation of the zero depressed
at 100° can be produced by heating the thermometer during three
days to 80°, four days to 60°, and five days to 40°.
It will be seen that, the greater the interval between the tem-
perature which has produced a depression and that at which the
thermometer is maintained to accomplish the reelevation, the
slower is the movement; and it may not be complete if the
interval notably exceeds 100°. These data have been utilized in
the following manner to prepare some thermometers for the study
of the real depressions of the zero. In order to cause the
abnormal tension produced during the blowing of the glass to
disappear, the instruments nos. 1 and 5 were heated 11 days to
355°; nos. 13 and 15 were heated three years to 206° and 266°;
nos. 31 and 32, before being filled with mercury, were heated 100
hours to 440°, and cooled as gradually as possible during 100 hours ;
and finally all were heated for one day to 306° and the zero-points
observed. In order to reelevate completely the zero from its
position depressed by the heating to 306°, all the thermometers
were heated and kept for four days at 218°, eighteen days at 100°,
five days at 80°, seven days at 60°, six days at 4U°, nine days at
20°, three days at 10°, and two days at zero.
Here only one series of experiments can be cited; they are
summed up in the following Table: the first column contains the
numbers of the thermometers; those which follow give the de-
pressions corresponding to the temperatures indicated at the top
of the columns.
40° 60° 80° 100° 160° 218° 260° 306° 355°
1..... 0°00 006. 0:19 031 074 112 133° PGA
Dieta. 0:04 0:08 018 0:29 0°56 0°76 O91 1:14 151
13.....0°02 0:03 017 0°31 069 0-87 1:09-1:30 2-15
i ee 001 0:05 018 031 075 O97 112 140 2-05
31.....0°02 0°06 0°22 0°37 0°84. 115 1:46, P77 ae
os .- 0:28 069 0:98 1:21 1:56 2-06
Neglecting thermometer no. 5, which is of German soda glass, the
numbers for all the others, which are of glass containing oxide of
lead, are sufficiently concordant to permit the table to be employed
for estimating, with but a very slight error, the depressions which
will be produced by heating thermometers manufactured at Paris.
The relation between the temperatures and the depressions might
be expressed by a general formula; but simple interpolation
suffices for practical needs.—Comptes Rendus de V Académie des —
Sciences, May 8, 1882, t. xciy. pp. 1298-1301.
Intelligence and Miscellaneous Articles. 79
ON THE OSCILLATIONS OF THE PLANE OF POLARIZATION PRO-
DUCED BY THE DISCHARGE OF A BATTERY : SIMULTANEITY OF
THE ELECTRICAL AND OPTICAL PHENOMENA. BY D. BICHAT
AND R. BLONDLOT.
We proposed to ourselves to study the rotation of the plane of
polarization in a transparent body under the action of the current
from the discharge of a Leyden jar. The experiment was arranged
as follows. ;
Between a polarizer and an analyzer at extinction the transpa-
rent body is placed in a bobbin with a long and fine wire which is
connected with the armatures of a battery. An exciter interca-
_ lated in the circuit permits the discharge to-be produced when the
difference of potential is sufficient. At the instant of each dis-
charge the eye, placed in front of the analyzer, perceives a vivid
reappearance of light, which shows that the plane of polarization
has been deflected.
This fact having been proved, we sought to analyze it. For that
purpose we placed before the optical apparatus a mirror rotating
about a vertical axis. The polarizer was furnished with a slit, like-
wise vertical, the image of which was observed in the mirror by
means of a telescope. By a suitable arrangement we compelled
the spark to burst forth at the moment when the mirror, in its con-
tinuous rotation, occupied such a position that the image of the
slit was visible in the telescope. We thus saw in the rotating
mirror the reappearance of light due to each discharge.
What we observed was this:—In general, in the field of the
telescope a series of broad luminous bands are seen, separated by
narrower dark bands. The appearance reminds one absolutely of
that which is observed when the light of the spark is examined.
Tt is known that in that case the successive Juminous bands corre-
spond to currents alternately in opposite directions: the discharge
is oscillatory. We have ascertained that it is the same with the
plane of polarization. In fact, if the analyzer be rotated a small
angle in a certain direction, the images of the even order are seen
to be weakened, and at the same time the images of the odd order
to increase in brightness. If the rotation take place in the oppo-
site direction, the images of the odd order are weakened, and those
of the even order become brighter.
The plane of polarization, then, undergoes successive rotations
alternately in opposite directions; it oscillates about its normal
position. To each oscillatory discharge corresponds an oscillatory
movement of the plane of polarization.
This being admitted, is there simultaneity between the electric
and optic phenomena? or does the movement of the plane of po-
larization manifest itself in an appreciable time after the electric
action? We have solved this question in the following manner :—
Tothe apparatus employed for the preceding experiments we added
an arrangement permitting to be seen at the same time, in the
rotating mirror, the bands furnished by the light of the spark and
those due to the oscillation of the plane of polarization. For this
80 Intelligence and Miscellaneous Articles.
purpose the exciter was placed so that the spark, by means of a
suitable optical system, illuminated a vertical slit. A fixed mirror
sent back the light proceeding from this slit upon the rotating
mirror, and thence into the telescope. The movable mirror being
at rest, the vertical images of the two slits were seen in the field
distinctly. By regulating the position of the fixed mirror, these
two slits, which had the same breadth, were brought to be each
precisely in the prolongation of the other.
During the rotation of the mirror, at the moment when the bat-
tery is discharged, each of the images dilates im the horizontal direc-
tion. ‘Two systems of bands alternately luminous and dark are
thus seen one above the other: the one is due to the light of the
spark ; the other proceeds from the polarizing-apparatus.
The experiment shows that the brilliant bands of one of the systems
forms exactly the prolongation of the luminous bands of the other, and
that it is the same with the dark bands. If the mirror be rotated
more and more rapidly, the breadth of the bands increases, but the
correspondenee of the two systems still remains perfect. Therefore,
with the close approximation which our apparatus permits us to
obtain, we may conclude that the two phenomena, electrical and
optical, are simultaneous,
In order to measure that approximation, we slightly displaced
the fixed mirror, so as to destroy the correspondence of the two
images. It is clear that the displacement produced the same effect
as any delay that might have existed between the two orders of
phenomena. We thus secured that a delay of =51,,; of a second
should be quite appreciable; we can therefore affirm that the delay,
if it exists, is less than =,4,, of a second.
The experiments were made with heavy flint glass and bisulphide
of carbon successively as the transparent body. M. Villari, by
causing a cylinder of flint glass to rotate between the poles of an
electromagnet*, ascertained that at a sufficient velocity the pheno-
menon of rotatory polarization ceases to exist ; hence he concluded
that, to produce magnetization of the flint glass, a time comprised
between 0:001244 and 0-00241 of a second is required. Now the
sensitiveness of our method permitted us to appreciate a displace-
ment corresponding to a forty-fourth part of that time.
An unpublished experiment of MM. P. Curie and Ledeboer
accords with our conclusions. Substituting for the copper disk of
Foucault’s apparatus a glass disk, and causing it to rotate at the
rate of a hundred turns per second, they observed no diminution
in the rotation of the plane of polarization. It seems, then, that
another explanation of the very interesting experiment of M.
Villari must be sought.
We are moreover in accord with him upon this point, that the
rotation of the plane of polarization ceases at the same instant as
the electric action—Comptes Rendus de V Académie des Sciences,
June 12, 1882, t. xciv. pp. 1590-1592.
* Pogg: Ann, exlix. p. 324 (1873).
THE
LONDON, EDINBURGH, axp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
————
[FIFTH SERIES.]
f
AUGUST 1882.
X. Remarks on Absolute Systems of Physical Units.
By A. F. SUNDELL*.
ppee great importance of the absolute system of physical
units, introduced by Gauss, and developed by William
Weber, Kohlrausch, Maxwell, and Jenkin, is no doubt fully
recognized by every physicist. It is therefore the more sur-
prising that the so-called dimensions of the physical units are
so little employed in practice, notwithstanding the demonstra-
tion of their great utility given by Prof. Kohlrausch in his
well-known Leitfaden der praktischen Physik. These dimen-
sions may be regarded as the actual names of the units ; and
where they do not accompany the statement of the numerical
values of magnitudes, the data are as incomplete as if, in giving
a length or a surface, the unit of length or of surface employed
were not mentioned.
The works of the authors named contain all that is necessary
for the practical employment of the absolute system. But inas-
much as there are several different systems of absolute units
employed in physics whose mutual relationships have not been
sufficiently clearly pointed out, although definite indications
of the connexion between them are to be found, especially in
Weber’s Elektrodynamische Maassbestimmungen, and in Max-
well’s great work, ‘A Treatise on Electricity and Magnetism,’
_ I propose to put forward here an elementary theory of abso-
lute systems of physical units.
* Translated from a separate.impression from the Acta Soc. Scient.
Fenn. Tom. xii, (Helsingfors, 1881), communicated by the Author.
Phil. Mag. 8. 5. Vol. 14. No. 86. Aug. 1882. G
82 M. A. F. Sundell on Absolute
1. Various physical conceptions have resulted from the
endeavour of physicists to represent the results of their re-
searches mathematically as simply as possible, and to extend
them. Most physical conceptions, even if not required for
this special purpose, are at any rate absolutely necessary for
a satisfactory formal demonstration of physical laws. If, for
example, we seek to represent the law of a given uniform
motion mathematically, the equation
s=cb. J \.
is sufficient ; in which s represents the distance described in
the time ¢, and c is a constant dependent on the units employed
for sand t. If by means of this equation we determine the
value of the constant c by means of the distance described in
a given time, we are then able to calculate the distance for any
time ¢. The equation (1) may then be regarded as the ma-
thematical representation of the law of the given motion. But
with the value found for the constant, the equation can be
used only for this particular motion, and not for any other
uniform motion. But for any other motion of the same kind,
an equation of the same form may be used,'but with a different
value of the constant c. It is in fact impossible to give a
general formula for uniform motion with only the two con-
ceptions of distance and time. But if we employ also a third
conception, 4, proportional to the ratio of distance to time, we
obtain the formula d
h=c #? . 6 a eae (2)
which is sufficient for any uniform motion. This conception
(1) is of course that of velocity. If from any particular uni-
form motion we determine the value of the constant ¢, we are
able to calculate from the formula (2) the value of any one of
the three quantities when the values of the two other quantities
are given.
Equation (2) may be regarded as the general formula of
uniform motion ; but it may also be regarded, on the other
hand, as an equation defining the conception of velocity, if we
take the conceptions of space and time as already in any way
defined. Each new conception in physics may be defined by
an equation containing this new quantity, together with other
quantities previously defined. Thus, for example, the con-
ception of acceleration may be defined by the equation
&
“u=C€ >
t? ]
which relates to uniformly accelerated motion with zero initial
Systems of Physical Units. 83
velocity. But since ; is proportional to a certain velocity
(viz. the final velocity), this equation may be better written
h
Bes) sat cy tee cee)
In order to extend these conceptions to every case, we must
often take account of infinitesimals. Thus, for example, to
extend the conception of velocity to the case of motion not
uniform, it must be defined by the differential equation
ds
ne dt. Ee eh iat tek lxetheatee (4)
Acceleration, when not uniform, is defined by the equation
dh 3
a=C i gs GE Chak Coats a ge (5)
But even in these new forms the equations express the same
things as in their simpler form. Velocity is proportional to
the increase of distance, and acceleration to the increase of
velocity in the unit time. The conceptions of force (£) and
mass (m) are connected by the equation
ae ee re eee a!)
This equation may be regarded as a definition of force, if mass
be taken as a conception previously defined—or, on the other
hand, as a definition of mass, if the conception of force has
been first defined in any way. Hach additional conception is
defined by a separate equation. Moreover, these quantities
may be connected by equations distinct from the defining
ee which express natural laws. Thus, for example, the
ewtonian law of gravitation gives the equation connecting
length, mass, and force, ;
me
k=c TL 2 : 4 ° . e a (7)
where & denotes the force with which a mass m attracts an
equal mass at a distance L.
2. We have thus a certain number (7p) of distinct equations
in which g quantities occur. Hach equation may contain a-
constant. The units of the different quantities may be chosen
at pleasure ; the numerical value of the constant in an equa-
tion depends on the units of the quantities occurring in the
equation. If, for example, we determine the constant of equa-
tion (2) from the velocity of light, and take the geographical
mile as unit of length, the second as unit of time, and the
84 M. A. F. Sundell on Absolute
velocity of light as the unit of velocity, we must put s=40000,
"3 2 oe 1 } Ss es
Pala li 1 2 hence c= 40000" Equation (2) becomes there
fore h= 400002? ° s=40000h¢; which holds good for any
uniform motion so long as distance, time, and velocity are
expressed in the units chosen. But if we take as unit of
length a quadrant of the earth’s meridian (1350 geographical
miles) without changing the other units, then we must put
s= Bee = ne and the constant ¢ has now the value a
As the constants of the equations thus change with the units,
so, conversely, by choosing appropriate units, particular values
may be given to the constants. If we choose the units so as
to make certain constants equal to unity, the corresponding
equations assume the simplest form, and the constants disap-
pear from them. Units so chosen are termed absolute units,
and form an absolute system. If we assume that p (the num-
ber of equations) is smaller than g (the number of quantities),
then we may eliminate all the constants by choosing the units
properly; g—p units remaining undetermined, and p units
having values determined by the condition that each constant
is equal to unity. But if we wish to have more than g—p
units, say g—p+w undetermined, then « constants must be
retained, which are then to be considered as independent con-
ceptions. Let us take a few examples. ‘The four conceptions
distance, time, velocity, and acceleration are connected by
the equations (2) and (8). If we wish to eliminate the two
constants, we must take as unit of velocity the velocity of the
uniform motion in which unit distance is described in unit
time; the unit of acceleration must be the acceleration of a
uniformly accelerated motion in which the velocity increases
or diminishes in unit time by unit velocity.
Then equations (2) and (3) may be written as follows:—
8
a ol
ee
and similarly equations (4) and (5) become
=
i= Se
di
a= oe ow eo ae
Systems of Physical Units. 85
Of the four units, any two are chosen at pleasure. If we
choose for units of length and time the metre and the second
respectively, then the unit of velocity becomes the velocity of
a uniform motion in which 1 metre is described in 1 second ;
and if the velocity of uniformly accelerated motion change by
one unit of velocity in one second, then its acceleration is
unity. But if we arbitrarily choose the second and the velo-
city of light as units, then, according to equation (8), the unit
of length is the distance (40,000 geographical miles) which
light traverses in one second. The corresponding acceleration
40000 x 7420 |. ate ih
[eee mes. as great as the
acceleration due to gravity. Weneed not follow out the two
other possible combinations.
By choosing suitable units of mass and force we may elimi-
nate the constants of equation (6), which assumes the form
Tasks ee aN go eae eee
The six quantities—space, time, velocity, acceleration, force,
and mass—are connected by the four equations (2), (3), (6),
and (7); if we wish to eliminate the four constants, we must
retain the four units already determined. Equation (7)
assumes then the form
will be, as we easily see,
y
ne
k= L . . . . . . . (13)
The units of mass and force must be chosen so that, on the
one hand (equation 12), unit force communicates unit accele-
ration to unit mass, and so that, on the other hand, unit mass
attracts an equal mass at unit distance with unit force. Of
the six units any two may be chosen at pleasure. But if we
wish to choose three units at pleasure—say those of length,
time, and mass—then we must retain one constant, for ex-
ample that of equation (7) (the “constant of attraction ”’);
for, since the units have been some of them chosen at pleasure,
and some of them determined by means of the three remaining
equations, the constant of the equation in question does not
usually become unity. We may then regard this constant as
a quantity defined by the equation
KL?
J nos fi a terk (14)
If we wish to choose four units at pleasure, say those of
length, time, force,and mass, we must retain one more constant,
for example that of equation (6).
By the introduction of absolute units the equations of defi-
86 M. A. F. Sundell on Absolute
nition are much simplified ; since the constants of the equa-
tions are partly eliminated, partly regarded as new concep-
tions, it may be said that the equations from which an absolute
system is derived contain no constants—that is, no numerical
factors; each side of the equation has only one term. We
will call these equations the fundamental equations. Together
with these equations there occur in physics. a large number of
equations or formule; but these are not distinct from the fun-
damental equations, but are formed from them by various
combinations and methods of calculation, integration, and so
forth: they are therefore not so simple as the fundamental
equations; the two sides may contain several terms, into which
various numerical factors enter. It is necessary in our choice
of units not to lose sight of these equations derived from the
fundamental equations ; only, in using them, we must express
the quantities in the units obtained from the corresponding
fundamental equations. If, for example, we employ the for-
mula for centrifugal force,
ak mh?
=—
we must express /, m, h, and the radius of curvature 7 in the
units which correspond to the fundamental equations (8), (9),
and (12).
In the same way, the general equation for uniformly acce-
lerated motion,
s=hot +4at’,
requires the units for s, ¢, h, ho, and a, which are obtained
from the fundamental equations (8) and (9).
3. According to what has been explained, in an absolute
system certain units may be chosen at pleasure ; these are
termed fundamental units. The magnitudes of all the other
units are determined by the condition that the constants in
certain equations of definition are to be equal to unity: such
units are therefore termed derived units*. We see that, in con-
sequence of the mode in which the absolute units are deter-
mined, the fundamental equations will be satisfied if in them
we replace the quantities by their units. If, for example, we
take equation (8) for velocity, it will also hold good if we
replace the quantities by their respective units. But if we do
this in the ordinary way, by putting h=1, s=1, and t=1, we
arrive at the identity 1=1, which is of no further use to us,
But if we put s= unit length, ¢= unit time, = unit velocity,
* Kohlrausch, Lertfaden, 3rd ed. p. 206; Maxwell, ‘Treatise on Elec-
tricity and Magnetism,’ i. pp. 2 & 5,
Systems of Physical Units. 87
we obtain the relation
unit velocity = sea ue
: unit time
unit length
unit time
magnitudes; and we may therefore regard this quotient as the
name of the unit of velocity, if this unit is derived from the
units of length andtime. Butif we take the metre as the unit
of lengthand the second as the unit of time, then the velocity
metre
second’
that a yelocity equal to 10 such units of velocity is to be
c metre
written 10 Z
second
unit length is called by Maxwell* the dimen-
unit time i
sions of the unit of velocity. If in all the fundamental equa-
tions we replace quantities by their units, we obtain a system
of equations according to which the absolute units are functions
amongst themselves of certain fundamental units. These
functions, which are obtained by solution of these last-named
equations, are the dimensions or names of the derived units.
For the sake of brevity we will, as a rule, denote the units
by the same symbols as the quantities ; but, to avoid confu-
sion, we will include the symbols of units in brackets. Thus
[2] will denote the unit of length.
As an example of the different systems of units and dimen-
sions, we will consider the group of the six conceptions of
length, time, velocity, acceleration, mass, and force. We will
choose [7], [¢], and [m] as fundamental units; then from the
four equations (2), (3), (6), (7) we may omit three constants,
say those of the first three equations ; and so we obtain as
fundamental equations the equations (8), (9), (12), (7). By
substitution of the units we obtain the following relations :—
=[5], e]=[7]; [k]=[ma], [k]= Eel (15)
By solution of these equations we obtain the following dimen-
sions:—
m=[F], l=[p], =[4], lal=[z.]: a6)
If we keep the same fundamental equations, but choose [7],
7. ێ, unit velocity and the quotient are identical
which means
derived from these units must be called
The function
* «Treatise on Electricity and Magnetism,’i. p,2, Compare Kohl-
rausch, Leitfaden, p. 207.
88 < M. A. F. Sundell on Absolute
[¢], and [%] for fundamental units, the dimensions become
m=({], tl=[4], tml=[F], el=[q]- aD
If, on the other hand, we leave the constant of equation (6)
standing, we obtain new fundamental equations (8), (9), (6),
and (13) for a system with three fundamental units, and the
equations of the units become
=[F], td=[F], (=Leme], [=[], G8)
where c, denotes the constant of equation (6). If, again, we
choose [7], [¢], and [m] as fundamental units, we obtain the
dimensions
w=[F]), tl=[p) @l=[F], tl= [Fr]: 9
We see that the dimensions of units change not only with
change of the fundamental units, but also when the funda-
mental units remain the same and the fundamental equations
are taken differently.
If we wish to regard only [7] and [¢] as fundamental units,
all four constants are eliminated; the equations (8), (9), (12),
and (13) become fundamental equations, and the dimensions
become
m=[-], fl=[5], fI= BE and jae [i (20)
On the other hand, if we assume four fundamental units, we
must leave two constants standing. If we take equations (8),
(9), (6), and (7) as fundamental equations, the equations of
units become
im=[-]; l= [7], [k]=[coma], (i= [ee . (21)
Tf [7], [4], [m], and [/] are the fundamental units, the dimen-
sions become ;
=[7], tal=[a], (el= [5], fal= [<5]. 22)
The choice of fundamental units is limited only by the consi-
deration that they must not all occur in the same formula.
Hence we see from equation (15) or (16) that [/] [#] and
[h], [2] [a] and [4], [7] [é] and [a], or [k] [m] and [a]
cannot be fundamental units at one and the same time; on the
Systems of Physical Units. 89
other hand, the last-mentioned group may be employed for
this purpose in the system corresponding to equation (8).
4, It is very important to be able to pass from one system
of units to another, and to determine the ratio between the
units of the twosystems. This problem presents the following
special cases:—
' I. When the new system contains one new fundamental
unit besides the fundamental units of the old system. Let L
be the value in the old system of the new fundamental unit
defined by the equation
Tia MO Nee eh hac ee Oa)
where M and N are quantities defined independently of L.
As the unit for L in the new system may be chosen at plea-
sure, this quantity is expressed by a new number L,; but the
numerical values of M and N are not altered. Hquation (28)
is therefore not satisfied by L, M, and N, but must be written
with a constant a,
ae NO ee Tate Os)
The system of fundamental equations is therefore changed :
the number of equations remains the same ; hut the number of
quantities is increased by one. Since we must regard a asa
new conception defined by equation (24), we must therefore’
increase the number of fundamental units by one. Conse-
quently the relations of the units as well as their dimensions
are partially altered. By comparing equations (28) and (24)
we find that
L r
Vici ad tt ct ose ay MD
whence, since the units are inversely proportional to the nume-
rical values of a given quantity, it follows that
(elie elt eels ayo cx tose eget oh ue)
where 7 is the numerical value of «.
The ratios of the remaining units are easily obtained from
the other fundamental equations without alteration. It is to
be remarked that the constant « is in general not an abstract
number, but that the dimensions of its unit are given by the
equation
oe Mee 1G a eee ai eamemee (20)
If, for example, we wish to pass from the system (15) into the
system (21), where, besides the three fundamental units [7],
[¢], and [m], we take [%] also as a fundamental unit, we must
start from the equation (12), which defines the conception /.
90 M. A. F. Sundell on Absolute
This equation becomes
ky= cya.
We have between the old unit of force and the new one the
relation
[4] =n[h],
where » denotes the numerical. value of c.. The new dimen-
sions of the units are determined by equation (22).
Example 1.—Let us take as the old unit of force
metre x kilogramme
(second)?
and as new unit of force the weight of a gramme at the Obser-
vatory in Paris; then, by equation (2), since m=0°001 kilo-
gramme, and a=g=9-808 ae ha
3 oe (second)””
[k]=1
[ky] =0-009808 Me enh = 0-009808 [2].
bo din tga coe : : Phy ]
Hence N= 5-9098083 and as the dimensions of ¢, are [ 74?
the complete value of the new constant becomes
és) 1 (second)” x gramme (Paris)
“= -009808 metre x kilogramme
if we call the new unit of force a gramme (Paris). We have
further,
1 gramme (Paris) =0°009808
metre x kilogr.
(second)? 7” |
metre xkilog. 1 Par (7
(second)? 0-009808 © = eee
II. One of the fundamental units of the old system is a
derived unit in the new system; the remaining units are com-
mon to both systems. Since the new system contains one
fundamental unit less, it must also contain one constant less.
The new system is therefore obtained by eliminating a constant.
Let :
aL=M’N* . .”, Sn
be the equation containing the constant « to be eliminated.
In the new system this equation assumes the form
L=MN de
and defines the conception L,; the dimensions of its unit are
Systems of Physical Units. oF
given by the equation
i ON ee ao 8)
eL=L,,
[peared TTS ei Ba tie Ba)
where, again, 7 is the numerical value of «. If we introduce
into this equation the dimensions of [ L,] as well as the dimen-
sions of [L], if this unit is also a derived unit in the old
system, we obtain at any rate a relation into which the funda-
mental unit enters, which is to be made a derived unit. We
can then determine from equation (31) the ratio of the units
in question in the old and new systems.
If, for example, we wish to pass from the last system with
four fundamental units to system (17), where [/], [¢], and
[£] are fundamental units, we must make [m] a derived unit
and eliminate the constant ¢c. from the equation k=cyma. We
accomplish this by putting cym=m,, whence
[mm |=n[m,],
where 7 is the numerical value of ¢. The new unit of mass
Now we find
2
[m,], according to equation (17), has the dimensions + |:
If we retain the last units, we have
pd 1 sec.” x gramme (Paris)
2 0:009808 metre x kilogramme ”
and
1 sec.” x gramme (Paris),
0009808 metre (32)
Sear
aie acess Gen) =0:009808 kilogramme.
metre
If we wish to make [¢] and not [m] a derived unit, we must
put c,a=a,, so that the equation k=c,ma becomes k=may,
defining the conception a.
We obtain then
[a]=n[a,];
and by introducing the dimensions of [a] and [a,],
1 kilogramme =
L
whence
1 1
1 fl? m?
is pi shits ak
Sia wil-x [4].
92 M. A. F. Sundell on Absolute
Retaining the former units, we have
metre? kilogr.* a
gramme (Paris)? . (38)
metre? x Bie 1orpriy Sy asonenn
/ 0009808
1 second=4/0-009808
gramme (Paris)
In the same way we find, if [7] is to be made a derived unit,
cee OTE a gramme (Paris) x sec.” —
} metre = 5.909808 kilogr. Legs
1 gramme (Paris) x sec,” — (009808 metre.
kilogr. :
It is to be remarked that the relations (27), (32), (83), and
(34) may be regarded as determinations of the four units from
any one of them.
III. By successive employment of the two preceding me-
thods we are able to exchange one fundamental unit for
another, while retaining the same fundamental equations.
In one of the examples given, we have in fact exchanged the
unit of mass (kilogramme) for the unit of force (gramme,
Paris) while retaining the two remaining units (metre and
second).
IV. By successively employing methods I. and II., we may
change the system of fundamental equations by transferring a
constant from one equation to another without altering the
number of the fundamental units. If, for example, we wish
to pass from the system (15) to the system (18), we first of
all eliminate the constant of equation (7) by method (IL),
and then introduce a constant into equation (12) by method L.
We may of course adopt the reverse method. The calculation is
most simple if it is possible to retain the same fundamental units.
If, for example, in the system of equations (8), (9), (12), and
(7) the constant is to be transferred from equation (7) to equa-
tion (8), we must make the following substitutions, [7], [m],
and [¢| being the fundamental units :—in equation (7), 7 whys
in equation (12), k=/yc, and hence - =a; in equation (9),
a=a,c, and hence . =h,; and in equation (8), h=/,c. We
obtain thus the fundamental equations
ls hy m
= = 3 = 4 Hines ee
1 C t? 1 +? 1 1> 1 2?
Systems of Physical Units. 93
and the dimensions become
ai-[E]. ot=[$]. mr=[2]. c2=[2)
as before.
5. The rules we have given make it possible to pass from
one system of units to another. The process, however, is
somewhat troublesome. When the magnitude of a physical
conception is given in one system of units and we wish to find
its numerical value in another system, the following is in
all cases the safest and quickest method of arriving at the
result * :—
If we assume three fundamental units and denote them by
P, Q, R, then the dimensions of a derived unit N are of the
form
N=P’Q’R’,
where @, , c are positive or negative rational exponents. If
we assume units of other magnitudes p, g, 7, and if P=ep,
Q=79, R=gr, where e, f, and g are constants, then
N= et fea’, Pp" gq? Ge,
_Ifp,g, and rv are fundamental units, the new derived unit
has the dimensions p*, 9’, 7°, and
N= pgs 217;
or the given unit N is ef’ 9° times as large as the new unit 2.
If one of the new units, for example p, be itself a unit derived
from the units g, 7, and a new fundamental unit s, by means
of the formula
yi= by plist
then foaes
N79" . pt p= etf? ge. gett pete sf,
The new unit 7 is determined by the formula
n= ghthi gered:
consequently in this case also
N=*f% 9° . 2.
We obtain thus the following practical rule for obtaining
the value of a unit referred to new fundamental units:—In the
dimensions of the unit replace the old fundamental units by
their values in the new fundamental units, and carry out the
algebraic operations indicated as if the names of the units
were algebraic magnitudes. This rule gives not only the
ratio of the old unit N to the new unit 7, but also the dimen-
* Compare Kohlrausch, Leitfaden, p. 207.
94 M. A. F. Sundell on Absolute
sions of the new unit. Of course the rule holds good if the
number of fundamental units is greater or smaller than three.
Example 2.—The unit of force derived from the metre,
poe ealogt . If now we take
the centimetre, the gramme, and the minute as new funda-
mental units, we put
metre = 100 centimetres, kilogramme = 1000 Sra
second = ,5 minute,
and so obtain
1
second, and kilogramme =1
metre x kilogr. __ 100 centimetres x 1000 grammes
sec.” (25 minute)?
= 100 x 1000 x 602 (=360 x 10°) Centm. x gramme
(minute) 3
that is, the first unit of force is 360 million times larger than
the second.
If here we wish to exchange the former unit of mass, the
(sec.)? x gramme (Paris)
kilogramme, for the derived unit
metre
?
then by equation (82) we obtain
neanha, . (sec.)? x grm. (Paris)
metre x kilogr. 0:009808 metre
a ete alls e 2
- sec.” ; (sec.)?
pay or: gramme (Paris). Compare equation (27).
It is clear that the same rule holds for the reduction of any
magnitudes to new fundamental units.
Haample 3.
1 Daniell =112 x a eR (Gauss-W eber system)
= 119 x 108("001 metre) x (0'000001 kilogr.)*
sec.”
_ 12x10" metre# x kilogr.4
~ 10? x 10? sec.”
=112x 108 metre ae
3
metre? x
1 sec.” x grm.(Paris)\4
3 ‘009 i
=112 x 10! 0°009808 : metre
sec.
_ 11210 metrex gramme (Paris)? ,.. ..
= 70009808 oy Gov
system, Equation 32).
e
_ y
a
sty
Systems of Physical Units. 98
By the aid of this rule, the elimination of a constant is
more easily effected than as given above by II. If the con-
stant to be eliminated has the value
a=n[P*Q’R*],
where [ P], [Q], and [R] are the fundamental units, and if
we wish to make the fundamental unit | P|, for example, into
a derived unit and at the same time to eliminate the constant,
i. é. to make it equal to unity, we must put
1 4 e
[P]=n"@[Q°¢ Res],
where « becomes equal to unity.
If, again, we wish to eliminate the constant
de 1 sec.” X gramme (Paris)
>" ‘0009808 metre x kilogramme
introduced into example 1 by making the unit of mass a de-
rived unit, we do so by putting
E tian ath sec.” x gramme (Paris)
ae ’— §-009808 ~~~ metre
(compare equation 32); c, becomes equal to unity, and we
have a system in which the only fundamental units are the
units of length, time, and force. In order to make the unit
of time a derived unit, we put
1 seo? =0-009808 metre x Kilogr.
grm. (Paris)
or
metre kilogr.?
1 sec. =4/0-009808 ==
(compare equation 33), and so on.
e may follow a similar rule in using a physical formula
to find the value of an unknown magnitude. We introduce
the numerical values of the known magnitudes into the
formula, together with the appropriate dimensions or names of
the units, and solve the equation, thus finding at once the
value of the unknown magnitude and its dimensions.
Example 4.—Let us determine the value of the constant ¢,
from the equation 4,=c,ma (compare example 1). If the
force k;=1 gramme (Paris) act upon the mass m=0-001 kilo-
gramme, it produces the acceleration
: metre
a=g (Paris) 9°808 eae
96 M. A. F. Sandell on Absolute
If we put these values in the equation given, we have
1 gramme (Paris) =c, x 0°001 kilogramme x 9°808 I
1 gramme (Paris) =0:009808 nee login a oar
and
ib sec.” x gramme (Paris)
= 0:009808 metre x kilogramme
The rule given above is also of service in the exchange of
units, as is shown in the following examples:—
Example 5.—Let the velocity of light be taken as funda-
mental unit instead of the unit of fikdes We know that
Velocity of light= 40,000
Then we have the velocity
geographical miles.
second
metre! ““L*seooT ale 1
second 7420 second ~ 7420 x 40,000
and the acceleration
vel. of light,
9-808 metre = 9-808 awe ‘ rf
(see.)? (sec.)? ~ metre
ey us old's (velocity of of light)”
~ 7420? x 40,000? metre.
From this last number we may obtain the ordinary value as
follows:—
9°808 vel. of light? __ 9-808 x 40,000? geogr. mile”
7420? x 40,0007, metre — - 7420? x 40,000? sec.? x metre
__ 9808 x 40,000? x 7420? 9: 808” metre .
~ 7490? x 40,0007,
Example 6.—Let the acceleration due to ~— (Paris)
ae 803 = pace
unit of Bate: We obtain then, for example,
be taken as the fundamental unit instead of the
met.?
metre x kilogr, (Paris) _ —7 5a anelret
second
1 horse-power =75
x kilogr.( Paris) = 5(soe3 at x met.? x kilogr.( Paris).
= on acceleration due to gravity (Paris)? x metre?
x x kilogr. (Paris).
:
:
:
6. The systems of units most frequently employed in physics
are that due to Gauss and Wilhelm Weber, whose fundamental
units are those of length, time, and mass, and that employed
in many text-books (e. g. in Wiillner’s Experimental-Physik),
as well as by engineers, which has for fundamental units the
units of length, time, and force. In this last system the gra-
vitating force of a unit of weight is taken as the unit of force.
This system may therefore be termed the gravitation system.
The Newtonian equation (7) holds good for this system with
the introduction of a constant (constant of attraction). The
examples given above (examples 2 and 3) show how a quantity
given in the Gauss-Weber system may be transformed into
the gravitation system: the unit of mass of the first system
must in general be replaced by the derived unit of mass of the
second system. Conversely, if we wish to pass from the
second system to the first, we must replace the unit of force
by the derived unit of force of the first system. For this pur-
pose we employ relationships of the same kind as equations
(32) and (27).
The reduction is made most simply by employing the gravi-
tating force of the unit of mass (m) of the first system as the
unit of force (£,) of the second system. We have then
; In
[a] =o[#]=9| 5 |,
and hence ohois ce Sa eeee
eek;
Aad soe |],
where g expresses the numerical value of the acceleration of
gravity at the place. Since the name of unit of weight is ,
employed both for the unit of mass and for the unit of force,
these units may be easily distinguished from each other by
attaching to the name of the unit of force the name of the
place where the gravitating force of the unit of weight is equal
to the unit of force, as we have done in previous examples.
Example 7.
Systems of Physical Units. 97
_- metre x kilogramme (Paris
One horse-power =75 metre x kilogramme (Paris)
second
(gravitation system)
metre x kilogr.
~~ second?
second ey
=75 x 9°808(=735°6) more x kilogr.
second
(Gauss-Weber system).
The chief constant of the two systems is the constant of
_ Phil. Mag. 8. 5. Vol. 14. No. 86. Aug. 1882. H
metre x 9°808
=75
98 M. A. F. Sundell on Absolute
attraction—which is equal to the square of the so-called Gauss’s —
constant. The value of this constant is given by Gauss* as
0-017 Semi major axis of earth’s orbit,
mean day x sun’s mass?
Hence we have the attraction-constant
» semi- major axis of earth’s orbit
=(0°0172) ree, :
y” X sun’s mass
__ (0:0172)” x (19,900,000)? _ geogr. mile*
~ (86,400)? x 820,000 sec.” x earth’s mass
ie) (0:0172)? x (19,900,000)? x (7420)? metre’
~ (86,400)? x 320,000 x 4 x 8°14 x (6,370,000)? x 6000 sec.” x kilo
_ 615 metre®
~ 10" sec? x kilogr.’
if we take the mean mass of 1 cubic metre of the earth as equal
to 6000 kilogr. The force with which a mass of 1 kilogr.
attracts an equal mass at a distance of 1 metre is then
ae oie If we transform the value of the con-
stant of attraction into the gravitation system, we obtain
615 metre? —__ 615 metre?
10" sec.” x kilogr.~ 10” seo? ¢__1__ See.’ x kilogr. (Paris)
Px
9°808 metre
_ 615 x 9808 7_ 604 metre*
a 1 (= ro eee x kilogr. (Paras
7. Of systems with four fundamental units, that with fun-
damental units of length, time, mass, and force is not without
interest. In order to obtain such a system we must retain
two constants in the fundamental equations (2), (3), (6),
* Theorta Motus Corporum Celestium, p. 2.
t Willner (Lehrbuch der Experimental-Physik, vol. i. 1870, p. 145)
puts the mass of a cubic metre of the earth =, and hence finds for the
attraction-constant the value = , Which value, if the unit of mass
(=9'808 kilogr.) employed in the same work (vol. i. p. 59) is to be
retained, is 5808 times too great, and must be altered to ;
9808 | 6128 _ 601
1000 “ 10" ~ 10”
(very nearly the same as given above). The unit of mass,
1 Sec.’ x kilogr. (Paris) _ 9, :
Neer Sa 9°808 kilogr.,
ee attracts an equal mass at a distance of 1 metre with the force a
Toe ldlogr,
2
Systems of Physical Units. 99
and (7). If we choose for this purpose the constant of equa-
tion (6) (the force-constant) and that of equation (7) (the
attraction-constant), we obtain a system in which the dimen-
sions of the chief units are given by equation (22). We have
already found the value of the force-constant c, (example 1),
namely
Boone (second)” x gramme (Paris)
2= 0-009808 metre x kilogramme
— 1 (second)’ x kilogramme (Paris)
9°808 metre x kilogramme
According to equation (22), the dimensions of the attraction-
2
constant are [c¢ |= Ei ; we may find its new value as fol-
lows:—
615 (metre)? _ 615 (metre)? iS metre x kilogr.
“~ 08 (sec.2) x kilogr. 10" (kilogr.)? (second)?
_ 615 (meire)? ibe eras : u
= 410 (alogr.)? X 9-808 kilogr. (Paris) (equation 35)
site 615 _ (metre) x kilogramme (Paris)
0 9-808 (kilogramme)” ,
or
__ 627 (metre)? x kilogramme (Paris).
“a= 70" (kilogramme)’
The other mechanical equations of definition would remain
unaltered. Thus we should have:—
for the work A, the relation A=ks, with the dimensions
[A]=[41];
for the vis viva, wu=mh’,
for the momentum, g=mh,
m x
(a= [F];
and so on.
Such a system has this advantage for a beginner—that he
is able to express either a force or a mass in units of weight,
and so would escape the reduction (difficult to understand and
often forgotten) of a force from units of weight into units of
force of the Gauss-Weber system, or of a mass from units of
weight into units of mass of the gravitation system. The
following circumstance may, however, perhaps be considered
inconvenient. The constant of force passes over into the equa-
tions which give the connexion between work and change of
H 2
100 M. A. F. Sundell on Absolute
vis viva, and between the so-called time-integral of force”
1: dt and the change of momentum, as well as into certain other
mechanical equations which are derived from equation (6).
The equations are as follows:—
A= 4 cgm(h? —i) = Co(u aaa Uo),
fk dt=em(h—hy)=¢x(¢—4q)s
A=}(u—w),
fk dt=q—Q, :
in the usual systems with three fundamental units. That the
equations in question, as well as equation (6), are free from
any special constant in the usual systems is, no doubt, to be
formally mentioned ; but the circumstance is not of practical
importance. For physicists often, and engineers almost always,
express both forces and masses in units of weight, and the
reduction to absolute units necessary for the employment of
the ordinary formule introduces a constant in a disguised form.
8. The different systems of electrical measurement arranged
by Wilhelm Weber, which are connected with the magnetic
system of Gauss, are of special interest.
We have the following equations between the chief concep- _
tions of this group of phenomena :—
instead of
w=ockL?, .. . . wn
é =chkL’,: .-. . on
pae5 2 )
2
i.
2
Pao, » + ay
Ee, ... nn
where w denotes the quantity of free magnetism or strength
of a magnetic pole, ¢ the quantity of electricity, and i the cur-
rent-strength; J is the length of an element of the current-
path, L the distance between two elements of the current, two
magnetic poles, or between a current-element and a magnetic
pole; 4 is the attraction or repulsion between current-elements,
magnetic poles, or electric masses. The magnetic pole is to
* Thomson and Tait, ‘Theoretical Physics,’ § 29.
q + «it
Systems of Physical Units. 101
be supposed to be in the line drawn from the centre point of
the element acting on it, and at right angles to it; the two
current-elements which act upon each other are to be regarded
as parallel to each other and at right angles to the line joining
their centres.
The complete formulz are
t
cha WH sin 8, eerie Rare a Satie Cake ae)
ae ie |
ck= +5 (cose—$ cos 0 cos 0); - hott St (408)
where e, 8, and @, are known angles. Equation (41) relates to
the motion of a closed circuit in the neighbourhood of cur-
rents or of magnets ; 7 is the strength of the induced current,
k the electrodynamic action of the inducing currents or mag-
nets on the induced conductor, estimated according to the
direction of the motion; A is the velocity of motion, and E the
induced electromotive force:
Since the units of length, time, velocity, and force are
already fixed by a system of fundamental equations, we have
six equations connecting the four new conceptions, p, ¢, 2,
and E. In forming the corresponding fundamental equations
we must therefore retain two constants. The electrostatic (or
mechanical) system is obtained by retaining the constants of
equations (36) and (40). In the electromagnetic system we
retain the constants of equations (37) and (40). A very conve-
nient system is obtained by retaining the constants of equations
(38) and (40) ; this system may be called the Gauss-Weber
system: it is completely worked out in Kohlrausch’s Leitfaden.,
Lastly, we have the electrodynamic system with the constants
of equations (37) and(39). The values of the constants are as
follows in the Gauss-Weber system:—c=4 (equations 40 and
40a), and o=* (equation 38), where ¢ is the total quantity
0
of electricity (positive and negative) passing per second with
the unit current of this system. Weberand Kohlrausch have
found
gio millimetre,
—— second
(42)
_* Wiedemann, Lehre vom Galvanismus und Elektromagnetismus, vol. ii.
diy. 2. p. 457. Weber himself takes into account only one form of elec-
ie e 10
tricity, and puts therefore pee
2
—— (Abh. der kénigl. sachs. Ges. der Wissensch. vol. iii. Also in
Zoliner, Principen einer elektrodynamischen Theorie, pp. 93-131).
(more exactly 15°537 x 10!°)
eS,
102 M. A. F. Sundell on Absolute
By the aid of IV. we easily find the following values of ‘
constants in the other systems :—
Electrostatic system,
ae : ; ;
C= (equation 36), c= 5 (equations 40 and 40a);
0
electromagnetic system,
1
c= (equation 37), o=5 (equations 40 and 40);
0
electrodynamic system,
2 mn
c= & (equation 37), c=,/2 (equations 39 and 39a).
&%
We obtain a formula of induction suited for practical use
by replacing the force & in equation (41) by its value caleu-
lated from the formula (394) or (404).
Since the constant of equation (41) has the value unity in
all four systems, it follows that the work performed by the
current in unit time is equal to the product of electromotive
force into current-strength. Moreover the equation corre-
sponding to Ohm’s law which determines resistance is of the
same form in all three systems.
The relations of the chief units of the electromagnetic,
electrodynamic, and electrostatic systems, together with their
dimensions, are given in Prof. Wiedemann’s Lehre com Gal-
vanismus und Elektromagnetismus, vol. ii. div. 2. pp. 467-471;
they are also given for the electrostatic and electromagnetic
systems in Maxwell’s * Treatise on Hlectricity and Magnetism,’
vol. ii. pp. 239-245.
The occurrence of the constant e, in so many of the for-
mul connected with electricity would seem to show that these
formule could be derived from some natural law. Wilhelm
Weber finds this in his fundamental electrical law,
_ &&9 a dL poe ?L ty
a rab 161 Car) 2ae $I
Here : is the quantity of positive or negative electricity
(measured electrostatically like e, and e,) which traverses the
circuit in unit time when the current-strength is equal to the’
1
J/2
electrodynamic unit current, 7. e. is equal to electromag-
; : L248 ee
netic unit. Consequently we have ~=—“~ or — =,
a 2/2 6 ‘
: Systems of Physical Units. 103
where é is to be taken in accordance with equation (42). The
fundamental law may then also be written
b= V8) 1— 5 Be (2 Beg toe |, 43)
9. Systems with two fundamental units result by elimina-
ting one constant from the fundamental equations for systems
with three units. Various systems with two fundamental
units may be formed by elimination of the constant of attrac-
ig
tion. If in the value of this constant ( _ ae a or ) we
put
615 metre? 615 millim.’
108 ‘sec 10% second?’
1 kilogr. = (44)
this constant becomes unity, and we obtain a system with the
two fundamental units of length and time. The unit of mass
derived from the metre and the second is consequently
metre? 10%
second? 615
The unit of force 1 kilogramme (Paris)
kilogr.x metre _ 9°808 x 615 metre* |
kilogramme.
=e (Second)? ..~ 10" sect?
consequently the new unit of force is
metre* LON
second: — 9:808x 615 kilogramme (Paris).
This system is employed for attraction-problems by Thomson
and Tait (‘ Theoretical Physics,’ §§ 459, 774)*. The densityt
—— iY le
of water (=1000 10" sec
(thus independent e the unit of length). In order to com-
pare this number with the number given by Thomson and Tait
2 becomes in this system
(§ 774) we must multiply it by a since Thomson and Tait
put the mean specific gravity of the earth equal to 5-5. We
* Compare also H. Weber and Kohlrausch (Zollner, Prineipien ewer
elektrodynanuschen Theorie, p. 129); Maxwell, ‘Treatise on Electricity
and Magnetism,’ vol. i. p. 4.
+ Density is here taken to mean mass of unit volume of the substance
(Maxwell, p. 5).
104 M. A. F. Sundell on Absolute
thus obtain for the density of water the number
6 ,, B15 1 ey a 1
De 5-5 10” sec.2_-108 sec.”
which agrees exactly with Thomson and Tait’s number. It is
to be observed that the dimensions of the electric and magnetic
units in this system have exponents which are whole numbers.
In the Gauss-Weber system the dimensions of [mJ and [e] are
the same as of [m]; for we have the dimensions [‘ |; for [ H’]
3
E , and so on.
Example 8.—The Weber unit of current
bic mm.? x mgr. be re metre? x kilogr.?
sec. 0% sec.
paOlbd | 615 _V61 615 mee
TF a0 eom Tor (equation 44).
If we wish to return to the ordinary system, we must observe
equation (44). We may calculate as follows :—
V/ 615 615 meee ./ 615 metre? a metre?
(current-strength) =
10" see 10? ree sec.
ae Jas 615 (metre? ); metre? _ /615 ;
10" \ sec? sec. 100
7 kilogr.4 x metre? 2 ki
s 103 kilogr.2 x metre cigs 1 x kilogr.4
/ 615 sec. 102 second
(Weber unit of current).
The constant of attraction may also be eliminated by putting
1 second = ay [Gb meiner metre? _ V615 millimetre’
or kilogr.4 2 10° milligr.2 ?
so that the unit of time becomes a unit derived from the unit
of length and the unit of mass,
1 metre? yes —> seconds.
ais aa 615
metre x kilogr. heecimeaee
second? 615 metre??
The unit of force 1
; Systems of Physical Units. 105
from which the new unit of force
kilogr” _ 615 metre x kilogr.
metree 108 sec.”
Peale:
~ 9-808 x 10%
The dimensions of the other principal units become
7
cl=["], =[5]. l= tl=m)
(according to the fundamental equations of the Gauss-Weber
system),
‘ m m2
l= E yb i=
and so forth. A quantity of electricity is given in ordinary
units: we find the electrostatic unit
kilogr. (Paris).
millim.? x milligr. 3
second cs =~ 615
i milligr.,
or
7615 millim.? x milligr?
1S sec.
1 milligramme = Weber units;
10°
" V/615
action at a distance as 1 Weber unit of electricity.
Instead of eliminating the constant of attraction, we may
obtain a system with two fundamental units by eliminating
the constant
: ae
= Bly ge
Tf, in doing this, we wish to make the unit of time a derived
unit, we must put
1 second =31 x 10”? millimetres.
Time must therefore be expressed as a length, the new unit of
: ain 1
time 1 millimetre = 31x 10 See
The units of the four electric systems have the same dimen-
sions and the same magnitude, with the exception of the units
of the electrodynamic system. The dimensions of the most
important units are as follows:—
106 M. A. F. Sundell on Absolute
[h]= [0m] (abstract number),
faj=[5], =[F], =, (Al=fol:
constant of attraction [¢,]= [- | » fel=[4]=[m2?],
. ms
c= [54] =(81.
We see that, by eliminating the constant (¢), the distinction
of the units by their dimensions is lost for the most part—a
result which was to be expected, since e, has no independent
dimensions, but is to be regarded as a velocity.
10. The systems with two fundamental units have yet an-
other constant; if this be also eliminated, we have a system
with only one fundamental unit. If we start with the system
given above, with the fundamental units of length and time,
we may eliminate the remaining constant cy by the relationship
1 sec.=31 x10" millimetres. . . . . (45)
We thus obtain a system in which the unit length is the only
fundamental unit. The three electrical systems now combine
into one. The dimensions of the units are as follows:—
=P]. (abstrastajumber), le) aan tal=[7],
[mJ=[4], [A]=1], [AJ=[4, [el=[4]=(2],
[‘J=[E]=[2"].
The distinction of units by their dimensions is now completely
lost; velocity, force, current-strength, and electromotive force
are abstract numbers; time, mass, work, quantity of electricity,
and magnetic pole are to be regarded as lengths.
ac ee i
The unit-mass 1 ae (= : = 5 kilogr.) becomes equal to
1 sas
312 x 10” millim. Consequently the unit of mass
ry _fmilhimn. i. Bh? 10 a:
iimallim. == 31 x 10” =a 61S a 157 x 10”)kilog.,
or nearly one fourth of the earth’s mass (650 x 10” kilogr.).
Weber’s formula may now be written
pa eiea ae uae oe
ara Se 2L en
Weber himself simplifies the formula thus: —
Poise] gs el ee
r= fe { (2) ae}.
If we compare this formula with formula (48), we find that
,
1
d
3
Systems of Physical Units. 107
it is not ¢,, but eV 2 which is eliminated by putting 1 sec.=31
x 10°Y2 millim.=44x 10" millim. The new unit of time is
oe sec. The constant of attraction, too, is eliminated
by Weber by introducing a unit of mass
2x 31? x 10”
615
(nearly half the earth’s mass™). These last two formule ap-
pear to us equally simple; but the first of them, as we saw
above, has the advantage of combining the three electrical
systems into one. In returning to the ordinary systems,
attention must be paid to equations (44) and (45).
Example 9.—The quantity of electricity 1000 millimetres
millim.? x mgr.# We
sec.
(=314 x 10”) kilogr.
is to be expressed in electrostatic units
have 1000 millim. electricity
5 : s 3 *77* 3
ETO) ee — 31? x 10 x 1000 et (equation 45)
millim.” sec.”
ey millim.? 10?
272 23
= x 10 r ———
sec.” sec. W625
x 31?
ae
2
*W7: s .
93 Millim.* x kilogr.
sec.
x10
(equation 44)
_ 10°x 31? x 10% x = 10% x 31?\millim.? x mer.2
W615 V 615 )
It is to be observed that a system with two or with only one
fundamental unit is not completely determinate, unless its
connexion to the ordinary systems with three fundamental
units is given by relations such as equations (44) and (45).
The systems with three fundamental units are therefore to be
regarded as the fundamental systems of mechanics.+
11. The ordinary units of mechanics are not convenient nor
* Weber and Kohlrausch (Zollner, 7. ¢. p. 130).
+ The above systems with less than three fundamental units may be
regarded as the result of taking the unit of length, the unit of velocity,
and the unit-of-attraction constant as fundamental units. Tf, for example,
we take the millimetre, the velocity e,, and the attraction-constant C, as
fundamental units, we obtain, frome, =615 x10~4mm.* x see.—? x kilogr.~},
1 kilogr. = 615x10-4mm.5 x sec.2Xe, 7 ; and from e,=31 x10" mm.x
sec._’, 1 sec. =31x10"x mm. xe>'; which expressions become iden-
tical with (44) and (45), if we omit c, ande, from the dimensions. The
constants ¢c, and e, should be left in the fundamental equations, so as not
to disturb their homogeneity.
sec.
108 M. A. F. Sundell on Absolute
sufficient to give a quantitative representation of all the phe-
nomena of physics; but we are obliged sometimes to introduce
arbitrary units. Among these may be reckoned the unit
angle, which is very useful in considering circular motion, for
which purpose it replaces the unit of length. From the unit
angle and the unit of time we derive the units of angular velo-
city and angular acceleration; since, further, moment of inertia
corresponds to mass, and moment of rotation to force, we obtain
a complete analogy with motion in a straight line, and equa-
tions analogous to the equations (2), (3), and (6). This ana-
logy is lost by regarding the angle as an abstract number.
The conceptions derived from the phenomena of heat.—A
quantity of heat w is proportional to the elevation of tempera-
ture T which it can cause ina mass m. We obtain thus the
equation of definition,
wo=ceml,
where ¢ is a factor depending on the material nature of the
body, which we will call the capacity for heat. The dimen-
sions of the unit of heat are determined by the equation
[w]=[emT].
We have here three new units, of which we may choose two
as fundamental units. Ofthe three possible combinations, we
have determined upon one, and choose units for capacity [¢
and temperature [I] at pleasure, so that the unit of heat My
becomes a derived unit: it is the quantity of heat required to
raise by one unit the temperature of the unit mass of a sub-
stance having unit capacity. The units of temperature in use
are well known; for unit of capacity we take the capacity
of water ; the capacity of a body is therefore expressed by the
same number as its so-called specific heat. As examples fur-
nished by the science of heat we may take the following :—
The heat necessary to raise 10 kilogr. mercury (capacity
=0°033 capacity of water) from 0° C. to 100° C. = 0:033 x
10 x 100(=383) kilogr. x Centigrade degree x capacity of
water.
Coefficient of linear expansion of iron=0-000012 _ ae
degree C.
1 1
aie ee x . Se
0000012 2 denies Bua x 0000012 degree ail
1
Sa | paws Wea eae Sots
3 x 0:000012 dearea.
Latent heat of ice =79°25 degrees C. x capacity of water.
We obtain the work A which is equivalent to a quantity of heat _
w by multiplying this quantity by the mechanical equivalent
Systems of Physical Units. 109
of heat Q, peas
= Qu.
The dimensions of Q are
[e)
We usually put
Q=494 metre x kilogramme (force)
ze kilogramme (mass) x degree CU. x capacity of water
iF Ball oe! English foot x English pound (force)
eee OL X (= 778) Engl.pound(mass) x deg.F. x capac. of water”
This value does not agree with either of the two ordinary
mechanical systems, since both the unit of force and the unit
of mass are here fundamental units. Butif we introduce either
metre x kilogr. (mass)
1 kilogramme (force) =9°81 x (second)
or
1 (second)? x kilogr. (force)
Peo 3
1 kilogramme (mass) = 9 SE
we obtain in both cases
: Pee a (metre)?
ee OY) sec.” x degree C. x capacity of water’
which value may be employed either with the Gauss-Weber
system or with the gravitation system.
In stating physical magnitudes, we frequently see arbitrary
units employed besides the absolute units: it is important in
using such units to state their names completely, the names
being often formed according to the theory of dimensions.
Ezample.—LHlectrolytic (chemical) unit of current
__ cubic centim. of electrolytic gas a milligramme copper
minute minute ?
The rules for the reduction to new units are then always
applicable, as the above examples in heat show, and render the
calculation rapid and certain.
Helsingfors, January 1881.
Postscript.—After the above was in type the author became
acquainted with Dr. Herwig’s work, Physikalische Begriffe und
absolute Maasse (Leipzig, 1880). The units of the science of
heat are stated somewhat differently by Herwig: the equiva-
lent Q is first eliminated, so that the units of quantity of heat
and of work become identical; secondly, the capacity of water
is taken as a conventional unit, and its name is omitted from
the dimensions.
LG
XI. Moseley’s Theory of Steady Flow. By Major ALLAN
CunnincHam, R.E., Honorary Fellow of King’s College,
London*.
A NEW Theory of the Steady Flow of a Liquid was pro-
posed by the late Canon H. Moseley, in an important
essay published in this Magazine in 1871-72+. The paper was
valuable as an attempt to form a rational theory of the steady
motion of a real fluid, and to deduce results of great scientific
and practical interest from it. Formule were arrived at for
the Velocity at any point in a Pipe flowing full, and for the
Discharge both of a Pipe flowing full and of an Open Channel,
and for some other quantities of less importance.
In the investigation it was assumed that:—
I. Pipes.—In long uniform pipes at uniform slope, flowing
full,—
1. The motion is a steady motion in lines parallel to the axis of
the pipe.
2. The surfaces of equal velocity are similar, and similarly
situate, to the enclosing margin.
3. The measure of tangential resistance to the fluid at the en-
closing margin is (A, + 44,0").
4. The measure of tangential resistance to fluid particles flow-
ing past each other is (A+p. (6v)?).
. The whole of the kinetic energy lost by any particle of the
fluid under subheads 3 and 4 is probably converted into
heat energy, or, at any rate, lost as kinetic energy.
CA
II. Open Channels.—In long uniform open channels at uni-
form slope,—
6. The discharge is one half of the discharge of a pipe flowing
full whose lower half is the open channel in question, and
upper half is similar to the lower (reversed).
The evidence as to the reality of the assumptions Nos. 1, 2,
5 is not stated: they are apparently only working hypotheses.
No. 3 is accepted from Poncelet’s experiments on the friction
of a fluid on a solid. No. 4 is merely an assumption that the
expression for fluid-friction is of the same functional form as
that between a fluid and a solid. No. 6 is accepted from
Darcy’s experiments on pipes and open channels.
It must be remarked, in passing, that there is really no evi-
dence as to the existence of steady motion in parallel lines
even in pipes flowing full, and that in the case of open chan-
* Communicated by the Author.
+ Vol. xlii. 1871, pp. 184 and 349; vol. xliv. 1872, p. 30,
|
|
’
;
:
On Moseley’s Theory of Steady Flow. 111
nels, at any rate, all modern experiment points* to the con-
clusion that the motion is essentially unsteady and that the
stream-lines interlace freely in all directions. Next, hypothesis
No. 2 is contrary to the evidence of Bazin’s experiments.
In Bazin’s work two diagrams are givent of cross sections of
two rectangular iron pipes (flowing full) laid with two sides
horizontal, with velocity-measurements made at many points
on several horizontal and several vertical lines thereof figured
thereon: now the contours of loci of points of equal velocity
traced thereon are all rounded (like ellipses); so that hypo-
thesis Ne. 2 disagrees with nature.
From these hypotheses Nos. 1 to 5, the primary result is an
expression for the velocity at any point in a pipe flowing full ;
and thence follows, by a simple integration, an expression for
the discharge through the same. By help of No. 6 (which is
a result of pure experiment) this last result is extended so as
to give a formula for discharge in open channels.
It will be seen that the results for pipes (flowing full) are
strictly dependent on the hypotheses Nos. 1 and 2 of steady
motion in parallel lines, and of the surfaces of equal velocity
being similar and similarly situate to the enclosing margin;
whilst the formula for discharge in open channels involves no
assumptions as to the actual motion therein, but depends only
on the correctness of the theory of the moticn in pipes flowing
full together with the connecting link No. 6 (derived from
experiment).
From the uncertainty of the assumptions, it is evident that
the only test of the correctness of the theory is the comparison
of numerical results therefrom with observation.
The extensive small-scale experimental resultst of MM.
Darey and Bazin on pipes and open channels not exceeding
2 metres in width nor 4 metre in depth were applied (in the
original essay) in numerical verification of the formule quoted
—viz. for Velocity at any part of a circular pipe flowing full,
and for Discharge both in pipes flowing full and in open chan-
nels. The result was apparently satisfactory; that is to say,
there was certainly a remarkable approximation on the whole
(with occasional very large discrepancies) between the expe-
rimental and theoretical results. A sound theory of flow of
* See ‘Roorkee Hydraulic Experiments,’ vol. i. chap. vi., for a summary
of the evidence.
} Recherches expérimentales sur [écoulement de Teau dans les canaux
découverts, pl. xviii.
{ Recherches expérimentales relatives au mouvement de Veau dans les
tuyauxr, by H. Darcy. Paris, 1857.
Recherches exp&imentales sur Tl écoulement de Teau dans les canaux dé-
couverts, by H. Darcy and H. Bazin. Paris, 1865.
12 Major Allan Cunningham on
water would be of such great scientific interest, and its ulti-
mate result—a good formula for Discharge—would be of such
great practical use in engineering, that it is well worth while
to thoroughly test this new theory : it will be shown that the
approximate agreement above noticed is quite illusory.
The primary result of the investigation is, as stated, a for-
mula for the velocity v at any point at a distance 7 from the
centre of a pipe of radius R flowing full, the central velocity
(in the same cross section) being v,, viz.
U4. ET,
Upon different hypotheses, and by a quite different investi-
gation, M. Darcy proposed* the formula
V=V. {i-m(Zy
and applied the same (his own) experimental results in verifi-
cation.
It is quite clear that these two expressions, differing so
greatly in form, cannot both be correct rational formulz; and
yet they both give numerical results agreeing sufficiently with
Darcy’s experimental results to have satisfied their proposers.
But the fact is, that the numerical test relied on from Darcy’s
experiments is (though this seems to have escaped attention)
avery poor one. Darcy’s velocity-measurements were made
at only five points in a vertical line through the centre of each
pipe, viz. at the centre and at points symmetrically above and
below the centre at 4 and 2 of the radius from the centre ;
thus embracing only the middle 2 of the diameter in question,
within which the change of velocity is very small, and the
velocity-curve (or locus of the equation) is therefore very flat.
Thus almost any very flat curve would agree tolerably well
with the observations in the middle 2 of the diameter, especi-
ally when the comparison is made (as in the present instance)
between ordinates measured in so large a unit as a metre, as
the difference (in metres) would then only be small decimals.
The dissimilarity of the two curves is in this case very striking,
their convexities being actually turned opposite ways. Thus
Moseley’s curve is concave downstream with a cusp at the
middle, whilst Darcy’s is convex downstream with an apse at
the middle. On plotting Darcy’s observations they will be
found to give curves generally very flat, convex downstream
with an apse at the middle; so that Moseley’s velocity-formula
does not agree with nature.
All the rest of the investigation depends on this primary
* Recherches expérimentales &c., by H. Darcey, p. 128.
Moseley’s Theory of Steady Flow. 113
velocity-formula, and therefore fails as a rational theory along
with it. It might, however, happen that the other results
might prove to be good empirical formule. The only others
admitting of test are the formule for Discharge, which are
given in several forms, as suited for pipes of various sections
(cireular, rectangular, &c.) fiowing full and for open chan-
nels. A large number of the discharge-measurements of
MM. Darcey and Bazin in circular pipes flowing full and in
small rectangular and trapezoidal open channels, are compared
in the original essay with the results computed from the for-
mul ; and here, again, there is a remarkable approximation
in the results. This turns out, however, to be no criterion of
approximation on the large scale, as will appear below.
Some extensive large-scale experiments on flow of water in
large canals of various widths up to 200’ and depths up to 11’,
and various discharges up to 7000 cubic feet per second, made
under the author’s superintendence near Roorkee in Northern
India, in 1874-79, and recently published”, afford a test for
the formula for discharge in open channels on the large scale.
The formula given is
Discharge in cubic BY :
8 D/=355.{1-(14 2B’) 2? } «0g
metres per second R )
where
B/ = wetted border, R’ = hydraulic mean depth, both iz
metres
v9 = central surface-velocity in metres per second;
D/ = discharge in cubic metres per second.
The formula is a very laborious one for computation; but its
failure on the large scale can be readily shown, without com-
plete computation, as follows:—lIt is obvious that the quantity
(1+2R’).e-*®' is always a + quantity, rapidly decreasing as
R’ increases: hence the above expression gives a result always
Vi
B
less than 4 Re: vy cubic metres per second, and therefore
(changing to British measures) the
Discharge, in cubic : Si) (iyo) eevee: ae
feet per second : D is always <9 * R* S087
or <5°d82 = «U0;
where B, R, vp are here measured in feet.
- * Roorkee Hydraulic Experiments, 1881, 5 vols. (published at Tho-
mason C, E. College, Roorkee, N.W. P., India, 1881).
Phil. Mag, 8. 5. Vol. 14. No. 86. Aug. 1882. i
114 On Moseley’s Theory of Steady Flow.
A few selected instances from the Roorkee experiments™,
with widely differing data (as to width, depth, velocity, and
discharge), are given in the table below.
Data. | Value of | Discharge-
Site. 5-382 B,, mneasurement
\ Bel B tou So
Solani left aqueduct ............... 100-2} 6°75 | 4:05 O24 | 2328
Solani right aqueduct ..... ...... 105°8| 7-96 | 452 |. 323- | 3429
Solani embankment, main site... 190°3| 934 466 512 ) 7169
Fifteenth mile, new site ......... | 1820} 9:49 | 4:91 507 ) 7187
TST aires eee er eee 196°4| 9°02 | 3:67 430. |! 5611
SAOUUBILG, Cotes perce Nese ees eee | 200°2| 7°82 |. 5-43 473 | 4631
| Kamhera site | ..0...........s0c000- 695) 484 | 3-40 | 263 | 961
It will be seen that the computed values of 5°382 Rey
which should be all greater than the discharge-measurements
(D), are actually only from about + to + of the latter; so that
the formula is evidently useless for application to large bodies
of water.
The Roorkee experiments also furnisht important (nega-
tive) evidence on the vexed question of the supposed convexity
of the water-surface in an open channel. Canon Moseley states
(in the same essay{) that, as a result of theory,—
“ As the pressure is everywhere less where the velocity is greater,
it is evident that there will be a tendency in the liquid on the
surface to flow from the sides of the channel towards the
centre, and that thus the velocity of the surface-water at the
centre will be diminished, and the water heaped up, drowning,
as it were, the point of greatest velocity in the section.”
Now two of the results above indicated—yiz. the constant
transference of surface-water § from the edges towards the
centre and the depression|| of the maximum velocity below the
surface—have been amply verified experimentally. But as to
the “ heaping-up”’ of the surface-water at the centre, or, in
other words, as to the surface-convexity (the existence of which
seems to be accepted by writers on hydraulics), the author has
not been able to find any certain experimental evidence. Some
special experiments were accordingly made by him to test the
point, at a site extremely favourable for the trial, in a canal of
about 170’ surface-width and 11/ depth, with a central sur-
* Roorkee Hydraulic Experiments, vol. i. p. 297.
T Op. cit. vol. i. chap. viil. passim.
{ Philosophical Magazine, [4] vol. xliv. p. 44.
§ Roorkee Hydraulic Experiments, vol. i. chap. xvii. arts. 14-14,
|| Op. eit. vol. i, chap. xii. passim.
_
Mr. T. C. Mendenhall on Edison's 7 aeieier: 115
face-velocity of about 4°5 feet per second. The experiment
(fully detailed in the Roorkee work*) was a very delicate one,
on account of the incessant slight oscillations of the water-
surface ; but every possible care was taken. The result of
twelve trials on one day and twenty-four on another, was that
the mean water-surface (7. e. average of the oscillations) at the
eentre and edges was (on a calm day) most probably level.
XII. On the Influence of Time on the Change in the Resist-
ance of the Carbon Disk of Hdison’s Tasimeter. By T. C.
MENDENHALL, Columbus, O.T
1 ae five years ago Hdison announced the discovery of
“ the remarkable property possessed by carbon when pre-
pared in a special manner, in virtue of which its electrical
resistance was greatly lessened by subjecting it to an increase
of pressure. Among the numerous interesting applications of
this discovery which were quickly made, none was more pro-=
mising or more interesting than the tasimeter devised by
Hdison himself. The extreme sensitiveness of the carbon to
the slightest changes in pressure gave rise to the hope that
the instrument would far exceed in delicacy those previously
in use for the detection of minute quantities of heat.
Mr. Edison was a member of the Draper Hclipse Expedi-
tion in the summer of 1878, and used his tasimeter during the
total eclipse of July 29 in that year, attempting to measure
the heat emitted by the sun’s corona. His report to the
director, Dr. Henry Draper, was published in the Proceedings
of the American Association for the Advancement of Science
for the same year. This report shows that the attempt was
by no means as successful as could have been desired, the
principal obstacle being apparently the difficulty in the adjust-
ment of the tasimeter so that the galvanometer-needle would
remain at zero, and to secure its return to that point after it
had been deflected. In fact, the zero adjustment was only
made by the use of a peculiar shunt of variable resistance
ingeniously contrived by Mr. Edison for the purpose.
The writer is not aware of any other systematic attempt to
secure quantitative results through its use; and, as far as
known, the instrument has been generally regarded as pecu-
liarly inconstant and unreliable in its indications.
Having in his possession a tasimeter constructed after the
* Op. cit. vol. i. chap. viil. arts. 4, 4a. f
+ From Silliman’s American Journal of Science for July 1882, having
been read, by invitation, at the April meeting of the National Academy.
12
a
116 Mr. T. C. Mendenhall on the Resistance of
model of that described in the report referred to above, the
writer undertook a short time ago to investigate the quantita-
tive relation between pressure and resistance for the carbon
disk which belonged to it. In a series of preliminary experi-
ments, the use of the toothed wheel and screw, by means of
which the pressure is communicated to the disk, was found to
be extremely objectionable on account of the impossibility of
exactly reproducing a given pressure. This portion of the
instrument was therefore entirely removed, and an arrange-
ment made by means of which any definite pressure might be
quickly brought to bear upon the disk or removed fromit. A
slender brass rod was placed in a vertical position upon the
centre of the upper contact piece, the upper end of which
rested lightly in a small conical cavity made on the underside
of the scale-pan of a balance. The weight was suspended
above by a fine thread passing over a pulley; so that by raising
or lowering it, the pressure was applied or removed as was
desired. The carbon disk was made one of the branches of a
Wheatstone’s bridge, as described by Mr. Edison. In lowering
the weight, care was taken to make the movement slow enough
to avoid any shock to the disk. When the apparatus stood
with the weight lifted, the adjustment of the galyanometer to
the zero was made without any difticulty, the resistance of the
disk appearing to be quite constant. When the pressure was
applied, however, the adjustment became very troublesome ;
and after a few trials it was discovered that time was a very
important element in the problem. The addition of a pressure
of fifty grams reduced the resistance to nearly one fourth of
what it was in its normal condition instantly; but it was found
that the minimum was not reached at once. The resistance
continued to fall during the first two or three minutes with
considerable rapidity, and after that more slowly. A series of
experiments was accordingly undertaken for the investigation
of this phenomenon. After a number of trials, the bridge was
adjusted so that when the key was closed simultaneously with
the application of the pressure the needle of the galvanometer
would remain momentarily at zero; for the instantaneous effect
of this pressure seemed to be quite constant. Ina few seconds,
however, the needle began to move, showing that the resist-
ance was diminishing. With this constantly decreasing resist-
ance it was, of course, difficult to obtain balances which were
very accurate: but generally one could be obtained within a
minute after the application of the pressure, and another a
minute or two later, and so on. The operation was repeated
many times, and a number of points for the curve shown
Resistance.
the Carbon Disk of Wdison’s Tasimeter. 117
below were obtained, which, though necessarily somewhat
scattering, were so situated as to render its general form
almost certain. In almost every instance, immediately after
the removal of the pressure the normal resistance was again
measured; and it was found that while time was necessary for
the resistance to reach a minimum after the application of the
pressure, the disk seemed to recover its maximum normal
resistance instantly upon its removal.
“D0
40
20
10
3:00 10 m. 20 m. 30 m. 40 m. 50 m. 60 m,
Time.
Curve showing the relation between Resistance and Time.
After the construction of the curve showing the relation
between time and resistance, and on the supposition that it -
correctly represents that relation, it was easy to know what
the adjustment of the bridge should be at the end of any
given time; and thus the difficulty of that adjustment disap-
peared,
When tested in this way, the curve was found to be correct
within the errors of experiment. ‘The following table exhibits
the resistances after various times, the instantaneous resistance
being called 100. The resistance before the addition of the
pressure of 50 grams was 11:67 ohms, which immediately fell
to 3°52 ohms upon the application of the weight.
7
Om.
118 Mr. T. C: Mendenhall on Edigon’s Tasimeter.
in el Resistance. Deine, Resistance.
MNS coupe saeye 100 1D . ccepecenee
ene ia 966 | 90 |.
1 eh 95-4 | 25
IO aoe cette 949 | SO | ssccesaeeee
EN et bay agit 35
SENSE Be ae ST AQ)’ \ octcodguadeue
eed: fected JE 50 °c cwineseoene
"fot Poe oe yieuoadtn min 60 «sessensee
Pe aie Past vinnie 93°6 10 sac
ee tee sects E we 93°4 SO ccncsoaeeeee
yp eS 93°3 90 icccseneeee
Wate re tatarcens 93°1
It will be seen that the resistance falls a little more than
3 per cent. in one minute, about 5 per cent. in three minutes,
and about 10 per cent. in one and a half hours; and it seems
tolerably certain that even then a minimum is not reached.
In two or three instances the time of continuous pressure was
prolonged to twenty-four hours, the resistance at the end being
slightly lower than at any previous reading. Finally, the
apparatus was left with the weight applied for one week,
No measurements were made during that time; but at the end
the resistance was found to be decidedly lower than it was at
the end of two hours after the application of the pressure ;
and it is especially to be noticed that, on the remoyal of the
pressure, the normal resistance of a week before was instantly
recovered. In this case the pressure applied was 100 grams.
The resistance before the application of the pressure was 11°08
ohms. Upon applying the pressure, it immediately fell to
2°34 ohms. In two hours this had been reduced to 2°10 ohms;
and at the end of a week it was 1:°930hm. Thus in two hours
it was reduced by about 10 per cent.; and after one week it
was again about 10 per cent. lower.
It appears, therefore, that the element of time plays an
important part in the phenomena exhibited by the carbon disk;
and it seems highly probable that this has been one of the
principal causes, if not the chief cause, contributing to the
inconstancy and unreliability of the indications of the tasi-
meter. The experiments made thus far indicate a fair degree
of constancy in its results when this factor is considered. The
writer hopes to be able to make further examination concern-
ing the extent to which all the conditions necessary to its use
may be controlled.
The resistance of carbon under pressure has been made the
Mr. W. J. Lewis’s Crystallographic Notes. 119
subject of investigations recently by Mr. Herbert Tomlinson
and Professor Silvanus Thompson. The conclusion reached
by both is that the diminution of resistance is really due to
the contact between the electrodes ; and it appears that Pro-
fessor W. F’. Barrett has arrived at a similar conclusion, as a
result of experiments made upon a “button of compressed
lampblack.”’ Without knowing any thing about the nature of
these experiments, the writer desires to record his belief that
this theory does not entirely account for the facts stated above.
Besides, it seems a little difficult to understand how so small
a pressure as fifty grams, added to an already existing pres-
sure of about the same amount, can increase the area of con-
tact between a flat plate and a flat disk nearly four times, to
say nothing of the “recovery ’’ which takes place so promptly
upon the removal of the pressure.
XII. Crystallographic Notes. By W. J. Lewis, A.*
[Plate III.] q
(PSE UDOBROOKITE.—A pupil of mine, whilst making
a list of the apatites in the Brooke collection preparatory
to their registration, called my attention to a specimen of
asparagus-stone from Jumilla, Murcia, on which were some
minute black crystals of apparently rhombic symmetry. They
were clearly not hematite, which is frequently found in thin
laminz in the matrix from this locality. The measurements
obtained show it to agree well with the mineral discovered by
Dr. Koch (Groth’s Zeitschrift f. Krys. iti. p. 806), which he
has called pseudobrookite.
The crystals are very small, and consist of simple prisms
with the makrodiagonal pinakoid, strongly striated parallel
to their intersections, and terminated by minute bright dome-
planes (figs. 1 and 2). They have a considerable tendency to
more or less parallel growth; and the opposite planes of the
prism are not, as a rule, accurately parallel. They are brittle,
and seem to haye no good cleavage.
The quantity so far obtained from the specimens in the Cam-
bridge collection is very small (not more than one grain), and
it has been impossible to get a chemical analysis made. A
preliminary examination by Dr. Hugo Miiller confirms, to a
certain extent, the belief that it is identical with Koch’s pseu-
dobrookite. The following table gives the angles observed
and calculated, as also the corresponding angles given by Dr.
Koch:—
* Communicated by the Crystallological Society, having been read
June 3, 1882,
120 Mr. W. J. Lewis’s Crystallographic Notes.
Lewis. Koch.
—_--— ——
Calcu- Observed Calcu- Ob-
lated. means. lated. served.
ram 2549 *25 49(meanofdSbest) 25 51 26 31
| 25 454 (mean of 20)
HB wiirdd Bde (wah 44 6 44 6
ae 69 14 69 2 (mean of 5) 68 50 68 56
es 41 57 *41 57 (mean of 6) 42 20 41 19
me 1 12 71 74 (mean of 6)
me, 108 48 108 42
The development requires us, in my opinion, to take m as
(110). The plane e¢ might conveniently have the indices
(1038); and the elements would then be:—
System rhombic.
D=(010, 011)=29° 5"5; E=(001, 101)=48° 59%6;
F=(100, 110)=25° 49’,
OF a: bi: 'e=1 2/2060 : 1
The mineral is specially interesting, as, from Dr. Koch’s
analysis, it seems to be a compound of ferric oxide and titanic
acid, and to be therefore a dimorphous form of ilmenite. Its
crystal-elements do not approach those of Brookite sufficiently
near to justify us in considering it isomorphous with the latter
mineral. It offers, therefore, a fresh instance of the peculiar
connexion which exists between oxide of iron and oxide of
titanium.
Ludlamite.—In the Brooke collection is a specimen with a
label in Heuland’s handwriting, “ Phosphate of Iron on a fossil,
Stésgen near Linz on the Rhine, new.’ The phosphate of iron
is in minute pale green translucent crystals, haying the charac-
teristic three-faced-wedge habit of ludlamite on the free termi-
nations. The best crystals of Cornish ludlamite, as described
by Prof. Maskelyne, give angles which vary greatly, owing
to more or less parallel growth. The crystals from Stésgen,
although half a dozen different crystals have been tried, have
such imperfect faces that no measurements have been yet ob-
tained which render a comparison with the ludlamite from
Cornwall possible. They seem to have a good cleavage,
which, however, manifests the irregular growth of the minute
crystals by the indefiniteness of the reflexion obtained from
the cleavage-face. They are deposited on the sides of a cayity
in the midst of a small mass of greenish-grey matrix, which
consists of bundles of coralloid structure containing appa-
rently a quantity of the same substance. I hope during the
©
\
,
Mr. W. J. Lewis’s Crystallographic Notes. 121
course of the long vacation to be able to settle definitely the
crystallography of the mineral.
Idocrase—The Brooke collection contains a small crystal of
idocrase, apparently from Zermatt, which has minute planes
adjoining the base which do not seem to have been hitherto
noticed. They are striated, and the measurements obtained
are not good. Using p and p, to denote two of the planes in
a zone with c, and p,, one of the others, the measurements
obtained were cp=6° 3! (best), cp, =6° 19’, and pp,,=9° 26’.
The form (117) is that which agrees best with these measure- ©
ments; the angles required by it being (001, 117)=6°10Y,
and (117,11 7)=8° 422’.
Zoisite.—In the Cambridge collection is a small specimen of
zoisite in small bright green crystals imbedded in calcite.
One of them had terminal planes; and by careful extraction
from the calcite, I obtained a crystal showing four terminal
pyramidal faces. The faces were rough, and deeply striated
parallel to the edge lying in the brachydiagonal plane, so that
the measurements obtained were not good. They agree, how-
ever, sufficiently well with those given by Brégger (Groth’s
Zeitschrift, ii. p. 471); and they have led me to the conclu-
sion that Brooke must have been mistaken in giving the angle
wk=56° 30’, an angle which has been assumed in all the
mineralogical works to give the elements of the crystal.
DesCloizeaux observed a poor dome-plane, of which I seemed
to have doubtful indications, and has given a table of angles
ealeulated from Brooke’s data. The positions of the faces are
shown in the stereographic projection (fig. 3). The angles
given by M. DesCloizeaux are compared in the following table
with those of Brégger and with those observed and calculated
by me. Means of Angles Angles cal-
Calculated. observed adopted by — culated by
angles. Brogger. Dx.
Tbs *58 8 58 94 758 Wie oe 48 28
[sk 1436 14 36
LSS, 63 44 63 35 63 26 63 44
fen 713" 9 73 104 ta<9 (2 282
73 19 (Miller)
sw 56 42 56 524 56 324 55 134
ww, 66 36 66 14 66 55 69 33
pam ADE G2 D4 Bi UO eects 61 1
ww; 55 35 ee) 55 57 57 58
ae 56 75 35 (Miller) 75 438 13 23
wk 57 544 Pes ee ye AUG & oan 6 Tee Rs *96 30
LL, 58 19 60° near (Dx.) aaen 61 3
ei
122 Mr. W. J. Lewis’s Crystallographic Notes.
The plane a is doubtful. The planes & were only measured
on one side of the crystal; and a, possibly a result of repeti-
tions of the opposite / planes, was found on the other side.
The difference in the angles ww,, and ww; given by Brooke’s
data and those adopted by me suffice, I think, to justify my
belief in an erroneous impression as to the prism-plane which
gave the reading 56° 30’. The angles ) s and bw are unmis-
takable, and are those used in determining the elements ; the
remaining angles found by Brégger and myself agree as nearly
as can be expected with those calculated. .
Quartz.—In the Cambridge collection are two crystals of
quartz, each of which has a well-developed plane whose indices
were determined by the late Prof. Miller to be (50,19, 19).
Professor Miller seems never to have published this result ; nor
has any record of the measurement which led to it been found
amongst his papers. I therefore remeasured the crystals, and
obtained an angle which agrees almost exactly with that
required by the indices (50,19,19). The larger crystal is a
broken prism about 40 millim. long by 8 millim. across. The |
face y on this crystal is about 1°5 millim. long by about ‘75
millim. broad, and is smooth and bright. Near the edge [by]
it is slightly rounded. As shown in the diagram (fig. 4), it
has to the left a large rough x plane and a long somewhat
narrow s plane. The 7 plane above y is developed so as to
all but blot out the other terminal planes, and is traversed by
a few horizontal lines, due to repetition of r and some plane
in the zone [ry]. At the extreme top the plane 7 is more
strongly striated, and is penetrated in a perfectly arbitrary
way by small crystals of quartz which are ill developed. In
the zone [z7,] are three minute planes, angular measurement
of which places them in the position s, /, uv. These planes,
however, do not succeed one another in this order, but form
re-entrant angles, uw being that adjacent to 7,, / next, and s
last, and adjacent therefore to l,.. The planes uw and J are
strongly striated parallel to the edge [b,,s|. The planes
observed on this crystal are )(211), +(100), z(221),
y(501919), 6 (8138), s=a(421), 2(42 1), u(6,17,12) or
(5, 14, 10), /(8 10 6).
The smaller crystal is a slender prism about 15 millim. long,
The plane 7 on it is not so well developed as in the former
crystal, and it is considerably more rounded near the edge [by].
The image, however, given by it is quite distinct. The plane
s to the right of y is very largely developed; and # and x
appear as very narrow planes below it. The crystal is a
combination of b(211), (100), 2(221), (5019 19),
v(412), v(16 5 8), and a plane near ¢.
e
aa
Mr. W. J. Lewis’s Crystallographic Notes. 123
The planes observed on these two crystals are given by the
stereographic projection (fig. 5).
Mr. Thomas Davies, of the British Museum, lent me a
erystal which showed a very prominent plane below the s
plane, as also some narrow ones, looking somewhat like stria-
tions, between them. The distribution of the faces on this
crystal is shown by the stereographic projection (fig. 6). It
is acombination of ) (211), (100), (221), s=a(412),
g==2(324), (536), (724), (412), y(15 8 8). ;
Direct observations of ¢ and s’ in the zone [0,, s] were
too little reliable to be of any service. These planes were
therefore determined by observations of the angles they make
with 6 and z,. The plane s’ is somewhat doubtful. The faces
wand n are yery rounded, and no reliable measurement could
be made.
The planes (50 19 19), (824), (536), (724) are not
given by M. DesCloizeaux ; and this is possibly the first time
that their existence has been recorded. The following table
gives the observed and calculated angles for these planes:—
Calculated. Observed.
‘ es 30 234 on the larger crystal.
eee 80 253 1 30 20% on the smaller crystal.
ames OO 15 =) Sk
Pees. 20 O4 28 53
be (0G) 5 33.47 33 57 not good.
| r,u(61712) 88 9 Bile OZ. 6% Bovurgs
Lr,u(5 1410) 38 29 _s
moe. = » 10 19 10 16
Re A cas
mee... . 84 33 35 O near.
ae. D2. 39 52 43
Ba(53-6) .. 50 44 0520
Pe 2 4)... 39.108 39 104
a. 30 42 30 282
2, ree 28 0
[ 194
XIV. On the Dimensions of a Unit of Magnetism in the Elec-
trostatic System of Measures. By R. CLausius*.
fee articles in the June number of the Philosophical
Magazine, respecting my determination of the dimen-
sions of the electrostatic unit of magnetism, induce me to give
some further explanations on the point of view from which I
started in that determination. -
One of the greatest advances of physical science was Am-
pere’s establishment of the connexion between magnetism and
current electricity, and his pointing out that, in respect of its
action, a small magnet can be replaced by a small closed elec-
tric current, of which the quantity and intensity stand in the
following relation to the strength of the magnet:—the pro-
duct of the intensity and the surface round which the current
flows is equal to the moment of the magnet. In consequence
of this principle, magnetism need no longer be regarded as a
peculiar and separately existing agent, but to the word mag-
netism a notion can be attached the definition of which is to
be drawn from electrodynamics.
But then it is evident that this definition must be such as
to correspond with Ampére’s proposition universally, and in-
dependently of the system of measures employed, and not
such that a current and a magnet which are equivalent when
one system is employed become of different values on the em-
ployment of another. On this condition I haye based my
determination of the static unit of magnetism.
Now, with respect to Maxwell’s treatment of the matter, he
has in several passages of his work quoted Ampére’s proposi-
tion as a correct one, without anywhere adding any limiting
remark to the effect that the proposition is to be regarded as
valid only in the electrodynamic system, and not in the elec-
trostatic. His units, however, he has determined in such wise
that Ampére’s proposition is satisfied only in the electrody-
namic system, while in the electrostatic the quantities which
according to Ampére should be equal are represented by ex-
pressions which have different dimensions, and hence their
values are changed in quite different ways by an alteration of
the fundamental units. .
How Maxwell arrived at his formula for the electrostatic
unit of magnetism, which deviates from Ampére’s proposition,
it is impossible to say with certainty, as no explanation about
it is given in his work. Nevertheless, as I have already said
in my previous paper, it can be inferred from the context that
* Translated from the German MS, communicated by the Author,
“4
a
rer
my
ee)
On the Dimensions of a Unit of Magnetism. 125
the way in which he has brought into the calculation the force
acting between an electric current and a magnetic pole deter-
mined the derivation of his formula.
If we suppose given an electric current of intensity 7 pass-
ing along a straight line of infinite length, the force exerted
by the current upon a magnetic pole m at the distance L of
the straight line will be represented by 2imL7’, provided that
zand m be measured in electrodynamic measure. If, then,
each of the three quantities 7, m, and L is a unit of the kind |
of quantity in question, the expression takes the value 2 and
represents 2 units of force. Hence, introducing the formula
of the unit of mechanical force [MLT™], we can write
2\imL-*|=2|MLT 7],
from which follows
lan |=(ML?AT"*],
and, if for [7] we substitute [eI~"],
[em]=[MLT*].
This is the equation of Maxwell’s, cited in my preceding
paper, in which for [{e] he has inserted the expression of the
electrostatic unit of electricity in order to get the electrostatic
unit of magnetism.
It is, however, to be remarked that in forming this equation
the formula of the unit of mechanical force is put for an elec-
trodynamic force, and thereby the equation obtains the cha~
racter of an electrodynamic equation, into which we must not
directly put electrostatic units.
In opposition to this, Mr. Everett says that my equation
derived from Ampeére’s proposition stands, in respect of the
property of being electrodynamic, on a par with Maxwell’s,
But this I must controvert. Ampére’s proposition enunciates
that the forces exerted by-a magnet and by the corresponding
electric current are equal to one another, but does not represent
those forces by any formula. Maxwell’s equation, on the con-
trary, rests, according to the above derivation, upon the intro-
duction of a definite formula for the electrodynamic force,
namely the formula of the unit of mechanical force ; and it is
this circumstance that makes it an electrodynamic equation,
in the sense that it is not suitable for application to electro-
static units, as the determination of the latter rests upon the
representation of a quite different force (the electrostatic force
exerted by two quantities of electricity upon each other) by
the formula of the unit of mechanical force.
In Mr. J. J. Thomson’s article another objection appears, in
126 On the Dimensions of a Unit of Magnetism.
the words “ Mr. W. D. Niven has pointed out to me that the
value given by Clausius for the dimensions of a magnetie pole
does not make the magnetic force between two such poles of
the dimensions of a force, which ought clearly to be the case.”
I cannot understand this objection. In the electrodynamic
system of measures the force between two magnetic poles [ma]
is represented by the formula of mechanical force. Now, if
in the electrostatic system also the force between two magnetic
poles [m,] is to be represented by a formula of the same
dimensions, then must | m,] have the same dimensions as [ mg],
which is no more the case with Maxwell than with me, and
also cannot be the case; while if instead of [m,]| the quantity
is put which I have denoted by v. d. [m,] (the value of the
electrostatic unit of magnetism reduced to electrodynamic
measure), the expression of the force between two magnetic
poles assumes again the dimensions of the mechanical-force
formula. Mr. Niven might have made the same objection
against the electrodynamic unit of electricity as he has made
against the electrostatic unit of magnetism.
J. J. Thomson raises also an objection of his own. He says
that, in determining magnetic force the magnetic permeability
yw of the medium in which the current is placed must also be
taken into account ; and then he adds :—* Thus the force be-
tween two magnetic poles depends on the medium in which
they are placed; but, according to Maxwell, the magnetic
force between a current and a magnetic pole does not.” In
this sentence a distinction is made between the force of a mag-
netic pole and the magnetic force of a current, which is quite
foreign to Ampere’s theory. According to that theory a small
closed current can completely replace a small magnet with
respect to the forces exerted by it upon other magnets or
closed currents, so that it is no longer necessary, in order to
explain the magnetic actions of a body, to assume the presence
in it of a special agent to be designated by the name of mag-
netism, but instead of this we can suppose that the molecules
are encircled by electric currents, and that these exert the
actions in question. It is of course contradicting this to say
that the magnetic forces proceeding from an electric current
act according to other laws than those which govern the forces
proceeding from a magnet.
For all these reasons I must continue to maintain that, if
physicists accept Ampére’s theory (which is certainly done by
most physicists, and, as I believe, was done also by Maxwell),
they must, to be consistent, accept also the formula determined
by me for the electrostatic unit of magnetism, instead of the
formula set up by Maxwell.
XV. On Double Refraction, produced by Electrical Influence, in
Glass and Bisulphide of Carbon. By H. BroncersMa*.
[Plate IV. fig. 5 a-h.]
I
ee phenomena first observed by Kerrt, and described in
his papers entitled “ A new Relation between Hlectricity
and hight,” I have submitted to a reexamination. The im-
portance of the subject, and the failure of the attempts of
yarious physicists to repeat Kerr’s experiments, so far as these
relate to solid bodies, have induced me to undertake this inves-
- tigation.
The willing readiness of the Directors of the “ Teyler’s
Stichting” at Harlem to place an apartment and the necessary
instruments at my disposal has made it possible for me to
accomplish this labour, which, as I hope, has resulted in pro-
ving that the doubt of the correctness of Kerr’s results was
not well founded.
If I mistake not, Gordon was the first who repeated Kerr’s
experiments, and, indeed, in spite of all his carefulness, with
a negative resultf. Ina work published subsequently§, he
returns to the subject. After describing the phenomena which
he had once observed when the glass was perforated by the
spark, he says:—‘“ A fresh glass plate was at once drilled, in
hopes of repeating the experiment in the lecture next day ;
but, owing to sparks springing round, we did not succeed in
perforating the glass, and therefore saw only the faint return
of light described by Dr. Kerr.” The words which I have
italicized make it in some degree doubtful if the phenomenon
observed by Gordon must not be attributed to accidental
causes. I have found that a piece of ordinary plate glass is
rendered doubly refracting only by the electric spark passing
in proximity to it, or when a heated wire is brought near the
late.
: Mackenzie|| also did not succeed in obtaining Kerr’s pheno-
menon. He thought it was produced by heat only.
_ An investigation by Rontgen{] likewise gave negative
results. He also believes that some accidental influences were
at work in those experiments.
* Translated from Wiedemann’s Annaler, 1882, no. 6, pp. 222-235.
+ Phil. Mae. [4] vol. 1. p. 337 (1875).
{ Phil. Mag. [5] vol. ii. p. 208 (1876).
§ A Physical Treatise on Electricity and Magnetism, by J. EH. H. Gor-
don, vol. ii. p. 247.
|| Wiedemann’s Annalen, ii. p. 356 (1877). 4] Ibid. x. p. 77 (1880).
128 M. H. Brongersma on Double Refraction
in a copious memoir*, Quincke briefly touches on this part |
of Kerr’s investigation. He says:—“ In fact, plate glass and
bisulphide of carbon show, according to Dr. Kerr’s observa-
tions, opposite electric double refractions; in my experiments
I found this confirmed for flint glass and bisulphide of carbon.”
After the many negative results attained by others, it is be
regretted that Quincke has not described in detail his method
of experiment with glass, as in the other parts of his inyesti-
gation.
Lastly, Grunmacht did not succeed in observing the phe-
nomenon.
After this I think I ought to communicate my own results,
and the more so since, according to them, Kerr himself has
not seen these phenomena in their whole extent.
In a piece of common plate glass 14 centim. high, 6 centim.
broad, and about 1 centim. thick, two holes about 3 millim. in
diameter were drilled coaxially, parallel with the largest lateral
surface, so that their ends remained 5 millim. distant from one
another. Into each of these openings a small quantity of
mercury was introduced, and then thin-drawn-out glass tubes
were fixed therein with a mixture of shellac and wax, through
which fine copper wires 15 millim. in length were carried till
they reached into the mercury. They were then thickly
coated to their ends, together with a portion of the glass plate,
with the mixture above mentioned. Moreover the plate was
varnished, except at the two places which bounded the field of
view.
Much care was necessary in doing this, in order to ensure
the possibility of obtaining a satisfactory difference of poten-
tial. The investigation had to be interrupted several times,
partly because the insulation was not sufficient, and partly
because the plate was perforated by electric sparks.
The glass plate was set up midway between two nicols 15
and 11 millim. in diameter respectively, so that the incidence
of the light-rays was perpendicular, and the space between the
wires or electrodes occupied the centre of the field. Thelight —
of an albo-carbon lamp (which was placed ina sort of Duboseq
lantern), before passing through the polarizing nicol, fell upon
a lens, so that the real image ot the round aperture of the lan-
tern coincided with the centre of the plate. Afterwards, with
the aid of a second lens, mounted in front of the analyzing
nicol, a magnified image was observed by the eye; and it was
soon found that by this alteration the method was improved.
The electric charge was obtained by means of a Holtz machine,
with the conductors of which the copper wires were connected, —
* Wied. Ann. x. p. 537 (1880). + Ibid. xiv. p. 110 (1881),
: in Glass and Bisulphide of Carbon. 129
In the first experiment the planes of polarization of the
erossed nicols made an angle of 45° with the horizon (first
position). Without a glass plate there was, in the middle
of the field, a dark spot; the borders of the field were not
completely dark. When the glass plate was inserted, there
appeared, principally in consequence of the drilling, pheno-
mena of double refraction as in fig. 5c.
- Soon after the Holtz machine was brought into action the
field changed : first the dark portion between the electrodes
divided into two parts; and two dark tails made their appear-—
ance, which joined the electrodes to one another above and
below, leaving a strongly illuminated space of elliptical form
between them. Gradually these tails receded from each other
at one of the electrodes, the ellipse approaching more to a
parabola. Fig. 5a shows the phenomenon as it appeared
when the difference of potential was the- greatest possible.
After about three minutes’ powerful working of the machine,
the field underwent no further perceptible change; the maxi-
mum action had therefore been attained. After a sudden
discharge the phenomenon vanished, at first rapidly, and then
more slowly; and within three minutes every thing was again
as before the experiment.
Having placed before the analyzing nicol a plate of calc
spar polished perpendicularly to the axis, I saw, on repeating
the experiment, the black cross in the plate change into a hy-
perbola; so that the light must have been elliptically polarized.
When, instead of the calc-spar plate, I took a vertically
compressed glass plate, and slowly increased the pressure, the
tails of fig. 5a approached one another, at last they assumed
the above-mentioned elliptic shape, and with still stronger
pressure the phenomenon disappeared.
If the cale-spar plate was now again placed before the ana-
lyzing nicol without any pressure taking place upon the
_ compensating glass plate, with increasing difference of poten-
tial the black cross, as remarked above, was converted into a
hyperbola. By gentile vertical pressure of the compensating
glass plate the hyperbola was again converted into the black
cross.
If the polarization-planes of the nicols were directed hori-
zontally and vertically (second position), the phenomenon
appeared as in fig. 50.
The phenomena of double refraction with the first position
were seen by Dr. Kerr incompletely ; and he did not succeed
in observing thuse which accompany the second position,
perhaps because his field of view was too small to take in the
whole. By placing the glass lens in front of the analyzing
Phil. Mag, 8. 5. Vol. 14. No, 86. Aug. 1882. K
130 M. H. Brongersma on Double Refraction
prism and mounting the plate movable horizontally and verti-
cally, by which different parts could be successively brought
into the field, I succeeded in improving his method. It is,
however, very possible that the kind of glass used by Kerr
was not without influence upon the result. According to my
experiments a piece of very hard English glass, of the same
thickness (18 millim.) as that employed by Kerr, becomes
strongly doubly refracting in consequence of the drilling.
With it the described phenomena were only faintly shown.
Of other glass plates, some, which in consequence of the
drilling had become much more strongly doubly refracting
than those above mentioned, yielded perceptible but much less
distinct results.
The above is besides in complete accordance with the result
derived by Kerr from his experiments—namely, that glass
under the action of electrical influence behaves like glass which
is compressed in the direction of the lines of force.
The difficulties in this investigation are not inconsiderable.
For it is necessary to make the difference of potential very
great ; and then many a glass plate is perforated by sparks.
Besides this, it is not easy to insulate sufficiently the conduct-
ing connexions. To this must be added that many glass plates
become so strongly doubly refracting in consequence of the
drilling as to be useless for the investigation. This was the
case chiefly with plates whose apertures were drilled with a
metallic instead of a diamond drili, presumably in consequence
of the great pressure attending the employment of the former.
The influence of the nature of the glass I have not yet been
able to observe.
Kerr saw in these phenomena a confirmation of Faraday’s
theory respecting dielectrics. That great physicist already
regarded it as probable that under the influence of electricity
an isotropic body passes into the anisotropic state, so that it
behaves like a doubly refracting crystal. He did not, how-
ever, succeed in confirming this by experiment. Still, in my
opinion, it is not sufficiently proved that these phenomena
cannot be of a secondary order. The motions of the mole-
cules, on their arrangement in a limited portion of the plate,
may have for their consequence a development of heat; and
this, again, may be the cause of the observed double refrac
tion, as Werner Siemens has already experimentally demon-
strated by the heating of the insulating medium of a condenser
accompanying the charge and discharge*. I hope that a con-
tinued investigation will soon enable me to enunciate a defi-
nite view.
‘ * Berl. Monatsber. 1864, p. 614.
wn Glass and Bisulphide of Carbon. 131
ET:
In his subsequent memoirs* Kerr treats of double refrac-
tion of liquids produced by electrical influence. Rdntgen has
repeated Kerr’s experiments. He made use of a larger nicol
than Kerr employed, and by so doing gained the important
advantage of being able to have a better view over the whole.
The results of the two investigations agreed in the main.
Only, with the horizontal and vertical position of the polari- .
zation-planes of the nicol, Kerr observed no or only an
irregular light-phenomenon; while according to Rontgen’s
observations the phenomenon with this position of the nicol
was complementary to that accompanying the first position.
Rontgen, however, appears not to have seen this phenomenon
in its entirety, as will be shown subsequently.
In my experiments a square glass jar 5 centim. broad and
9 centim. high, filled with bisulphide of carbon, was employed.
In the centres of two parallel sides, apertures of about 3 cen-
tim. diameter were made, which were again closed by glass
plates 0-2 centim. thick. The jar was set up midway between
the nicols, upon an ebonite stand, so that the light-rays fell
perpendicularly onto the thin glass plates. Apertures were
also made in the centres of the two other sides, to admit the
electrodes. The latter were tightly screwed on copper wires,
which, inclosed in thin glass tubes, were fixed in the apertures
with sealing-wax. Hach of these copper wires was connected
with one of the conductors of the Holtz machine.
In order to avoid particles of dust, the bisulphide of carbon
had to be repeatedly filtered from a bottle into the experiment-
vessel and vice versa. Finally the vessel was filled with bisul-
phide of carbon from a third bottle.
In the first experiment one electrode was a brass disk of
12-7 millim. diameter and 7:8 millim. thickness, the other a
sphere of 8°5 millim. diameter. The axis of the disk was hori-
zontal ; and its prolongation passed through the centre of the
sphere. The polarization-planes of the nicols were constantly
perpendicular to one another, and made an angle of 45° with
the horizon, and consequently also with the direction of the
lines of force in the centre of the field of view. As soon as
the machine worked, the phenomenon represented in fig. de,
as nearly as possible, was observed. The middle of the field
was brightly illuminated, and mest brightly in the immediate
vicinity of the electrodes, which is not given in the figure.
* Phil. Mag. [4] 1. p. 446 (1875); [5] viii. pp. 85, 229 (1879); [5] ix.
p. 157 (1880).
+ Wied. Ann. x. p. 80 (1880).
132 M. H. Brongersma on Double Refraction
Two black tails issue from the sphere, at points the radii be-
longing to which make an angle of 90°, which is bisected hy
the axis of the disk. ‘Two other black tails issue from the disk,
whose directions at the beginning likewise form an angle of
45° with the horizon. A glass plate placed before the analy-
zing nicol, upon the centre of which the rays fell perpendicu-
larly, had, with an extremely gentle horizontal pressure, the
following influence upon the phenomenon:—With slowly in-
creasing difference of potential, first a small black bow, nearly
in the form of a semicircle, with its centre in the point of the
surface of the spherical electrode where the prolongation of the
disk-axis cut that surface, was observed. Further, this bow
divided into two branches connecting two points of the sphere
with two points of the disk. These branches receded con-
stantly further from one another till at length fig. 5e again
came into view. If the glass plate was pressed somewhat
more forcibly, the two first-mentioned phases of the pheno-
menon, and with still stronger pressure the first only, namel
the black bow, were observed. If the pressure was still further
enhanced, the entire field remained uniformly illuminated,
even when the potential-difference was the greatest possible.
If, with a great potential-difference, the horizontal pressure
upon the glass plate is slowly increased, the same phenomena
follaw in reverse order, from fig. 5e to the above-described
black bow, which is seen to become slowly smaller till at last it
vanishes,
If on the repetition of the experiment without the com-
pressed glass plate the potential-difference is slowly increased,
the same transitions can be remarked, as it appeared to me, as
were observed when a gently compressed plate was employed;
only the first transitions were slight and less distinctly marked,
so that already with a proportionally slight difference of poten-
tial the phenomenon is seen as in fig, 5e, at first faint, but
gradually coming out sharp and clear. If the origin of the
black tails at the sphere be joined to its centre, the angle which
the lines thereby formed make with the horizon, on the poten-
tial-difference diminishing and without a horizontally com-
pressed glass plate, or with the potential-difference constant
and with increasing horizontal pressure upon the glass plate,
becomes smaller; but in no case, not even with the greatest
possible potential-difference, does this angle become greater
than 45°.
If the glass plate was exposed to a vertical pressure, with
increasing pressure the tails issuing from the sphere and those
issuing from the disk removed further from one another, so
that the illuminated intervals at the sides of the electrodes
in Glass and Bisulphide of Carbon. 133
became smaller (as in fig. 5e). At last these tails were com-
pletely squeezed against the electrodes; and with still stronger
pressure they disappeared. With a greater difference of po-
tential they emerge again, to again vanish in consequence of
stronger pressure. Both with horizontal and with vertical
pressure of the glass plate, a slight difference of potential with
gentle pressure has the same effect as a great potential-differ-
ence with stronger pressure. The latter agrees with what was
found by Rontgen.
When I substituted for the compressed glass plate a plate
of cale spar cut perpendicularly to the axis, I convinced myself
that here also the light was elliptically polarized. Before the
machine worked, the coloured rings with the black cross ap-
peared. When the machine commenced working, the latter
changed into a hyperbola; the ends of the two branches
of the hyperbola receded further from each other as the
potential-difference increased.
If the polarization-planes of the nicols were brought into a
horizontal anda vertical position, the phenomenon of fig. 5f
showed itself already at a slight potential-difference ; at a
greater difference it became sharp and distinct. With this
position Kerr did not obtain any evident results, probably
because in his experiments the field of view was too small for
him to see the whole of the phenomenon. But how it was
that Réntgen* saw only the black horizontal line that issues
from the sphere is so much the more inexplicable, as he with
different electrodes, and with vessels of different widths, always
. found the same results. I have repeated this experiment with
electrodes corresponding exactly in dimensions with those em-
ployed by Réntgen. Yet this did not alter the phenomenon,
any more than an alteration of the distance of the electrodes
from 2-7 to 5 millim. In frequent repetitions of this experi-
ment it was always seen by me unchanged ; and even the
results obtained with two spherical electrodes agree with this,
as will be subsequently shown.
With horizontal and vertical pressure upon the glass plate
while it again occupied the previously mentioned position, the
phenomenon was unchanged if the glass was placed so that
the black cross was midway between the electrodes.
When the direction of the pressure upon the glass plate
made an angle of 45° with the horizon, the figure was unsym-
metrical. ‘This is also the case when the nicols are gradually
moyed out of the second into the first position. The figures
then form a transition between fig. 5e andfig.5f. The latter
also accords with Réntgen’s results.
* See fig 5 of his paper.
134 Double Refraction in Glass and Bisulphide of Carbon.
In a further experiment the electrodes were brass balls of
8:5 millim. diameter. With the nicols in the first position
fig. 5g appeared; in the second, fig.5. Horizontal and ver-
tical pressure upon the glass plate had the same effect as in
the first experiment. I obtained completely accordant phe-
nomena also with spherical electrodes of larger dimensions.
If one electrode was a sphere of 14 millim. and the other a
sphere of 8°5 millim. diameter, this made just as little dif-
ference.
At first I thought that a movement of the electricity from
one of the electrodes to the other would have a great influence
upon the phenomenon. This induced me to make the follow-
ing experiments.
Two cylindrical electrodes were placed coaxially. One of
their opposed surfaces was furnished with fine points. Fig. 5d
shows the phenomenon which was observed with the nicols in
the first position. That which appeared with the second posi-
tion was very similar to fig. 5/7.
In the next experiment two thermometers whose spherical
bulbs had an external diameter of 13 millim. were employed
as electrodes, their mercury being conductively connected with
the Holtz machine: thereby neither a dark nor a spark-dis-
charge could take place through the liquid; so that the poten-
tial-difference could be raised very high. The striking-distance
of the machine was now as great as when the condensers were
not connected to the electrodes. The phenomena observed,
both with the first and with the second position of the nicols,
agreed with those obtained with spherical electrodes (figs. 5g
and 5h). Only with the first position of the nicols was the
field illuminated between the electrodes, while the black tails —
at the sides of the electrodes were much less distinctly visible.
With the second position such a difference was not to be per-
ceived. On repeating this experiment with spherical copper
electrodes completely inclosed in glass tubes, I obtained the
same results.
Further, it is noteworthy that the liquid, which in the expe-
riments with uncovered electrodes was constantly in motion,
now remained at rest. Only during a few seconds, as the
machine was beginning to work, were very delicate undula-
tions to be seen when the polarization-planes of the nicols
formed an angle of about 90° with one another, so that the
field of view was feebly illuminated previously.
That with Kerr’s and Roéntgen’s method of experiment a
dark discharge takes place through the liquid was ascertained
by both physicists ; and they deem this fact not unimportant
for the explanation of the phenomena. From the experiments |
aa
Ad
Notices respecting New Books. 135
just mentioned, however, it is evident that such a discharge is
not requisite, any more than a violent motion of the liquid.
That view would also be untenable for this reason, because
we have here to do with elliptically polarized, and not with
depolarized light.
If it is further shown that explanations which rest upon the
hypothesis that electricity may produce these phenomena indi-
rectly, are not confirmed by an experimental investigation, it
becomes more and more probable that we have to do here with _
a hitherto unknown action of electricity on the light-undula-
tions; and then Kerr’s phenomena, as Roéntgen justly says,
acquire an extraordinarily fundamental significance.
I hope soon to touch this subject again.
Harlem, March 1882.
XVI. Notices respecting New Books.
(i) Mathematical Papers by Wiut1am Kinepon Crirrorp. Edited
by Ropert Tucker, with an Introduction by H. J. STEPHEN
SmitH. London: Macmillan and Co. 1882. (8vo, pp. lxx, 658.)
(ii) Mathematical Fragments, being Facsimiles of his unfinished
Papers relating to the Theory of Graphs, by the late W. K. CLIFFORD.
London: Macmillan and Co. (Fol., pp. 22.)
T° those who remember the late W. K. Clifford’s appearance as
a rising mathematician of singularly brilliant promise, one
likely to extend the limits of knowledge in any of the various
fields of Mathematics to which he might be led to apply his powers,
his short career of little more than a decade would seem a mere
dream, but for the substantial evidence of his energy and pro-
ductiveness contained in the thick volume of more than six
hundred octavo pages (one third consisting of matter in close type)
which we have here to notice. And it is to be borne in mind that
the publication of this volume has been preceded by the collection
of two volumes of Lectures and Essays produced subsequently to
Clifford’s removal from Cambridge to London in 1871. The former
publication (of more popular matter, but handled invariably with
characteristic scientific precision and freshness), together with
the collection which forms the subject of the present notice, may
interest (and they are deeply interesting) from either of two points
of yiew,—one of which has occupied the pen of Prof. H. J. 8.
Smith in a masterly Introduction ; and the other will be more par-
ticularly here dwelt on—the study of the growth of a singularly
gifted genius as it derived fresh aliment from extended acquaint-
ance with the work and speculations of kindred minds, and visibly
waxed stronger and stronger in its own powers by their exercise on
problems of ever increasing height and subtlety.
136 Notices respecting New Books.
The absence of any kind of arrangement of these Papers with
reference either to subject or date is much to be regretted—* tan-
tum series juncturaque pollet.” For the absence of chronological
order an apology is offered in the Preface; and some amends
are made by a chronological Table therein drawn up, which
rather serves to show that the apology might have been rendered
needless, as far as any difficulty in assigning, with at least approxi-
mate accuracy, their dates to the few doubtful papers. At all
events, the chronological order of the greater part is clear of doubt;
and had this order been followed, the effect, on a reader able to fol-
low intelligently and appreciatively the matter of the Papers, would
have been a sense of harmonious development of an almost unique
genius among the English mathematicians of his generation.
Thus, in the earliest papers (contributed to the three leading ma-
thematical serials of this country, and covering the period from
1863 to the completion of his undergraduate career, with the next
year or two) reference is made to the higher geometrical text-books
only, which occupy the attention of the candidate for a good place
on the Tripos: they contain no strikingly new results, but rather re-
produce, with extensions and novelties of algorithm, results already
known. ‘These papers are of an exclusively geometrical character.
During the three or four years intervening between taking his
degree and his removal] to London (1871) his mathematical commu-
nications were made to the Cambridge University Philosophical, and
London Mathematical Societies, or to Section A of the annual British
Association Meeting—the one exception being a geometrical paper
commenced in the ‘ Messenger,’ October 1869 (erroneously assigned
to 1870 in the chronological list), in which he urges the greater
cultivation of the methods of Synthetic, or Organic, Geometry ;
and, drolly enough, makes a reference (no doubt second-hand) to
St. Thomas Aquinas, of all authorities on a geometrical question !
Among these papers occur two purely analytical:—the “ Proof
that every Rational Equation has a root” (which attracted much
attention at the time), and the closely connected (though separated
by some 140 pages in the reprint) “‘Case of Evaporation in the
Order of a Resultant.” In both these papers the subjects are treated
with a masterly conciseness. The ‘‘ Lecture Notes,” drawn up, as
we are informed, for tutorial lectures at Trinity College, Cambridge,
in 1870, show a gradually extended course of reading. They com-
mence with the emphatic words “Geometry is a physical science”
(probably adopted from Mill, ‘Logic,’ ch. xxiv.); and in them
Riemann is for the first time quoted—a mathematician whose
short but brilliant career of Professor Extraordinary at Gottingen
had terminated in 1866, after a few years of struggle against the
disease which was sapping his life, as, a few years later, it was to
lay Clifford in his grave. There is pervading these “ Notes” a
strong flavour of Hankel’s Vorlesungen iiber die complexen Zahlen
(1867), which probably accounts for the references to Riemann,
Gauss, Argand (otherwise a name almost unknown to mathema-
Notices respecting New Books. 137
ticians of the present generation, but whom Hankel characterizes as
the true founder of the method of representing a complex geome-
trically), Cauchy, and Grassmann.
The years 1871, 1872 produced only five short Mathematical
Papers, the most considerable being an extension to tridimensional
space of a plane theorem of the late Mr. Cotterill’s. In the Editorial
note to the first of these (p. 234) “nodal conic” should be “ nodal
cone.” In 1873 appear evidences—from his translation of Riemann’s
Essay ‘‘ on the Hypotheses which lie at the basis of Geometry,” and
the “ Preliminary Sketch of Biquaternions ”—of Clifford’s thoughts ~
having been directed to speculation on hyper-dimensional space,
a subject reverted to in a succession of papers down to the close
of his career—the last being the unfinished ‘ Classification of Loci”
(Phil. Trans. 1878). On the whole of this subject Prof. H. J.S.
Smith’s masterly analysis will be the reader’s best guide. To the
same year belongs the first of his two contributions to the Phil.
Trans., “On Mr. Spottiswoode’s Contact Problems.” The year
1874, though one of great activity in other scientific directions,
produced no published mathematical papers ; the abstracts of his
communications to the British-Association Meeting showing that
Clifford took his part in the Peaucellier “ revival” of the period,
and in following up the idea of bringing Chemical Equations under
a general formula.
The published mathematical papers of the next three years were
contributions to the Mathematical Society’s ‘ Proceedings,’ those
which attracted most attention being :—(1.) “ On the Transforma-
tion of Elliptic Functions” (1875)—suggested by a paper of
Dr. Liiroth’s in the Mathematische Annalen, Bd. I.,—followed by
* Notes” thereon (1876), in which Darboux’s priority both in
matter and method on certain points is acknowledged and the
geometric proof of the transformation-formule is restated and
completed ; (ii.) “ On the Canonical Form and Dissection of a Rie-
mann’s Surface ”—a most characteristic example of Clifford’s powers
in its kind. But these three years produced many papers left
incomplete by the author and now printed as left. Some, which
are mere fragments, were apparently the commencements of papers
to be offered to the Societies or Mathematical Journals ; others are
more probably compilations to form the bases of courses of
Lectures planned, but destined never to be carried out. A
singular and doubly melancholy contribution to the volume is the
late Miss Watson’s series of notes of the course of Lectures on
Quaternions which, as a student of University College, London,
she attended. This was probably the first imstance of public
instruction in Quaternions offered in England. In Edinburgh it
has been for some years a recognized subject in the Mathematical
Curriculum, having been introduced by the late Prof. Kelland and
by Prof. Tait—the most skilled adept in the method among
English mathematicians, and whose elementary Treatise has been
the source whence most of the younger mathematicians who have
138 Yotices respecting New Books.
paid attention to the method have derived their first knowledge of
its principles. It is one of the losses which University College,
London, has most to lament in Clifford’s death, that with him
has apparently died the effort to establish the elements of Qua-
ternions in its Mathematical programme. Strangely enough, in
France, too, the most flourishing School of Quaternions is not to be
found in Paris, but in the provincial Faculty of Bordeaux. Apart
from the interest of their authorship, it might be a question
whether Clifford would have wished these Lecture Notes to have
been published among his own papers. Whatever there is novel
in the treatment is probably incorporated in his ‘ Dynamic ;’ and a
cursory examination of a page or two indicates the necessity of a
revision of the Notes by some one conversant with the subject.
Thus at p. 502, “a point of no velocity” is an error for “no
acceleration,” and the whole paragraph is a corollary to one in the
following page; wherein, again, a reference to “ equation (2) ”
should be a reference to another equation not numbered, just
above. Such errata as O for O are either typographical or con-
sequences of the hurry of note-taking.
Of much more general interest will be the unfinished “ Algebraic
Introduction to Elliptic Functions,” in which, though Prof. Smith
finds that it “contains no new results and perhaps no original
methods of investigation,” the most recent contributions to the
subject by Rosenhain, Konigsberger, Schréter, Gopel, Cayley, and
Smith had been incorporated. This “ Introduction ” was probably
drawn up with immediate reference to his intended course of lectures
in University College. The third most considerable paper in the
Appendix, ‘‘On Power Coordinates in general,” should certainly
have been preceded by the Notes on the Theory of Powers
which follow it. The remarks (p. 555) with which the Editor
has introduced these ‘ Notes’ are very unfortunate : if ‘ they are,
in places, apparently inaccurate” and “it is not easy to see how
the equations in (1) and (4) are got, nor how the other equation
in (1) contains a linear relation between the powers of a point
with respect to a &c.,”—of course cela dépend; but if Mr. Tucker
had referred his difficulties in this case, as he did in others, to any
of the many mathematicians who would gladly have cleared them
up, it would have been pointed out to him that the results are
perfectly accurate to a factor pres (as it might have been expected
any such work of Clifford’s would be), and that the last equation
_in (1) has the significance assigned to it. In the last equation but
one of (4) as printed there is certainly an erratum of the sign (—)
for (x); but this would probably not be found in the MS.
Of great interest is the collection of Problems and Solutions
from the ‘ Educational Times ;’ and it appears that there is still
a goodly number of Questions proposed by Clifford remaining
unanswered, the solutions of some of which would perhaps be
found, in substance at least, among the Papers and Fragments now
for the first time published.
_
=
*
Notices respecting New Books. 139
It would be vain to attempt to convey in a cursory notice any
adequate idea of the contents of the thin folio of lithographed
facsimiles of the fragments on ‘“ Graphs,” a subject which formed
one of Clifford’s communications to the ‘ Proceedings’ of the British
Association in 1875, ‘‘ On the Graphical Representation of Inva-
riants.”
To those who are acquainted with Clifford’s mathematical papers,
it is needless to remark how invigorating, disciplinary, and sugges-
tive the study of them is—and that they are for the most part by
no means easy of reading, but, on the contrary, require a good
deal of hard work on the part of the reader to cover with shorter
steps the long strides with which he gets over his ground. The
reader of this collection is deeply beholden to Prof. H. J.S. Smith
for the lucid and helpful analysis of the contents with which he has
introduced them, and to Professor Cayley for his elucidatory notes
to many of the posthumous papers; also to Mr. Spottiswoode,
P.BS., as well for similar assistance as, we believe, for his liberality
in undertaking the cost of lithographing the Fragments on Graphs.
The labour which Mr. Tucker has contributed as editor it is super-
fluous to point out; and the circumstances which induced him to
undertake so heavy and responsible a charge are explained in the
Prefatory Letter. It is the best return we can make an editor
for such labour in our behalf, to point out whatever imperfections
and errata come under observation, for amendment in the Second
Edition, which the interest likely to be taken in this collection may
be expected to call for ere long.
[By the Editors’ kindness I have been permitted to see the
above Review in “ proof,” and to append to it the few remarks
which follow. ‘ Triangular” symmetry, I need hardly say, is
Clifford’s own title to his paper, though in line 9 he writes, “I call
eae rectangular symmetry.” In the Bibliography I state that
the lower date of publication is given: the Reviewer is no doubt
aware that alterations are frequently made by authors in their
papers in the interval which elapses between composition and pub-
lication: I think, but I am open to correction, that the paper (viii.)
was not published in its entirety until 1870. The Reviewer implies,
in writing of my remarks on p. 555, that I made the arrangement
without consulting any one else; but I can assure him that these
two papers were submitted to the, I believe, careful consideration
of one of my four referees; and it was on his advice that I took the
course I adopted and wrote the “very unfortunate” remarks. I
am now able to say that my difficulties have been cleared up, or
nearly so, by a young mathematician who is working on some of
Clifford’s les. For a second edition, if such should be ealled for,
the Reviewer’s remarks, and any further ones he may be willing to
send me, will be most acceptable.—R. TUCKER. ]
140 Notices respecting New Books. .
A Treatise on the Theory of Determinants, with graduated Sets of
Exercises for use in Colleges and Schools. By THomas Mutr,
M.A. Macmillan: London, 1882. (Pp. vi+240.)
THE subject of Determinants is every day coming more and more
to the front. As evidence of this we may instance the recent
works of Mr. Scott and Mr. W. Thomson, and the chapters in
Messrs. Burnside and Panton’s ‘Theory of Equations.’ Students are
no longer shut up to the advanced works of the masters in the
science nor restricted to the small morsels dealt out in two or
three of our algebraical textbooks.
In France M. Dostor has recently brought out his Hléments
de la Théorie des Déterminants avec application a U Algébre, la
Trigonométrie et la Géométrie analytique dans le plan et dans
Vespace; and in this country Mr. Muir, who has done so much
good original work, now puts forth the excellent text-book under
notice. Without going into any lengthened detail, we may say
that the Author does not touch upon the Geometrical applications
of Determinants; perhaps he considers that these have been dwelt
upon with sufficient fulness elsewhere, and is only anxious to
provide his readers with a full Algebraical imtroductory treatise.
The first two chapters dwell at considerable length upon Deter-
minants in general; but the third chapter treats much more
concisely of the various forms known as Continuants, Alternants,
Symmetric and Skew Determinants, Pfaffians and other Deter-
minants. Much of this chapter is the Author’s own work; and
the whole of it is very suggestive in its treatment. There is
apparently much of discovery still in store for the careful worker
in this corner of the mathematical field. Ample practice is
furnished for the reader in a capital collection of Exercises, to which
answers are appended at the end of the book. The fourth chapter
contains a slight historical sketch: this is interesting; but we are
inclined to regret that regard to space prevented Mr. Muir from
extending it. However, he has made some amends by the publication
in the ‘ Quarterly Journal of Mathematics’ (Oct. 1881) of a “ List
of Writings on Determinants ” (1693 to 1880), which was originally
drawn up for the present work. We have noticed only a few errata
and afew obscurities of expression. These can be removed ina
second edition, which will no doubt be soon called for. Could not
the work then be printed in a form better adapted for the
numerous lengthy formule ?
(Ra aes
XVII. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from p. 74.]
May 10, 1882.—J. W. Hulke, Esq., F.R.S., President,
in the Chair.
HE following communications were read :—
1. “On the Relations of Hybocrinus, Baeroerinus, and Hybo-
cystites.” By P. Herbert Carpenter, Esq., M.A.
2. “On the Madreporaria of the Inferior Oolite of the neigh-
bourhood of Cheltenham and Gloucester.” By R. F. Tomes, Esq.,
F.G.S.
3. “On the Exploration of two Caves in the neighbourhood of
Tenby.” By Ernest L. Jones, Esq.
4. “Note on the Comparative Specific Gravities of Molten and
Solidified Vesuvian Lavas.” By H. J. Johnston-Lavis, Esq., F.G.S.
From some experiments made on Vesuvian lava, Prof. Palmieri
in 1875 expressed the opinion that its specific gravity, when molten,
might be as high as 5-0, though when cooled it is only 2°7. The
author described the results of experiments made in December 1881
on some lava flowing across the Atrio del Cavallo. Favourable cir-
cumstances enabled him to gain a position above a perfectly molten
stream, the surface of which was protected from radiation by the
heated walls of a tunnel which the lava had already formed by
cooling of the crust. Onto this were dropped, from a height of
13 yard :—(a) light scoria; this floated on the surface until lost to
view (the stream could be watched for 150 yards or so) ; (6) fairly
solid lava, with some vesicular cavities; this slowly sank, until
after some distance it disappeared ; (c) the most compact lava that
could be found, in which, however, were a few small cavities; this
sank rapidly, the molten rock welling up round it. The author
considered that these experiments demonstrate that the cooled lava
is more dense than the molten, and that the apparently contra-
dictory results obtained by Prof. Palmieri were due to the fact that
the surface of the stream, by loss of heat, had become viscid, so
that the solid material floated, though of greater density. The
author concluded by citing other confirmatory evidence of his view.
May 24.—J. W. Hulke, Esq., F.R.S., President,
in the Chair.
The following communications were read :—
1. “On the Geology of Costa Rica.” By George Attwood, Esq.,
F.G.S., F.C.S., Assoc. Memb. Inst.C.E.; with an Appendix by W.
H. Hudleston, Esq., M.A., F.G.S., F.C.S.
The author commenced his journey at the town of Punta Arenas,
142 Geological Society:—
on the Gulf of Nicoya. This stands on a peninsula composed of
a calcareous sandstone, covered by a dark sand consisting of quartz
grains, magnetite, and decomposed felspar and augite. Inland is an
igneous rock which occupies, before long, both banks of the Rio
Barranca, and on the left bank extends to the sea; it is a greenstone
containing porphyritic crystals of augite and triclinic felspar, and
appears to contain too much silica for a true dolerite, being rather a
representative of one of the more basic forms of the augite-andesites,
resembling, in some respects, specimens from the English lake-dis-
trict described by the late Mr. Clifton Ward. On this rock, after
a time, are found boulders of a black augite-andesite; this appears
to be identical with the rock found in situ in the Aguacate Moun- —
tains. Here are gold- and silver-mines, which were described. In
the ravine of the Rio Grande lignites are found. Below this is a
series of ancient lakes, which on the Pacific slopes have been tapped
by the Rio Grande, on the Atlantic by the Rio Reventazon. Here
also the country rock is the greenstone already described ; and near
Cartago there are boulders of trachyte. The volcano of Irazu is a
trachyte, probably a quartz-trachyte, forming an important building-
stone. Augite-andesites are found at La Palma, about twelve miles
N.W. of the volcano. Irazu, a voleano at present passive, but with
blow-holes of gas, is between 11,000 and 12,000 feet in height.
Turrialba, of about the same elevation, is still feebly active.
The author is of opinion that the filling of the mineral lodes
(ancient fissures) in the Aguacate Mountains took place in Tertiary
times, probably Pliocene, and that this infiltration was contempo-
raneous with the eruption of the augite-andesites in the same region.
The quartz-trachytes and sandstones are certainly post-Tertiary.
2. “On a remarkable Dinosaurian Coracoid from the Wealden of
Brook in the Isle of Wight, preserved in the Woodwardian Museum
of the University of Cambridge, probably referable to Ornithopsis.”
By Prof. H. G. Seeley, F.R.S., F.L.S., F.G.S8., &e.
3. ‘ On the Newer Pliocene Period in England.” By 8. V. Wood,
Esq., F.G.S. (Concluding Part.)
In this part the author continued, from the first part of the paper
(published in the Journal of the Society for 1880), his examination of
the conditions which accompanied the emergence of England during
the retreat of the ice of the Chalky Clay, and described the damming-
up of the valleys which drain to the Wash by that ice after the
water-partings between their systems and those of the Severn and
Thames had emerged, whereby the fresh water in these valleys was
raised, so as to overflow the minor water-partings within their sys-
tems and cover them with gravel, such as that at Casewick, within
the Welland system (described by Prof. Morris in yol. ix. of the
Journal), and those of Cambridgeshire, described by Mr. Jukes-
Browne. He referred the freshwater bed at Casewick, covered
by this gravel, and the paleolithic brick-earth of Brandon and
Mildenhall (which is overlain as well as underlain by the Chalky
Clay) to the time immediately antecedent to this—the slight advance
On the Newer Pliocene Period in England. 143
of the ice which thus blocked up and raised the water-line within
the systems of the Welland, Nen, Ouse, and Cam having overridden
this brick-earth and covered it with the Chalky Clay.
He then described the gravel (f of his figures) of the Thames
valley, and showed that it was the continuation of the gravel previ-
ously described by him as synchronous with the Chalky Clay, and
which, as described by him in the first part of his paper, was over-
lain, and also wnderlain by that clay, it inosculating with those
gravels, up the valleys of the Lea and (Middlesex) Colne.
He then described the Cyrena-fluminalis formation, which he
showed as originating in a depression which raised the water-line in
the Thames valley at Grays and Crayford to about 100 feet above
the present sea-level, and proportionately higher on the west of
London ; and described the formation as consisting, at Grays, of four
divisions, which in their upward order he called 1, 2, 3, and 4,—
No. 1 being the gravel base, No. 2 mostly brick-earth with freshwater
shells, No. 3 yellow sand containing freshwater shells in the lower
part, but unfossiliferous and false-bedded in the upper, and No. 4,
a clay or loam, also unfossiliferous.
These, he showed, are mutually transgressive, both at Grays and
at Clacton, No. 3 at Clacton becoming estuarine by the intermixture
of marine shells with the Cyrena, and No. 4, a loamy gravel which is
unfossiliferous, while, from its greater transgression, No. 4 spreads
so widely over the gravel f that remnants of it occur at Slough,
West Drayton, and other places. He then traced the formation north-
wards in Suffolk; and from the Cyrena not being associated there
with other than freshwater shells (except at Gedgrave, where the
marine shells associated with it are derivatives from the Crag), he
inferred that the depression did not bring the sea into Suffolk or Kast
Norfolk. In West Norfolk and around the Wash, however, it did
so, the Cyrena being associated with the marine gravel at March.
The evidences of this depression bringing in the sea around the
Wash (which consist of the Nar brickearth and the gravel of
Hunstanton, March, and other places in the Fen country with
marine shells) extend to about 30 feet elevation. This gravel
at Overton, near Peterborough, passes down into a bed with
freshwater shells only, thus resembling the Clacton bed, and at
March contains the Cyrena in abundance. Northwards the for-
mation is represented by the Cyrena-gravel of Kelsea Hill, in Hol-
derness; and the evidences of depression rise in that direction to
near 100 feet, as a brick-earth, at Kirmington in North Lincoln-
shire, at between 80 and 90, containing mammalian remains ‘and
Scrobicularia piperata, with valves united, is regarded by the author
as part of the formation; and he instanced the ripple-marked pan
beneath this formation at Hessle as evidence of redepresssion or
transgression similar to that afforded by the Mollusca at Overton
and Clacton. He then described this gravel as extending up the
vales of York and Tees to about a similar elevation, and as passing
in them, as it doesin Holderness, under the clay of the minor glacia-
tion. Southwards he traced the formation as represented by the
144 Geological Society :—
shingly sand and gravel of Avisford and Bourne Common in Sussex—
the Selsea mud-bed with Lusitanian shells, near the present sea-
level, representing the first part of the formation, which the depres-
sion carried transgressively to Avisford. In the Thames and lower
Lea valleys he described, and showed, by many lines of section, how
considerable a denudation accompanied the rise from this depression,
so that not only most of the formation but also much of the gravel
f, of glacial age, on which the uppermost bed of this formation
rested, was washed away, the latter having for a great distance been
left on an escarpment facing the valley-sides. This denudation, he
showed, was in the same places repeated after the formation of the
gravel of the minor glaciation.
He then, under another division of the period (which he distin-
guished as that of the minor glaciation or reindeer age), described
the various formations, morainic, atmospheric, fluviatile, and marine,
due to a return of glaciation after England had, except in the
north-west, become all land. ‘The morainic part in the north-west
(which was the Upper Clay of Lancashire and adjoining counties) he
regarded as extruded beneath the sea up to that level at which it
contains shells, these having been dropped from floe-ice detached
from the shores, which drifted over it while thus undergoing extru-
sion; but in the north-east it was terrestrial, owing to this part
having emerged from the depression of the Cyrena formation before
the moraine reached Holderness, and therefore it contained no shells.
The ice giving rise to this moraine was of far less volume than that
of the Chalky Clay, and instead of seeking the sea as that did, when
the sea lay over the centre and south of England it passed to it in
its present position, one stream of it going straight out through the
Tees valley, and another down the vale of York and out by the
Humber, so as to overspread southern Holderness and the sea-board
of Lincolnshire. The fluviatile formation of this minor glaciation
is the gravel which overlies the Cyrena formation at Crayford and
Ilford (Uphallfield) up to the elevation of about 30 feet, and at
similar elevation lies up to the foot of that formation at Grays; and
it is that which forms the 40—45-foot terrace at Acton, where it
has yielded reindeer-remains. Owing to the rise from the depres-
sion under which the Cyrena-formation accumulated, which had
taken place when this gravel was formed, its level does not differ
greatly from that of the fossiliferous part of the Cyrena formation at
Grays and Crayford, so that in more inland districts, as at Oxford,
the two, though quite different in age, may be undistinguishable.
This gravel the author regarded as corresponding in position with the
beaches of the buried cliffs of Sangatte, Brighton, Isle of Wight,
Portland, and Sili Bay, these beaches and the gravel having originated
during a pause in the rise from the depression of the Cyrena forma-
tion. The floe-ice of this glaciation, driven onto these beaches, left
blocks on them, which becoming mixed with loam from rills pouring
in summer over the cliffs, is covered by the atmospheric formation
which accumulated as, by renewal of emergence, the sea receded from
these beaches. At the same time floes grounding on the Pagham
On the Newer Pliocene Period in England. 145
J
and Selsea flats, which, in correspondence with the shingle of the
Isle-of-Wight beach, were then submerged about 30 or 40 feet
below their present level, left the great blocks found in the clay-
gravel of Pagham and Selsea, which was then forming, and which
overlies the mud-bed with Lusitanian shells, and is itself overlain
by the atmospheric formation. He also showed by a line of section
that this gravel occupies a position several hundred feet below that
which the gravel of the great submergence and major glaciation oc-
cupies in the adjoining parts of Hampshire.
The atmospheric formation of the minor glaciation he regarded as
the brick-earth with angular fragments of stone and splintered flints
overlying the buried cliffs and their beaches. This is the “ formation
of great submergence ” (with land shells and Mammalian remains) of
Prestwich, and identical with the ‘‘ warp” of Trimmer and “ trail” of
Fisher in other parts of England. The origin of this he referred to
an annual thawing of the upper layer of the permanently frozen land-
surface, such as takes place in arctic countries net occupied by land-
ice, such as Siberia. Owing to the subsoil being permanently frozen,
no water can penetrate it, so that the thawing surface-layer becomes
sludge from the snow-melting and rainfall of summer, and slowly
slides from higher to lower places, thus exposing on the higher a
continually renewed superficial portion of the permanently frozen
soil to this action, and accumulating it in the lower. In sliding, this
material has collected not only the bones of animals such as the
reindeer and mammoth which lived on this surface, but also those
of the hippopotamus, which did not, but had lived during the Cyrena-
formation stage, from superficial deposits of that stage (from which
also they got by derivation into the gravel of this glaciation), in
illustration of which he refers to Siberian rivers now receiving the
remains of the extinct mammoth and living reindeer alike.
Penetratiug fissures in the rocks, this material has formed the
amorphous Caye-earth of the districts beyond where the moraine has
reached; and the author pointed out that, stalagmite being due to
percolation, none could form while the subsoil was thus permanently
frozen, which is the reason why the Cave-earth is devoid of it,
though always covered by it and sometimes underlain by it, such
underlay probably showing that the caves where this occurs were
not submerged at the commencement of this minor glaciation.
After giving various reasons which appeared to him to show that
the passing away of the minor glaciation took place while Lancashire
was still submerged up to an elevation of from 20 to 30 feet, but when
the east and south of England was at a somewhat higher level than
at present, he described a bed of flattened stones which cover all
anterior beds alike in the limestone districts of the south of Lincoln-
shire, and some gravel with flattened fragments of hard chalk in
North Lincolnshire and Holderness, which appear to him to indicate
a flooding of the country after the termination of this glaciation.
The author then offered some remarks on the coexistence of arboreal
yegetation with the land-ice of the first or great glaciation at the
| Phil. Mag. 8. 5. Vol. 14. No. 86. Aug. 1882. L
146 Geological Society:—
time when it uncovered the plateaux of Norfolk and Suffolk, appeal-
ing for the probability of this to the condition of South America,
where the inland ice passes in glaciers to the sea in the Straits of
Magellan and adjoining channels through dense forests. He also
pointed out that the evidences of the Newer Pliocene period, as traced
by him, lend no support to the climate-theories of Dr. Croll, Mr.
Wallace, or Mr. Murphy, but, on the contrary, conflict with them,
as do the respective extensions of the areas of glaciation in Western
Europe and Eastern America, while they are equally repugnant to
any theory of climate based on changes in geographical conditions ;
and he concluded by insisting on the British origin of all the ice
connected with either glaciation in England, and on the existence
of an open north sea throughout.
June 7.—J. W. Hulke, Esq., F.R.S., President, —
in the Chair.
The following communications were read :—
1. The President read the following note, forwarded by Don
Manuel F. de Castro, Director of the Geological Survey of Spain :—
“On the Discovery of Triassic Fossils in the Sierra de Gador,
Province of Almeria, Spain.”
«‘The metalliferous limestone of the Sierra de Gador, owing to no
fossil remains haying been found prior to this occasion, has been a
perfect puzzle to all geologists for the last fifty years.
“MM. Maestre, Amar de la Torre, Pernolet, Ansted, and Cooke
considered these limestones to belong to the Transition series, the
former taking it as a representative of the Mountain Limestones of
other parts of Hurope. M. Prado hinted that they might be De-
vonian ; whilst M. Willkomm,.in the geological map published to
accompany his botanical researches in Spain, considered them Silu-
rian, Lately MM. Botella and Vilanova, in their respective maps,
have marked them as belonging to the Permian series; whilst M.
de Verneuil, coming nearer to the truth, took the whole of the lime-
stones to the south of Granada and the Sierra de Gador as Triassic,
though in doubt (‘ Trias incertain ”).
‘Under these circumstances, I was commissioned by the Director
of the Geological Survey of Spain to investigate the S.W. portion of
the Province of Almeria, which comprises the Sierra de Gador. In
February last I had the good fortune of discovering abundant fossil
remains in different parts of the Sierra de Gador, which perfectly
fix the age of the metalliferous limestones of this part of Spain.
«‘The whole series of rocks forming this sierra, resting on the
mica-schists and slates of the Sierra Nevada, is a succession of black,
white, and purple talcose schists at the base, which alternate with
some beds of yellowish and porous limestone, and which pass
through a considerable thickness of grey limestones and slates, and,
precisely where the fossils have been found, to the metalliferous
limestone of Sierra de Gador, which appears to form the top of this
interesting formation.
“The fossils found belong to the following genera :—J/yophoria
Prof. C. Lapworth on the Girvan Sucession. 147
(M. levigata and M. Goldfussi), Hinnites, Monotis, Avicula (A.
Bronni), Myacites, Rissoa, and many others difficult to determine.
*« The places where the fossils have been found are the following :—
on the southern slopes of the Sierra de Gador, in the Rambla del
Canuelo; midway on the road from Felix to Marchal ; and in the
place named La Solana del Fondon, to the left of the river Andarax,
following the track between the mine Sebastopol and the town of
E] Fondon. * Joaquin Gonzato y XAVIER.”
2. “The Girvan Succession.—Part I. Stratigraphical.” By
Charles Lapworth, Esq., F.G.S., Professor of Geology in the Mason
Science College, Birmingham.
The Lower Paleozoic rocks of the neighbourhood of Girvan, in
the south of Ayrshire, have long been famous for the remarkable
variety of their petrological features, and for the abundance and
beauty of their organic remains; but the strata are so intermingled
and confused by faults, folds, and inversions, that it has hitherto
been found impossible to give a satisfactory account of the geological
structure of the region.
The most remarkable formation in this Girvan area is a massive
boulder-conglomerate, several hundreds of feet in thickness, which
forms the high ground of Benan Hill, and ranges throughout the
district from end to end. Employing this formation as a definite
horizon of reference, the author showed, by numerous plans and
sections, that it was possible for the geologist to work out the
natural order of the strata, both above and below this horizon, and
to construct a complete stratigraphical and paleontological scheme
of the entire Girvan succession. This succession is composed of the
following members, arranged in descending order :—
(1.) Upper Girvax Rocks.
(D.) Dattty Series (1500 to 2000 feet), including the
(3) Straiton Group, consisting of grey flags, shales, and grits,
with Beyrichia Kledeni, Cardiola, &e.
(2) Bargany Group, of pale flagstones, shales, and mudstones,
with Retiolites Geinitzianus, Cyrtograpius Grayi, &e.
(1) Penkill Group, of purple mudstones, grey flags, and grey-
wackes, with Crossopodia, Protovirgularia, &e.
(C.) Nzwzasns Serres (1000 to 1500 feet), embracing the
(8) Camregan Group &c., of yellow thick-bedded grits and
dark shales, with a band of caleareous rock ; abounding in
Pentamerus oblongus, Atrypa reticularis, Rastrites maximus,
and Monograptus Sedqwickit.
(2) Saugh-Hill Group, composed of alternations of coarse
pebbly grit and zones of grey and black shales, with a
coarse conglomerate at the base. Its commonest fossils
are Stricklandinia lens, Pentamerus oblongus, Favosites
gothlandicus, Monograptus leptotheca, &e.
(1) Mulloch-Hill Group, ee of shelly sandstones underlain
2
148 Geological Society:—
by a coarse boulder-conglomerate, and containing hosts of
Brachiopoda &c., chiefly Meristella angustifrons, Atrypa
hemispherica, Nidulites favus, &e. o
(I1.) Lowrr Girvan Rocks.
(B.) Anpuriiay Serres (1800 to 2000 feet), embracing the
(4) Drummuck Group of soft grey mudstones &c., with Trinu-
cleus seticornis, Ampyx, Staurocephalus, Dicellograptus, &c.
(3) Barren or Shalloch Flagstones.—A great thickness of alter-
nations of grey or green flagstones and shales, generally
destitute of fossils. ‘i
(2) Whitehouse Group.—Purple and green shales and mud-
stones, striped flagstones and calcareous beds, with Dionide,
Dindymene, Atglina, Agnostus, Dictyonema, Dicellograptus, —
and Pleurograptus.
(1) The Ardwell Group of dark Graptolitic flagstones and
shales, with occasional fossiliferous seams affording
examples of Dicranograptus, Leptograptus, and Climaco-
graptus, &e.
(A.) Barr Serres (800 to 1000 feet), composed of the
(4) Balclatchie Beds.—Highly fossiliferous pebbly grits and
nodular shales, with Lingula Ramsayi, L. canadensis,
Siphonotreta nucula, Remopleurides, Glossograptus, &e.
(3) Benan (or Green) Conglomerate.—Massive boulder-beds of
great thickness, unfossiliferous.
(2) Stinchar (ov Craighead) Limestone Group, composed of
compact limestones, nodular and calcareous flagstones and
shales, with Maclurea Logani, Ophileta, Orthis confinis,
Tetradium, Didymograptus, Clathrograptus, &e.
(1) Kirkland (or Purple) Conglomerate—Coarse boulder-heds
and sandstones, generally of a purple colour.
It was shown that the highest beds of this succession are faulted
against strata of Carboniferous age. The discussion of the relation-
ship of its lowest beds to the igneous and metamorphic rocks of
Ballantrae was deferred to a future paper. The author pointed out
how perfectly this reading of the succession explained the anomalies
hitherto supposed to obtain among the fossils of the Girvan region.
When the organic remains collected from these strata by previous
investigators (notably the magnificent Gray collection) are referred
to their natural horizons in this stratigraphical succession, it is
found that each of the great petrological divisions of the Girvan
series has a collective fauna peculiarly its own, and that the general
zoological gradation is identical with that of the acknowledged
sequence in the typical Lower Paleozoic areas in Wales and the
West of England.
The Lower Girvan rocks are clearly of Ordovician age ; while the
Upper Girvan rocks as distinctly appertain to the Silurian. The
Barr Series corresponds to part of the Llandeilo-Bala of Wales: and
-
Mr. HE. Wilson on the Rheiies of Nottinghamshire. 149
the Ardmillan Series is of Caradoc -Bala age. The Newlands Series
answers to the Llandovery formation of Murchison, containing
similar fossils and corresponding local breaks in the succession.
The Purple Shales of Penhill correspond in systematic position,
petrological features, and fossils with the Tarannon; and the
Straiton Beds represent the lower division of the Wenlock.
The development of the paleontological features of the several
zones of life in this succession, and the demonstration of their
correspondence with the zones already recognized in the synchronous
Lower Paleozoic strata of Moffat, the Lake-District, Scandinavia,
and elsewhere were reserved by the author for a second part of this
memoir.
3. * Notes on the Annelida Tubicola of the Wenlock Shales, from
the Washings of Mr. George Maw, F.G.S.”. By George Robert
Vine, Esq.
4, “ Description of part of the Femur of Nototherium Mitchell.”
By Prof. Owen, C.B., F.R.S., F.G.S., &e.
5. “On Helicopora latispiralis, a new spiral Fenestellid from
the Upper Silurian beds of Ohio, U.S.” By E. W. Claypole, Esq.,
B.A., B.Sc. (Lond.), F.G.S.
June 21.—J. W. Hulke, Esq., F.R.S.,
President, in the Chair.
The following communications were read :—
1. “On Thecospondylus Horneri, 2 new Dinosaur from the
Hastings Sand, indicated by the Sacrum and the Neural Canal of
the Sacral Region.” By Prof. H. G. Seeley, F.R.S., F.G.S.
2. “On the Dorsal Region of the Vertebral Column of a new
Dinosaur, indicating a new genus, Sphenospondylus, from the
Wealden of Brook in the Isle of Wight, preserved in the Wood-
wardian Museum of the University of Cambridge.” By Prof. H. G.
Seeley, F.B.S., F.G.S.
3. “On Organic Remains from the Upper Permian Strata of
Kargalinsk in Eastern Russia.” By W. H. Twelvetrees, Esq.,
E.GS.
4, “The Rheetics of Nottinghamshire.” By E. Wilson, Esq.,
F.GS.
During the last few years several sections of the Rheetic beds, in
addition to those already known near Gainsborough and Newark,
have been exposed in making railway-cuttings. These were described
by the author. The beds usually assigned to the Rheetic consist of :—
Lower Rhetic, greyish or greenish marls; Middle or Avicula-con-
_torta series; and Upper Rhetic (white Lias), a series of variable
shales and light-coloured limestones. The author pointed out that in
the Nottinghamshire district there is always a clear line of division,
and sometimes indications of erosion, between the Avicula-coniorta-
series and the so-called Lower Rhetic beds, while the latter graduate
‘down uninteruptedly into the Upper Keuper Marls, Further, they
150 Geological Society :— ic:
are practically unfossiliferous, while in the other series there is evi- —
dence of marine life and the remains of a fauna ranging upwards —
into the Lias. Hence the author proposed to class these Lower —
Rheetics with the Trias, and regard the Rheetic series as commencing ©
with the base of the Avicula-contorta group.
5. “On the Silurian and Cambrian Strata of the Baltic Provinces
of Russia, as compared with those of Scandinavia and the British
Islands.” By Dr. F. Schmidt. Communicated by Dr. H. Woodward,
F.R.S., F.G.S.
The Cambrian and Silurian strata in question are found stretching
over an area 400 miles long by 80 miles wide. The country oceu-
pied by these strata is a nearly uniform plain covered by glacial
deposits ; but sections are presented by the sea-cliffs, which are from
90 to 150 feet high. The strata consist mainly of marls and lime-
stones, arenaceous deposits being rare; and they form a continuous
series from the base of the Cambrian to the top of the Silurian, the
whole of these strata being in conformable succession and unconform-
ably overlain by the Devonian. Although the representative of the
Cambrian or Primordial Silurian contains neither Paradowides nor
Olenus, nor, indeed, any Trilobites whatever, but only Lingulide and
Graptolites, yet its stratigraphical position leayes no doubt as to its
age. The Lower Silurian or Ordovician is the richest of the diyi-
sions, the strata of this age forming a perfectly continuous series.
The author divides these beds into the stages B, C, D, E, and F,
several of which are divisible into substages. Of the Stage B the
lowest bed, 1 to 10 feet thick, consists of the Glauconite-bands con-
taining the casts of Foraminifera described by Ehrenberg, which
correspond to the Ceratopyge stage of the Scandinavian geologists.
‘Above this, and closely connected with it, is the Glauconite-limestone,
from 12 to 40 feet thick. Next comes the famous Orthis-limestone,
a thin bed with a very interesting fauna, corresponding to that of
the Phyllograptus-schists. The author’s beds C, D, E, and F can be
paralleled with the strata of Scandinavia, but have no exact repre-
sentatives in the British Islands. The stage E appears to represent
the Bala of England or the Trenton of North America. Although ©
there is no stratigraphical break, there is a marked paleontological
division between the Upper and Lower Silurian, there being no ~
strata of imtermediate age represented. The Upper Silurian is
divided by the author into the stages G, H, I, K, which can be
exactly correlated with the strata of Scandinavia. The stages G, H ©
do not appear to have precise representatives in the British Islands; —
but Tis undoubtedly equivalent to the Wenlock, and K to the Ludlow.
In the Baltic provinces there are no representatives of the passage-
beds and Lower Devonian, but the Silurian strata are unconformably
covered by the Old Red Sandstone with Coccosteus, Asterolepis
Bothriolepis, Homosteus, and Heterosteus, there being a marked oyer-
lap between the two series. The author argues in favour of con-—
sidering the Cambrian, Ordovician, and Silurian as forming, in the ~
Baltic provinces, one ‘“‘ system.” The author is able to construct a
Mr. T. F. Jamieson on the Glacial Period. 151
section connecting the Silurians of Russia and Scandinavia, and pass-
ing through the islands of Gothland and Oesel. The paper is accom-
panied with a map and a tabulated list of the fossils found at the
several horizons which have been distinguished by the author. He
points out which of these species are found ranging into other areas,
and proposes eventually to publish figures and descriptions of the
characteristic Russian forms. The first part of the author’s paleon-
tological work has just appeared in the shape of a memoir describing
60 species of Trilobites of the genera Phacops, Cheirwrus, and Encri-
nurus. The total number of species of the Trilobites is about 150,
of which only about 15 occur in the Upper Silurian.
6. “On Chilostomatous Bryozoa from Bairnsdale (Gippsland).”
By A. W. Waters, Esq., F.G.S.
7. * The Silurian Species of Glauconome, and a suggested Classi-
fication of the Palxozoic Polyzoa.” By G. W. Shrubsole, Esq.,
F.G.S., and G. R. Vine, Esq.
8. “On the Cause of the Depression and Re-elevation of the
land during the Glacial Period.” By T. F. Jamieson, Esq., F.G.S.
The author commenced by noticing the theory advanced by Adhé-
mar and Croll, according to which the submergence was due to the
effect of a polar ice-cap causing a displacement of the earth’s centre
of gravity and thereby drawing the ocean towards the ice-covered
pole, and proceeded to show that this theory is opposed to the geolo-
gical evidence, according to which the amount of submergence has
been unequal in adjacent areas and along the same parallels of
latitude, showing that the movement has been in the land and not
in the sea. The facts of submergence also prove that no such cap
of ice could haye existed at the time in the northern regions.
Sundry other objections were also pointed out. The author then
went on to state his own hypothesis, which is to the effect that the
depression of the land was caused by the weight of ice laid upon it,
and the re-elevation by the disappearance of the ice. The amount
of depression would depend partly on the weight of ice and partly
on the elasticity or yielding nature of the ground beneath it. He
then proceeded to consider what was the weight of ice that probably
existed, and referred to the elastic and flexible nature of the earth’s
crust, as evinced by earthquakes &c.
He further considered the relation of time to pressure, and touched
upon the probable rate of subsidence, which he supposes to have
been yery slow and gradual. The recovery of level, he thinks, would
also be very gradual, and probably, in most cases, not complete.
He next proceeded to show how his hypothesis is borne out by an
appeal to geological evidence in various countries, taking England,
Treland, North America, and Greenland as examples. He further
pointed out its application to the facts connected with the loess beds,
Fjord latitudes, and lake-basins, and concluded with some obserya-
tions on the remarkable connexion between glaciation and submer-
gence in all countries,
[ 152 ]
XVIII. Intelligence and Miscellaneous Articles.
ON SOME EXPLOSIVE ALLOYS OF ZINC AND THE PLATINUM
METALS. BY H. SAINTE-CLAIRE DEVILLE AND H. DEBRAY.
QOME time before the sickness of my dear and illustrious master
Henri Saite-Claire Deville, we had undertaken to return to
some points in order to complete our old researches respecting pla-
tinum. Our work, as regards the division of the osmides, was
almost finished, when it was interrupted by his sickness and death.
I have had to terminate it; and today I present the result to the
Academy.
It is known that the osmides cannot be divided by mechanical
action. If for example, one essays to pound them in a tempered
steel mortar, the osmide of iridium penetrates into the material
without being either blunted or broken.
If, however, it be fused with 25 or 30 times its weight of zine,
and if after the mixture has been kept for some hours at an
incipient red heat it then be more heated in order to volatilize all
the zinc, there remains a spongy mass, easily divided, and, in this
state, completely and with facility attacked by the mixture of
nitrate and binoxide of barium which we have employed for
oxidizing the two metals of the osmide and to render them soluble
in acids. As it is easy to eliminate baryta from its solutions, the
analysis of the osmide then becomes possible.
What is the part played by zinc in this division? by what
mechanism is it effected? are questions which we had not then
examined, contenting ourselves for the moment with a practical
result sought in vain by Berzelius, which facilitated our entering
upon that study of the platinum metals which has occupied us for
many years.
I. Some osmide of iridium is thrown into some zinc heated to
dull redness and which has been previously well cleaned with sal-
ammoniac. A brisk disengagement of heat is produced. The
mass is kept melted at this temperature during five or six hours,
in order to attack completely the large grains of osmide. The
cold button is then dissolved in dilute hydrochloric acid. The
solution of the zinc takes place with great violence; and there
remains a blackish residue having the appearance of graphite,
which contains all the noble metals of the osmide. The greater
part of the iron existing in this material is dissolved at the same
time as the zinc; on the other hand, there remains a notable
proportion of zinc combined with the metals of the osmide, and it is
not remoyed by prolonged contact with concentrated hydrochloric
acid.
This residue, well washed, and dried at 100°, diffuses in the air
a slight odour of osmic acid. Heated to nearly 300° it suddenly
ignites, almost with explosion, spreading fumes of zinc and abun-
dant vapour of osmicacid. As this deflagration took place in vacuo,
without any sensible liberation of gas, and of course without the -
iM
bee
Intelligence and Miscellaneous Articles. 153
production of oxide of zine and osmic acid, we must conclude that
at about 300° the substance undergoes a change of state accom-
panied by a large disengagement of heat. In air the change of
state is immediately followed by combustion, which augments the
evolution of heat.
The residue is only partially attacked by concentrated nitric acid
or aqua regia. It is quickly and completely oxidized when
thrown into a mixture of fused potass and potassium nitrate ;
ir must even be thrown in in small portions, the mixture being
but little heated, to avoid too strong a deflagration when the divided
material touches the surface of the oxidizing liquid. If one wishes
to make use of this residue either for the analysis of the osmide or
to extract the metals which it contains, it is better to mix it with
anhydrous baryta and barium nitrate: one can then heat it with-
out fear of losing the substance, which is then attacked totally and
easily.
This substance is evidently a complex. mixture of various alloys
which zinc is capable of forming with the platinum metals; we
were therefore induced to examine more closely those different
combinations.
II. Osmium simply dissolves in zinc. When the fused button
of this metal with osmium in a state of division is acted upon by
hydrochloric acid, there remains pure osmium with a crystalline
appearance.
Palladium and platinum, treated in the same manner, leave a
residue consisting of alloys which undergo no isomeric modification
when heated in vacuo. Rhodium, on the contrary, and iridium and
ruthenium especially, as one of us has already proved *, combine
with zine with much liberation of heat; and when the zine button
is dissolved in hydrochloric acid, residues are obtained which are
susceptible of undergoing a true isomeric modification accompanied
by a brisk liberation of heat, without loss of gas, when heated in a
vacuum above 300°. Before the liberation of heat, the blackish
residues would be more or less readily attached by aqua regia.
They lose this property after the liberation of heat, and then take
the metallic appearance.
The thermal phenomenon which accompanies the change of state
of the iridium residue is so marked that it may serve for the
recognition of the presence of small quantities of iridium in
platinum (1 or 2 per cent. for example). The metal to be assayed
is dissolved in a large excess of zinc; and the button is acted upon
by dilute hydrochoric acid; the residue, well dried, raised to a
temperature above 300° in a platinum capsule becomes incan-
descent at various points. Ruthenium and rhodium produce
similar effects.
Til. In brief, osmium is the only platinum metal which does
not retain zine when its alloy with a large excess of zinc is treated
with an acid capable of dissolving that metal. The other metals
obstinately retain a notable proportion of it (on the average 10 to
* Comptes Rendus, t. xc. p. 1150,
154 Intelligence and Miscellaneous Articles.
12 per cent.); and the metals which are insoluble in aqua regia
(rhodium, iridium, and ruthenium) then remain in the state of
peculiar products, without metallic lustre, which seem to be an
allotropic modification of the true alloys possessing a metallic
appearance.
The action of zine upon the osmide of iridium is thus accounted
for naturally. If the heat liberated in the combination of iridium
and zinc much exceeds the heat of combination of osmium and
iridium, the osmide, in conformity with the laws of thermo-
chemistry, will be destroyed by the zinc; the osmium dissolves
and may crystallize in the excess of metal; the iridium and the
‘ other metals remain combined with the zinc. It is the residue
from the action of the hydrochloric acid upon this alloy with excess
of zine that constitutes the explosive substance above considered.
In fact the heat liberated in the union of zine with iridium,
ruthenium, and rhodium, which are the dominant metals of the
osmide, is truly enormous: on adding, for instance, 1 part of iridium
to 30 or 40 per cent. of melted zinc at a temperature below a red
heat, there is combination accompanied by actual incandescence of
the whole mass of metal; it is the same with the two other metals.
Tf all the zinc be driven out by heat (as was done by us in our old
experiments), the hardly fusible metals of the osmide, free or
alloyed, remain ina state of extreme division, in which they are
much more readily attacked than the natural osmide.
Tn an early Note we shall speak of facts observed in the solution
of the platinum metals in copper.—Comptes Rendus de V Académie
des Sciences, June 12, 1882, t. xciv. pp. 1557-1560.
ON THE REACTION-CURRENT OF THE ELECTRIC ARC. BY M. JAMIN,
WITH THE ASSISTANCE OF M. G. MANEUVRIER.
The two currents, in alternately opposite directions, given by
Gramme’s self-exciting machine are absolutely equal; consequently
they do not decompose water, and a tangent-compass intercalated
in the circuit undergoes no deflection, since the contrary effects
following at very close intervals destroy one another. This de-
struction of the effects is kept up when one or several burners are
put into the circuit, provided that the two carbons are equal, dis-
posed in exactly the same manner, and are heated equally.
If eight or ten Bunsen elements be introduced into the total
circuit, they communicate to the compass a deflection 6 when the
machine is at rest, and a deflection 6’, absolutely equal to é, when
the machine is working.
é. é'.
First experiment ......... 32 33
Second experiment........ 38 38°45
Third experiment ........ 33 34:10
This equality proves that the resistance of the wires of the
machine does not vary, whether the machine be at rest or in motion ;
a
Intelligence and Miscellaneous Articles. 155
it proyes also that the two effects of the machine and the battery
are superposed and independent.
If we now suppress the battery, but ignite in the circuit a burner
formed of two unequal carbons—one stout (0-004 metre), the other
thinner (0:002 metre),—this asymmetry suffices to determine a
permanent deflection of the compass, just as if a battery had been
intercalated. The two systems of mutually inverse currents given
by the machine cease, therefore, to be equal; that which is directed
from the thick carbon to the thin, from the less hot part to that
which is more so, prevails over the system of which the direction is
opposite. A differential current results, indicated by the compass,
and the more intense as the difference of thickness of the two car-
bons is more marked ; it reaches its maximum between a large mass
of retort-carbon, which becomes little heated, and a crayon termi-
nating in a fine point, which attains the highest temperature. The
same phenomenon is obtained, and in the same sense, when an are
is produced between a mass of any metal and a carbon point. As
it is difficult to maintain the constancy of the arc, the intensity of
the differential current is very variable; the following results must
be regarded as only a first approximation :—
Lead. Tron. Carbon. Copper. Mercury.
29° 30° 31° 60° 70°
In general the differential current is weak or none when the are
is but of little extent; it increases with the distance of the elec-
trodes. For zinc it is at first as intense as with copper; but it
falls suddenly, probably on account of the oxide with which the
metal is soon covered.
The deflection depends on two things :—1, on the mean electro-
motive force of the differential current; 2, on the resistance intro-
duced into the current by the are which is formed. It is easy to
compare that force and that resistance in the different cases in the
following manner :—
We introduce into the total circuit a battery of x pairs, having
an electromotive force nA. According to whether it acts in the
direction of the differential current or in the opposite direction, we
have
ss wetnA je w—nb
dies Re
When « is greater than 7A both deflections have the same sign,
and we find
it 7
1 2
a etnA k+
—=k= 7
a e—nA’ is a aes
©
bnt if @ is less than 7A, the two deflections have opposite signs—
ES es Es ena Pe Noo
Ch nA—“ k+1
156 Intelligence and Miscellaneous Articles.
IT employed fresh and well amalgamated Bunsen elements ; the
experiment, not susceptible of great precision, on account of the
variations of the are, gave the following values of the electromo-
tive force v of the differential current evaluated in Bunsen ele-
ments :—
Lead. Tron. Carbon. Copper. Zine 1. Zinc 2. Mercury.
2°5 32 5°0 50°6 66:2 YT 103°7
The first three substances are nearly equal; the last three are very
active. Copper is equivalent to 50 bunsens; zine to 66 at the
commencement of the action, falling to 5. As to mercury, it pre-
sents an enormous and very constant value; the differential current
has a mean electromotive force equivalent to 103-7 bunsens. The
same determinations conduct us to an estimation of the introduced
resistance. We have, in fact,
R is in the imvyerse ratio of 7~—7’.
Now the total resistance R was composed (1) of that of the wires
of the machine, (2) of that of the battery, (3) of that of the electric
are. The last alone is variable, and increases or diminishes the
value of R; it will therefore be the more the less i—7 is. Here
are the calculated values of ¢—7':—
Carbon. Tron. Lead. Copper. Mercury. Zinel. Zine 2.
0-406 0°307 0°283 1:41 0-89 1:02 0°56
It would follow from these numbers that carbon, iron, and lead
offer the greatest resistance, copper and mercury the least.
The differential current can only be explained in two ways——
either by a difference in the resistance, or else by inequality in the
inverse reactions of the arc in the one direction or the other.
In order to ascertain if the resistance of the are varies with the
change of direction, I caused a continuous current to pass, first
from the carbon to the mercury, afterwards from mercury to carbon.
A compass, placed in derivation, measured the intensity in the two
cases. I could not measure any appreciable difference. But these
experiments presented a remarkable peculiarity : when the current
passed from mercury to carbon, the arc had a very pronounced
green colour, and the volatilization of the metal proceeded vigo-
rously ; in the contrary case the arc was reddish, and there was a
less abundant production of vapour. This renders evident the
asymmetry existing in the two cases. Now, when the alternating
currents of a Gramme machine are directed through this burner,
the arc is green, which proves that the current going from mercury
to carbon predominates oyer that which goes in the opposite direc-
tion ; and as there is no difference in the resistance of the are, it is
-
Intelligence and Miscellaneous Articles. 157
in a peculiar property of the alternating currents that the reason of
the differential current must be sought.
Each of the two systems of currents stores up, at the instant of
its commencement, a certain sum of energy, which is set free when
it ceases, and is maneseed by a contrary current, or, as Edlund
says, by an inverse electromotive force. “Thus a first current —>
initially very feeble, gradually 1 increases, and, when it ceases, gives
rise to an inverse reaction <-, which adds itself to the current —
developed by the machine at the same instant. If, then, one of the
systems of current — presents a weaker reaction than the contrary
system <—, it will be less weakened and more reinforced, and will
determine the direction of the differential current.
Whatever may be the explanation of these facts, it is clear that,
once produced by an are with mercury, the differential current
entirely changes the action of the machine, that one of the systems
of currents is, if uot extinguished, at least considerably weakened,
and that the other system is constituted by successive currents of
greater intensity and duration. Also every additional electric are
introduced presents the same aspect as that of the batteries—that
is to say, greater brightness and heat at the positive pole, with
transfer of matter to the negative pole. The machine, previously
incapable of decomposing water, becomes capable of decomposing it
like a battery with an electromotive force equal to 100 Bunsen
pairs; it can, like the batteries, determine all the chemical actions
we will, magnetize soft iron, reduce metals, convey force—in a
word, replace a continuous-current machine in its applications.
There are two types of magneto-electric machines: those of the
one kind, derived from the Gramme system, can give directly cur-
rents constant in direction ; the others, like those of Nollet or Méri-
tens, can engender only alternating currents: the latter are appli-
cable only to the production of light; it has been in vain attempted
to employ them for chemical operations by directing the currents
with a commutator. It is evident that this commutator might be
replaced automatically by one or more arcs formed between a bath
of mercury and acarbon point™. It remains to ascertain what are
the economical conditions of that transformation.— Comptes Rendus
de V Académie des Sciences, June 19, 1882, pp. 1615-1619.
ON THE MOTION OF A SPHERICAL ATOM IN AN IDEAL GAS.
BY G. LUBECK Tf.
The author considers an atom of mass M, moving through a gas
at rest, of which the atoms are of mass m. W ith respect to the
impact, he avails himself of the principle of vis viva, of that of the
centre of grayity, and, lastly, of the principle that communication
* These experiments were made at the laboratory of the Sorbonne.
1 Festschrift des Fried,-Werd.-Gynn., Berlin, 1881, pp. 295-812.
158 Intelligence and Miscellaneous Articles.
of motion takes place only in the direction of the common normal
to the two cylindrical atoms at the instant of the impact. The
atoms then behave like perfectly hard elastic spheres; no internal
motion takes place. First the number Yt of the collisions is cal-
culated (in the known manner) which the atom M experiences when
during a unit of time it moves through the atoms m with the con-
stant velocity Q; and it is remarked that 3t is a minimum for
oa=0.
It is then assumed that the velocity of M is continually altered
in quantity and direction by the collisions, but at the same time a
certain mean velocity A, in the direction OX, prevails. Those de-
viations from the mean motion effected by the impacts the author
names the ‘oscillating motion” of the atom M. [To some extent
in this way behaves an atom of one kind of gas which is diffused
with a certain velocity through another—Tue Rerorrer.| The
probability f, that the atom M has the velocity-components U,, V,,
W, in the directions of the axes of coordinates the author finds by
a method first employed by O. E. Meyer. He first finds the pro-
bability that the atom, in arbitrarily chosen time-elements, has
successively the velocity-components
U,, Va Ws w., A pie Ae eee Us Ls W,,
equal to the product
Sur Dave Fnt
As the most probable distribution of velocities he designates that
for which this product is a maximum. But now the sought-for
function f is not variated, but the differential quotients of the above
product with respect to the variables contained therein are, under
the corresponding accessory conditions, put equal to 0, which gives
fa=ce—AUU—a)3+(V—B)2+(W—y)7],
By F the author denotes the ratio of the time during which the
velocity-components of the atom M lie between the limits U and
U+dU, V and V+dV, W and W+dW to the whole time ofthe
motion of that atom; and he finds from the above, putting
U=Q.cos 6’, V=Qsin6'cosg’, W=Qsin 6’ sing’,
w= V kmQ, a=NkmA, b= a
ce
-\ F : ; :
e— (*) e—K(wPau—2 cos '+07)y? dy sin 6' dO! dd’.
as
For the quiescent gas, Maxwell’s distribution of velocities is
assumed :—the number of the atoms in the unit of space for which
the X component of the velocity lies between uw and u+du is
N = Ane e—kmu® du,
fate
:
Intelligence and Miscellaneous Articles. 159
If L be the mean vis viva of the atom M, this gives for the mean
vis viva L—3(MA*) of its oscillating motion the value 3M/4).
The mean vis viva, however, of an atom m is equal to 3/4k. In
order to find the dependence of L on A, the author seeks the pro-
bability dU, dV, dW, that, it the atom M before the impact had
the velocity-components U, V, W, the resulting impact is exactly
such that the velocity-components after it le between the limits
U, and U,+dU,, V, and V,+dV,, W, and W,+dW,. Consider-
ing first an impact occurring upon any surface-element of the
sphere, and then summing all ‘the collisions resulting upon all the
surface-elements so that the condition mentioned is fulfilled, he finds
odU, dV, dW,= (“4 9) RN es Tem
Zit
im | M +m U(U,—U)4+ VW(V,—V)+ W(W,—- W)7°
e-~ km ene 5 Q+ 1 |
m Q
aU,dV,dW, .
Qx ?
in which R is the radius of the atom M,
Now, as the atom M in the course of the time-unit collides FN
times with m so that before the impact the velocity-components of
the former lie between the limits U and U+dU, V and V+dV,
W and W+dW without any further condition,
FRodU, dV, dW,
is the number of impacts which M during the unit of time suffers
in such wise that the velocity-components before the impact lying
between the limits U and U+-dU. Vand V+¢dV, W and W-+dw,
after the impact lie between the limits U, and U i +dU,, V, and
V,+dV,, W,and W,+dW,. Ifwe integrate over all the differ-
entials contained in "E, we obtain the number of impacts after
which the velocity- components lie between the limits U, and
U,+dU,, V, and V, +dV,, W, and W,+dW, without any ‘other
condition ; and since this must be equal to the number of impacts
at which the velocity- -components before the impact lie between
the same limits, without any condition for those after the impact,
we get
EN, =dU, dV, aw, ( ; ( : { “ERS.
ow?
If in this equation, which holds for all values of U,, V,, W,, we
assign to each of these quantities the value 0, we get, after carry-
160 — Intelligence and Miscellaneous Articles.
ing out the three integrations,
yn (eras,
M+im nP\o
o=: ra — =e 4 CE oe
ce (7 ) mv
Qn
From this we find
<oM, OM _p_M
m’ AX
in which
that is, the part of the mean vis viva expended upon oscillating
motions of the atom is in general less than, and for A=0 is Bay
to the mean vis viva of anatom m. For A=o it is equal to
The author demonstrates also that |
Mi: |
L— = A .
with A increasing must always constantly diminish. :
By integrating Ft over the three differentials therein contained,
the author finds the number Z of the collisions-which the atom M
suffers in unit time, and by threefold integration of F.Q the sum
S of all the lengths of path of the atom during the unit of time.
p=S/Z is the mean path between two collisions. Simple values
were obtained only for A=0.
Since the atoms m form a resting gas, it is clear that the atom
M will continually lose more and more of its own proper velocity
through the collisions. The author calculates, first, how much a
collision of any kind changes the X component of the velocity of M.
This quantity, multiplied by the number of collisions of that kind
in unit time, and integrated over all kinds of collisions, gives the
diminution dA/dt which the proper velocity of the atom M under-
goes on the average in the unit of time, and which the author, like
Stefan (in his theory of gas-diffusion), designates the resistance of
the gas to the atom M. If A is very small, the calculation gives
dA a*
a —gA, A=A,e-?t
while :
13 \ 4M MW
p= v «NR ut am m ae Re ‘2
VkM m @ _M
m
—Wiedemann’s Babldtter, 1852, no. 6, pp, 451-455,
co
+
THE
LONDON, EDINBURGH, axnp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
SEPTEMBER 1882.
XIX. On the Electricity of Flame.
By Jcutus Ester and Hans GEITEL*.
[ Plate IV. figs. 1-4.]
§ 1. Introduction.
N the electricity of flame there is already a long series of
memoirs ; but in many respects they contradict one
another, both in regard to the results and’also to the views
advocated by the different authors as to the cause of flame-
electricity. As Holtzf has briefly given a very perspicuous
digest of all the memoirs which refer to the electrical beha-
yiour of flames, a reiterated historical quotation of them in this
place may certainly be dispensed with.
The origin of the electrical difference can be accounted for
by the following three causes:—
(1) The electricity of flame is caused by the process of
combustion as such (Pouillett, Hankel).
2) It arises from the flame behaving to the metals intro-
duced as electrodes like an electrolyte (Matteucci||). To this
explanation, evidently, no other meaning can be attached than
that the different layers of the flame excite differently by con-
tact the wires immersed in them. For shortness, we will
* Translated from Wiedemann’s Annalen, 1882, no. 6, vol. xvi. pp. 1938=
222.
+ Carl’s Rep. xvii. pp. 269-294 (1881).
t¢ Ann. de Chim. et de Phys. xxxy. p. 404 (1827).
§ Pogg. Ann. lxxxi. p. 212 (1850). || Phil. Mag. 1854, vii. p. 309.
Phal. Mag. Ss. Ve Vol. 14, No. 87. Sept. 1882. M
162 MM. Elster and Geitel on -
in future designate this as the “electrolytic” theory, and, in
correspondence therewith, speak also of “ electrolytic” excita-
tion by the flame.
(3) Its explanation is found in a thermoelectric difference
of the electrodes (Buff)*.
The theories which are deduced from the unipolar conduc-
tivity of flame we may be permitted to pass without notice,
since, as will result from the following investigation, sources
of error may have prevailed here, causing the conclusions
drawn from them to appear doubtful.
Besides these differences in respect of theory, however, the
different observers also adduce experiments which are abso-
lutely irreconcilable with one another. This goes so far that
even in regard to the question whether the positive or the
negative electricity is that which is proper to fame no unity
prevails.
The reason of this lies in the fact that all the observers have
overlooked a point that plays a very essential part in the elec-
tricity of flames, namely the behaviour of the shell of air
which immediately envelopes the flame.
The maximum of electromotive force is always found when
one wire is introduced into the Jatter, and another into the
interior of the flame, as will be shown in the following. At
the same time, however, with the electrodes in this position
the resistance of the hot layer of gas separating the wires is
uncommonly greater ; so that we can hardly reckon on mea-
suring the intensity of the current with the aid of a multiplier ;
it is perhaps a consequence of this circumstance that.all the
observers who have investigated flame-electricity by means of
that instrument have lost sight of the point above named.
As hitherto, so far as is known to us, the electricity of flame
has not been examined with an electrometer permitting exact
measurements, it appeared to us of importance to test the
electric behaviour of flame with Thomson’s quadrant-electro-
meter, and eventually to verify the correctness of one of the
theories above cited.
§ 2. Apparatus and Method.
In order to keep the charge of the needle of the electro-
meter constans, it was connected with one of the poles of a
Zamboni’s battery consisting of 2400 pairs of plates, the other
pole of which was led ia earth. The double deflection pro-
duced by a normal daniell varied 4 or 5 scale-divisions dnring
* Lieb. Ann, lxxx. p. 1 (1851) & xe. p. 1 (1854).
the Electricity of Flame. 163
the time of the investigation, and amounted in the mean to
112. To this normal daniell, putting its electromotive force
=100, all the data given in the following communication are
referred. The scale was placed at 2 metres distance from the
mirror ; and the deflection left and right from the position of
rest was measured by means of a suitable turn-plate.
In order to convey the electricity of the flame to the quad-
rants, of which one was, as usual, connected with the earth,
straight wires were mostly employed, or electrodes from
liquids, which, fixed in suitable stands well insulated upon
cakes of resin, could be raised and lowered at pleasure.
The experiments were made with well-insulated Bunsen
burners and with alcohol flames. The flames of the former
issuing from apertures of the usual width proved too flicker-
ing, and therefore the measurements too uncertain. On this
account a very small Bunsen burner was prepared from a glass
tube of 4 millim. width. Its upper extremity was surrounded
by a platinum sheath, in order to avoid colouring the flame
by the gradually heating glass. When one electrode [the
“ base-electrode ”’ | (B, fig. 1) was immersed in the foot of the
flame, and the other in its apex [the “apex-electrode”’] *(S,
fi. 1), with the turn-plate in one position the foot of the flame
was connected with the earth, and the apex insulated ; with
the other position the reverse took place.
§ 3. Longitudinal Polarization of the Flame.
Hankel states that when one platinum wire is introduced
into the apex of a flame and one into its base, a galvanometer
indicates an electric current passing from above downwards.
From this it might be inferred that the flame is polarized
lengthwise.
The corresponding experiment with the electrometer gives
apparently the same result ; but in this case two very striking
points are to be remarked.
The first point is this :—lIf the experiment be arranged as
represented in fig. 1, the apex mostly appears, as in Hankel’s
experiment, negative to the base; but very often, and appa-
rently without any external cause, the reverse takes place.
The second is that when the metal from which the flame
issues is connected with that quadrant which is conducted to
earth, while the insulated electrode is introduced at different
heights s above the base, by suitably shifting the insulated
electrode within a cross section the appearance of a constant
potential within the flame is easily attained.
M2 |
164 MM. Elster and Geitel on
Thus the electromotive force (H) was determined as fol-
lows:—for
millim.
je EK=104
s= 20 HK=104
s=60 E= 94 (wire at the extreme apex).
Lastly, as a third noteworthy point may be added that the
electromotive force is independent of the size of the flame, and,
consequently, of the amount of the burning gas. This is evi-
dent from the following experiment:—
By regulating the admission of the gas, over the same
aperture of the burner three flames of different height 1 were
produced, and their apices connected with the insulated pair
of quadrants by a clean plate of platinum. There were found,
for
20 h=95 h=70
13°7 R= 715 =a
consequently the electromotive force E independent of the |
height h of the flame. Two subsequent series of experiments |
gave the same result. Here the arrangement of the experi-
ment was that shown in fig.2a. There were found, for
Ist series. 2nd series.
h=20 B=142 H=Ziee
h=40 H=145 H=219:2
h=70 H=142 K=216-0
~The reason of the value of E being here so much higher will
appear subsequently.
§ 4. Polarization of the Flame in the Cross Section.
If the flame were polarized lengthwise, the surfaces of equal
potential would be given by planes perpendicular to the axis
of the flame. On examining cross sections of this sort, the
surprising result was obtained that, if the two platinum wires
laterally introduced penetrate the flame to an equal depth, the
difference of potential within one and the same cross section
=0, but that with a slight horizontal displacement of either
electrode a difference of potential often appears, which equals
that produced by the vertical displacement or far exceeds it.
The latter takes place whenever one of the electrodes no longer”
dips into the flame, but into the enveloping shell of hot air
(A A’, fig. 1). The layer of air immediately enveloping the
flame plays therefore an essential part in the electrical be-
haviour of the flame.
_ the Electricity of Flame. 165
Hence, in order to avoid possible errors, it appeared advi-
sable to cover as much of the electrodes as was not within the
flame with an insulating coat, which could easily be done by
fusing the platinum wires into glass tubes. The wire project-
ing out of the glass was just long enough to reach from one
margin of the flame to the other.
If, now, two such platinum wires were placed opposite one
another in one and the same cross section of the flame, and one
of them was continually moved further and further from the
other, with its complete withdrawal from the flame a very con-
siderable increase of the electromotive force occurred ; it rose
from 12 to 192; and the electrode which was in the layer of
hot air was positive.
Accordingly, a flame gives the maximum of action when
the apex-electrode is introduced into the hottest part of the
flame, and the base-electrode into the sensitive hot layer of air,
_ about as represented in fig. 2a.
Let it be further remarked that with this arrangement of
the experiment a reversal of the polarity of the flame was never
observed by us, and that all carburetted-hydrogen flames ex-
hibited the same behaviour.
§ 5. On the Change of the Polarity of a Flame.
It was mentioned in $ 3 that one and the same flame appears
sometimes positive, sometimes negative. Since, then, the
wire introduced into the air envelope becomes highly positively
electric, it is clear that uncommonly much will depend on how
the electrodes are introduced into the flame. If it is wished to-
have the apex of the flame negative, the apex-electrode must
be completely enwrapped in the flame; in the other case,
especially if the base-electrode dips quite into the flame, the
electric excitation of the enveloping air stratum may prepon-
derate, and consequently the flame appear positive. If this is
the true explanation, it must be possible artificially to change
the polarization of a flame.
Of the experiments with alcohol-flames we note the follow-
ing; the positions of the platinum electrodes are given in
fig. 2a,b,c,d,e. In fig. 2a the base-electrode B is in air at
about 4 millim. distance from the margin of the flame, and
will now be gradually pushed in till (fig. 2 ¢) it touches both
margins of the flame. The apex-electrode S has had this
same position from the beginning. The electrode B was then
left in this situation and 8 gradually drawn out of the flame
until it was all in air (fig. 2e). The deflections were as fol-
lows:— !
166 MM. Elster and Geitel on
Position of rest of the electrometer-needle: 511°0.
Daniell = 100.
Position of Orientation of Electromotive
electrodes. needle. force.
a 439-0 +144
b 4.85°0 + 52
c 510°5 + 1
d 547:0 — 72
e 572°0 —122
(The sign placed before E gives the direction of the electric
excitation of the electrode b.)
Or, in words:—
As long as B is outside of the flame it is positive, 8 negative
(fig. 2 a).
When B is in the margin of the flame, the deflection dimi-
nishes, but B still remains positive, 8 negative (fig. 2b).
When B and § are equally immersed in the flame the needle
returns to its resting-position (511); deflection 510°5. There-
fore, with the position fig. 2c, H=0.
If § is now drawn back into the margin of the flame
(fig. 2d), it becomes positive, B negative; the polarity of
the flame is therefore reversed. And when, finally, 8 is quite
outside of the flame (fig. 2), it is strongly positive ; conse-
quently it behaves exactly as did the electrode B in the initial
position (fig. 2 a).
With asuitable position of the electrodes, consequently, the
flame is shown to be not polarized lengthwise at all. This
proves that the longitudinal polarization of the flame is only
apparent, called forth by the unequal immersion of the two
electrodes. At the same time the second point, the constancy
of the value of the potential in the flame, is hereby explained.
The reversal of the polarity can likewise be shown with a
gas-flame; only it does not bring back the electrometer-needle
quite to its position of rest, a small + deflection of from 5 to
10 seale-divisions always continuing to subsist.
A bisulphide-of-carbon flame shows the reversal of the
polarity in ike manner as a spirit-flame, which is interesting
inasmuch as in it the chemical process is fundamentally dif-
ferent.
Leaving quite out of consideration provisionally a proper
electricity of flame, the electrical phenomena in question might
be essentially conditioned by contact of the metals with the
hot air and the gases of the flame. Itmight then be expected
that the electromotive force would depend on the nature of the
metals, as well as on that of the burning gases,
ee
the Electricity of Flame. 167
A series of very carefully made experiments have most de-
cisively confirmed both these conclusions.
§ 6. Dependence of the Electromotive Force upon the Nature
of the Metals.
Ifa platinum electrode is brought into the base of the flame
or into the sensitive stratum of air while the apex is, as exactly
as possible, at the same place conducted to earth, considerably
different values are obtained, according to the nature of the
conducting metal. In the series of experiments recorded in
the following table the position of the electrodes was that
represented in fig.2a. 3B, as well as the flame itself, remained
unmoved during the whole time of a series of experiments,
while the apex-electrode 8 consisted successively of wires of
platinum, iron, copper, and aluminium. The experiments
were made with the non-luminous flame of the small Bunsen
burner described at the commencement.
TABie I.
The flame-apex electricity Electromotive force for D=100.
conducted away by Series of experiments.
f. Il. EEL EV.
Platinum . . 49°6 116-0 157-2 188-4
heme.) «O43 139-0 173°8 232-0
Copper . . se 153-2 208°8 264:0
Aluminium. . 171°0 237-0 268°8 3640
In all four series the flame shows itseif very highly electric
when conducted away by aluminium, less so with conduction
by copper, still more feebly on the employment of iron ; and
the smallest values are obtained with conduction by platinum.
When both electrodes dip into the flame the result is com-
pletely analogous; and it is just the same when, instead of the
non-luminous gas-flame, a luminous gas-flame or a spirit-
flame is employed. The peculiar position of aluminium also
with such an arrangement of the electrodes and the employ-
ment of such flames follows from Table II.
TABLE IT.
: He Apex of flame conducted-from by Electrodes
Kind of flame. Platinum. Aluminium. as in
Ordinary Bunsen burner 74:2 149-2 ‘ig. 26
Luminous gas-flame . . 49°6 112°2 Fig. 2b
Spirit-flame ... . 160°0 278°0 Fig. 2a
The base-electrode, in all the series of experiments, consisted
of a platinum wire. As the wires employed were not of equal
thickness, we made another series of experiments with three
plates, of exactly equal thickness, of aluminium, copper, and
168 MM. Elster and Geitel on
platinum, which were introduced into the apex of a pure-
alcohol flame. In the gas-flame there was always a fusion of
the aluminium, altering the shape of the electrode. The pos-
sible source of error herein contained also disappears when a
spirit-flame is employed. The determinations of the electro-
motive force of the flame were:—when its apex was conducted-
from by
; The platinum plate . . 120°1.
The copper plate. . . 166°0
The aluminium plate . 301°5
Sodium and magnesium are more negative than aluminium,
as will be seen from the following numbers:—
Flame conducted-from by Electromotive force.
Platinum wire (fo SS ee
‘Aluminium wire’) .°e 2) ae
Magnesium ribbon . . . . 221
Sodigm . 0. 325 pijeh. Se
The last two metals were introduced into the lower part of
the flame, in order to prevent their ignition. The sodium was
a piece of the size of a bean, with a bright cut surface.
The relative position to one another of all the metals em-
ployed is specified by the following numbers :—
{ Gold (not pure) }
Platinum «,, dat
Silver (not BP
Purchased wires of { Iron . . » « 10
Copper... ..) s.r
Aluminium. . —. js: eee
| Magnesium. . . . « 920
Sodium . 500
A Desens dlawienees =100
It is consequently put beyond question that the electric
condition of a flame depends essentially upon the nature of the
metal conducting from it; but that nevertheless the quality
of the surface of the electrode which is in air plays also an
essential part was evidenced by the following experiments:—
If the insulated base-electrode in air be wetted with water
or a salt-solution while the apex of the flame communicates
with the earth, a very considerable diminution of the electro-
motive force immediately takes place, especially when a solu-
tion of potassium chloride is employed.
A perfectly clean platinum wire, employed as the base-
electrode, gave H=184; when it was wetted with distilled
water, Hi instantly fell to 134, passed through the values 148
the Electricity of Flame. 169
160, and was finally constant at 170. That the former value
184 was not again reached after the evaporation of the water
may probably be accounted for by a shght impurity of the
(commercial) distilled water.
Still more striking was the phenomenon when a solution of
potassium chloride was employed. Here likewise an instan-
taneous diminution of the electromotive force from 184 to 74
took place; and when the wire was once hastily drawn through
the flame so that small particles of fused potassium chloride
overspread it, the electromotive force fell quite to 16. This
yalue could not be increased by any shifting of the electrode;
so that the cause of this great diminution cannot possibly be
the unavoidable change of place of the electrode concerned. -
Finally, let us mention one more circumstance belonging
to this—namely that freshly annealed wires, used as electrodes
in the air stratum, always give higher values than those which
have remained a longer time (say ten minutes) exposed to the
air—the explanation of which behaviour, even in the case of
platinum, can only be found in an alteration of the quality of
the surface.
§ 7. Repetition of the Experiments with Liquid Electrodes.
In order to completely avoid the contact of the flame-gases
with metals, liquid electrodes, of the form represented in fig. 3,
were employed. By the pressure of the liquid column in the
glass tube R a drop was pressed out of the fine aperture a,
which was then brought into the air surrounding the flame,
and as near as possible to its base. A U tube served to put
the flame of a Bunsen burner constructed entirely of glass
into communication with the earth, one leg of which ascended
the inner cavity of the burner. Both the glass electrodes were
filled with distilled water, into which clean platinum wires
(Pt) dipped. When the two water columns in the electrodes
were connected directly with each other, the electromotive
force called forth by the heterogeneity of the platinum elec-
trodes amounted, at the maximum, to 0°05 daniell.
Now, in all the experiments, the electrode which was in air
was charged in the same sense as a metallic electrode; it
likewise was positive, though the electromotive force was cer-
tainly much weaker. The mean yalues from three series of
experiments were the following:—
Bil efi ueagik 3) Gy
while two platinum electrodes at the same flame gave values
which lay between 150 and 180.
A similar series of experiments were performed with a
170 MM. Elster and Geitel on —
spirit-flame, in which direct contact of any metal with the
flame was likewise avoided. The conduction to earth took
_ place by means of a platinum plate dipping into the alcohol of
the lamp, and connected with the earth-conduction by a pla-
tinum wire. In addition to the electrode represented in fig. 3,
a wet string wrapped tightly round a glass rod was employed.
The electromotive force was then determined:—For the
Water electrode inair . H=24,
Wet strmginair . . . H=58;
For a platinum electrode H=99.
That lower values likewise result for the latter than in the
previous experiments cannot be surprising, since in this
arrangement of the experiment there is no second metal dip-
ping into the flame itself.
A direct determination of the combination platinum, water,
alcohol, platinum gave a maximum of 11:6 for a daniell=100;
so that the observed electromotive force cannot be produced
by this.
In employing the wet string, care must be taken not to
place it tangentially near the flame; for then small fibrils
might project into the flame itself, by which, for the reasons
above discussed, a reversal of the polarity of the flame might
easily be induced.
The above-communicated values being so much lower than
on the employment of platinum electrodes may be accounted
for by the conduction to earth by distilled water or alcohol
being always very imperfect. On this account it seemed
advisable to examine the behaviour of a water electrode over
against a platinum electrode. If the apex of the flame is con-
ducted-from to earth by a platinum wire, the water electrode
which is in air is positive only so long as the platinum wire is
completely enveloped by the flame ; if it be drawn so far out
that it also is entirely in the hot-air stratum, the polarity of the
electrodes is reversed—the platinum wire being positive, the
water electrode negative. Tor example, in an experiment of
this kind, by the drawing-back the electromotive: force was
raised from —142 to +60 (the signs refer to the metal elec-
trode). From this it follows that metals in contact with hot
air become more strongly positive than liquids, but that liquids
in contact with heated gases exhibit nevertheless a similar
behaviour to that of metals. Accordingly we must not directly
infer, from the fact that flames show themselves electric even
when all metals are avoided, the existence of a peculiar elec
tricity of flame.
The complete analogy of behaviour between metal and water
the Electricity of Flame. LA
electrodes appears also from the kind of metal which conducts
from the flame to the earth having an essential influence upon
the result. When the base-electrode was formed by water,
and the electricity conducted from the apex of the flame by
different metal plates of equal thickness, determination of the
electromotive force E, when the conductor was
A piikiivam plate, save H= 73°6,
An aluminium plate, gave H=176°8.
The electromotive force of the combination aluminium, flame,
hot air, water, platinum is therefore as much again as that
between platinum, flame, hot air, water, platinum, completely
in accordance with the previous experiments with two metal
electrodes.
§ 8. Dependence of the Electromotive Force on the Nature of the
Flame.
Since the electromotive force of flame depends on the nature
of the metal introduced into it, it is to be expected that, when
the constituents of the flame-gases are changed, an alteration
of the electromotive force must also occur. Such an altera-
tion can be readily brought about by introducing, for example,
a bead of soda into the flame, ona well insulated wire. Indeed
a deflection of the electrometer-needle then takes place imme-
diately ; only with sodium there is the great inconvenience
that within a short time the entire atmosphere of the room is
so impregnated with sodium vapour that the flame burns with
a strong resemblance to a sodium-flame, which affects the trust-
worthiness of the results. On this account a salt to which
flame is less sensitive was chosen, namely potassium chloride.
lt was first ascertained, by a series of careful experiments,
that the introduction of a well-cleaned and insulated platinum
wire into the flame did not alter the electromotive force. It
may be suflicient to allude to this point here, as we shall sub-
sequently return to it.
When the electrodes are in the position shown in fig. 2a,
and a bead of potassium chloride is introduced on an insulated
platinum wire, the needle receives an impulse which indicates
an increase of the electromotive force; but it quickly goes
back again, and, indeed, far below the value of the deflection
which had been given with a pure fame. According to this,
there was a diminution of the electromotive force ; but it was
only an apparent diminution ; for if the bead of potassium
chloride be now taken out of the flame, the needle approaches
still nearer to its resting-place. This indicates that with the
electrode which was in air an alteration must have taken
place. Upon ita thin dash of potassium chloride has formed,
172 MM. Elster and Geitel on
so that the platinum wire, introduced into the flame, burns for
a moment like potassium. As soon as the colouring of the
flame is over, the same wire, used as the electrode in air, again
gives the usual (mostly somewhat higher) values.
The apparent diminution of the electromotive force is con-
sequently caused by the coating of the electrode which is in
air with potassium chloride, corresponding to the experiment
recorded in § 6.
In the following Table, E denotes the electromotive force
of an absolutely pure non-luminous gas-flame; H;, the electro-
motive force of the same flame ‘when a bead of potassium
chloride is introduced; E’, the electromotive force of the flame
after removal of the bead, but with the electrodes B and 8
(fig. 2a &e) covered with Ka Cl. Accordingly E,—H’ repre-
sents the increase of electromotive force produced by the intro-
duction of the Ka Cl. at
a - se: tea cleat oie
iP 150 60 26 34 Fic, 2
(NE LP dey4: yi des ig BD gan cae
III. 182 142 0 open Fic. 2
IV. LAS ABO aes ree Oe
The reason that the values of H;,—H’ show so little accord-—
ance lies in the impossibility of making two series of experi-
ments under exactly the same conditions. Besides depending
on the position of the electrodes, H;,—H/ depends, ina more _
complicated manner, on this—into which part of the flame
the potassium-chloride bead is introduced. Nevertheless the
above numbers prove that an increase of the electromotive
force is produced by the vaporization of the potassium chloride
in the flame. This can also be verified on the employment of
liquid electrodes.
Different flames being employed, the following values were
obtained for the electromotive force when platinum electrodes
were introduced in the position fig. 2 a:—
Flame. E.
(1) That ofa Bunsen burner . . 180-200
(2) A luminous gas-flame . . . 180-200
(3) Stearine candle-flame. . . . 180-200
(4) Spirit-flame. . . .. . . 180-300
(5) Magnesium-flame . . . . . 20- 30
(6) Bisulphide-of-carbon flame . . 85-100
With magnesium the experimental difficulties are yery
great. Here it could not beascertained with certainty whether
the air-electrode was excited positively, as was at other times
the case with all flames, or negatively.
4
=
7
“~
the Electricity of Flame. 173
§ 9. Combination of several Flames.
We have still to mention that flames can be combined in
exactly the same manner as galvanic cells—the base of one
flame being connected with the apex of the second, the base
of the second with the apex of the third, and so on, by wires.
Three Bunsen burners, connected in this manner by copper
wires, gave the following deflections at the electrometer:—
jl burner .. . 80 seale-divisions.
Zpurners . . .. 156 z (160)
Se aree Res EAS o2 (240)
With perfect equality of the burners the numbers in brackets
might haye been expected. Twenty-five spirit-flames, com-
bined in this way into a battery, produced at the electrometer
a deflection too small to be measured by mirror and scale. At
all events the intensity of the current which set in was, on
account of the great resistance within the flames, very little.
A sufficiently sensitive multiplier to prove the latter point was
not at our disposal.
§ 10. Summary of the Results.
1. The longitudinal polarization of flame is only apparent,
and is called forth by unequal immersion in the flame of the
wires employed as electrodes.
2. The flame appears to be strongly polarized in its cross
section; and the electrode which is in the stratum of air im-
mediately enveloping the flame is always positive to the elec-
trode in the flame.
3. In agreement with the points 1 and 2, the electromotive
force is independent of the magnitude of the flame.
4, Change of polarity of the flame can be called forth by a
suitable displacement of the electrodes, and likewise finds its
explanation in points 1 and 2.
5. The electromotive force of the flame is dependent on the
nature of the metals used as electrodes, and on that of the
burning gases. It appears singularly powerfully electric
when aluminium or magnesium is made use of as the metal
conducting from it; singularly feebly when the electrode in
air is covered with a salt (potassium chloride).
6. Unequivocal electrical effects are likewise obtained from
the flame when waiter electrodes are employed and every metal
excluded; and the electrode which is in air is likewise positive
to that in the flame. All the above propositions can be con-
firmed with liquids, so far as their nature permits.
¢. Flames can be combined after the manner of galvanic
174 MM. Elster and Geitel on
elements; consequently a number of them can be united to
form a “ flame battery.”
$11. Thermoelectrical Behaviour of Platinum Wires
separated by a Stratum of Hot Air*
The phenomena above discussed can be naturally explained
both from the thermoelectric and the electric theory; but we
soon arrived at the conviction that, so long as experiment was
made on the flame itself, a decisive experiment for the one or
the other theory could not be instituted, especially if the
existence of a peculiar flame-electricity (hitherto excluded
from our considerations) were assumed in order to aid in ex-
plaining the phenomena. Hence it was necessary to consider
the matter from another point of view, and to discover a
method by aid of which wires at different temperatures in hot
air could be examined as to their respective electrical beha-
viour. Of course in this case the hot air would not proceed
from a flame, and therefore would not be mixed with the pro-
ducts of combustion.
Starting from these views, we employed the apparatus repre-
sented in fig. 4.. ab is afine platinum wire stretched between
two copper wires w and y, which can be rendered incandes-
cent by a battery of two Bunsen elements B. At the point u,
its electricity, and with it also that of the battery, was con-
ducted to earth and connected with one pair of quadrants of
the electrometer. A second platinum wire, c, was connected
with the insulated pair of quadrants, and could be brought to
any degree of proximity to the wire al. This moyable wire
was placed so as to be as near as possible to the point w; ifa
thermoelectric difference then arose from the incandescence of
the wire ab, it was necessarily announced by the electro-
meter.
There is, however, in this experiment a source of error to
be mentioned. As it would be inadmissible, and even (with
precision) impossible, to place the wire ¢ exactly opposite to
the point w, a difference of potential might also possibly arise
from the circumstance that the potential-ditference of the
points w and v on the stretched wire ab traversed by the cur-
rent would be measured through the intervention of the con-
ductivity of the heated air. In order to be independent of
this, a turn-plate W, was inserted in the circuit, by which the
direction of the current in the wire ab could be altered. If
The electric excitation here occurring is taken into consideration in
this eas only so far as it is immediately connected with the electricity of
flame. The general treatment of this phenomenon is reserved for a future
communication.
|
:
:
;
:
the Electricity of Flame. 175
with one position of the turn-plate the value of the potential
is + z, it will be converted into —z by rotating the turn-plate;
that is, the direction of the electrometer-deflection must be
right or left according to the position of the turn-plate W,.
The circumstance here discussed, indeed, rendered a small
correction necessary. Assuming that the wire c would behave
like a platinum electrode introduced into the hot stratum of
air of a flame, we can denote the value of the potential upon
it by +e. To this value +e the value of the potential at the
point v will be added or subtracted from it, according to the
position of the turn-plate W;. If we denote by s, and s the
deflections of the electrometer corresponding to the two posi-
tions of the turn-plate, we have
@+@=8, €—#f=,
consequently
S; +s:
eae,
>
If the earth-conduction is brought, not to the point u, but,
say, to the point 7, this method still remains applicable; only
now x frequently =e, which for the moment slightly disturbs
the ciearness of the experiment.
The result was now obtained that a platinum wire ¢, brought
near to the incandescent wire, received a powerful positive
charge, consequently behaved like the base-electrode of the
flame. The agreement goes so far that even the values of the
electromotive force lie within the same limits. Nay, the
analogy between the two phenomena is still closer; for nearly
all the experiments above given for the flame can be repeated
with such an incandescent wire.
The electromotive force, besides depending on the distance
of the wire c from the wire ab, turns out to be dependent
on:—1, the state of incandescence of the wire ab; 2, the
quality of the surface of the wire c.
The correciness of these propositions follows from the fol-
lowing Table, in which the numbers are, for clearness, reduced
to equal sensitiveness of the electrometer. (A double deflec-
tion of the daniell= 100.)
Tase IIT.
Series 1 (ze). Conduction to earth in the point + (fig. 4).
tte. t—e. é. Position of the wire c.
+151-0 —10°0 161-0
+150°6 —16'1 i007 millim. above ab (fig. 4).
+169°5 + 60 163°5
+155°0 — 30 1580
Lig Ue beg Bee ae
41630 + O8 163°] 4 millim. laterally from « b.
176 MM. Elster and Geitel on ‘
When the wire c was brought half a millimetre below the ™
wire ab, there was no constant orientation of the electrometer-
needle. The following are the maximum values obtained :—
w+. r—e. é.
129 —9 138
Series 2 (e>«). Conduction to earth in the point wu. De-
pendence on the state of incandescence of the wire a b.
Incandescence of the wire ab. e+. e—a. é.
Dallzed/* <2 £°o> Se 42 96
Bright red... 86 83 169
White “72 Rte Ss 42 116
The last series of experiments show that, with the same
position of the wire ¢ (4 millim. above ab), the value of e is
lower at a white heat than at a bright red heat—a very sur-
prising circumstance, but confirmed by many control expe-
riments.
If the wire c be covered with a coat of potassium chloride,
the electromotive force sinks considerably; in one experiment
it fell from 188 to 34.
The wire ¢ was now replaced by a water electrode (fig. 3)
or a wet string. The experiments showed indubitably that
liquids also, separated from glowing platinum by a stratum
of hot air, become electrically excited; only this excitation,
exactly as with the flame, is much less. The results were,
with
e+. e—X.
é.
ca platinum electrode . . 85 84 169
cawater clectrode . . . 26 15 41
A NOb SINE 54. winnie ke. MER 24 50
Accordingly, from the fact that flames show themselves di-
stinctly electric even when all contact with metals is avoided, tt
must not at once be concluded that they have an electricity pecu-
liar to them.
Let it be further remarked that, both when the wet string
and when the water electrode was employed, the amount of
the potential-difference between ab and the wire in contact
with the liquid of the electrodes, when directly connected by
water, was determined before the definitive experiments. The
deflection of the electrometer-needle amounted for it to only
a few divisions of the scale; so that no source of error could
spring from this.
The phenomena here discussed, which had not, to our know-
ledge, been before observed, stand evidently in the closest con-
the Electricity of Flame. 177
nexion with an experiment described by Edlund *—namely,
that when the incandescent carbon points of the electric lamp
are connected by a multiplier immediately after the extinc-
tion of the flame-arc, a strong thermoelectric current is indi-
cated. It follows also from the above-communicated experi-
ments thatif the carbon points in the flame-are are in different
degrees of ignition (it is well known that the positive is the
hotter; this condition is therefore fulfilled), an electromotive
counterforce must arise, the quantity of which essentially
depends on the nature of the conductors between which the
flame-are passes—a deduction which has already been verified
by Edlund.
The positive electrode, as the hotter, must behave like the
incandescent wire in our experiment—that is, be thermoelec-
trically negatively excited,—which indicates the rise of an
electromotive counterforce.
~§ 12. Dependence of the Electricity of Flames on the State of
Incandescence of the Electrodes.
Haying thus shown that platinum wires, as well as water
electrodes, in contact with hot air are electrically excited, we
return to the electricity of flame.
The method discussed in the preceding section permits also
the determination of the electromotive force of the element
“incandescent platinum, hot air, flame-gases, incandescent
platinum,” if the wire ab is introduced into the stratum of
hot air, and the wire c into the apex of the flame.
As long as the wire ab (fig. 4) does not glow, it is positive
to the wire c in the flame; but as soon as it becomes incan-
descent a negative value is added to the positive value of the
potential; therefore the potential-difference between the two
electrodes must undergo a diminution. This inference was
completely verified by experiment.
In the following, Ei denotes the electromotive force of the
flame when c is incandescent and the wire ab not, and e the
electromotive force of the flame when both wires are incan-
descent. Of necessity e would be =H if the incandescence of
the wire ab had no influence; yet there resulted :—
Series I. Series II.
E. e. KE. é.
254 - 148 134 47
246 147 122 50
216 116 114 37
* Poge, Ann. cxxxi. p. 586 (1850), & cxxxiii. p. 853 (18651),
Phil. Mag. 8. 5. Vol. 14. No. 87. Sept. 1882. N
178 : MM. Elster and Geitel on
consequently always a considerable diminution of the electio-
motive force.
The difference of the numbers in one and the same column
arises from the circumstance that for each new determination
the wire ab was brought into a somewhat different place at
the margin of the flame.
An experiment which likewise proves the dependence of
the electromotive force on the state of incandescence of the
electrodes, but which is not so free from objection as the
above, is the following:—The electrode 8 (fig. 2a) was re-
placed by a platinum pan, and the electromotive force E deter-
mined. Water was then introduced into the red-hot pan,
and, as soon as it boiled, the quantity E measured again.
When the whole of it was evaporated and the pan again red-
hot, the first experiment was repeated for a control. In this
the turn-plate W (fig. 1) was placed so that the platinum pan
was conducted-from to earth. A long series of experiments
constantly gave the same result, namely a considerable dimi-
nution of the electromotive force with diminution of the tem-
perature of the pan. For example,
(1) With the pan red-hot . ... .. . . H=216
4 yy, at 100°.”
3 », Yved-hot (control-experiment) . H=213
Re) ty » . red-hot... » « w= 5).
Re ab 100°. * St.
we ,, red-hot (control-experiment) . H=197
These experiments, without the confirmation afforded by
the preceding experiment, did not appear to us definitive,
because an alteration of H might possibly be effected by the
evaporation of the water and by the wetting of the outside of
the pan. But from the former experiment it was already
evident that the electromotive force is the greater the greater
the difference of temperature between the electrode in the flame
and that in the air.
§ 13. Thermoelectrical Behaviour of Wires within a Flame.
In contradiction to the fundamental experiments adduced
in the last section stands the fact that, in spite of great differ-
ences of temperature, no thermoelectric excitation takes place
when both electrodes dip equally into the flame. With the
electrodes arranged as represented in fig. 2¢ it is easy to place
the electrode B so that it does not glow while § is intensely
white-hot ; but in spite of this the electrical forces which arise
are yery slight, as the following experiment shows:-—
the Electricity of Flame. 179
Electrode § (fig. 2¢) white-hot. Base-electrode B
In the flame (fig. 2c). In air (fig. 2 a).
Marck... 5 H’=44
Red-hot . . H’=+3 H= +150
White-hot. . H’=—6
The sign prefixed refers to electrode B.
Also when the electrodes are in one cross section of the
flame and at the same time dip completely into it, in spite of
great differences of temperature the electromotive force is very
small. If the wires 2b and c (fig. 4) were brought into the
coolest (lowest) part of an alcohol-flame, EH was ascertained to
be 23. By a suitable shifting of the wire ¢ this could be
reduced to 6, notwithstanding that ¢ was not red-hot while
ab was put intoa dazzling white incandescence by an electric
current. The reason for this surprising behaviour appears to
be that the flame-gases, being relatively good conductors in
comparison with the hot air, prevent the electrical difference
from being completed. This would also be confirmed by the
fact that, in the experiments with wires in air, the maximum
is found when the wire a6 is bright red-hot. White-hot wires,
when the electrodes are in the same position, constantly give
lower values for the electromotive force, as we have already
by the conductivity of the surrounding air being so augmented
by the strong heating that it forms as it were a secondary
closing of the circuit.
§ 14. Cases in which the Thermoelectric Excitation predomi-
nates over the Electrolytic, and vice versa.
The view last discussed explains also very naturally the
experiment mentioned in § 4, that the electromotive force
rises from 12 up to 190 as soon as the electrode B (fig. 2a)
is drawn quite out of the flame. The moment this takes place,
the secondary closing formed by the flame is removed, and
the thermoelectric force corresponding to the temperature-
differences of the electrodes comes fully into action.
If this explanation be not admitted as the correct one, it
may appear doubtful if with a jlame the thermoelectric exci-
tation does not entirely fall away, and the electrolytic exclu-
sively condition the electric behaviour of the flame. But if
the experiments related in § 12 tell against this, others also
can be instituted which it would be difficult to explain without
admitting a thermoelectric excitation. They are the follow-
ing :—
if the apex of the flame be conducted-from to earth by a
N2
180 MM. Elster and Geitel on
platinum pan, and a fine platinum wire, dazzlingly white-hot,
be brought below it into the extreme margin of the flame,
the platinum wire shows free positive electricity. According
to the previous experiments, however, a white-hot wire ought
to appear negatively charged with respect to the red-hot pan.
In this case, therefore, the electrolytic excitation outweighs
the thermoelectric. But if the difference of temperature
between the two electrodes be made still greater (which can
easily be done by cooling the platinum pan with water), the
polarity of the flame is reversed, the white-hot platinum wire
is consequently now negative, as the thermoelectric theory
requires it to be.
In an experiment of this sort the following values were
obtained :—
(Ly? Pan redAhot V3) Pee Be
Platinum wire white-hot . (+) f
(2) Pan cooled by H, O (+)
G
Platinum wire as above
The values of EH are considerably lower, because in this
experiment both electrodes are in the flame. At the same time
the margin appears negative to the interior of the flame—a
behaviour which cannot be obseryed under ordinary con-
ditions.
It can, further, be shown that an intensely white-hot plati-
hum wire tn air is negative to one not red-hot in the flame.
Ifthe wire ab (fig. 4) was stretched at about 3 millim. distance
from the margin of the fame, and ¢ introduced into the foot
of the flame so as to be completely enveloped by the flame-
gases but at the same time not to become red-hot, then like-
wise the polarity of the flame was reversed as soon as ab was
rendered brilliantly incandescent by the current. With the
wire ab dark the electromotive force amounted to about 1
daniell ; with it white-hot, to about 0°17-0-2 daniell, but with
the deflection in the opposite direction to the former: there-
fore in this case the thermoelectric again outweighs the elec-
trolytic excitation.
From these and all the preceding experiments it follows
that we cannot explain the electric behaviour of flame by
assuming either an exclusively thermoelectric or an exclusively
electrolytic excitation, but that we must perforce regard both
as cooperating in producing the total electrical state of the
flame.
15. On the proper Electricity of the Plame.
If we imagine two platinum wires introduced into a flame
and the stratum of air which enyelopes it, there arises, accord
the Electricity of Flame. 181
ing to the above conception, a thermoelectrico-electrolytic
element composed of
Cold platinum | Hot air+ Hot air | Flame-gases +
Flame-gases | Red-hot platinum.
If we fix our attention upon the single members of this com-
bination, it is proved by the experiments that an electric exci-
tation takes place between cold platinum with hot air, on the
one hand, and incandescent platinum with flame-gases, on the
other; while the question is still undecided whether an elec-
trical difference exists between the hot air and the flame-gases
even without wires or liquids being in contact with those gases.
This question is identical with that whether a proper electricity
does or does not belong to flame.
In order to bring this point also to a decision, let us here
adduce a few more experiments, which decidedly speak against
the existence of a proper electricity of flame.
On the hypothesis that to the stratum of air A A’ (fig. 1)
enveloping the flame a certain quantum of positive electricity
is brought by the process of-combustion or by mere contact,
at least a partial equalization of the electricities must take
place, even if we take into consideration the bad conductivity
of the two strata of gas, as soon as one or more well-insulated
wires are passed ‘transversely through the flame. But the
potential-difference existing between the electrodes 8 and B
(fig. 1) is not at all or only very slightly altered thereby.
Let E be the electromotive force without the transverse wire,
and Hp the electromotive force with it (platinum).
One series of experiments gave
Big h69-0 164°8 1684 mean 16774,
Hyp=162°0 1 ae Ee hee mean 161°6,
consequently a diminution of about 3 per cent.
A second series, when two very carefully cleaned and well-
insulated platinum wires were passed transversely through the
flame, gave:—
E. Ep. EK—Ep.
Hxperiment I. 168°5 168-0 +0°5
ie 158-4 158-9 —0°5
1g 182°0 182°0 0:0
Each of the above numbers is the mean of five readings ;
and the position of the electrodes was somewhat altered from
one experiment to another; hence-the difference in the num-
bers in the same column, ‘Therefore a partial equalization of
182 MM, Elster and Geitel on
the electricity does not take place through the introduction of
the transverse wires.
Further, in contradiction to the existence of a proper electri-
city of flame is the fact that when platinum wires as homoge-
neous as possible are used as electrodes, and are also approxi-
mately in the same state of incandescence, the electromotive
force of the flame sinks to a minimum. The electromotive
force of the combination
White-hot platinum | Hot air+ Hot air | Flame-gases+
Flame-gases | White-hot platinum
was ascertained to be 0:0018 daniell—a value which lies within
the limits of errors of observation, and consequently may be
put = 0. In this determination, of course, it was necessary
to employ the method discussed in § 11.
For e the following values were obtained :—
eta, e— i. é.
+9°5 —9-0 +0°5
—1:7 —0:2 —1:9 + Daniell = 100;
+73 = 55 +1:8
consequently e=0-0013 daniell. According to this, the elec-
tromotive force of the member
Hot air | Flame-gases
may be put =0, and consequently a proper electricity of the
flame be left out of consideration. |
The most important circumstance contradicting the existence
of a proper electricity of flame may be that the reversal of the
polarity of the flameis not connected with the reversal of the
combustion-process.
A flame of air burning in an atmosphere of illuminating-
gas exhibits the same polarity as illuminating-gas burning
in air.
An incandescent platinum wire in burning air was strongly
negative to the metal (copper) out of which the flame issued ;
and a second wire, introduced into its sensitive stratum,
received a strong positive charge, just like the base-electrode
of an ordinary flame. The details of this experiment were as
follows :—
First the electromotive force of an ordinary gas-flame
issuing from a glass tube provided with a copper jet, with the
electrodes in a determined position (fig. 2 a), was measured.
A current of air was then passed through the tube, which was
placed in a space filled with illuminating-gas, and the air-
current ignited by the spark of an induction-apparatus. No
source of error was given rise to by this (as we conyinced
wi
the Electricity of Flame. ~ 183
ourselyes by numerous preliminary experiments), since the
two electrodes were metallically connected with one another
and with the earth before the flame was kindled. As the
shape of the small bluish flame was quite different from that
of a gas-flame in air, it was necessary to shift the base-elec-
trode somewhat, in order to attain an analogous position to
that in the first experiment.
For the electromotive force of the
Gas-flame in air, we found H=148
Air-flame in gas, _,, Bet?
In both cases the glowing wire was negative, the not glowing
one positive, consequently the apparent polarity of the flame
the same.
Lastly, another noteworthy circumstance should be men~
tioned: namely, the polarity of the air-flame appears reversed
when the flame-electrode is in the lowest and, therefore, cool-
est part and is not red-hot. We have seen, in § 13, that, with
an analogous position of the electrodes in an ordinary flame,
the dark wire in the flame was always negative to one in hot
air, There we had the combination
Platinum, Hot gas, Hot air, Platinum.
But with the air-flame we have
Platinum, Hot air, Hot gas, Platinum,
consequently the same elements in inverse order, from which
the reversal of the polarity of the fame results spontaneously.
§ 16. Theory and Conclusions.
On the basis of the above experiments the following theory
on the electricity of flame can be set up.
By the process of combustion in itself free electricity within
the flame is not generated; on the other hand, the flame-gases
and the air stratum immediately enveloping the flame possess
the property, when in contact with metals or liquids, of exci-
ting it similarly to an electrolyte. To this electrolytic exci-
tation is added a thermoelectric excitation, produced by the
state of incandescence of the electrodes. The quantity and
kind of the electric excitation is then
(1) Independent of the size of the flame;
(2) Dependent on the nature, and the quality of the surface,
of the electrodes ;
(3) Dependent on the nature of the combustion-gases ;
(4) Dependent on the state of incandescence of the elec-
trodes.
184 Lord Rayleigh on the Equilibrium of Liquid
These conclusions are confirmed by numerous experiments;
and no experiment has been found to contradict them.
The decision in favour of this theory was supplied by the
fact that glowing and cold wires separated only by heated air,
with the exclusion of combustion-gases, showed an electrical
difference. Here also the latter is dependent on the nature,
and the quality of the surface, of the electrodes employed, and
on their state of incandescence. A too strong heating of the
wires, and, therewith, also of the separating air stratum, proved
unfavourable to the development of free electrical tension—a
circumstance prooably due to the augmentation of the con-
ducting-power of that separating stratum. In accordance with
this, wires introduced into the flame, so long as they are both
immersed in the combustion-gases (which are relatively good
conductors), never give the maximum of potential-difference ;
rather this enters only when one of the wires comes into con-
tact with only the outer air stratum of the flame (which is
endowed with a very high resistance).
The occurrence of a thermoelectric counterforce within the
galvanic flame-are is also naturally explained by the above
theory.
The questions proposed at the commencement are therefore
to be answered thus :—Hankel’s theory is not in accordance
with experiment; and the two kinds of excitation assumed
by Buff and Matteucci must be regarded as simultaneously
causing the apparent electricity of flame.
Wolfenbiittel, February 1882.
XX. On the Equilibrium of Liquid Conducting Masses charged
with Electricity. By Lorp Rayieian, F.R.S.*
pe consequence of electrical repulsion, a charged spherical
mass of liquid, unacted upon by other forces, is in a con-
dition of unstable equilibrium. If a) be the radius of the
sphere, Q the charge of electricity, the original potential is
given by
mF
ao
If, however, the mass be slightly deformed, so that the polar
equation of its surface, expressed by Laplace’s series, becomes
r=a(1+F,+F,+...+F"+...),
* Communicated by the Author,
;
Conducting Masses charged with Electricity. 185
a = 2 f1—s(n—1 (( 24 ey
and the ae energy of the cee ee from the
equilibrium position is
pee. —_ —S(n—1) (Fae.
In actual liquids si instability, indicated by the negative
yalue of P’, is opposed by stability due to the capillary force.
If T be the cohesive tension, the potential energy of cohesion
is given Ge
then
=0°T = (n—1)(n4+ 2) i) Frdo*.
If F, &% cos(pt+e), we have for the motion under the
operation of both set of forces,
= me See 4202 Gat
ments. When Q is great, the spherical form is unstable for
all values of x below a certain limit, the maximum instability
corresponding to a great, but still finite, value of n. Under
these circumstances the liquid i is thrown out in fine jets, whose
fineness, however, has a limit.
The case of a cylinder, subject to displacement i in two dimen-
sions only, may be treated in like manner.
The equation of the contour being in Fourier’s series
p=a(1l+F\+...+Frt..),
we find as the expression for the potential energy of unit
length
2
pak ad 2 Sie! Dilees 2d0
Q being the quantity of electricity resident on length /.
The potential energy due to capillarity is
=hraT 2(n?— ye
2a
and for the vibration of type x under the operation of both
* See Proc. Roy. Soc, May 15, 1879.
186 Lord Rayleigh on an Instrument capable of
sets of forces,
fs aed _ 2’
p oi | (n+1)T Pa
The influence of electrical charge in diminishing the sta-
bility of a cylinder for transverse disturbances may be readily
illustrated by causing a jet of water from an elliptical aper-
ture to pass along the axis of an insulated inductor-tube,
which is placed in connexion with an electrical machine. The
jet is marked with a recurrent pattern, fixed in space, whose
wave-length represents the distance travelled by the water in
the time of one vibration of type n=2. When the machine
is worked, the pattern is thrust outwards along the jet, indi-
cating a prolongation of the time of transverse vibration.
The inductor should be placed no further from the nozzle than
is necessary to prevent the passage of sparks, and must be
short enough to allow the issue of the jet before its resolution
into drops.
The value of T being known (81 C.G.S8.), we may calcu-
late what electrification is necessary to render a small rain-
drop of, say, 1 millimetre diameter unstable. The potential,
expressed in electrostatic measure, is given by
Va 2=,/(16ra,1)=20.
0
The electromotive force of a Daniell cell is about ‘004; so
that an electrification of about 5000 cells would cause the
division of the drop in question.
XXII. On an Instrument capable of Measuring the Intensity of
Aerial Vibrations. By Lorp Rayieren, F.R.S.*
HIS instrument arose out of an experiment described
in the ‘ Proceedings of the Cambridge Philosophical
Society’ f, Nov. 1880, from which it appeared that a light
disk, capable of rotation about a vertical diameter, tends with
some decision to set itself at right angles to the direction of
alternating aerial currents. In fig. 1, A is a brass tube closed
at one end with a glass plate B, behind which is a slit C
backed by alamp. D is a light mirror with attached mag-
nets, such as are used for reflecting-calvanometers, and is sus-
pended by a silk fibre. The light from the slit is incident
* Communicated by the Author.
+ See also Proc, Roy. Soc. May 5, 1881, p. 110,
Measuring the Intensity of Aerial Vibrations. 187
upon the mirror at an angle of 45°, and, after reflection,
escapes from the tube through a glass window at H. It then
CG
falls upon a lens F, and throws an image of the slit upon a
scale & Ata distance DH, equal to DC, the tube is closed
by a diaphragm of tissue paper, beyond which it is acousti-
cally prolonged by a sliding tube I.
When the instrument is exposed to sounds whose half wave-
length is equal to CH, H becomes a node of the stationary
vibrations, and the paper diaphragm offers but little impedi-
ment. Its office is to screen the suspended parts from acci-
dental currents of air. At D there is a loop; and the mirror
tends to set itself at right angles to the tube under the influ-
ence of the vibratory motion. This tendency is opposed by
the magnetic forces; but the image upon the scale shifts its
position through a distance proportional to the intensity of
the action.
As in galvanometers, increased sensitiveness may be ob-
tained by compensating the earth’s magnetic force with an
external magnet. Inasmuch, however, as the effect to be
measured is not magnetic, itis better to obtain a small force of
restitution by diminishing the moment of the suspended
magnet, rather than by diminishing the intensity of the field
in which it works. In this way the zero will be less liable to
be affected by accidental magnetic disturbances.
So far as I have tested it hitherto, the performance of the
instrument is satisfactory. What strikes one most in its use
is the enormous disproportion that it reveals between sounds
which, when heard consecutively, appear to be of the same
order of magnitude.
June, 1882,
[ 188 ]
XXII. On the Determination of Chemical Affinity in terms of
Ellectromotive Force.—Part V1. By C. R. Auber Wricut, |
D.Sc, (Lond.), F.R.S., Lecturer on Chemistry and Physies
in St. Mary’s Hospital Medical School*.
On the Relations between the Electromotive Forces of various
kinds of Cells analogous to Daniell’s Cell but differing there-
from in the nature of the Metals used, and the Chemical Affi-
nities involved in the Action of these Cells.
I. Cells containing Cadmium as one of the Metals, the Salts used
being Sulphates.
118. Dice experiments described in Part V. (§§ 106-109)
were repeated, using, instead of normal Daniell
cells, analogous arrangements containing plates of cadmium,
opposed in some instances to copper, in others to zine, solu-
tions of the respective sulphates being employed to surround
the various plates used. With each of these two classes of
cells (cadmium-copper and zinc-cadmium cells) the same
result was obtained as that already recorded in the case of
Daniell cells containing zinc- and copper-sulphate solutions—
viz. that so long as the two solutions are of the same strengtht
the actual state of concentration of the fluids does not
exert any appreciable influence on the E.M.F. generated with
given plate-surfaces ; at least the influence exerted is consi-
derably less than the errors of observation and the variations
due to unavoidable variations in the nature of the plate-sur-
faces, and does not amount to as much as +°0015 volt even
* Communicated by the Physical Society, haying been read at the
Meeting on June 24, 1882.
+ It is convenient to define solutions “of the same strength” not as
solutions of the kind usually spoken of by chemists as ‘ equivalent” to
one another, 7. ¢. containing in a given volume quantities of dissolved
matter in the ratio of the chemical equivalents of the substances dissolved
(e. g. 159°5, 161, and 208 parts of anhydrous copper, zinc, and cadmium
sulphate respectively), but as solutions in which the dissolved matter and
the water present are in the same molecular ratio, i.e. which are expressible
by parallel formule, such as CuSO, 50H, O, ZnSO,50H,O, and
CdSO, 50H,O. With weak solutions the two definitions are practically
the same—but not so with more concentrated fluids, especially when the
molecular weights of the dissolved matters are concn different (like
CuSO, and CdSO,). Solutions of zinc and copper sulphate of the same
molecular strength are practically identical in specific gravity ; but a solu-
tion of cadmium sulphate is considerably more dense than one of either
zine or copper sulphate of the same molecular strength. Thus solutions
of the strengths ZnSO, 50H, 0, CuSO, 50H, 0, CdSO,50H,O have at
18° specific gravities respectively close to 1-170, 1:167, and 1-208; with
stronger solutions the excess of density of the cadmium solution is still
more apparent.
On the Determination of Chemical Affinity. 189
when tolerably, concentrated soiutions of strength MSO,
50H, O are compared with similar solutions of only one
twenty-fitth the strength, MSO, 1250 H, O.
On varying the nature of the surface of the cadmium plate
(by employing bright cast metal, electro-deposited cadmium,
or amalgamated cadmium), it was found that whatever result
was produced in the cadmium-copper cells by a given altera-
tion of the cadmium plate, every thing else remaining unal-
tered, precisely the same numerical result, but with the opposite
sign, was produced in the zinc-cadmium cells by that alteration.
Thus, substituting electro-cadmium for bright cadmium plates
in the cadmium-copper cells caused an increase in the H.M.F.
varying from ‘002 to ‘006 volt in numerous experiments, and
averaging ‘004 volt; whilst with the zinc-cadmium cells the
same substitution caused a decrease in the H.M.F. varying be-
tween almost the same limits, ‘002 and ‘007 volt, and averaging
almost the same value as before, viz. ‘0045 volt. Similarly,
on substituting amalgamated cadmium plates for bright cad-
mium in the cadmium-copper cells, the average effect was a
decrease of ‘0415 volt when the mercurial amalgam was fluid,
and of ‘015 volt when it had become solid and crystalline on
standing ; whilst with the zinc-cadmium cells, substitution for
bright cadmium of amalgamated metal caused on an average
an increase in H.M.F. of ‘043 volt when the amalgam was
fluid, and of ‘016 volt when it had become solid and crys-
talline.
Cells containing Cadmium opposed to Copper.
119. On comparing together a number of similar pairs of
cells containing in the one case electro-copper and in the other
amalgamated copper, it was found that the average difference
was sensibly the same as that observed when the same two
kinds of copper plates were opposed to zinc (§ 107), viz. that,
ceteris paribus, the cell containing amalgamated copper read
on an average ‘001 volt lower than the one containing freshly
deposited electro-copper: the actually observed differences
ranged from +°003 to —‘003 volt, but were more usually
negative.
As just stated, when the cadmium plate was amalgamated a
decrease in H.M.F. was brought about, averaging ‘0415 volt
when the amalgam on the surface of the plate was fresh and
perfectly fluid, and ‘015 when perfectly solid and crystalline.
Intermediate numbers were given by plates on the surface of
which crystallization of the amalgam had begun but was not
complete, the gradation being regular as the crystallization
progressed.
190 Dr. ©. R. A. Wright on the Determination of
The following table gives the average result, in volts*, of
upwards of forty series of observations and comparisons, mostly
extending over three to four hours, during which time the
readings of each particular cell remained sensibly constant:—
Variation in E.M.F. due to the use of cadmium
and copper sulphate solutions of different
strengths, both solutions being of equal | Less than
molecular strengths in any given casef 270015.
(strengths varying from MSO, 47H, 0, to
MSO, 1250030)fi5). 0 au oo
Maxi-| Mini-
mum. mum.
Range.|
Effect of substituting for electro-copper :—
Amalgamated copper (surface wet eye 4-003 |—-003 006 |—-001
HiquIdeMercury)) s.1sAsara tec cece evompe mses
Effect of substituting for bright cadmium :—
Fresh electro-cadmium ..........svscseeeeeeeeeees +006 | +002) 004 |+°004
Amalgamated cadmium (surface wet with —-050'—-033| -017 |—-0415
BTU, MOLCURY: (a6 satohadcmcedacenom ease ance
Amalgamated cadmium (solid and ora} —-020 —-005 015 |—015
fepllinte);¢ eed. ores ne ae cast on desometee res
Electromotive force of combinations :—
Electro-copper—Electro-cadmium ............ 756 °750| 006 | -7525
i 2 Bright cadmium ...... bee: ‘753 °745| ‘008 | °7485
53 - Amalgamated cadmium iy as f ;
(liquid amalgam)...... “17| 701} 016 107
£ ~ Amalgamated cadmium oe ae .
(solid amalgam) ...... } 740} 727) 013 / 7335
Amalgamated copper—Electro-cadmium ........./ ‘754| -749| -005 ‘7515
f i" Bright cadmium ......... 752) *744| 008 | “7475
if ; Amalgamated cadmium | os : 4
(liquid amalgam) ... } (15) 701} “014 706
a se Amalgamated cadmium}! »~o-! »on| . ‘
(solid amalgam)...... } isi 721) O10 7325
When cells containing bright or electro-cadmium and elec-
tro-copper plates were allowed to stand for twelve hours or
* All the observations given in this paper are reduced to the same
standard as that employed in Part V.—yviz. the average reading at 15°5
of a number of Clark’s cells taken as 1:457 yolt, the particular Clark
cells used being the same throughout.
+ The specific gravities at about 19° of these fluids are close
following :—
MSO, 47H,O when M is cadmium: spec. gray, = 1/217.
’
8
to the
do. when M is copper: spec. gray. = 11753 solution
nearly saturated,
MSO, 1250H, 0: in each case below 1:01.
2
Chemical Affinity in terms of Electromotive Force. 191
longer periods, a slight alteration in the H.M.F., due to for-
mation of films of oxide on the surfaces of the plates, was
usually noticeable. As with the normal Daniells (§ 108), the
effect of the oxidation of the copper plate was to reduce the
E.M.F. by a few thousandths of a volt; on the other hand, the
formation of a film of oxide on the surface of the cadmium
plate produced an increase in the H.M.F. of from ‘001 to -004
volt ; so that in many cases the cell with partially oxidized
plates gave sensibly the same value as a newly set-up cell, the
diminishing effect of the oxidation of the copper being just
about counterbalanced by the increasing effect due to the oxi-
dation of the cadmium. In this respect cadmium behaves in
the opposite way to zinc (§ 108).
Relations between the E.M.F. of Cadmium-Copper Cells and
that corresponding to the net Chemical Action taking place
therein.
120. According to Julius Thomsen’s determinations (Journ.
prak. Chem. ii. p. 233, and xi. p. 271), the heat of displace-
ment of copper from copper-sulphate solution (CuSO,,400H,0)
by cadmium is as follows, in gramme-degrees per gramme-
molecule :—
Cds O,SOQvaq. 45) $<.)5.,,895500
@n.O SOs adsu, esse: 09,960
Difference = 33,540
the difference corresponding to 16,770 gramme-degrees per
gramme equivalent, or ‘740 volt*. As with normal Daniell
cells (§ 114), a small quantity () is to be added to this, repre-
senting a variable correction dependent on the physical con-
dition of the deposited copper. Hvyidently the average values
above cited (*7475 to °7525), obtained with bright and electro-
cadmium, are sensibly the same as the value ‘740+2, thus
deduced as representing the net chemical action taking place
in the cell; 7. ¢., as with zinc-copper cells, the whole of the
energy developed in the cell is adjuvant under the conditions
obtaining in the above experiments.
In order to compare the results obtained with the amalga-
mated-cadmium cells with Julius Thomsen’s figures, the heat
of solution of cadmium (precipitated from the sulphate by
zinc, crystalline) in twenty-five times its weight of mercury
was determined by means of the calorimeter, 20 grams of
* The value 4410, used in the former parts of these researches for the
factor for converting gramme-degrees into C.G.S. units, is employed
throughout the present paper; vide § 103, footnote.
192 Dr. C. R. A. Wright on the Determination of —
cadmium and 500 of pure mercury being employed for each
experiment. To insure solution it was found necessary to wash
the cadmium with dilute sulphuric acid just before use ; other-
wise portions remained unwetted and undissolved by the mer-
cury. The final result arrived at as the average of several
concordant observations was, that an evolution of heat to the
extent of 610 gramme-degrees per gramme-molecule (112
grammes) of cadmium took place during solution. Hence,
were cadmium sulphate formed from mercurial solution of
metal instead of crystalline precipitated metal, the heat of for-
mation expressed as Cd,O,SO3aq. would be 89,500—610=
88,890 (admitting that Thomsen’s value 89,500 applies, with-
out correction, to the metal in the crystalline condition of that
experimented with). Consequently the heat of displacement of
copper by cadmium from the sulphate is 32,930 per gramme-
molecule, or 16,465 per gramme-equivalent, corresponding to
‘726 volt. The observed values varied between ‘701 and *717,
averaging ‘707 with electro-copper and ‘706 with amalgamated
copper—again not differing from the value deduced from the
thermal data by an amount materially outside the limits of
experimental errors, especially those due to variation in the
heat of formation of salts according as the physical state of
the metal employed varies. :
It is, however, to be noticed that the above heat of solution of
crystalline cadmium in mercury only corresponds to an H.M.F,
of 0135 volt; whilst the average difference in E.M.F. caused
by the substitution of fluid amalgamated cadmium for erystal-
line electro-metal was *7525 —"707=:0455 volt, a considerably
greater amount; so that amalgamating the crystalline metal
appears to produce a greater effect on the H.M.F. than corre-
sponds to the heat of solution. Just the same result is pro-
duced when cadmium and zine are opposed (§ 121); on the
other hand, the effect on the H.M.F’. of amalgamating silver
is sensibly the same as that corresponding to the heat of solu-
tion of silver in mercury (§ 129). Probably the difference
in the cases of silver and cadmium is due to the oxidizability
of the latter by dissolved air, thus rendering the outer surface
of the crystalline masses somewhat different from the interior,
Cells containing Cadmium opposed to Zine.
121. The following table exhibits in brief the results of
upwards of thirty series of observations, mostly lasting over
several hours, during which period the E.M.F, developed by
any given cell remained sensibly steady :—
_———s
~- -
Chemical Affinity in terms of Electromotive Force. 193
Variation in E.M.F. due to the use of cad-)
mium and zine sulphate solutions of different Eee ian
strengths, both solutions being of equal mole- i
cular strengths in any given case (strengths { volt
rying from MS0O,50H,O to are 2
va
1250H,O) ...
| = Sor |
Maxi-| Mini- ‘Range. Aye-
mum. mum. | rage
Effect of substituting for bright cadmium :— | |
Fresh electro-metal ..............2---2e0eeeee- '—002 —-007 -005 |—-0045
Amalgamated cadmium (liquid) ............ +052 +°036| 016 |+:°04
ie a (solid, crystalline) + -024 +-009| ‘015 |+-0165
|
Electromotiye force of combinations:— | /
Amalgamated zine—Bright cadmium ......| °367| 361/006 | °364
oe Be Electro-cadmium ...| °362} °358| 004 | -360
; # Amalgamated cad-]| , RA |S Pree ge
, anes Gaia} | | 414) 401) 013 | 4079
- Amalgamated cad-|| . Eat unee spate
” ; and) } | 388 | 373 | 015 | 3805
These figures accord closely with the results deducible from
Julius Thomsen’s thermochemical data, together with the
heat of solution of cadmium in mercury above quoted ({ 120);
thus:—
Free metallic cadmium. eae ee.
fee Usaqg.-. . -. =106090 106090
Set) SOzaq. :... ... = 89500 88890
Difference . . 16590 17200
Difference per gramme- 905 :
equivalent . . . sate an
Corresponding with volt "365 379
The observed electromotive forces* thus do not differ from
* Regnault has shown (Amn. de Chim. et de Phys. [3] xliv. p. 453)
that the E.M.F. of a cell containing “ concentrated” solutions of zinc and
cadmium sulphates and plates of these metals was 55, when that of a
similar cell with zinc and copper sulphates and plates was 175 (a particuiar
thermopile being employed as unit). Taking the E.M_F. of the latter
cell as 1-115 volt, that of the former must have been -350 volt—a value
differing from those observed by an amount not outside that possibly due
to inequality in the molecular strengths of the two metallic solutions.
For, by the use of more dilute cadmium-sulphate solutions (the zinc-
sulphate solution remaining the same) an appreciable fall in E.M.F. was
found to be produced, the lowest value being 42=-268 volt with solution
diluted to ;4,; on the other hand, decreasing the strength of the zinc-
sulphate solution produced far less effect. These and the author’s some-
what different results on this point will be discussed in a future paper.
Phil. Mag. 8. 5. Vol. 14. No. 87. Sept. 1882. O
194 Dr. C. R. A. Wright on the Determination of
those corresponding with the thermal values by amounts ma-
terially outside the experimental errors. As with the copper-
cadmium cells, however, the observed difference in H.M.F.
between electro-cadmium (crystalline) and amalgamated cad-
mium (liquid) is notably greater than that corresponding with
the heat of solution of precipitated crystalline cadmium in
mercury, being ‘407—*3595 ='0475 as compared with °0135
volt,
Volta’s Law of Summation of Electromotive Forces.
122. The foregoing experiments clearly show that, as far as
cells containing zinc, cadmium, and copper plates are concerned,
Volta’s law of summation holds, at any rate when the plates
are immersed in solutions of their respective sulphates, the
solutions being of equal molecular strength ; that is, the sum
of the electromotive forces generated with a given pair of zinc
and cadmium plates, and with that same cadmium plate anda
given copper plate, is equal to the H.M.F. generated with the
given zinc and copper plates; or, otherwise,
{ Zn Cd. Zn
Od jsfiy ih Ctirtac ten kee
where the symbol { (iq Tepresents the E.M.F. generated with
a given kind of zinc plate opposed to a given kind of cadmium
plate, each plate being immersed in a solution of its sulphate
of constant molecular strength.
Thus the average results for Daniell cells quoted in Part V.
and the above figures give the following comparisons:—
Nature of Plate-surfaces. a rg
eveloped. Miesanl *
; ] 3 Daniell.
Zine. Cadmium. Copper. Pasi fae Ss
Amalgamated.| Electro. Electro. 38595 ‘7525 =| 1:112 | Amalga-
a Bright. " "364 ‘7485 | 1:1125} mated zine
s Amalgamated cg 407 707 1/114 Jand electro-
(fluid), copperl-111
s Amalgamated 3 ‘380 ‘7335 | 1°1185| to 1-116,
(solid). averaging
Mean ... | 11130) 1-114.
Amalgamated,| Electro. |Amalgamated.| +3595 7515 | 1111 meee
a Bright. ‘4 “364 ‘7475 =| 1:1115| mated zine
is Amalgamated " ‘407 706 1113 jandamalga-
(fluid). mated cop-|
és Amalgamated aut 380 ‘7825 | 1:1125) per 1:110
(solid), to 1:115,
Mean ... | 1:1120} averaging
1113.
Chemical Affinity in terms of Electromotive Force. 195
A number of direct experiments were also made on this
point, using éwin cells constructed as follows :—Three beakers
were arranged containing solutions of copper, cadmium, and
zine sulphates of the same molecular strengths, and plates
of electro-copper, bright (or electro-) cadmium, and amalga-
mated zine respectively. The copper and cadmium beakers
were connected by a siphon tube (with ends covered with
bladder) filled with the cadmium sulphate solution ; and the
cadmium and zinc beakers were similarly connected by a
siphon tube containing the zinc sulphate solution. The cop-
per, cadmium, and zinc plates were then connected with cups
Nos. 1, 2,and 3 respectively of a switch-board like that repre-
sented in fig. 3, Part V. (§ 106); so that by connecting cups
1 and 2 with the electrometer the E.M.F. of the cadmium-
copper cell was determined, whilst when cups 2 and 3 were
connected the E.M.F’. of the cadmium-zine combination was
determined. These readings having been made several times,
the zine and copper plates were transferred to another pair of
beakers, containing the same zinc and copper sulphate solu-
tions united by a zinc-sulphate siphon, so as to constitute a
normal Daniell cell after Raoult’s pattern, and the H.M.F. of
this combination determined. Several pairs of zine and cop-
per plates were thus used—each pair being read first in the
zine-cadmium-copper combination, then in the normal Daniell
cell, and then again inthe ternary combination. In each case
the difference between the sum of the average electromotive
forces of the zinc-cadmium and cadmium-copper couples dif-
fered from that of the zinc-copper combination by quantities
no greater than the errors of observation of the electrometer-
scale (about +0°1 per cent. when a sufficient number of read-—
ings were taken) ; whilst the average of the small differences
observed with different pairs was actually 0, the small + and
— differences due to errors of observation completely balancing
one another. This final result (that no discernible difference
was to be found between the sum of zinc-cadmium and
cadmium-copper couples, and zinc-copper couples containing
the same plates) was obtained in each of several sets of expe-
riments made respectively with solutions of molecular strength
MSO, AT H, O, MSO, 100 isi O, and MSO, 1250 H, O.
Rate of Fall in E.M.F’. through so-called Polarization occurring
in Zinc-Cadmium and Cadmium-Copper Cells for definite
amounts of Increase in the Rates of Current-jlow.
123. The experiments made with normal Daniell cells
described in Part V. (§§ 103-105) were repeated with zinc-
cadmium and with cadmium-copper plates (exposing surfaces
=
196 Dr.C. R. A, Wright on the Determination of
of 2°5 and 5:0 square centimetres). The results were similar
in character to those obtained with the Daniell cells, no
appreciable falling-off in H.M.F. occurring with a current-
density of less than some 5 to 10 microampéres per square
centimetre of plate-surface, but very considerable amounts
being observed with stronger currents. ,
Thus the following table exhibits the values obtained in four
experiments—the first three with zinc-cadmium plates, the
fourth with cadmium-copper plates, solutions of sulphates of
the respective metals employed being used throughout:—
Zine plates ......... Amalgamated.) Amalgamated. | Amalgamated.| ......
. Amalgamated. | Amalgamated. :
Cadmium plates ...| Electro { Fluid amalgam. |Solid amalgam. | Bright.
Copper plates’ s...i8h « Gastane — Ole See Se See Electro.
Sp. gr. of zine sul- : :
phate solution... } = a LLG | ean
Sp. gr. of cadmium rae 4
sulphate solution } on in T32 132
Sp. gr. of copper 1-17
| ‘sulphate solution | 7" fetes eee
Resistance of cell, i rs) :
in OhMs: ....:-.0e 95 hg 110 v4
MaximumE.M.F., 905
iniivolia:’!....626s 366 418 395 “741
Current-density, in
microampéres per Observed amounts of Fall in E.M.F.
square centimetre.
10 0 0 0 001
20 0 001 ‘001 004
40 ‘001 002 003 008
100 002 004 ‘007 014
200 004 007 ‘O11 020
400 012 013 017 030
1000 026 030 030 049
2000 049 "059 055 ‘O77
4000 088 ‘099 094 "128
The values are represented graphically by the curves marked
I., I1., I1I., and IV. respectively in the annexed figure.
A number of experiments were made with cells containin
solutions not of equal molecular strengths (like those describe
in § 110), for the purpose of finding how much of the dimi-
nutions observed with the larger current-densities might pos-
sibly be due to the strengthening of the solution round the
dissolved plate, and the weakening of the liquid round the
other plate, which takes place whilst the cell is in action.
The general result was that the maximum possible diminution
due to these causes could not exceed about ‘04 volt. The
Chemical Affinity in terms of Electromotive Force. 197
details of these experiments and of others allied thereto will
be discussed in a future paper.
*300
*250
“200
"150
Volt.
“100
"050
0 1000 2000 3000 4000
Microampéres per square centimetre.
Effect of varying the Size of one of the Plates, the other
remaining constant.
124. The experiments described in Part V. (§ 115) were
repeated with various cells containing Seapets eee or
zine-cadmium plates instead of zinc- -copper ones. The follow-
ing values obtained in four such experiments illustrate the
results obtained, indicating that the effect of halving the area
of the plate on which metal is deposited is, as with the Daniell
cells, greater than the effect of halving the area of the dissolved
plate, when the former plate is not mercurialized*. The zinc-
cadmium cells, however, differ from ordinary Daniell cells in
this respect—that, whils : amalgamating the copper piate of a
Daniell cell does not materi ially alter the relative effect of
halving its area, amalgamating the cadmium plate of a zinc-
cadmium cell greatly diminishes the relative effect of halving
its area, in such sort that, when solid crystalline amalgam is
used, the effect of halving the area of the cadmium ‘plates,
instead of exceeding, becomes sensibly equal to the effect of
halving the area of the zinc plate, whilst when liquid amal-
* Tt is noteworthy in this connexion, that when nearly pure wrought-
iron plates, immersed in ferrous sulphate solution, replace the zinc plates
and zinc sulphate solution of normal Daniell cells, the effect of halving the
area of the iron plates sometimes exceeds that produced by halving the
area of the copper plates
198 Dr. 0. R. A. Wright on the Determination of —
gam is used the effect of halving the area of the cadmium
plate becomes sensibly less than the effect of halving that of
the ziné plate.
Cadmium-Copper. Zine-Cadmium.
Amalgamated zinc— | Amalgamated zinc—
Bright cadmium— | Amalgamated zinc— | yj amalgamated | Solid amalgamated
Garrsit: Electro-copper. Electro-cadmium. Seatac, a eee
in micro= | ———$—$———___—_—_—— ee
amperes. Effect of halving Effect of halving Effect of halving Effect of halving
area of area 0 area of area of
a poo See
————— oe ee a — — —
Cadmium.| Copper. Zine. Cadmium.| Zinc. Cadmium.| Zine. | Cadmium.
1000 | -005 008 004 005 005 | 003 005 | 006
2000 | -010 013 007 ‘008 009 ‘005 ‘O11 ‘O15
5000 016 "022 ‘012 ‘013 ‘018 ‘O11 021 ‘019
10000 020 031 020 025 "027 ‘015 026 025
20000 039 051 030 040 035 ‘022 032 032
II. Cells containing Silver as one of the Metals, the Salts used
being Sulphates.
125. Three sets of cells, after Raoult’s pattern, were con- |
structed, containing respectively zinc-silver, cadmium-silver,
and copper-silver couples, the respective plates being immersed
in solutions of silver sulphate saturated at ordinary tempera-
tures, and of copper and zinc sulphate of strengths molecularly
equal thereto (the silver solution contained 7:25 grammes of
Ag,SO, per litre, and hada sp. gr. near to 1:0067); the com-
position was uniformly MSO, 2860 H,0.
On making series of determinations of the E.M.F.’s of these
cells, the following results were arrived at as the effects of
varying the nature of the silver surfaces, deduced from the
average values of a large number of observations (upwards of
50 sets of comparisons).
Liffect of substituting Electro-Silver for Bright Silver.
Zinc opposed. Cadmium opposed. Copper opposed.
Maximum ... +°017 +015 +:012
Minimum ... +:°003 +:°005 +004
Range. see esa. 014 ‘010 ‘008
Average...... +008 +009 +0075
Chemical Affinity in terms of Electromotive Force. 199
Effect of substituting Amalgamated Silver (fluid) for
Bright Silver.
Maximum ... +°102 +110 +105
Minimum ... +°092 +°095 +:°092
Range......... 010 015 013
Avyerage...... +°099 +°101 +1025
Considering the perceptibly wider ranges of variation in
these experiments than those usually observed in the zinc-
cadmium-copper cells previously described, it is evident that
the effect of varying the nature of the silver plate is sensibly
independent of the nature of the other metal.
Sometimes, but not invariably, the amalgamated silver
plates became solid and crystalline (greenish yellow) on the
surface: this result was apparently brought about much more
rapidly when the silver was immersed in concentrated zine
sulphate solution than under any other of the conditions ob-
taining in the various experiments. When this change took
place the H.M.F. set up by opposing such a plate to zinc in
cells containing sulphates of zinc and silver was always inter-
mediate between that set up in the same fluids by plates of
bright silver and of fluid amalgamated silver. The average of
several comparisons was as follows :—
Efect of substituting Amalgamated Silver (solid) for
Bright Silver.
Maximum...........+ +:°025
Winnie = 552 ..5520% +:014
EGAN an eee sae an os ‘O11
AVGRISC® sevaeee-t2e- +°021
In this respect silver is analogous to cadmium when the
latter is opposed to zinc (§ 121); but the average amounts
of increase in H.M.F’. due to fluid and solid amalgam are in
each instance considerably greater with silver than with cad-
mium (‘099 and -021 for silver as compared with :043 and
-016 for cadmium).
On substituting electro- for bright cadmium in the cadmium-
silver cells, identically the same average effect was observed
as in the cadmium-copper cells (§ 119), viz. an increase in the
E.M.F. of from ‘002 to 006, averaging ‘004 volt. Similarly, on
substituting amalgamated for electro-copper in the copper-silver
cells, practically the same numerical difference in the H.M.F.
was brought about as was formerly observed in the zinc-
copper cells (§ 107) and the cadmium-copper cells (§ 119),
but in the opposite direction, the E.M.F. being raised in the
200 Dr. C. R. A. Wright on the Determination of
copper-silver cells and lowered in the other two kinds: the
alteration in the E.M.F. varied between +°005 and —*003,
averaging +°0005.
126. On allowing newly set-up cells to stand for several
hours, different results were brought about in each of the
three cases according as the silver was opposed to zinc, cad-
mium, or copper. In the first case the E.M.F. invariably fell;
the maximum value was observed immediately after the cell
was set up, and continued sensibly steady for a variable period
of time, a distinct diminution becoming perceptible sometimes
after half an hour, sometimes only after two or three hours.
With cadmium the value after several hours was somewhat
greater than that set up at first and during the subsequent
hour or so; and with copper the value attained after several
hours was still greater than that exhibited during the first hour
or two. The following numbers represent the average altera-
tions thus observed, being the differences between the average
readings during the first hour and during a period of from
3 to 5 hours after setting up :-—
Amalgamated Zine opposed.
Bright silver. Electro-silver. Amalgamated silver. Mean.
—010 —'014 —'012 —°012
Bright Cadmium opposed.
+:°003 +001 +003 + 002
Hlectro-Cadmium opposed.
+°008 +004 +003 +°003
Electro-Copper opposed.
+009 +°007 +007 +008
Amalgamated Copper opposed.
+011 +°009 +:°005 +008
These alterations were traced to the variations in the nature
of the surfaces of the plates opposed to the silver; for on
taking out, for instance, an amalgamated zinc plate after 5
hours, and replacing by a freshly amalgamated plate, the
E.M.F. was restored to sensibly the same value as at first ;
and similarly with the other metals. On the other hand, on
taking out from two cells, for instance, a zine and a copper
plate after 5 hours, and replacing them respectively in two
beakers containing zinc and copper sulphate solutions of the
same molecular strengths, and connected by a siphon tube, the
E.M.F. of the cell thus formed was found to fall short of the
Chemical Affinity in terms of Electromotive Force. 201
average value of a normal Daniell cell with fresh plates by an
amount sensibly equal to the sum of the numerical alterations
that had occurred in the zinc-silver and copper-silver cells
jointly. It is specially noticeable that, whilst in zinc-copper
cells the alteration in the surface of the copper (probably
through oxidation) on standing diminishes the E.M.F., in
copper-silver cells the alteration is in the opposite direction :
with zinc and cadmium the direction of this alteration when
opposed to silver is the same as when opposed to copper.
It would seem from all these results that the effect of a given
alteration of the surface of one of the plates of a voltaic pair
upon the H.M.F. of the pair is independent of the nature of the
other plate as regards its numerical value, although the nature
of this second plate regulates the direction of the variation in
the H.M.F’. produced (increase or decrease), and also exerts
an influence upon the rate at which the alteration of the plate-
surface takes place. Thus it was repeatedly observed that,
whereas an amalgamated zinc plate (or an electro-copper one),
when forming part of a normal Daniell cell, did not become
sensibly oxidized, so as to diminish the H.M.F. of the cell,
until after several hours at least had elapsed, a precisely similar
plate immersed in the same liquid, but forming part of a zinc-
silver cell (or of a copper-silver cell), did become perceptibly
oxidized in much less time. In other words, although no
measurable current was generated in either case, yet the
different amounts of strain (so to speak) set up in the chain
of liquid particles between the two plates, according as one
was silver or not, did affect the rate of change in the surface
of the more oxidizable metal (presumably by varying the
rate at which it combined with the oxygen dissolved in the
fluid).
127. The following Table exhibits the average results ob-
tained in about 150 sets of observations and comparisons, only
those values made during the first hour (or sometimes: less)
after setting up being taken into account, and all subsequent
values being rejected where any diminution through oxidation
&c. began to be perceptible *. The values cited as the average
effects of substituting for bright silver electro- and amalga~-
mated (liquid) silver are the means of the three sets above
quoted (§ 125) obtained respectively with zinc, cadmium, and
copper :—
* Notwithstanding all care, it is probable that the average results with
the zinc-silver cells are too low by a few thousandths of a volt, and those
with the other cells slightly too high (vide § 128).
8 Ry it ie
: Fae
4 Sa
<
202 Dr. C. R. A. Wright on the Determination of
Maxi-| Mini- :
citar] paeaee Range.| Average.
Effect of substituting for bright silver :—
I GCERO-BILVOP® 250 c0s a dopndics matebehe Saeeeeee +:°017 |+-003| ‘014 | +:008
Amalgamated silver (liquid) ............... ‘+100 |+-092} 008 | +°101
a jg} | COMED ER. Seeeaaeeeee +025 |+°014} ‘011 | +°021
Effect of substituting for electro-copper :—
Amalgamated copper .........sssscesecesenee +005 |—-003} ‘008 | +-001
Effect of substituting for bright cadmium :—
WMlectro-cadmigimMy. can. esc.de. ee senaas de +:006 }+°002| 004 | +-004
Electromotive force of combinations :—
Amalgamated zine—Bright silver......... 1540} 1518] 022 1-528
ss 55 Electro-silver ...... | 1550] 1°529} -021 1°536
# 24 Amalg.silver(liquid) 1°640| 1°615 | -025 1627
i > y~«(solid).| 1°555| 1-544] O11 | 1-549
Bright cadmium—Bright silver............ | 1173) 1:163| 010 | 11675
Be . Electro-silver ......... | 1:185| 1°169| O16 1:1765
: . Amalg. silver (liquid). 1-278} 1-261] ‘O17 | 1:2685
Electro-cadmium—Bright silver ......... 1-176 | 1:164| -012 11715
4 5 Electro-silver ......... 1:186 | 1-176} -010 1:1805
5 5 Amalg. silver (liquid)) 1:277| 1:267| ‘010 | -1:2725
Electro-copper—Bright silver ............ 422 -411) O11 416
5. . Electro-silver ............ 429) -411/ 018 4235
2 ae Amalg. silver (liquid)...| -535} °513| :022 5185
Amalgamated copper—Bright silver ...... | °420| -411| -009 “4165
- », Hlectro-silver ........., 480) -414) -016 424
| 7 », Amalg. silver (liquid)) °535| ‘513) °022 519
Volta’s Law of Summation.
128. The values in this table, together with those quoted
above for the zinc-cadmium and cadmium-copper cells (§§
119 and 121) and those given in Part V. for zinc-copper
cells (§ 107), clearly prove that Volta’s law holds in the case
of the sets of combinations
Zn Cd Zn
A os >
iol oninge Ae As
n u is n
~) eine Ag = Ag
Cd : Cd
(C) Cu an Ag a Ag
at any rate within the range of possible error due to the
somewhat larger ranges of fluctuation in the E.M.F. of silver-
containing cells than were observed with zinc-cadmium-copper
cells, and to the fact that, although alterations of the oxidi-
zable plates in the cells containing silver was avoided as far
as possible by only carrying on the observations for one hour
and sometimes less, still it was not practicable wholly to avoid
this source of inaccuracy. Thus in the three cases respec-
tively the following figures are obtained :—
203
1200--+ = donor osvioA Wy
_
: 900-+ } _ C891 61d: GILT cH *poyeores pau .
: 9200. tor | GEE9-T qgi¢. HEL |-(omby) poywonedigemny |" “oxjoory)
Ss 100:+ \ ROT { LEGT PGP S111 . “‘poyeurus[eoy "
my ¢T00-+- GLE O&aP- PITT ‘0.10010 “OxQOOTOT Be
: 8 a100.+ | GOT { G6G4- 1 GOP CVT ih ‘poyw ues uuLy sf
S GOO: -+- : ; Od. I 9] py p it ] a “qo Ley, ‘OMPOOTHL ‘poynuneseuy
S : : ; : “IOATIS ‘sod
s OOUOLOT ICT TOATIO: OU, tung os dd 0 oi oe “LOATIO ‘xoddog ‘OUlZ,
5S o 9 1 @)
o ee Ss ease So SE Se See ee — ——ae
< ZPOO:-+ = ooulorayrp ose0Ay
§ g00:+ 120.1 { GEO OLE: I C688: 4 “0x00 (07 .
‘§ 6200-+ GEO: T GB0G-T poe — |f(pmby]) poyeurwsyeury | gydag ‘
pe Selolttinn 980-1 OPoT GOBT-T goas. i "Oajooy gy -
& Gp00:+ GOPa-T GOLT-T POG: ‘OMHOOTT, “qs itgy 2
— (800+ 870.1 Te@-1 QTAT-T 608: A *Oagooyy ;
= g800.+ Oa] QLOTT POG: qystagy “a siagy *poyeuredyeury
A eg sal el feateseie amy raed
‘ 3 : ‘ “ f “LOATIS TOU TUL ; :
3 OOUOOICT AOATI-OULIZ, tng -wuntpe -puo-oug TOATIC “TUNTUApTy “OUT,
L *podoporop sooxoyy OATLOMOAYOOT HL *HOOTJANS-OYV[T JO O4NGG jy ard
"WV osed
.
Dr. C. R. A. Wright on the Determination of
204
oe ee ET cee ee
ZE00-— = soud1eyTp oSvroay
0200-— | geet { COLET 6I¢- CTL. : ‘poyeuredeury ‘:
G100-— | J TLG-1 GgTg: CoGL, ‘(pmby) poyworespemy | so.yoora
0900: \ CORL-T { GGLL-T PGP: C1GL- e *poyeuuspeury .
Gh00-— OLLI cr GCL, ‘OnjOO[ GL “OL}OOTHT is
@800-— \ OTLL-T { 891-1 GOLF CIGL. : *poywuesyeary i
£00: — Gg9L-T IF: OGaL,. ‘qysig. “O.LJOO TL 01100] 9
G00.— } cgogt 4 G996-T 6I¢- CLEL- ‘ ‘poyeurespeury ba
G100-— t 196-1 ggt¢. GQPL. ‘(pinbyy) poyeumespemy | — “oa qooygy .
BS Sl paeRRART4f- MEET ¥GP- GLP: i ‘poywuespeary “
oF00-— CLT rr CSP: “01091 “OaPOOTET ‘
9800: — \ CLOLT { FOLT SOTF- oLPL. " “poyeiayseury S:
£00-— : GPOLT OIF: G8PL- ‘qs “Ol JOOT TT ‘WsIg
“MOATE *IOATL ‘
“eouodOTICT aggraves ‘wing aa La ae. *IOATIS ‘roddog *‘mUIMIOIpLp,
*podoypoaep so0LO KT PATJOULOLJOO [HL “S90BJANS-04V] qT JO Otny@ NT
ty OSBr)
Chemical Affinity in terms of Electromotive Force. 205
Average difference in case A ...... = +°0042
” ” ” B eeceee = +:0027
” ” ” C esesee = —:0032
Means<:-.<- = +°0012
On carrying out twin-cell experimenis like those described
in § 122, it was found that when a silver plate was placed in
the central beaker, and either copper and zinc, copper and
cadmium, or zinc and cadmium plates were used in the other
beakers, together with solutions of the respective metallic |
sulphates of the same molecular strengths, the difference
between the electromotive forces determined in the twin cell
was always sensibly equal to the H.M.F. developed by the pair of
plates other than silver employed when taken out and opposed
to each other in an ordinary cell containing the same metallic
solutions ; and this was found to be the case, not only with
freshly-prepared plates, but also with plates that had been
immersed for hours and had become oxidized on the surface.
For instance, in a pair of experiments with amalgamated zine,
bright silver, and electro-copper plates:—
Cells newly set up. After 24 hours,
Zine-copper in single cell . . 1°115 1-098
Copper-silver in twin cell . . °417 "425
DERE. fie estat BSS2 1523
Zine-silver in twin cell . . . 1°534 1°522
Difference . . —:002 +001
Similar results were obtained in several other experiments
of the same kind, both with zinc-copper plates opposed to
silver and with the other two pairs (zinc-cadmium and
cadmium-copper). The average difference in each case was
considerably less than +:°001 volt.
Relations between the Electromotive Forces of Zinc-Silver,
Copper-Silver, and Cadmium-Silver Cells and those corre-
sponding to the net Chemical Actions taking place therein.
129. In all the cells hitherto examined in this series of
researches there has been shown to be a sensible equality
between the electromotive forces generated with clean plate-
surfaces of pure metals and those corresponding to the net
chemical and physical actions taking place therein. A priori,
Bee
206 Dr. C. R. A. Wright on the Determination of —
there does not seem to be any evident reason why the same
state of things should not exist in the case of cells containing
silver plates. ‘Thomsen’s thermo-chemical valuations, how-
ever, indicate that the electromotive forces corresponding to
the three equations
Zn aE Ag SO,
Ga le ee
Ow 4 Se,
are considerably higher than those actually observed and
tabulated above, thus :—
2Ag + Zn8Ox,
2Ag + CdSO,,
2Ag + CuSO,,
Zince-silver. Cadmium-silver. Copper-silver.
Zn, O,SO,aq. = 106090 | Cd, O, SO, aq. = 89500 | Cu, O,SO,aq. = 55960
Ag,,O,SO,aq. = 20390 | Ag,, O, SO, aq. = 20390 | Ag,, O, SO; aq. = 20390
Diff., per gramme-
molecule ......... } 85700 69110 35570
Diff., per gramme- 2
equivalent......... } 22800 34555 17785
Corresponding to volt 1:890 1524 784
Tn each of the three cases the calculated H.M.F. is from *34
to ‘37 volt above the observed values when silver plates not
amalgamated are used, indicating that even when only infi-
nitesimal currents are generated a large amount of energy is
nonadjuvant. It will be shown in a future paper that this
behaviour is more or less marked in other kinds of cells con-
taining silver plates and silver compounds, although the mini-
mum amount of nonadjuvancy observed in any given case is
variable with the nature of the saline compounds in the cell*.
In order to see whether the rise in H.M.F. produced by amalga-
mating the silver plate is due simply to the heat of formation of
silver sulphate being less when the silver is dissolved in mer-
cury than when it is free, determinations of the heat of solution
of silver (precipitated from the nitrate by copper, crystalline)
were made. It was found a little difficult to get every trace
of silver used dissolved in mercury when 20 grams of silver
and 600 of mercury were employed, even though the surface
of the former was washed with dilute nitric acid. With
smaller amounts of mercury only incomplete solution was
* Raoult has already obtained numbers (Ann. Chim. et Phys. [4] ii.
317 and iy. 592) indicating that the “ galvanic heat ” (§ 17) of a cell con-
taining copper, silver, and the nitrates of their metals is sensibly below the
value due to the net chemical action taking place. These and other similar
observations will be discussed in a future paper.
~
Chemical Affinity in terms of Electromotive Force. 207
effected, more or less pasty amalgam being formed, and a smaller
heat-development being then noticeable. The most trustworthy
determinations made indicated that during the solution of
108 grams of silver, 2070 gramme-degrees are evolved.
Hence the heat of formation of silver sulphate, when the
silver is dissolved in mercury, is, per gramme-molecule,
20390 —2 x 2070 =16250; so that the heat of displacement of
silver from silver sulphate, when the metal is ultimately obtained
in mercurial solution, is greater than the values above calcu-
lated for zinc, cadmium, and copper respectively as precipi-
tating metals by 4140 gramme-degrees per gramme-molecule,
or 2070 per gramme-equivalent, corresponding with ‘0915 volt.
The average difference in H.M.F. between cells otherwise
_ alike, in which crystalline electro-silver and amalgamated
silver (fluid) are respectively used, is almost identical with
this, being ‘101 —-008=-093 volt. Asalready noticed (§ 120),
silver and cadmium differ in their behaviour in this connexion
when amalgamated, the inequality between the effect on the
H.M.F. actually produced by amalgamation of cadmium and
that corresponding with the heat of solution in mercury
being probably due to the oxidation of cadmium by dissolved
air.
Rate of Fall in Electromotiwe Force through so-called “ Polari-
zution”’ for definite Amount of Increase in Rate of Current-
Jlow.
130. In order to see whether the electromotive forces of the
cells above described are rendered less (when no current
passes) than they otherwise would be, through the interfering
action of dissolved air or some other similar obscure cause, a
number of experiments were made like those described in
Part V. (§§ 103-105), with the general result of showing that
the deficiency observed in the H.M.F. actually generated when
no current passes (as compared with that calculated from the
thermo-chemical data) is at any rate not due to any such
cause, inasmuch as the H.M.F. generated when a current does
pass is always more or less below that set up when no current
passes, just as with normal Daniell cells and with the zinc-
cadmium and cadmium-copper cells above described. Thus,
for example, the following numbers were obtained in three
experiments, in each of which bright zinc plates were em-
ployed, and one in which electro-copper plates were used, the
silver plates being in each instance uppermost and surrounded
by saturated silver sulphate solution.
208 Dr. C. R. A. Wright on the Determination of
Fluid surrounding |Zine-sulphate solu-|Zinc-sulphate solu- Zine-sulphate solu- } .
the zine plates. tion, sp. gr. 1°42.) tion, sp. gr. 1°42.) tion, sp.gr. 1:10.) fo 9 *"""""
Fluid surrounding f{ Copper sulphat
Bue copperipiatespy PTS T° OL TEER Pe ae sol., sp. gr. 1°17
Nature of silver|Hlectro-silver (cry-|Solid crystallized Solid _ crystallized/Electro-silyer (er
plates. stalline. amalgam. amalgam. stalline).
Resistance, : in
ohms, of column) : : : ‘
of fluid between 669 160 766 710
plates ............
Maximum E.M.F. 1°500 1511 1-546 ‘401
Ourrent-density, Observed amounts of fall in Electromotive Force.
in microampéres.
USUAL | etic lites eceneh S49 9|) ok ees 012 005
50 016 ‘010 021 O11
100 025 018 026 019
200 041 036 037 030
400 062 ‘067 059 047
600 080 097 O77 063
1000 116 144 112
2000 209 258 177
These numbers are represented graphically by the curves
marked respectively V., VI., VII., and VIII. in the figure.
On trying experiments, like those described in § 110, to see |
how far the falling-off in E.M.F. when a current is generated |
could be due to the accumulation of zinc (cadmium or copper)
sulphate round the plate opposed to the silver, it was found
that the maximum possible effect due to this cause could not
exceed about ‘04 volt with zinc and cadmium, and ‘02 with
copper. These experiments, and others of a similar nature,
will be discussed in a future paper.
On comparing the eight curves represented in the figure
with those previously described as obtained with various forms
of Daniell cell (Part V. § 105), it is noticeable, first, that the
curves obtained with the zinc-cadmium cells underlie all the
others (I., II., and III.); secondly, that the curve with the
cadmium-copper cell (IV.) is practically identical with one of
the Daniell-cell curves—indicating consequently that, whilst
the substitution of copper for cadmium in a zinc-cadmium
cell raises the position of the curve (7. e. increases the rate of
fall in E.M.F. according as the current-density increases), the
substitution of cadmium for zinc in a Daniell cell does not
materially alter the position of the curve ; thirdly, the curves
with the zinc-silver and copper-silver cells overlie all the
others, whilst the copper-silver curve (VIII.) is not widely
different from the zinc-silver curves (V., VI, and VII.)—
indicating that, whilst the substitution of silver for copper ina
— oe
e
Chemical Affinity in terms of Electromotive Force.
208
Daniell cell largely raises the position of the curve, the effect
of substituting copper for zinc in a zinc-silver cell is very much
less marked. In other words, the nature of the dissolved metal
agects the rate of decrease in E.M.F. with increasing current-
density much less than does the nature of the deposited metal ;
whilst the less the heat of formation of the salt of the latter that
is decomposed by the passage of the current, the more rapid
appears to be the rate of fall in the E.M.F. of the cell as the
current-density increases. As regards the first part of this
general conclusion, it is precisely what also results from the
majority of the previously described experiments on the effect
of halving the area of the dissolved plate, as compared with
that produced by halving the area of the plate on which metal
is deposited. The following experiments with cells containing
silver plates also give the same general results.
Effect of Varying the Size of one of the Plates in Cells con-
taining Silver as one of the Metals, the other Plate remaining
unaltered.
131. By operating in the way described in § 115, the fol-
lowing results were obtained in four sets of observations with
zine-silyer and copper-silver cells, showing that, in all cases,
halving the area of the silver plate produces a sensibly greater
decrease in the E.M.F. set up with a constant rate of current-
flow than is effected by halving the area of the plate opposed
to the silver.
| ZINC-SILVER.
/ Amalgamated
Amalgamated Amalgamated
zinc—crystalline zinc—crystalline Electro-copper—
| electro-silver.
pet aaa amalgamated | amalgamated
edd Be silver. | silver.
CoprER-SILVER.
aMPEFes: eect of halving Effect of halving Effect of halving Effect of halving
} area of | area of area of
|
|
|
|
1000 | -009 | O11 | -007 | 026 | -008
2000 | -012 -024 | 009 | 045 | -012
3000 | -014 | 038 O11 | 059 | “015
5000 016 064 | 020 | -103 | -021
s000~-| -028 -093 | -038 | 186 | -029
Wane | eo 52 | ec Scar] eeccee | 034 |
047
070 |
"151
ee :
Zinc. | Silver. | Zine. Silver. | Zine. | Silver. Copper.|
019
‘036
area of
Silver.
004 | 01
010 023
7017 | 028
|
|
Summary of Results.
132. The foregoing results may be thus summarized :—
Cells containing zinc and cadmium or cadmium and copper
Phil. Mag. 8. 5. Vol. 14. No. 87. Sept. 1882.
E
210 ~=Dr. CO. R. A. Wright on the Determination of
plates, immersed in solutions of the sulphates of these metals
respectively, are closely analogous to ordinary Daniell cells
(containing zinc sulphate solution). Slight variations in the
H.M.F. generated are introduced by varying the condition of
the plate-surfaces; but in all cases the maximum H.M.F.
actually generated with clean pure plate-surfaces and with
solutions of equal molecular strengths is close to that calculable
from the net chemical action taking place in the cell when
generating a current. When the cadmium plates are not
amalgamated, or are covered with crystalline solid amalgam,
the electromotive forces are close to ‘75 and *36 volt for
cadmium-copper and zinc-cadmium cells respectively, the
values corresponding to the net chemical actions as deduced
from Thomsen’s thermo-chemical results being substantially
the same. When the cadmium plates are covered with fluid
amalgam, the electromotive forces are lower in the first case
and higher in the second by upwards of *04 volt—a quantity
distinctly exceeding in magnitude the H.M.F. corresponding
with the heat of solution of cadmium in mercury, although of
the same sign.
(2) The electromotive forces of zinc-silver, cadmium-silver,
and copper-silver cells containing the respective sulphates of
these metals differ from those of zinc-cadmium, zinc-copper
(Daniell), and cadmium-copper cells in this respect, that the
maximum electromotive forces generated (the fluids being of
equal molecular strength) are not sensibly the same as those
calculated from Julius Thomsen’s thermal data, but in every
case fall short by an amount not far from ‘35 volt. When
the silver plates are not mercurialized, or are coated with crys-
talline amalgam, the electromotive forces (which vary slightly
with the precise nature of the plate-surfaces) are, in the three
cases, near to 1°53, 1:17, and 0°42 volt respectively, the
metallic solutions being of equal molecular strength. When
the silver plates are covered with fluid amalgam, the electro-
motive forces are in each case about ‘09 volt higher than the
values obtained with electro-deposited crystalline metal, this
increase almost exactly coinciding with the increment corre-
sponding with the heat of solution of silver in mereury.
(3) As long as the cadmium and zinc [or copper] solutions
employed are of the same molecular strength within the limits
indicated respectively by MSO, 50H, 0 and MSO, 1250H, 0,
the E.M.F. developed with a given pair of cadmium and
zinc [or copper] plates is sensibly independent of the actual
strength of the solutions, these cells behaving precisely like
Daniell cells in this respect. With Daniell cells the solutions
are practically of the same molecular strength when they
Chemical Affinity in terms of Electromotive Force. 211
are of the same specific gravity; but with the other cells
containing cadmium this is not so, cadmium-sulphate solution
being uniformly more dense than either zinc or copper solution
of the same molecular strength.
(4) The effect on the H.M.F. of a cell of a given alteration
in the nature of the surface of either a zinc, copper, cadmium,
or silver plate is sensibly the same numerically whichever
other one of these four metals be opposed to it; but the direc-
tion of the alteration is opposite according as the plate is the
anode or the kathode of the combination. .
(5) Volta’s “ Law of Summation” universally holds within
the limits of experimental error in all the cases examined ;
that is, the electromotive forces of zinc-cadmium, cadmium-
copper, and copper-silver combinations are such that, for any
given kinds of plate-surfaces, the sums of the two first, of the
two last, and of the three together are respectively equal to
the electromotive forces of zinc-copper, cadmium-silver, and
zinc-silver combinations.
(6) Zine, copper, and cadmium plates alter superficially
(probably in consequence of oxidation by dissolved air) more
rapidly when opposed to silver than when opposed to any
other one of these four metals, on being immersed in solutions
of their respective sulphates forming one half of a cell on
Daniell’s principle—no current being generated by the cell,
the measurements being made by means of a quadrant elec-
trometer.
(7) With all the cells examined the behaviour when gene-
rating a current is analogous to that of a normal Daniell cell:
when the current-density exceeds a few microampéres per
square centimetre of plate-surface, a more or less marked
diminution in the E.M.F. ensues, the falling-off being the
greater the greater the current-density. With moderately
strong currents the diminution far exceeds the maximum
possible amount due to accumulation of dissolved salt round
the plate dissolved, and exhaustion of solution round the other
plate. Coeteris paribus, the rate of fall in H.M.F’. as the
eurrent-density increases is the more rapid the lower the heat
of formation of the metallic salt decomposed in the cell so as
to deposit the metal, and is comparatively but little affected
by the nature of the dissolved metal.
(8) The effect of halving the area of the plate on which
metal is deposited is usually to cause a greater diminution in
the H.M.F. than is produced by halving the area of the dis-
solved plate; amalgamated cadmium plates in zinc-cadmium
cells, however, form an exception to this rule.
P2
i Bie 24
XXIII. An Integrating Anemometer. By Watrer Baty*.
| [Plate V.]
HE object of the instrument described in this paper is to
resolve the velocity of the wind in two directions at
right angles to one another, and to obtain the time-integral of
each part separately.
The instrument contains a horizontal plane, in which are
two slits NS and E W, forming a cross to be placed with its
arms towards the cardinal points. In these slits are sliders
F, G, connected by a bar of constant length. Ovis the centre
of the cross, H the centre of the bar. The locus of Hisa
circle with centre O. A weathercock or some equivalent
mechanism is to keep H in such a position that the radius
O H is in the direction of the wind. The sliders carry beneath
them wheels, B, C, whose planes are perpendicular to their
respective slits, and whose centres are beneath the pivots
joining the slits to the bar. [See figs. 1, 2, 3, Plate V.
Fig. 1 gives a perspective view of the instrument, omitting
some points: fig. 2 gives a view of the top of the instrument;
and fig. 3 gives a section of a slit and slider, and shows the
wheel carried by the slider.] The wheels B, C rest on a disk,
A (fig. 1), which revolves about a vertical axis immediately
below O. The disk A is to be rotated by Robinson’s cups, or
some equivalent mechanism, so as to have a velocity propor-
tional to that of the wind. The pieces which carry the wheels
B, C should be allowed some play in a vertical direction; and
the contact of B and C with A can then be maintained either
by their own weight or by the use of a spring. The number
of rotations of B in a given time is proportional to the time-
integral of the resolved part of the wind in one direction (say,
north); and the number of rotations of C is proportional to
the time-integral of the resolved part of the wind in a direc-
tion at right angles to the first (say, west).
Let Q be the angular velocity of the disk A; w, o/ the
angular velocities of the wheels B, C; m, m’ the number of
their rotations in a given time ¢; } their radius, a the length
of the bar; @ the angle between the direction of the wind and
(say) the north; then bdo=asin@.©, and bo’=acosé.0;
and the integrals required are
are th, b
( QO sin 6dt= ( —-o dt= —-Tm
2 Joe a
* Communicated by the Physical Society, having been read at the
Meeting on June 10, 1882.
Effect upon the Oceun-tides of a Liquid Substratum, 218
and
t th b
{ Deosddt= | —o/dt = — 7m’.
0 0 & a
Therefore m, m/ are proportional to the required integrals.
Hach slider might carry a train of wheels to record the
number of rotations; or an electrical arrangement might be
made in which each wheel should complete a circuit at each
rotation and the number of contacts should be recorded. In
the latter case, as no distinction is preserved as to the direc-
tion in which the wheels revolve, it becomes necessary to have
four circuits, one for each cardinal point, with a recorder in
each, and to have one connected with each arm of the cross.
A working model of the instrument above described was
- exhibited at the Meeting, and was fitted with an electrical
arrangement such as I have mentioned.
Ihave since discovered that the slits, sliders, and bar above
described may be replaced by a train of cogged wheels. (Fig. 4
represents the upper, and fig. 5 the under surface of the train.)
A bar turns in a horizontal plane about O, and is kept in the
direction of the wind. This bar carries three wheels, H, K, L,
having the same axis. The Jength of the bar from one pivot
to the other is supposed to be an inch andahalf. The wheels
H, K are rigidly connected; and L lies between them and turns
independently. Hand K are 1 inch, and L is 3 inches in
diameter. L rolls on the inner edge of P, and H rolls on the
inner edge of Q, the diameters of P and Q being 6 and 4
inches respectively. Two wheels, M and N, whose diameters
are 2 inches, are carried by the wheel L, and have their centres
at the extremities of a diameter of L. M and N are in the
same plane as K, and are therefore touched by it. As the bar
rotates, M and N move without rotation, and their centres
move in straight lines passing through O at right angles to one
another, and are ata fixed distance apart, and have the line
joining them bisected by the bar, which is the direction of the
wind. Hence M and N maybe used to carry the wheels B, C
(fig. 1) instead of their being carried by the sliders F and G.
XXIV. On the Effect upon the Ocean-tides of a Liquid Sub-
stratum beneath the Earth’s Crust. By the Rey. O. FisuEr,
MA... F.G.S.*
(1) ig a work which I have lately published, entitled ‘ Physics
of the Farth’s Crust’ {, | have maintained the theory
that the crust is thin, and floats in equilibrium upon a slightly
* Communicated by the Author.
+ Macmillans, 1881,
See
214 ‘Rey. O. Fisher on the Effect upon the Ocean-tides |
denser substratum of molten rock, the elevations on the sur-
face of the crust being due to compression, and being sup-
ported through flotation by corresponding protuberances (which
I call “roots of the mountains ’”’) projecting downwards into
the denser liquid—a mode of support long ago suggested by
Sir G. B. Airy *.
The most formidable difticulty in the way of this theory has
been said to be the necessary occurrence of tides in such a
substratum; and it has been thought that, the crust being
carried up and down in sympathy with the substratum, the
ocean-tides would be almost entirely masked, and that there
would be no appreciable rise and fall of the water relatively
to landt.
The explanation of the difficulty which I had offered in the
book itself was, that the tides in the substratum would involve
a horizontal transference of fluid backwards and forwards,
and might be expected to be of small amplitude, owing to the
viscosity of the substance and to its confinement beneath the
crust I; and I felt so convinced, from geological considera-
tions, that the substratum must be at least plastic, if not liquid,
that I did not think it needful to go further into the question.
But in consequence of the weight of authority by which this
objection has since been enforced, I have been induced to
examine it more closely, and to endeayour to discover what
indications, if any, the ocean-tides might be expected to give
of the existence, or otherwise, of such a substratum.
(2) The “canal theory”’ of the tides appears to be the
most suitable to solve, in a general way, the question at issue;
for what we have to do is to investigate the motion of layers
of liquids (the substratum and the ocean)under the influence
of tide-producing forces.
An article upon the tides by Mr. D. D. Heath appeared
in this Magazine§ in 1867. He intimates that it was founded
upon Airy’s treatise in the Encyclopedia Metropolitana. I
shall take the liberty of adopting the introductory paragraphs
of his analysis, merely changing a symbol. ‘The liquid is
treated as “ confined to a narrow channel running round the
equator, supposing the moon vertical over it and moying uni-
formly in her orbit, so that her apparent motion will be also
uniform and somewhat less than that of the earth’s rotation.”
Ҥ 3. And first as to the geometrical characteristics of a
fluid wave uniformly propagated westward at any rate («).
* Phil. Trans. Roy. Soc. vol. exly. p. 101.
aS Nature,’ vol. xxv, p. 423, 1882 ; also New-York ‘Nation,’ June 15,
t ‘Physics of the Earth’s Crust,’ p. 23.
§ Fourth Series, vol. xxxiii, p. 165, March 1867.
of a Liquid Substratum beneath the Earth’s Crust. 215
“Taking any point on the ‘equator as origin, let « measure
the longitude | linear] westward of any other point, and let
« be the mean depth of the water [or liquid] and y the small
elevation of the surface above the level at 2 as a definite
moment of time.
“For the wave to be propagated with a persistent form
and at the rate a, the height at w must, in a time dt, change
from y to the value which y now has at a distance adé behind
it, or z—ad¢t from the origin; that is,
WU ee iee == — Dadi + ke.
dt
or
dy _—s_— dy
di —=—- a Age ° e . ° e e * . (A)
And if this relation exist everywhere between the differential
coefficients, the condition will be fulfilled for finite intervals.
“Not only the heights, but every other measure or mark of
disturbance must be propagated onwards at the same rate, if
the wave is to have a permanent character; so that if v be the
average forward velocity of the particles in a vertical section
at 2, we must have
dv dv a
ee ee ee (B)
Tt is assumed in Mr. Heath’s paper, and, I believe, usually,
that «, the depth of the canal, is “ buta very few miles.” This
assumption is avoided in what follows, not being compatible
with the problem we have to solve ; for although it will appear
that the assumption that « is small might have been made,
yet this could not have been readily foreseen.
(3) The assumptions which will be made are :—That the
horizontal velocity of all the particles of water in a vertical
column are the same; that the vertical and horizontal veloci-
ties are small, and that the elevation or depression of the sur-
face above or below the mean level is also small; so that pro-
ducts of these quantities and of their derivatives may be
neglected.
From this it follows that, expressing partial differential
coefficients by brackets, since
dw dv dv
dv __ (dv :
= (Ge) approximately ;
216 ‘Rey. O. Fisher on the Effect upon the Ocean-tides
and
o) aaa «)
aye dz)”
Henceforth the brackets will be omitted.
Let Ox be the mean level of the surface,
O O’ be the depth of the canal =x,
OM=z,
MP=
m L=z
Let w be the vertical velocity of the liquid at Z at the time
t, and in the time d¢ let the surface rise from P Q to RS.
Then the volume of liquid which enters QZ in the time dé
is
v(e+y—z)dt+w dea dt ;
and that which goes out is
v(K+y!—z)dt,
v' and y’ being the values of v and y at «+dz, or
dv
d
And their difference is SP, or
dy
re dx dt.
Therefore, neglecting the products vy and v’y’, we get
dv dy
ae (k—z)= Fig
It is obvious that when z=0, then w=0, and _ is not a
function of z; whence the two relations,
7
:
y
) of a Liquid Substratum beneath the Earth’s Crust. 217
ad ee a Keys
d. d.
But we know (A) that == —a.
Wherefore from (1),
Be OU.
dx” « dx’
Cos a)
dz « da”?
oF oa vary. . a te ie ole spen os)
By the same reasoning as that by which we haye concluded
ayy | du ee
that ee tap? likewise conclude (B) that
de, de
Gn dm
ere
= 7 Age ue . . . ° . ° (4)
(4) The equations of fluid motion in two dimensions will
be, p being the density and p the pressure at Z:—
ldp _ dv dv dv
Riga fit dei de 8 agit 4)
1 dp dw dw dw
phe edna Cae ass + ~ Se)
In our problem p is constant. Considering a tide formed
over a rigid bottom, the horizontal forces are the difference
between the moon’s horizontal attractions at the point 2, z,
and in a parallel direction at the earth’s centre, and the
friction.
The moon’s differential horizontal attraction is — se sin 2a,
M being her mass, a the earth’s radius, D the moon’s mean
distance, and the longitude west of the moon’s meridian.
Tt will be negative, because it acts in an easterly direction.
Call it —psin 20.
The horizontal friction, if taken as proportional to the velo-
city v of the liquid (which is true of low velocities), 7 being
the coefficient of friction, is fv, or (by (3) of § 3), = y. When
Se ee
a ee
218 ~—‘Rey. O. Fisher on the Effect wpon the Ocean-tides
y is positive, or the liquid flowing westward, this force acts
eastward, and vice versa; so that its sign is always opposite to
that of y. It will therefore be expressed by — a PL Hence
X=—ypsin 20—f—y;
also ZL=—
Therefore, neglecting the small products, and substituting for
= and 2 the values lately found, the equations are reduced to
Ldp a” dy
5 da = Hh Sin2o—f cyt ay . oe te (1)
dp _ ae” (Dy
p dz = e 5 Pas ° . . . ° . . (2)
Integrating (2), and taking the integral from 0 to 2, we
obtain
Lpaglety—2+ = (et y)'—2)s
*. differentiating with respect to x, and neglecting the small
products,
1dp_ dy Kay
p dx I dx > da®
‘If there should be a floating crust of any kind capable of
adapting itself freely to the wave, the pressure arising from
this cause must be added to p; but it disappears when diffe-
rentiated.
. ’ 1
Hence, putting aw for vw, and equating the values of 5 e2
the differential equation to the wave-surface is
a’ \ldy ax ay _
ie “y+(g— =) eget SS dw —H sin Zo.
Assume
y=A cos 2o—B sin 20,
*. y=r/ A? + B? cos (20 + 28),
where ‘
tan 26= %
And we find aoe
K
tan 26= Sa pe . (8)
é
of a Liquid Substratum beneath the Earth’s Crust. 219
whence
me ee
y= 2( ce aga? cos 26 cos (2@+ 26).
J 2 ac
(5) Suppose c to be the maximum value of y when friction
is not taken account of. Then
And the maximum value of y when friction acts will be
EXC OWENS aia ee PE i bed (1)
Equations (3) and (4) show that, as friction is increased, 26
tends towards 90° or 6 towards 45°; while at the same time c’,
the maximum tide above mean level, diminishes to zero.
Hence as friction (or viscosity) increases, the vertex of the
tidal spheroid moves eastward, the ellipticity of the tidal sphe-
roid simultaneously decreasing, until, when friction is infinite,
its vertex reaches 45° east of the moon, and the tide disappears
altogether. The same general result appears from Mr. Dar-
win’s table (p. 16)* to hold good in the case of bodily tides,
if there should be such in the earth.
(6) We notice that our result is independent of the density
of the liquid, and that the weight of a floating crust, if con-
sidered flexible, would not aftect it—the reason being that
such a crust would aid in depressing the hollows just as
much as it would hinder the elevation of the ridges. It would
have an effect analogous to an additional load to the bob of -
a pendulum.
The coefficient of « in the denominator of the expression for
ce shows that the term may be neglected, although « itself be
not small. For e is the space over which the wave travels in
one second, while a is the radius of the earth.
Neglecting this term, c and likewise c’ are positive or nega-
tive according as
9
4
a
k>or<—:
g,
2
Consequently, when «< there will be low tide under the
* “Qn the Bodily Tides of Viscous and Semi-elastic Spheroids, and on
the Ocean-Tides upon a yielding Nucleus,” Phil, Trans, Roy. Soe. part 1.
1879,
220 ~—Rey. O. Fisher on the Effect upon the Ocean-tides
a” oo j q
moon, and when «> ~ there will be high tide under the moon.
In the case of the semidiurnal tide ~ is about 12 miles.
2
When «=~ the result fails; for c becomes infinite, which
is contrary to the assumptions on which the solution has been
obtained.
(7) Let us now look to the effect of a tide in the crust of the
earth upon the ocean-tide, to see whether the tide formed ina
liquid substratum would so far diminish the ocean-tide thatthe
observed amount of the ocean-tide would disprove the existence _
of a liquid substratum. The manner in which such a dimi- —
nution of the ocean-tide would be produced in an extreme case |
appears thus:—Suppose that the earth were liquid, and that |
there were an extensible film within it at a depth from the
surface equal to the ocean depth. Then, on the equilibrium :
theory, the entire sphere would be deformed as a whole, and
the measurable tide would be merely the excess of the defor-
mation at the surface beyond that at the depth at which the
film lay; which excess would be inappreciable.
In considering this question, it is necessary to take account
of the attraction upon the ocean of the part of the tidal earth-
spheroid exterior to the sphere to which it is tangential. The
problem has been worked out by Mr. G. H. Darwin in part ii.
of his paper “ On the Bodily Tides of a Viscous Spheroid’’*.
He considers the moon as moving uniformly in the equator
and raising tide-waves in a narrow equatorial canal. The
greatest range of the bodily tide is taken as 2H; and it is sup-
posed to be retarded after the passage of the moon by an
angle A which corresponds to 6 inthis paper. The expression
at which he arrives for the motion of the wave-surface of the
ocean relatively to the bottom of the canal (observing that he
measures the ordinate downwards instead of upwards as I
have done), when the symbols are replaced by those here
used, becomes
x See )
K+ pa (F cos 28 595 cos (2H +26)
+ “sin 26 sin (2@+ 28) ie
The apparent tide relatively to land can therefore be written,
* Phil. Trans. Roy. Soe. part i. 1879, p. 22,
of a Liquid Substratum beneath the Earth’s Crust. 221
t
putting, as before, a C
hae cos 20 5 COs (20 +28) t.
dh _
To find its maximum height put ans ss)
A O=c4 —sin 20 + 7 008 (20 +28) b.
ape
Squaring, and adding, and calling the high tide H, we have
ae {1-5 2" (2c0s28— 7)
5 ap Dau! .
from which the diminution of the ocean high tide by the earth-
tide, or c—H, can be found.
(8) The canal theory of the tides is doubtless less applicable
to the fortnightly than to the semidiurnal tide. Nevertheless
a certain fortnightly tide would be raised in an equatorial
canal; and since we are seeking the pro ratd diminution only,
and not the absolute height of the tide, we may assume that
this result will be applicable to the fortnightly tide ifwe assign
corresponding values to the symbols. It is evident that the
earth-tide must be of the same period as the ocean-tide which
is affected by it; so that H, c, and H will belong to tides of
the same period.
The foregoing equation is suitable to find the diminution of
the ocean-tide by the earth-tide, whether we consider the tidal
deformation of the ocean-bottom to arise from a bodily tide in
a non-rigid, but solid, earth, or from a tide in a liquid layer
beneath the crust, and of a depth which is small compared with
the radius. The latter is the theory of the constitution of the
earth which I have maintained in my ‘ Physics of the Earth’s
Crust,’ and against which the tidal argument has been held to
present a formidable objection. It is therefore with this sup-
position that Iam concerned. ‘The canal theory of the tides,
dealing with a layer of liquid, seems to be the suitable one
upon which to estimate the deformation of the crust through the
tide in the liquid substratum—that is, to give the value which
we ought to assign to H. Let, then, 7 be the tide which would
be formed in such a substratum were it of uniform depth,
perfectly liquid, and frictionless. Then, from what has been
already proved,
EK=7 cos 26.
222 ~—Rey. O. Fisher on the Effect upon the Ocean-tides
Now
ap K
ee a 2 yf
7 o(e—-£)_45*
# sol
Substituting for E, and observing that 7 vides out, we have
2 ‘"«cos?d 4 K ) \
wae ae tats i,
a eft 5 a oe 5 a Ko
o> eae — Sea
= es 2 an
This expression is therefore applicable to find the diminution
of an ocean-tide of any period, if we give a corresponding
value to «, because the moon’s force is not involved in it*.
(9) The theory of “ mountain-roots,” described at the com-
mencement of this paper, requires that the liquid substratum
should be at least about 60 miles deep. Nowif @ be the velo-
city of the semidiurnal tide, ~ is about 12 miles. Hence «
2
will be at least five times ~. And if we omit the considera-
2 pye
tion of friction, then cos 26=1, and a = is very small, so that
H=c{1—23t=bhe.
The semidiurnal tide would therefore, under these cireum-
stances, be diminished to one half.
If the depth of the substratum were, say, 120 miles, the
tide, when friction is neglected, would be diminished by 4, or
it would have 2 of its undiminished value.
(10) But, no doubt, friction would have a very considerable
effect upon a tide of short period in sucha substance as molten
rock, confined both above and below between a rigid nucleus
and the floating crust. The factor cos?26 would therefore
greatly lessen the term expressing the diminution of the
tide. The mountain-roots likewise, following the contour of
the land masses of the globe, would so confuse the tidal phe-
nomena, both in the substratum and in the ocean, that little
* “Tf QO be the moon’s orbital velocity, and I the inclination of the plane
of the orbit to the earth’s equator, then the part of the tide-generating
potential on which the fortnightly tide depends is
2M ayy? sin? I(4 — cos? 4) cos 20%,”
8 <3
where m is the moon’s mass, c her distance, w the mass per unit of volume
of the earth, 7 the radius vector, and @ the colatitude (Darwin, “On the
Bodily Tides,” &c., loc, cit. p. 15).
of a Liquid Substratum beneath the Earth’s Crust. 228
reliance can be placed upon the above estimates. It is, how-
ever, necessary to remark that all the accidents to which I
have referred would tend to diminish the earth-tide, and to
lessen the consequent diminution of the ocean-tide, and so to
weaken any argument against the theory of a liquid sub-
stratum derived from the circumstance that a diminution of
the semidiurnal tide has never been detected.
(11) It appears, however, to be chiefly upon the fortnightly
tide that reliance is placed for answering the question whether
the earth is rigid or not, because friction and the interference
of continents will have a much smaller effect upon that slow
tide. Now the fortnightly tide in an equatorial canal would
have a velocity of about 54 feet per second. If we substitute
this value for «, neglecting the effect of friction, and putting
k=60 miles, we obtain
H=¢ex 0'6:
If we use a larger value for x, the result will be but little
affected.
(12) The effect of friction would not altogether disappear
even in the case of the fortnightly tide ; and the supposed
mountain-roots, which appear to be a necessary accompani-
ment of a liquid substratum, would still interfere with the for-
mation of the tide, and diminish the value of E, and lessen the
diminution of the ocean-tide.
Suppose, then, that if there were no friction in the sub-
stratum, the ocean-tide would, as shown above, be diminished
to 0-6 of its undiminished value. Let us inquire what the
coefficient of friction in the substratum would need to be to
bring the ocean-tide up to 0:7 of its undiminished value. Now
H=c{1— 27 cos? 26(2—#)} nearly.
Hence the diminution varies as cos’ 26. By our supposition
= = Cos" 26,
or |
26= 380°.
Now (§ 4)
Dpiaate s:
tan 26= DG taRy:
and 2’, the equatorial velocity of the fortnightly tide, =54:28 *
feet per second; «=60 x 5280 feet; and a=209 x10 feet;
g =32'2 fect. From this equation we find
f= 0°0178 tan 28.
224 Effect upon the Ocean-tides of a Liquid Substratum.
And if 28=30°,
f=0°010316,
= yp) nearly.
What is meant by such a coefficient of friction may be thus
realized. Mr. Heath remarks that it is only necessary to con-
sider the friction on the bottom of the canal. The effect is
assumed to be to check equally all the liquid in each vertical
column, as if it were all directly subject to the action of the
bottom (and of the crust at the top also in the case of the
substratum). This, as he says, “can hardly be true, though
probably the resulting calculation exhibits something closely
resembling the case of nature; for it is the average forward
velocity on which the form of the wave depends.” But it
seems to me that the reciprocatory nature of the motion of the
liquid will nearly confine the effect of friction to the two sur-
faces, because scarcely will the retardation have been propa-
gated far before it will be reversed in direction. The case
will be somewhat analogous to the propagation of seasonal
variations of temperature into the earth’s surface.
We have then, integrating the equation
dv
Fea +)
ees 6
dE? h.l. Fe
where C is the initial velocity. Whence, if f=0°01, such an
amount of friction would reduce the velocity to one half in
100 x h.l. 2, or 69°3 units of time. Tor instance, if a stream
of the material were flowing over level ground witha velocity
of one mile an hour, it would be reduced to half a mile an
hour in 69°3 hours. As the layer of liquid may, from what
has just been said, be likened to a solid layer whose upper and
under surfaces are lubricated by a sufficient thickness of the
liquid, this would seem to be a low degree of viscosity for such
a substance as molten rock.
In the case of the semidiurnal tide «= 1520 feet per second;
and if we put f=0-01, 26 will be about 87°, and cos?26=0°0024.
This factor will render the diminution of the ocean-tide prac-
tically inappreciable.
(13) The final result therefore is that, upon the canal theory
of the tides, if there be a liquid substratum of 60 miles or
more in depth beneath the crust, and resting on a rigid
nucleus, upon the supposition (of course impossible) that the
i i at
=.
ee,
:
¥
3
.
e
On the Dimensions of a Magnetic Pole. 225
substance is perfectly without friction, the fortnightly ocean-
tide in an equatorial canal would be reduced to about 0°6 of its
ealeulated amount. It would require a coefficient of friction
of 0-01 to bring this tide up to 0°7 of its calculated value. But
the same amount of friction would have so great an effect in
reducing the semidiurnal tide in the substratum, that the
ocean-tide of that period would not be perceptibly affected.
This is entirely in accordance with the « priori reasoning sug-
gested in my book, as referred to at the beginning of this
article. Without friction, however (a condition impossible in
nature), the semidiurnal tide would be reduced to one half its
calculated value.
Should then observations on the fortnightly tide lead to the
conclusion that it is reduced to somewhere about 0°7 of its cal-
eulated value, it would appear that such a result would on the
eanal theory agree perfectly well with the theory of a liquid
substratum upon a rigid nucleus. And, further, under these
circumstances no appreciable diminution of the semidiurnal
ocean-tide could be expected.
The entire range of the fortnightly tide at Teneriffe, upon
the supposition of a rigid earth, would be, according to Sir
William Thomson, 4°5 inches*.
August 12, 1882.
XXV. On the Dimensions of a Magnetic Pole in the Electro-
static System of Units. By J. J. THomson.
To the Editors of the Philosophical Magazine and Journal.
Trinity College, Cambridge,
GEN TLEMEN, August 21st, 1882.
INFER from Prof. Clausius’s letter in the last Number
of the Philosophical Magazine that he has misunderstood
my position with regard to the question of the dimensions of
a magnetic pole in the electrostatic system of units. I did
not attempt to show that Maxwell’s value was in accordance
with Ampere’s theory as Prof. Clausius interprets it, but en-
deayoured to show that Maxwell’s value was the necessary
consequence of the principles laid down in his treatise; and
to point out what modification of Ampére’s theory these prin-
ciples leadto. From what Prof. Clausius says about Ampere’s
theory being independent of electrodynamic considerations,
it would seem that he understands the theory to state that every
small magnet is an electric current, and not that the magnetic
effects of every small magnet may be represented by those of
* Natural Philosophy, § 845, ed. 1867.
Phil. Mag. 8. 5. Vol. 14. No. 87. Sept. 1882. Q
226 On the Dimensions of « Magnetic Pole.
an electric current, since this statement is only intelligible on
electrodynamic considerations. The theory in this form seems
rather hypothetical for the foundation of a system of units.
Prof. Clausius does not think it objectionable that his formula
for the magnetic force between two poles is not in the electro-
static system of units of the dimensions of a force. But since the
attraction between two poles is as much a force as the attraction
of the sun on the earth, if the expression mm’ / 7” is not of the
dimensions of force on the electrostatic system, it is clear that
this formula no longer represents the force between two poles,
and that another factor must be introduced to make the ex-
pression of the right dimensions. Now it is one of the great
advantages of Maxwell’s system that all his formule are true
as they stand, and do not require the arbitrary introduction of
a factor on passing from one system of units to another; these
factors introduce themselves naturally through symbols repre-
senting some physical property of the body or medium. As
Maxwell does not dwell on this point in his book, I may be
pardoned if I quote a few illustrations of it.
Using the notation of Maxwell’s treatise, the force between
/
ee ; Ae
two electrified particles = —,, where « is the specific induc-
Kr”
tive capacity of the substance. Now in the electrostatic
- - ay 8p P
system the dimensions of e are (M?L?T~’), and « is of no
dimensions in mass, space, and time. In the electromagnetic
system the dimensions of e¢are M*L2, and « is of dimensions
L~*T?. Thus in both these systems the expression ee! / «r?
is of the dimensions of force; and the factor changing from
the one system to the other makes it appearance in the «x.
The same thing is true for the force between two magnetic
poles. The expression for the force is mim’ / wr’, where pw is
the magnetic permeability of the substance. In the electro-
static system m is of dimension [M?L?], and p of dimensions
[L-°T*]; in the electromagnetic system m is of dimension
[MsL?T~"], and w of no dimensions; thus in both systems
the expression mm’ / ur? is of the dimensions of force. Other
illustrations might be given; but the reader can easily verify
the statement that in Maxwell’s system every equation is true
as it stands; and consequently, whenever we have a purely
dynamic effect, the expression for it will be of the same di-
mensions in both systems of units.
I am, Gentlemen,
Your obedient servant,
J. J. THomson.
eae
[ 227 J
XXXVI. A new Form of Magnetic Torsion-balance and Magne-
tometer. By FREDERICK JOHN SMITH*.
N the torsion-balance, such as used by Coulomb to measure
magnetic forces, two poles of the suspended magnet are
acted on. The end the author has had in view is so to place
one pole of the suspended magnet thatit shall not be acted on
by horizontal pull. A magnet of rectangular shape, N BS,
fig. 1, having a brass counter-
weight A B, is suspended by the Fig. 1.
filaments C D so that the south
pole is in the axis of rotation of
the whole mass; thus the magnet
may be regarded as having only
one pole that can be acted on by
horizontal force. In addition to
this, a little mirror is so placed |
on an axis, O M, and attached to
S by a short lever P, that the
ratio of the deflection of N to the
rise of the whole mass is at once
shown on the scale, R, by the
usual reflecting method. In the
magnetometer for determining
the pole-strength of magnets the
same kind of rectangular magnet is used, attache] to a single
horizontal wire, A B, fig. 2; the magnet is furnished with a
mirror-scale and lamp.
| Fig. 2.
NPS, rectangular magnet; S, mirror; R, scale and lamp.
The instrument is used thus:—The weight at Q and the mag-
net N’S’ being removed, the magnet NPS is set ina hori-
zontal position by means of the torsion-wire ; then a known
weight, Q, is placed at M, MP=PN, and the deflection on
the scale is recorded ; then the weight is removed, and the
* vole Gg by the Author.
2
a
228 Notices respecting New Books.
same deflection produced by bringing up the N pole of the
magnet N’S’. The magnets are made of equal pole-strength
and tested in the usual manner; the distance between them is
taken in centimetres, the weight Q being in parts of the
gramme. In the formula which shows the relationship be-
m xm!
a?
strengths, d distance between them), if m=’ as in this instru-
(where /= force, mm’ pole-
tween magnetic forces, f=
2
ment, then fa: and if 7 be replaced by Qg (i. e the
numerical value of the weight x gravitation), the formula
becomes Qg= ay from which m is known in absolute measure.
With the pole-strength thus obtained the strength of other
magnets and solenoids can be readily compared. In order to
secure great strength, the frame which carries the torsion-wire
is a gun-metal casting, having a rib at the back.
Taunton, July 27, 1882.
XXVII. Notices respecting New Books.
A Treatise on the Distillation of Coal-Tar and Ammoniacal Liquor.
By Groree Luner, Ph.D., F.C.S., Professor of Technical Che-
mistry in the Federal Polytechnic School, Zurich. London: Van
Voorst, 1882.
D* LUNGE is so well known, not only from his published
investigations, but also from his ‘Treatise on the Manufac-
ture of Sulphuric Acid and Alkali, that we were desirous of ascer-
taining how he would handle the subjects of coal-tar and ammoniacal
liquor. A careful examination of his book enables us to pronounce
most favourably upon it; and we regard it asa very valuable
contribution to the literature of coal-tar and its derivatives.
Dr. Lunge commences his work by a preliminary chapter of 25
pages entitled ‘“ The Origin of Coal-tar,” in which he discusses the
differences between the tars derived from peat, browncoal, bitu-
minous coal, and real coal, and also the effect of the temperature
at which the coal is distilled upon the resulting products. We
quite coincide with the author that the system well-nigh universally
adopted, of squeezing the maximum quantity of gas out of the coal
and letting the tar come out as it may, isa bad system. We may,
perhaps, be hardly prepared to accept the dictum recently uttered
at the annual meeting of gas-managers by a well known American,
that, before long, gas will become the “ residual” and coal-tar the
principal object in the carbonization of coal; nevertheless it is, we
think, indisputable that coal-tar is a necessity of the age, and will
become rapidly of greater and greater value.
In Chapter II. a table is given of the constituents of coal-tar.
—— ee
ee se
Notices respecting New Books. 229
This table is the most complete that has yet been published. It must
be remembered, however, that itincludes the products of Boghead and
other bituminous shales as well as those of true coals. After the
table, is given a brief but sufficient account of the chemical and
physical characters of the principal substances mentioned in it.
The sketch of the history and properties of benzene is very com-
plete, and includes a clear description of the views of its constitu-
tion propounded by Kekulé, Claus, and Ladenburg. The author is
quite right in saying that it would be well-nigh impossible to find
one’s way through the interminable field of the aromatic compounds,
if Kekuleé’s theory of the constitution of benzene had not brought
light and order into it.
Chapter IIT. is devoted to “ The Applications of Coal-tar with-
out Distillation.” It is well written and very interesting, and,
describes the various attempts that have been made to utilize it for
fuel, varnishes, &c.; it is, however, becoming tco valuable for these
~and similar methods of getting rid of what was once regarded as a
nuisance.
The chapter on the “ First Distillation of Coal-tar ” is so minute
that there is even a section on the “ Carriage of Coal-tar.” Even
the best form of casks is discussed; and we are informed that:
** Long barrels are said to be pulled more easily than those more
bellied.” Does the author mean rolled instead of “‘ pulled”? The
sentence seems rather obscure. The distillation of tar by steam
and fire is fully described ; and the best forms of stills, condensers,
and rectifying apparatus are illustrated by engravings.
In treating of Pitch, the manufacture of artificial asphalt, and
of the so-called asphalt-pipes used for conveying water, acid, air-
blasts, for covering underground telegraph-wires, &c. &e., is de-
scribed, and instructions are given for the preparation of artificial
fuel. The distillation of pitch for the production of anthracene oil is
fully treated ; and engravings are given of Fenner and Versmann’s
apparatus.
Chapter VI. is devoted to the working-up of the anthracene oil,
which is effected by cooling to cause the solid hydrocarbons to de-
posit; the whole is then pressed, and the liquids are returned to
the heavy oils, or employed as lubricants, or are redistilled. The
solid portion constitutes rough anthracene, and may be sold as such,
or be submitted to further purification. The preparation of anthra-
cene has, however, been very fully treated of by Auerbach, whose
excellent treatise has been translated into English, and is in the
hands of every one interested in the subject. ‘The chapter on Creo-
sote oils is a valuable one ; but we think the author is scarcely suffi-
ciently alive to the comparatively smail part played by phenol in
the preservation of wood. Certain it is that long after the phenol
has so far disappeared that it is aimost impossible to detect it even
by the most delicate tests, the wood continues to remain sound for
many years. We are also of opinion that those modern specifica-
tions for creosote oils which insist that no naphthalene shall be
deposited at 40° F. have been issued under a false impression of
230 Intelligence and Miscellaneous Articles.
what constitutes a good creosote oil, and would exclude oils of the
highest preservative character. We have lately examined timber
“pickled” 30 years ago with creosote oils from the London tar,
and which oils when cooled to 40° F. yielded a very large amount of
naphthalene; and yet the wood remains perfectly sound to this day.
The directions for the preparation and estimation of pure phenol
(carbolic acid) are very minute, and include the results of the most
recent workers on the subject. The author also describes the
methods of preparing carbolic soap and disinfecting powders.
The chapter on Ammoniacal Liquor is well written, and contains
a full account of all the substances contained in it; directions are
also given for estimating its value, and for working it up. This
latter part of the work is fully illustrated with engravings.
» In conclusion, we congratulate the author upon having produced
a work which is absolutely indispensable to all manufacturers of coal-
tar products.
Worked Examination Questions in Plane Geometrical Drawing.
By F. E. Hutme. Longmans, Green, and Co.: London.
- Tuts work consists of three hundred questions taken from old
examination papers, two thirds of which have figures correspond-
ing to them, said to be solutions of the problems. There is no attempt
at classification ; on the contrary, it has been purposely avoided by
the author, and for a reason with which we do not hold. There
are no demonstrations, and in most cases only scant directions ; and
even these are given where least, and omitted where most, needed.
Many of the constructions are empirical, and incapable of being
demonstrated ; hence, from a mathematical point of view, they are
not solutions at all. Scale Questions, those bugbears of Candidates
for Military Examinations, ought to have been collected, and com-
plete solutions of typical cases given. What good results from
answering precisely similar questions over and over again? Not-
withstanding its many defects, there is much in the book to re-
commend it. The questions are such as are certain to be encoun-
tered in Woolwich and Sandhurst papers; and the constructions
are well drawn and conveniently placed for easy reference.
XXVIII. Intelligence and Miscellaneous Articles.
ON THE DURATION OF THE PERCEPTION OF LIGHT IN DIRECT
AND INDIRECT VISION. BY AUG. CHARPENTIER. :
AFTER various experimenters, I have sought to determine the
time that elapses between the appearance of a light before the
eye and the making of a signal by the subject of the experiment as
soon as he perceives the light. There was interest in ascertaining if
the duration of the perception was different for the centre and for
the excentric portions of the retina, if exercise could modify that
duration, and if the modification would or would not be limited to
the part exercised.
For these experiments the eye, place at the centre of a Landolt’s
perimeter, looked into a large box lined with black, in the bottom
of which a perforation had been made, about 1 square centim. in
section, usually closed by a plate lined with black, which plate,
heayy and metallic, was retained in its position by the attraction of
an electromagnet, but without coming into immediate contact with
the latter, so that as soon as a person placed behind the box inter-
rupted the current animating the electromagnet the stopping-plate
instantly fell and disclosed the window placed before the eye which
was under experiment. A current supplied by a laboratory Gramme
machine, after passing through the electromagnet, put in action a
small Deprez signal, the pen of which left its trace on a regis-
tering cylinder with a Foucault regulator. The signal immediately
announced the interruption of the current, and consequently the
precise moment of appearance of the light. Then the subject under
experiment, directly after perceiving the light, restored the current
in the signal through a derived path, by pressing on a spring the
index finger of his right hand; precisely at this moment a new sign
is traced upon the registering cylinder.
The interval which had elapsed between the interruption and
reestablishment of the current, measured by comparison with the
vibrations of a Marey electric chronograph, indicated directly the
time which had been required for the subject to perceive and signal
the light. For shortness, I shall call that time simply the dura-
tion of the luminous perception.
Here are the principal results which I have obtained in this in-
vestigation :—
(1) For one and the same person, under the same conditions,
the duration of the perception varies from single to double without
any apparent regularity. But ifin one and the same experiment the
mean of a sufficiently large number of successive determinations be
taken (ten for example), a duration constant during the whole time
of the experiment is found. I have found for myself, in direct
yision, a mean duration of 0°13 second with daylight.
(2) The duration of the direct perception varies according to the
individuals. I have seen it vary, according to the persons, from
0-09 to 0°15 second.
(3) The duration of the perception is sensibly the same for the
right and for the left eye when they are sound.
(4) The duration of the luminous perception is notably increased
by another cerebral occupation imposed on the subject during the-
experiment. Thus, when he speaks, when he listens attentively to
a reading or a discourse, while at the same time applying himself
to the experiment, he must have, for the reaction, 0-04 or 0:06
second more than before.
(5) The duration of the luminous perception is always more con-
siderable in indirect than in direct vision ; it is more considerable
in proportion as the point of the retina struck by the light is more
distant from the centre. This cannot be due toa difference of sen-
sitivity, since, as I together with M. Landolt have shown, the retina
is everywhere nearly equally sensitive to light.
(6) The difference between the duration of indirect and that of
direct vision showed itself especially considerable at the beginning
of our experiments. There was then between the duration of per-
Intelligence and Miscellaneous Articles. 231
232 Intelligence and Miscellaneous Articles.
ception for the centre and for a point situated 80° on the outer
side in the visual field a difference of nearly 7 hundredths of a
second. That difference was notably lessened by repetition of the
same experiments during a month and a half; at the end of that
time it was not more, for my left eye, than 2 hundredths of a second.
(7) If exercise attenuates the difference of duration of direct and
indirect perception, it never annibilates it ; so that the first con-
stantly takes place more rapidly than the second. The influence
of exercise asserts itself rapidly from the first sittings; afterwards
it takes effect rather slowly, and then affects direct as well as indi-
rect vision.
(8) Having established at the commencement that the duration
of perception is the same for the left as for the right eye, I made,
almost every day during a month and a half, fifty determinations
on two well-defined points of my left eye only, excluding all other
points of my two retinas. I thus exercised exclusively, a very
great number of times, the centre of the left eye and the point of
the left retina corresponding to 80° in the external part of the
visual field (the internal part of the retina), At the end of that
time I could estimate the influence of exercise by comparing the
duration of the luminous perception on the same points in the
right retina, and even on other points in both retinas. That dura-
tion was, for the centre of the left eye 0°129 second, for the centre
of the right eye (not exercised) 0-148; at 80° outside for the left
eye the duration of perception was 0-160 second ; at 80° outside, for
the eye not exercised, 0:210 second. Therefore exercise had notably
shortened the duration of the reaction of the points experimented on.
(9) I wished to see if the abbreviating influence had extended
over the left eye to points which had not been exercised. Now the
duration of the reaction was found to have been shortened in the same
proportion for all the points of the inner half of the left retina (the
outer side of the visual field), but not for the points of the outer half.
Consequently the exercise of an excentric point affects the different
points of the same retinal hemisphere, but not those of the other
hemisphere.
(10) The shortening influence had extended to the outer hemisphere
of the retina of the right eye, while the inner hemisphere reacted much
more slowly than the same part, exercised, of the left eye.
These facts can hardly be explained, except by admitting Wol-
laston’s theory respecting the incomplete crossing of the fibres of
the optic nerve in the chiasma, and supposing that the exercise of
one part of the retina does not act merely on that part itself, but
rather on the whole of the nervous centre, which receives both the
fibres from the half of the retina containing the exercised point and
the fibres from the half on the same side of the opposite retina.
Most of these experiments were simultaneously made by my
assistant M. Bernardy, who aided me throughout, but, unfortu-
nately, being able only to utilize the right eye for these researches,
did not control points 8 and 10.—Comptes Rendus de Académie
des Sciences, July 10, 1882, t. xey. pp. 96-99,
+ ey
Intelligence and Miscellaneous Articles. 233
AN AIR-THERMOMETER WHOSE INDICATIONS ARE INDEPENDENT
OF THE BAROMETRIC PRESSURE. BY ALBERT A. MICHELSON.
The appearance of an abstract of a paper by Pettersson* on a
new air-thermometer has led me to publish, sooner than I had
contemplated, a notice of an instrument far simpler and more
manageable than that which is there described, and which likewise
retains the important advantage of giving indications which are
independent of the external pressure.
The instrument consists of a glass bulb and stem, the former
about 40 millim. and the latter about 2 millim. in interior diameter.
The bulb contains dry air at a pressure of about 100 millim. of mer-
eury ; and this air is separated from the upper portion of the tube
by a column of mercury about 100 millim.in length. The mercury
remains above the air, notwithstanding the large diameter of the
bore, owing to the resistance to deformation of the meniscus. The
space above the mercury is a vacuum.
Thus the pressure of the air in the bulb is constant, and is equal
to that of the column of mercury above it. I the bore of the stem
is not of uniform section, the length of the column will change ; but
this length is easily read off, and gives at once the true pressure.
The pressure need not be limited to 100 milim.; butif it be much
greater the instrument becomes inconveniently long.
The only precaution to be observed, beyond what is used in an
ordinary mercurial thermometer, is that the stem must be kept ver-
tical.—Silliman’s American Journal, August 1882.
Case School of Applied Science,
Cleveland, O., July 4, 1882.
ON A PROPERTY OF THE ISENTROPIC CURVE FOR A PERFECT GAS
AS DRAWN UPON THE THERMODYNAMIC SURFACE OF PRESSURE,
VOLUME, AND TEMPERATURE. BY FRANCIS HE. NIPHERT.
The equation of this thermodynamic surface is
PUK Ae arses io eee (1)
where p, v, T represent the pressure, volume, and absolute tempe-
rature, and where R is directly proportional to the volume of a
unit mass (or inversely proportional to the density) of the gas at a
standard temperature and pressure.
By differentiation, (1) becomes
R RT
Gp — Ge eee oa Rae toe (2)
v uv
For convenience, putting
Roy, Blip
Uv
(2) becomes
dpa Mtl Balan 4 eee ae (3)
1. To find the direction of maximum slope with respect to the
v, T plane at any point on the surface. For this purpose pass a
* Annalen der Physik und Chemie (Beiblatter), No. 5, 1882.
+ From Trans. of St. Louis Academy of Sciences, read April 3, 1882.
234 Intelligence and Miscellaneous Articles. i. lin
plane through any point in the surface, and at right angles to the —
v, T plane. Its trace upon the v, T plane is
T=P+av, 355.4 4, (4)
p being indeterminate, where a is the tangent of the angle which ~
the trace makes with the v axis, or
ll ee (5)
From (3) and (5) we have
dp=(Aa—B)dv, ...,.- 550000 0nee (6)
Calling 8 the slope of any element of the intersection of the
plane and the surface, dz being the projection of the element on
the v, T plane, we have
which by (5) becomes
__ ap 1
dv ‘ V1l4+a°
= Ae Be (8)
In determining the direction of maximum slope at any point,
‘it is evident that A and B will be constant, which gives as the
required condition,
ds _ A+Ba
ied =0,
da (1+a)?
or
a=—A,
B
Substituting the values of A and B, we have
(= y= ta, oat (9)
For very low pressures, the direction of maximum slope P
z
becomes more and more nearly at right angles to the plane of p, v;
while for high pressures this direction becomes more and more
nearly parallel to the plane of p,v. The direction of maximum
slope is constant along a line of constant pressure.
2. To find the direction of the isentropic line at any point on
the surface, as related to the direction of maximum slope deter-
mined in (9).
Poisson’s equation,
Tvt—1= const., . .\.35 ae (10)
is a-projection of the isentropic line upon the plane of v,T, where
k is the ratio of the specific heats =1°41.
Calling «' the tangent of the angle which any element of this
Intelligence and Miscellaneous Articles. ~ 235
projection makes with the v axis, we have
bd Ue
6S An ee
dv
This yalue of a! is obtained by differentiating (16), and is found
to be
r Pp
an a ee CIE! Cee Oacy, PA (11)
Here also the condition of constant pressure gives a constant
value for a’. Hence, at any point along any line of constant pres-
sure, the production of an element of the isentropic line upon the
uv, T plane makes a constant angle with the projected line of great-
est slope at the same point.
From equations (9) and (11) it follows that
k=
tani
from which it will appear that for either very high or very low
pressure the isentropic line runs at right angles to the direction
of greatest slope. The condition that it shall coincide with the
direction of greatest slope is
tan 7 =
SONeIStS bbe sein” (12)
tani=Vk—1= =
or R
p = SSS SA oe en Ole eed ee iZ
- Vi—1 ( )
For air this pressure is about 3:2 millimetres of mercury; and
for other gases it is proportional to the volume of a unit mass at
2 standard temperature and pressure.
The thermodynamic surfaces of various gases will lie the one
above the other, those having the largest value of R being upper-
most. If we now substitute the value of p’ of (13) in the original
equation of the surface, we haye
DN Ty SA TPO Nal eaves. (14)
which is independent of R. Hence, for all gases which follow the
law represented in (1), the lines on their respective surfaces, where
the isentropic lines coincide with the direction of maximum slope
(18), will all lie in a common plane passing through the axis of P
and at right angles to the plane of v, T, its trace upon the latter
plane being represented by (14).
If the gases have a common temperature while in this condition,
(14) shows that they will also have a common density, which, when
T is 273°, will be 0:000058 gramme to the cubic centimetre.
Jt will be observed that for air the pressure indicated in (13) is
_ practically the same as that at which Maxwell’s law for viscosity |
begins to fail. This, however, is a mere coincidence. The two
phenomena have nothing in common, as is evident both from theo-
retical considerations and from experimental results.—Silliman’s
American Journal, August 1882.
236 Intelligence and Miscellaneous Articles.
ON THE INFLUENCE OF THE QUANTITY OF GAS DISSOLVED IN A
LIQUID UPON ITS SURFACE-TENSION. BY S. WROBLEWSKI.
Tt has long been known that the solution in a liquid of a gas
which is superposed to it diminishes the tension of its surface.
M. E. Desains observed, twenty-five years since, that the rise of
the meniscus terminating water at its contact with air was a little
less than that formed with hydrogen, and a little greater than that
formed with carbonic acid—that is to say, that it was lowered in
proportion as the gas was more soluble. I have found that, in all
the liquids which I have studied, the surface-tension in contact
with air is a little greater than in contact with carbonicacid. Lastly,
M. Quincke has shown that, in the case of ammonia and hydro-
chloric acid (which are highly soluble in water), the diminution of
the surface-tension increased with the quantity of gas dissolved.
On the other hand, a number of cases can be cited in which the
more or less complete absence of the faculty of absorbing gases is
always accompanied in a liquid by relatively great surface-tension,
and conversely. Thus liquids whose coeflicient of absorption is
considerable (ether, alcohol, the oils) have a feeble surface-tension.
Saline solutions, which absorb much smaller quantities of gas than
water, have a greater surface-tension than the latter; and their
tension increases with the quantity of the salt dissolved, while their
capability of absorbing gases diminishes. By reducing the surface-
tension of water by the addition of alcohol, the solubility of gases
in the mixture thus formed is increased. And mercury, which, of
all liquids, has the greatest superficial tension, is almost incapable
of absorbing gas. |
The study of the correlation between these two classes of pheno-
mena may be commenced, on the one hand, by determining the laws
governing the solubility of a gas in a liquid, and, on the other, by
measuring the surface-tension of a liquid in contact with a gas, the
solubility of which in the surface-layer of the liquid can be regu-
lated at pleasure by increasing or diminishing the pressure upon
the gas. These experiments are so much the more easy to perform,
as the saturation of the surface-layer of the liquid is effected instan-
taneously, and the tension, depending only on the condition of that
layer, follows with the same velocity every change in the pressure
which determines the value of that solubility.
Up to the present time no one has considered the question in
this light. On the contrary, it has been attempted to establish a
theory of liquids which, while based on the facts which militate in
favour of the existence of that correlation, denies the correlation
itself. That theory, attributing to pressure a direct influence upon
the surface-tension, leads to consequences at variance with the facts.
Thus Kundt, having observed that the height to which a liquid as-
cends in a capillary tube diminishes in the same proportion as the
pressure upon the gas is increased, has drawn from this fact the
following consequences :—
There is an influence of pressure upon surface-tension. The
observed diminution ought to be regarded as a tendency of the
liquid to pass into the gaseous state. If the compression could be
7 ae = a
ee ee
carried far enough, not only all liquids, but solids also, such as salts,
would finally be reduced at ordinary temperature to the gaseous
state, as takes place under the action of heat. Finally, at a little
higher temperature (M. Kundt made his experiments at one tem-
perature only), cohesion being diminished by the increase of tem-
perature, the decrease of surface-tension under the influence of
pressure would take place still more quickly.
Haying recently determined the solubility of carbonic acid in
water under pressures of from 1 to 30 atmospheres, I proposed to
myself to make evident and establish the correlation of these two
classes of phenomena. Meserving the description of the method
employed and the numerical data for a special memoir, I will only
enunciate here the results of my experiments.
Under pressures of 1-30 atmospheres, there exists a remarkable
relation between the laws of the solubility of carbonic acid in water
and the surface-tension of that liquid. That relation can be expressed
thus :—
1. The product obtained by multiplying the surface-tension a by
the pressure P under which the carbonic acid is placed is proportional
to the saturation-coefficient S corresponding to that pressure—that is,
aP=AS,
where A is a coefficient which depends on the temperature and in-
creases with it.
According to the first law of the solubility, the temperature remain-
Intelligence and Miscellaneous Articles. 237
ing constant, P decreases in proportion as the pressure increases*.
Experiment shows that the decrease of «1s proportional to that of
P With the aid of this relation of the phenomena of capillarity,
those of the solubility of the gas can be calculated, and conversely.
2. The pressure remaining constant and -equal to n atmospheres (n
being greater than 1), it follows from the laws of solubility that the
quotient decreases with the lowering of the temperature.
A2P=n
aP=1
Experiment shows that in this case the ratio of the tensions cor-
responding to these pressures decreases also.
This result isin evident contradiction of M. Kundt’s theory,
since the lowering of the temperature, instead of retarding the
decrease of the surface-tension, accelerates it. The phenomenaare
therefore completely independent of the pressure, and depend only
on the state of saturation of the surface of the liquid—that is to
say, on the quantity of gas dissolved in the surface-layer.
The above relation does not end at the pressure of 30 atmo-
spheres. The solubility increasing less quickly than the pressure,
tends towards a certain limit, which at 0° seems to be reached at
* See my Note, Comptes Rendus, t. xciv. p. 1355.
238 Intelligence and Miscellaneous Articles.
the moment of the liquefaction of carbonic acid, since that liquid
does not mix with water. Experiment shows that the decrease of
the surface-tension, becoming slower with the increase of pressure,
tends also towards a certain limit, which at 0° is reached under the
pressure at which the liquefaction of carbonic acid takes place ; at
that instant the surface-tension of the water is reduced to about
one half *.
Bisulphide of carbon, which also does not mix with liquefied car-
bonic acid, behaves in a similar manner in contact with that gas.
The decrease of its surface-tension also takes place at 0° much
more quickly than ata higher temperature. It becomes slower,
and ceases under the pressure of liquefaction of the gas.
In my next Note I will show that the phenomena present them-
selves under a different form as soon as we have to do with a liquid
that mixes in all proportions with liquefied carbonic acid.—Comptes
Rendus del Académie des Sciences, Aug. 7, 1882, t. xev. pp. 284-287.
ON THE STRUCTURE AND MOVEMENT OF GLACIERS.
BY M. F.-A. FOREL.
M. F'.-A. Forel, of Morges, Switzerland, has recently published
(Bibl. Univ. 111., vii. p. 329) an important memoir upon glaciers,
embodying the results of observations by himself and M. Ed.
Hagenbach-Bischoff, with a discussion of these results and also of
those obtained by other observers. His argument rests plainly
upon the well-attested fact that glacial ice has a distinctly erystal-
line granular structure, the mass being composed of a confused
agglomeration of individual crystals, each optically distinct—and,
moreover, that the size of these crystalline grains increases from
the upper margin of the glacier at the limit of the névé, where they
have the size of a hazel-nut, down to the middle part, where the
size is that of a walnut, and further down to the extremity, where.
they are as large as a hen’s egg. For example, at the lower extre-
mity of the Aletsch glacier, or that of the Rhone, the grains have a
diameter of 7 or 8 centim. In regard to this gradual increase in
size of the individual crystals, the author remarks that two suppo-
sitions are possible: either the growth of some grains must go on
at the expense of others less favourably situated, one gaining what
the next loses, and absorbing as much heat as is disengaged by the
crystallization ; or each grain increases in size by means of the
water which reaches it from above from the surface of the glacier.
Of these two hypotheses, the first is rejected, on the ground that,
wherever observations have been made, they have shown the grains
to be all of sensibly the same size in the same region, and not to
be some small, others large, as this explanation would require.
Accepting provisionally the second hypothesis, the author re-
marks that for the increase in volume of the crystals there are
needed water, cold, and favourable conditions. About the last point
nothing is definitely known; but the others admit of further dis-
* The case in which one of these two liquids is superposed to the other
does not come within the scope of this communication.
Intelligence and Miscellaneous Articles. 239
cussion. The water is believed to be afforded by the melting of
the upper surface of the glacier under the influence of the heat of
summer. This water runs over the surface of the ice, descends
into the crevasses, and, if it be admitted that the ice contains
capillary fissures (a pot which is discussed later), much of it would
be absorbed by the mass of the glacier and used in increasing the
size of the crystalline grains ; the rest of the water flows off in the
subglacial torrent. The low temperature needed for the solidifi-
cation of the absorbed water is believed to be due to the continued
loss of heat during the winter, the glacier as a whole being a mass
the temperature of which can never be above zero, but may fall
considerably below. The question as to the mean temperature of
the ice at different seasons of the year is discussed at length ; and
the author concludes, for a variety of reasons which cannot be
quoted here, that the middle of the mass of the glacier has probably
a temperature at the end of the winter several degrees below 0° C.
This excess of cold would be partially expended in causing the soli-
dification of the water which, as already stated, is absorbed into
its mass and thus goes to increase its volume. The crystalline grains
are therefore to be conceived as growing by accretion, successive
layers being added to them at the expense of the water derived from
surface-melting, and in the process of the warming of the glacier
which goes on during the summer.
Assuming the correctness of the results of Hugi as to the increase
in size of the crystalline grains—that is, in brief, that they increase
from a diameter of 1 to one of 4 centim.,—taking 100 years for the
time of their development, the author finds that the annual increase
in volume is 43 per cent. Assuming, further, that the cold of
winter is all employed in bringing about this increase, it is calculated
that the hypothesis advanced is satisfied if the temperature of the
glacier descends in winter to —6°°8 C., or in round numbers —7° C.
This temperature, the correctness of which is obviously dependent
upon the accuracy of the assumed data as to the rate of increase of
volume, is too low to be accepted, and leads to the inference that a
part of the increase is accomplished by a process different from
that which has been described. Thus at the end of the summer a
considerable portion of the glacier must be at the temperature of
melting ice, and in the capillary fissures between the crystalline
grains there must be water; now, as the glacier cools down in the
autumn, the first effect of theloss of heat would be the solidification
of this water, and the consequent increase in size of the crystalline
grains. Taking into account this last point, the author considers
that the temperature that would have to be assumed for the glacier
at the end of the winter would be quite within the range of pos-
sibility.
The hypothesis which has been advanced depends upon the as-
sumption that the water can find its way into the interior of the
glacial mass through the capillary fissures separating the individual
grains. This point is one which is yet somewhat doubtful; and
the author, after considering the various observations of Agassiz
and others, which tell for and against the possibility of such a
240 Intelligence and Miscellaneous Articles.
penetration of the water, discusses the question from a more theo-
retical standpoint, and concludes that the assumption of the im-
permeability of the glacier is contrary to fact. He promises, further,
to make this a special subject of observation at a later period.
In regard to the cause of the movement of glaciers, M. Forel
places himself on the side of Hugi and Grad in supporting the
theory of expansion, although modifying somewhat their hypo-
thesis. On the old dilatation theory, it was the expansion of the
water contained in the capillary fissures at the moment of their
solidification to which the glacial movement was supposed to be
due. According to the view of M. Forel, however, this special
expansion plays a subordinate part; and it is rather the gradual
increase in volume of the crystalline grain, due to the molecular
affinity which causes a crystal to grow in the mother-liquor in which
it is placed.
In discussing further the application of the hypothesis, a distine-
tion is made as to the course of events during the youth and during
the old age of the glacier. The glacier may be divided into three
parts. The first is in the elevated region where the glacier has its
commencement, that of the névé. Here the heat of summer is
not sufficient to melt the whole volume of the snow which falls
during the year; only a part of the snow is consequently trans-
formed into water; and this penetrates into the layers below, and
is solidified there: the temperature is much below the freezing-
point. This is the region of the infancy of the glacier. Following
this comes the line of separation, where the heat of summer is just
sufficient to melt the winter’s snow, and there is no excess of heat
to attack the ice.
The second stage (that of the youth of the glacier) is found
below this line of separation, where the summer’s heat not only
melts the snow but also partially melts the ice ; the water so formed
is absorbed and assimilated by the ice ; and the temperature below
the surface is, even at the end of summer, below zero. In this
region the glacier is increasing in volume, and consequently moying
downward. Then follows a second line of separation, where the
water absorbed is all used in the increase of volume of the glacial
grain. At this point the subglacial torrent has its origin; and at
the summer's end the temperature is at 0°.
The third stage is that of the old age of the glacier, where the
supply of water exceeds that needed to bring the temperature of
the ice back to 0°; the excess of water flows off in the glacial
streams. The temperature of the ice is at 0° during the summer ;
and the excess of the summer's heat goes to cause the melting and
destruction of the glacier.
In concluding his interesting memoir, the author promises to test
his hypothesis by further observations and experiments, bearing
especially upon the questions as to the comparative size of the crys-
talline grains in the different parts of a glacier, and as to the possi-
bility of the penetration of the surface-w ater into the mass of the ice,
—Silliman’s American Jownal, August 1882.
THE
LONDON, EDINBURGH, asp DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
OCTOBER 1882.
XXIX. Notes on Practical Electricity. By R. H. M. Bosay-
queEt, Fellow of St. John’s College, Oxford.
ye work I have had in hand for some time past has been
the design and construction of clock-regulated uniform-
motion machines. As to these, I will only say that the con-
structions formerly described by me have been entirely
superseded by a new design. This is not yet ina state of
sufficient forwardness for ‘description, and I propose to reserve
it for another occasion. The working of these machines is
dependent on the application of a considerable amount of
electrical power. After seeing the Paris exhibition I decided
that in all probability a dynamo machine would be a better
source for laboratory purposes than batteries, which are in
my opinion a nuisance, and subject to most ‘serious defects
when used on the large scale. I accordingly set up an A
Gramme machine. I also have made a set of accumulators.
The practice of the employment of these instruments for
ordinary purposes gives rise to numerous points of interest;
and I propose to give a short account of my experience.
The laboratory steam-engine is able to supply sufficient
power to give a powerful electric light from the machine. I
take it that under these circumstances about 23 horse-power
are absorbed altogether. The nominal horse-power of the
engine is 2. It is scarcely sufficient to develop the full
power of which the dynamo is capable; but for laboratory
purposes it is quite sufficient.
__~Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. R
242 Mr. R. H. M. Bosanquet on Practical Electricity.
The A Gramme machine has four electromagnets, two above
and two below, whose axes are in one plane. In the same
plane is the axis of the Gramme ring armature. The resis-
tance of the machine is about 1°2 ohm.
The magnet-wires are directly connected with the armature-
brushes; and the terminals receive the wires after each has
passed through two magnets. Consequently all currents have
to pass through both magnets and armature, thus:—
Magnet Armature Magnet
Magnet Magnet
Terminal Terminal
For purposes which will be presently described, it was
found necessary to be able to separate the magnets from the
armature. The wires were therefore cut, by which means
the following combinations were obtained :-—
Magnet-terminals 4
Ma gnets--Armatue-7-laag
Armature-terminals
and
-— Magnet-terminals
al
L—___§- Magnets
-— Armatare.7—. ae
L_ Armature-terminals —
in which last arrangement the magnets are separately excited.
There are other forms, which will be described presently.
The resistance of the magnet circuit is about *75 ohm.
That of the double course through the armature is therefore
about ‘45 ohm, the total resistance being taken at 1°2.
The terminals are marked + and — respectively. When
the machine is acting in correspondence with these indications,
I call it “ straight,” and the upper pole-piece attracts the un-
marked end of a compass-needle. The residual magnetism
is very strong. I think the whole of the solid part is probably
made of cast iron.
Mr. R. H. M. Bosanquet on Practical Electricity. 243.
When the polarity gets reversed from any cause, I call it
_“yeversed.”” In this case the upper pole-piece attracts the
marked end of a compass-needle.
The directions of currents and rotation deserve some at-
tention.
_ The machine is driven in the direction opposite to that of
the hands of a watch, regarded from the pulley-end. It
gives currents in the one or the other direction according as
it is “straight” or “reversed.” This is obvious ; for with
reversal of the current both field-magnets and armature are
reversed, and the attractions which have to be overcome in
doing the work remain the same.
_ When a current is sent through the machine from a battery,
it always turns in the direction opposite to that in which it is
driven by the engine ; for whichever way the current goes
the attractions are the same as in the former case, and as
these are overcome by the engine in that case, it is clear that
they tend to turn the machine in the opposite direction to the
engine.
When the machine is driven
by a battery, with the hands of
a watch from pulley-end, it is
necessary so to adjust the brushes
that their ends may not -catch
in the commutator. I turn
up the ends of a spare pair of
brushes, and apply them to the
commutator in, this manner.
Otherwise the machine can be caused to turn in its normal
direction when driven by a current, by reversing the connex-
ions between armature and magnets ; this is made possible
by the cutting of the wire above described. The arrangement
may be formulated thus:—
Armature
eee
Magnets Magnets’
Terminal Terminal
The machine is constructed for driving one are light.
Although this is not a matter with which I am directly con-
cerned, the normal conditions may be of interest:—
R 2
244 Mr. R. H. M. Bosanquet on Practical Electricity.
Serrin lamp.
Revolutions about 900 per minute.
Current about 20 amperes.
Difference of tension between lamp-terminals about 40
volts.
These are the highest values obtained under favourable cir-
cumstances.
According to these numbers the resistance of the are is
about 2 ohms; that of the machine and connexions is about 1°5.
This corresponds to 800 volt-amperes, or rather more than.
1 horse-power, in the light itself (1 horse-power=746 volt-
amperes).
We observe here that little more than half the power ex-
pended is developed in the lamp.
Circuits of High Resistance.
Suppose I take a single British incandescent lamp (150
ohms cold, and about 80 ohms hot), the machine only just
raises it toa red glow, though a speed of as much as 2000
revolutions per minute be employed. The current developed
is much less than 1 ampere.
Here the high resistance kills down the current, and pre-
vents the proper excitation of the field-magnets. Hence the
advantage in this case of machines in which the magnets form
a shunt circuit of high resistance. It is easy to excite the
Gramme machine by putting the magnets into a_ shunt
circuit with a suitable resistance; but if a resistance-wire be
employed, the power developed in heating it is wasted. I
have therefore in many cases adopted the plan of putting
useful work into the shunt-circuit of the magnets. This may
sometimes with advantage consist of a number of incandes-
cent lamps in parallel circuit. Substituting for this a certain
number of accumulator-cells, we have the origin of a useful
method which I call charging in balanced cireuit, to which I
shall return.
Galvanometers.
The galvanometers I employ were made in the laboratory.
They are of a simple character, but quite sufficient for practical
purposes. There are three of them.
Tension Galvanometer.—A circular wooden channel about
‘11 m. radius, wound with wire of which 1 metre=roughly
10 ohms. Resistance=2900 ohms. This had its constant
determined by reading the current from 9 Daniell’s cells,
which are taken as representing 10 volts. Resistance of
Daniell’s cells determined and allowed for. For high ten-
Mr. R. H. M. Bosanquet on Practical Electricity. 245
sions a further resistance of 5000 ohms is interpolated in the
galvanometer circuit. Brass dial 3 inches in diameter divided
to degrees. Short steel needle with long pin-points. 50°
on the galvanometer, with the 5000 ohms external resistance,
corresponds very nearly to 50 volts. Other readings by the
tangent-law.
Two Quantity Galvanometers.—These consist each of a ring
of gun-metal, *11 m. radius; the conductors leading to them
are copper, and of tube-and-core form; brass dials, and steel
needles with long pin-points as before.
When dealing with large currents I placed a steel magnet
under one of these, so as to convert it into a high-quantity
instrument. Its constant was ascertained by sending the
same current through both instruments, the one without the
magnet reading as a tangent galvanometer in absolute mea-
sure.
Measures.
Although numerous measures of dynamo machines have
been published, the laws of any given machine cannot as
yet be predicted; and a few measures are given, which are
sufficient to illustrate the general course of the performance
of this machine under different circumstances,
First, we will consider the cases where the governor was
used. This may be taken to give 840 revolutions in all cases,
except where, the resistance being 3 ohms or less, the leverage
against the engine was suchas to reduce the speed materially.
Resistance in parallel circuit Tension between
with lamp. terminals. uanal ty
ohins. volts. ampéres.
¢ 24:5 3°8 |
6 d1-4 DD
4) 309 76
4 41:0 10°5
With lower resistance the speed cannot be maintained with-
out taking the governor off. In considering the total electro-
motive force developed, of course the whole resistance of the
circuit must be considered. The resistance of machine and
connexions may be taken at 1:5. Then, multiplying the
current by the whole resistance, we should have the total
electromotive force.
The work of Meyer and Auerbach leads for a given speed
to equations of the form @6=aH—b, where @ is an angle
whose tangent is the measure of the current, and E the total
electromotive force. I used the expression at first as it stands;
246 Mr. R. H. M. Bosanquet on Practical Electricity.
but now I think it better to eliminate E as follows:—Putting
E=CR, the above form gives CR= 5 = : or I = EE
where R is the resistance of the circuit, C the current, and @
the angle of a tangent-galvanometer by which the current is
measured.
To apply this to the above observations, we find the follow-
ing values of the total resistance, current, and 6:—
R. c 6. R=”
7-9 38 50° 7-9
7-0 55 60 73
62 7-6 674 6-2
53 10°5 73 51
(When calculating the resultant resistance of the parallel
circuit, we notice that it should be the same as the quotient of
the observed tension by the current. It does not differ in
any case by more than one or two tenths of an ohm. This
is sufficient, considering that no special accuracy was aimed
at. Further, it must be remembered that the wires of the
resistance are nearly or quite red-hot under these cireum-
stances, so that some discrepancy is to be expected.)
Calculating R from the formula
6—20
R=—q— ;
we obtain the numbers in the last column.
This result is tolerably satisfactory; but it is of little prac-
tical use where the motor employed is a steam-engine capable
of considerable variations of speed. With a gas-engine, or
other motor of very constant speed, the above method of find-
ing the approximate resistance for a given current would
probably be useful.
But with my engine, when the governor is not used, the
speed adapts itself to the work to be performed; so that, with-
in considerable limits, the only things to be considered are the
amount of steam turned on and the work to be done. To
illustrate this I will quote a series of experiments, in which
the object was to maintain the tension necessary for a
“ British” incandescent lamp, which is about 80 volts, with
different resistances in parallel circuit.
The least resistance with which this tension can be main-
tained is 5 ohms. It is easily seen that the resulting external
resistance here is nearly four times that of machine and con-
nexions; so that the total H.M.F. would require to be 100
volts, roughly, to get 80 between the terminals. For smaller
=
=
.
Mr. R. H. M. Bosanquet on Practical Electricity. 247
external resistances the total required would be larger ; and
this cannot be obtained. The load on the engine is heavy;
full steam is required ; and the speed is moderate.
Increase the 5 ohms to 6, leaving the steam asbefore. The
engine runs faster, and the required difference of potential is
kept up with about the same head of steam.
Increase to 7 ohms. Similar effect.
Increase to 10 ohms. The engine runs very fast; but the
required difference of potential is still easily maintained. Of
course here the total H.M.F. required is decidedly lessened.
As the resistance increases beyond this point, the speed re-
quired to maintain a difference of potential of 80 volts becomes
too great for convenience, and by the time it reaches 20 or
30 ohms it becomes impossible.
In view of this power of accommodation, the question as to
the precise resistance required to produce a given current at
a given speed becomes of little practical importance.
The explanation of the power of accommodation is, roughly,
as follows. The total E.M.F. is to be supposed constant. In
the preceding experiments it is not quite so, being 100 volts,
about, with the 5 ohms, and 90 or so with the 10. But the
conditions of constancy can be realized; for with the 10 ohms
I kept up the difference of potential of the terminals to 90 volts
for some time, this corresponding to about 100 volts total
H.M.F.; so that, in fact, this condition of constancy of total
electromotive force can be attained through a certain range
with a little attention.
Then the current developed follows Ohm’s law throughout
this limited range, with varying resistances; and the attraction
between the magnets and armature depends on the current in
each; so that a rough idea of the course of the values may be
formed by assuming the attraction proportional to the square
of the common current through both; and this is the reaction
against the engine. Consequently as the resistance in circuit
increases the current diminishes (Ohm’s law), and the statical
resistance to the engine diminishes, as we suppose for the
moment, in the square of the ratio of increase of resistance in
the circuit. Of course, the real values of the attraction depend
on the magnetizations of magnets and armature ; but the
above accounts in a general way for the increase of speed pro-
duced by introducing additional resistances into the circuit.
The increased speed is then utilized in obtaining the same
electromotive force from the diminished current, or rather
from the diminished magnetization.
It will be readily seen how importantly this power of accom-
modation may be utilized in the practical treatment of such
248 Mr. R. H. M. Bosanquet on Practical Electricity.
a question as the variation of the number of incandescent
lamps on a circuit. Take the case of lamps of 70 ohms.
Then 7 of these in parallel circuit constitute a resistance of
10 ohms, and 14 one of 5 ohms. Between these limits the
tension might be kept nearly constant by the automatic varia-
tion of speed above mentioned. I do not say that this is the
best way of attaining the result; but with means such as I
possess it is a valuable auxiliary. I believe as many as 29
such lamps can be driven from the A machine; but this must
require far greater power than is at my disposal.
Accumulators.
I have made 21 cells with lead plates coated with red lead,
and 9 of another kind, which I will describe presently. In
all cases the plates are wrapped in canvas. The lead I em-
ployed was 2 lb. to the square foot; each plate is about a square
foot in size; and the red-lead plates have 1 lb. of red lead on
each surface. The tags at the end were left rather narrow.
I found lately that all the tags of the oxidized plates were so
eaten away at the surface of the acid that they had to be re-
placed. I now use lead 3 lb. to the square foot for oxidized
plates; the tags are left 3 or 4 inches broad, and they are
additionally thickened at the junctions by burning on a piece
of lead on each side ; they are also varnished.
These cells were “ formed ”’ by charging in the same direc-
tion every day for a considerable time. ‘The maximum effi-
ciency was reached in about a month, after which no further
improvement was perceived.
These cells do not pretend to the excellence which is said to
be obtained by the cells of the Faure Company. If left
charged for any time, the sulphuric acid is rapidly and com-
pletely absorbed, leaving the water quite sweet, and consi-
derable quantities of sulphate of lead are formed. This is
slowly decomposed by fresh charging; but in the mean time
it appears to isolate large portions of the active material, and
considerably impairs the efficiency. Iam informed that, this
Jocal action does not take place with the cells supplied by the
Faure Company. The red lead on the hydrogen plates becomes
reduced to metallic lead,and that of the oxidized plates changed
into black peroxide *. Itis not until this change is complete
that the cells attain any considerable efficiency.
* Tam indebted to Mr. Fisher, of the Oxford-University chemical labo-
ratory, for the examination of samples of these substances. . The metallic
character of the reduced substance was proved by amalgamation with mer-
cury. The peroxide contained very nearly the proper quantity of oxygen,
but fell a little short—not more than would be explained by inevitable
impurity.
Mr. R. H. M. Bosanquet on Practical Electricity. 249
The cost of the construction is very considerable. I have
little doubt that they have cost me on the whole as much as
if I had bought them at the very high price charged. But
much of the expense could have been avoided. As it was, the
original construction cost under £2 per cell. About half the
outlay went to provide the wooden cases lined with lead. If
stoneware jars could have been procured, I think one third of
the original cost might have been saved. The “ forming ”’ of
the cells with the small power at my disposal was expensive.
I have not estimated the cost ; no doubt it could be done very
much more cheaply on the large scale.
The best return I have ever obtained amounted to about
one half the power expended. This was obtained after a
charge of short duration, the cells running one Swan lamp.
The current and tension were measured at intervals. The
return was about 70 per cent. of the electrical charge taken,
and, as I judge, about half the total power expended. But
this is by far the best return I have ever obtained. As a rule,
the return is only a small fraction of the power expended.
The other 9 cells are made with amalgamated plates of lead,
and “‘formed”’ by charging in opposite directions in the manner
practised with Planté batteries. These have less capacity than
the red-lead cells, and are troublesome to form; but on the
whole I am inclined to prefer them for laboratory purposes
to home-made red-lead cells. ‘They are much less trouble to
put together, and do not suffer from local action.
Having cells of different kinds in the system is a great
inconvenience. When the red-lead cells have suffered from
local action, they increase their resistance ; and if systems of
balanced charging are employed, in which two or more cir-
cuits are used, a progressive change takes place in the distri-
bution of currents, which requires constant watching. It
should be a first principle that all the cells should be as similar
as possible.
The red-lead cells have 11 plates in each cell, the others 15.
With all their imperfections these cells are extremely useful
for laboratory purposes ; and as this was my object in con-
structing them, I am on the whole satisfied with their per-
formance.
On charging Accumulators.
Suppose that the accumulators are entirely without charge,
and the machine polarized rightly, having its residual magne-
tism such that the + terminal gives a positive current and the
— one a negative current. Then in charging we join + (or
oxygen) to +, and — (or hydrogen) to —, and all goes
250 Mr. R. H. M. Bosanquet on Practical Electricity.
rightly. Now suppose that, after the accumulator has ac-
quired a sensible charge, we stop the dynamo machine with-
out breaking the connexions. The power of the machine to
drive back the battery-current was derived from its velocity,
which is gone. Consequently the battery-current discharges
itself through the machine in the opposite direction to the
proper current of the machine, and reverses the magnetism of
the machine. This change is recognized, as I have mentioned,
by the effects of the pole-pieces on a pocket-compass. When
the machine is “ straight,” the upper pole-piece attracts the
unmarked end of the needle. When it is reversed, it attracts
the marked end.
If the machine be then set in motion again, the effect is to
strengthen the current in the magnets. But this is now the
discharge current of the battery. Consequently the machine
proceeds to pump the electricity out of the battery.
This reversal is prevented in ordinary practice in two diffe-
rent ways. In charging by Gramme machines, in general,
two machines are employed, of which the one serves only to
drive a current through the magnets of the other. This cur-
rent is wholly independent of the charging current; and the
arrangement is consequently not liable to reversal.
The power which is employed in this case to maintain the
current in the magnets contributes nothing to the work; con-
sequently this arrangement is not economical. But in a large
establishment one small machine may be used to excite several
large ones, and the waste is reduced to a minimum.
The best method for charging in general would appear to
be the use of machines of the Siemens type, with the field-
magnets in a shunt circuit of high resistance ; for then the
reaction of the battery-current seeking to pass backwards
into the machine conspires with the forward current from the
machine, so far as the supply of the field-magnets is con-
cerned.
Diagram of Circuits in Shunt-Circuit Machine.
-—Accumulator—y
save agnets |
i
L____Armature peel
But as my machine is not thus arranged, I have had to
devise other means of doing the work. I have not seen any
account of these processes.
mo
Mr. R. H. M. Bosanquet on Practical Electricity. 251
The simplest mode of effecting the charge is to charge in
one series, starting by means of a resistance-wire in parallel
circuit, thus :—A wire of 5 or 6 ohms resistance, arranged so
that it can become red-hot without injury, is introduced be-
tween the terminals, and the machine driven at full speed.
A difference of tension is thus produced between the ends of
the wire, which must be greater than that of the accumulators
to be charged. This difference amounts with my machine to
70 or 80 volts, or even more. Then, if we have 80 volts and
6 ohms of wire, we get a current of a little over 13 amperes,
which is enough to excite the machine well.
The terminals of the battery are now joined up to the
terminals between which the difference of tension is estab-
lished, + to + if the machine is straight, + to — if reversed.
The existing difference of tension drives back the battery-
current, and a charging-current is set up. With the 30 cells
in series I find that the current traversing the accumulators
is about 10 amperes under these circumstances.
is Accumulators a
eee oo
Ma onets—Armature—Maguets
The machine is then traversed by the double current of
more than 20 amperes from both battery and resistance-
wire. Great statical resistance to the engine is consequently
developed, and the magnets are well excited; but the current
through the 6-ohms wire goes to waste, and in fact the wire
is kept nearly red-hot. A large power is required to maintain
this state of things. The last step is to remove the wire,
leaving the battery with the current of about 10 amperes
passing through it. The resistance at the machine is reduced
to about one fourth by the halving of the current, and the
engine quickens its speed ; but, on the other hand, in order
to maintain the difference of over 70 volts when excited only
by 10 ampéres, the machine requires a high speed.
Consequently there is a period of instability at the moment
of removing the resistance, and the machine is often reversed
before the high speed is established. The only means of
obviating this are (1) to cram on every available pound of
steam at the moment, (2) to execute the two operations of
joining up the battery and removing the resistance in such
quick succession that the speed has not time to fall. By the
use of both these precautions I have generally succeeded in
252 Mr. R. H. M. Bosanquet on Practical Electricity.
starting the charging in this form; but until I had acquired
considerable experience and a thorough understanding of the
conditions, I frequently failed.
When this arrangement is once started, and if sufficient
power is available to keep it going, it is not only the most
economical method of charging with this machine, but is more
economical than any other method, excepting the case where
the magnets form a shunt circuit of very high resistance
indeed.
The objection to the arrangement in question is that there
is a very small margin between the tension of the battery and
that of the machine which has to overcome it; consequently
at the slightest check to the steam, and frequently without
any apparent cause, the battery-current will overpower the
tension of the machine and reverse it. The motion of the
machine tends to reinforce the current of the battery in the
new condition, and the resistance of the machine is small;
so that a tremendous current, probably more than 50 ampéres,
is poured through the machine, and the electromagnetic
attraction resulting is powerful enough to stop the engine.
This reversing is indicated by a hiss of the belt on the pulley,
followed by the stoppage of the engine. The person in
attendance has immediately to break the circuit, or the whole
store of electricity would soon be poured uselessly away.
With the limited power at my disposal I have never been
safe from reversals in charging in series in this manner when
the number of cells to be charged amounted to twenty or more.
Another method of starting the charging in series is to
throw a current through the magnets from an auxiliary
battery or from a series of accumulators already charged, and
then introduce those to be charged. The connexions are as
follows:—
i. ace ee Auxiliary ———q
initial
charging current
current
Magnets
ss Armature 9
In this arrangement one terminal of the magnets must be
disconnected from the armature, and the magnets made up
into one circuit.
Mr. R. H. M. Bosanquet on Practical Electricity. 253
When the charging is started, the auxiliary battery is
removed. An instability of the same sort as that above de-
scribed takes place.
This method is not superior to the last, and is troublesome
from requiring the auxiliary battery.
A very simple mode of charging, where the cells are all
similar, is to make them up into two or more parallel circuits,
according to the electromotive force available. When there
are different kinds of cells this method is troublesome, as the
two circuits have to be exactly balanced, and this must be
done by trial. Further, the red-lead cells alter during charging
as if their resistance diminished, which I take to be caused by
the decomposition of the sulphate of lead with evolution of
sulphuric acid. It is then necessary to keep watch at the
galvanometers in the two parallel circuits and rearrange the
circuits when necessary, which is very troublesome. Latterly,
however, I have used this method more. With my machine
it would be more suitable for charging about 40 cells. The
charging is started with a resistance in the sume way as in
the first case.
The next method is an interesting one; I found it useful
when the cells were in good condition, with low resistance
and with about 20 cells; but I have used it also with 30 cells.
When the resistance of the cells is high, it is better to use the
last method with 30 cells.
I call the present method the method of balanced charging.
It arose in this way :—I began by putting the magnets in a
shunt circuit, with a resistance in the magnet circuit; then
accumulators could be charged in the main circuit (armature-
terminals), and the current spent in heating the resistance in
the magnet circuit went to waste. I therefore tried substi-
tuting cells for the resistance in the magnet circuit. I put
the two similar quantity galvanometers in the two circuits,
and varied the distribution of the cells until the deflections
were equal; so that all the cells were getting uniformly
charged. I found at once that under certain conditions a
balance was established, so that the tension-difference on the
two sides of the magnet circuits was small, and that, so long
as the balance was maintained, there was no tendency to
reversal.
The following scheme will explain one of these arrange-
ments :—
254 Mr. R. H. M. Bosanquet on Practical Electricity.
->———_——9 side cells
21°5 volts between magnet-terminals.
Magnets Magnets
: Armature :
|
laa principal cells -—-——_—_]
28°1 volts between armature-terminals.
In this case I had a balance when 9 ampéres of current
were passing in each circuit.
It is clear that the current through the magnets is due to
the difference of tensions between the two sets of cells; con-
sequently,
volts.
Tension of 12 cells=28-1 (measured)
” 9» =219 ”
6°6
and, dividing by the measured current of 9 amperes, we find
‘73 ohm for the resistance of the magnets. This corresponds
well with my direct measure of ‘74, and less well with the
resistance given by the makers, *77.
The balance is a function of the current; and if the power
in action be varied, the current in the principal cells changes
faster than that in the magnet circuit (or side cells). It is
to this circumstance that the stability of the arrangement is
due.
In order to give foundation for the theory of this arrange-
ment we have to represent the variation of the tension of the
cells with varying current. We may represent the course of
the changes sufhciently for this purpose, according to my
measures, by assuming that the tension varies with the —
charging current, so that it is 1°9 volt per cell when at rest
and 2°4 per cell when the current is 10 amperes, 7. e. it varies
dp volt per cell per ampere. The same rule expresses fairly
well the diminution of tension when the freshly charged
battery gives out a current. I shall return to the question
of the rationale of this, and for the present assume general
values, and that the change of tension is proportional to the
current.
Ee
Mr. R. H. M. Bosanquet on Practical Electricity. 255
Let E be the tension of one cell at rest,
z the current in the principal cells,
y the current in the side cells,
e the change of tension per cell per ampére,
m the number of the principal cells,
n the number of the side cells.
Then,
Tension of armature-terminals, or of principal cells
=m(H+ezx) ;
Tension of magnet-terminals, or of side cells
=n(H +ey).
Then, if R be the resistance of the magnets, since the diffe-
rence of these tensions drives current y through R,
m(H+ev)—n( H+ ey) = Ry;
or
(m—n)E + mex=(ne+ R)y;
: daz __net+R
dy | me
Put n=m—d, where d is the difference between the principal
cells and side cells; then
dz R-—ed
ee 3
dy me
which is >1 if R>ed.
In the case above given,
COO ua (4 ers
whence = =2 nearly, and the change of the current through
the principal cells is twice that in the magnet circuit.
Of course it is the change in the magnet-current that alters
the excitation, and gives rise to instability; so the more we
throw the change off the magnet-current, the more stable the
arrangement will be.
The behaviour of the balance as ascertained by experiment
corresponds with this theory. The magnet-current alters
more slowly than the other.
To deduce the magnitude of the balancing current in any
particular case, put y= in the equation
m(E + ex) —n(H + ey) = Ry;
(m—n)H+ {(m—n)e—Ri x=0.
256 Mr. R. H. M. Bosanquet on Practical Electricity.
Let m—n=d as before,
&|
iR="74, d=3, e="05,
a2=5K.
If we assume H=1°9, 2=9°5, which is near enough to 9,
the observed value, to show that we have a general represen-
tation of the facts. The constants are not determined with
sufficient closeness for accuracy.
Again, suppose we wish to charge with a larger current.
Put d=4 in the above; then we find for 2 the balancing cur-
rent 14:6. So that we have only to increase the difference
between the two sets of cells.
Again, supposing we wish to use a smaller current, put
d=2. Then «=6, nearly; or the balancing current is about
6 ampéres. Both of these conclusions have been verified
experimentally.
With reference to the assumption just made as to the de-
pendence of the potential on the current, and generally as to
the constants of the accumulator, if we calculate the resistance
of a cell of the accumulator from the data available, assuming
that the plates are 1 centim. apart, and that the sulphuric acid
has a strength even considerably less than 10 per cent., which
is its original value, we find a result which is extremely small.
In fact, specific resistance *
*2 per cent.=4:47 x 10”,
oie ete = oo ee
The intermediate value 10” represents our case with sufficient
approximation.
The edge of each plate is about 30 centim., and its surface
not far from 1000 square centim.; so we may consider the
conducting solid as consisting of one plate of unit thickness,
and surface somewhat exceeding 10,000.
0
The resistance therefore would be a =10°, or the thou-
sandth of an ohm roughly. This prevents us from assuming
that the change of potential caused by current is due to the
spread of the tensions along a resistance according to Ohm’s
law. And it appears probable that any change of tension due
* These numbers are taken from Prof. Everett’s ‘ Illustrations of the
C.G.S. System.’
Fit
-
Mr. R. H. M. Bosanquet on Practical Electricity. 257
to such a source is negligible, so long as there is acid in the
solution.
A key to the nature of the phenomenon may be found by con-
sidering what happens when the cells are being exhausted. If
a current of 10 amperes, such as I have used for charging, be
demanded from the accumulators, the tension falls off. Ifthe
demand continues, the cell becomes exhausted. If we let it
stand, it will recover itself, just as is the case witha Leclanché
cell, for instance*.
Now the simplest way of accounting for this, as well as for
the rise of tension in charging, is to suppose that the chemical
action, in which the storage consists, does not actually reside
on the surface, but penetrates to a certain extent into the sub-
jacent layers of the mass. It is easily conceivable that such
an action should be only capable of transference through the
mass at a certain rate; that when too large a current is de-
manded from the cell, the chemical change does not return
from the interior layers to the surface with sufficient rapidity
to maintain the current; and that when, on the other hand,
a high-charging current is employed, it cannot get away fast
enough into the substance from the surface, and is accumu-
lated there and forced to a higher intensity. It is simplest to
assume that this heaping-up is directly proportional to the
current which causes it.
So far as the excitation of the magnets goes, the method of
balanced charging is more economical than charging in series;
but as a double current passes through the armature, there is
some considerable waste in heating it.
The electromagnetic attraction of the machine is in this case
roughly double that of charging in series (assuming for the
moment that the magnetization is proportional to the current).
This gives the engine a better hold of its work in the case con-
sidered without making the load so very heavy as when the
double current passes through both magnets and armature.
The lead of the dynamo machine, or the angle at which
the brushes have to be set forward on the commutator, is about
double what it is under other circumstances. This is no doubt
due to the exalted magnetism of the armature due to the double
eurrent taking longer than usual to be affected by the compa-
ratively weak field-magnets through which only a single cur-
rent is passing. This appears to point to the reduction of the
* So, if we try to drive an arc light, we can get for a short time a cur-
rent of more than 20 ampéres and a good light; but the battery soon
begins to be exhausted, and a most curious effect sets in: the alternations
of exhaustion and recovery succeed each other with great rapidity, and
_ the carbons begin to chatter in a most extraordinary way.
Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. N)
258 Prof. G. Wiedemann on the Methods
lead by the employment of more powerful field-magnets. In
all cases the lead must be ascertained by its being the position
of least sparking, and the brushes set pretty closely to it;
otherwise the brushes are burned away, and the sparking is
unpleasant.
Having charged the accumulators, I divided them up into
circuits as required, and employ them to work my electro-
pneumatic and other appliances. I have driven every thing
for a week after a charge of a couple of hours; but on account
of the local action in the red-lead cells, this is not a very advan-
tageous course; and latterly 1 have preferred to charge for
half an hour in the morning of each day. If the charge is
meant to last, of course the currents must be used economically.
There are considerations, however, connected with the in-
evitable variation in the power of the current when any descrip-
tion of cells is used as a source of electricity, which make me
already doubtful whether this alternate procedure will answer,
and whether it may not be necessary to use the cells with the
machine running simply for the purpose of sluicing off small
currents with fairly constant differences of tension at their
sources from the main current of the machine. Itis even pos- —
sible that simple pairs of lead plates in acid without prepara- —
tion may be sufficient for this purpose. But the discussion of —
this matter must wait until my uniform rotation-machines are —
in a more complete state.
I will close with an experiment showing, ina manner suitable —
for the lecture-table, the development of a counter electromo-
tive force in the dynamo when driven by a current from the
accumulators.
I place a Swan lamp in parallel circuit with the machine.
Then, so long as the machine is at rest, the lamp does not burn.
But when the machine is in motion, as the velocity increases
the counter electromotive force is set up, and the passage of
the current through the machine more or less completely
barred. The lamp in the parallel circuit then burns up. If
the machine is stopped by a brake or overloading, the lamp is’
extinguished again.
XXX. On the Methods employed for determining the Ohm.
By G. WIEDEMANN™*.
A aes Congress of Hlectricians which met at Paris in the
autumn of last year adopted the electromagnetic units
based on the centimetre-gramme-second system for the con-
* Translated from the Elektrotechnische Zeitschrift, July 1882. Fro:
a separate impression, communicated by the Author.
employed for determining the Ohm. 259
stants of the galvanic current, as fundamental units, and ex-
pressed a wish that a special international commission should
be intrusted, in the first place, with the construction of a
standard ohm as unit of resistance. Since, then, further
consultation is to take place before very long, it seems desi-
rable to consider again the methods hitherto employed, with
their sources of error, from the experimental standpoint; their
mathematical theory has been sufficiently discussed.
I desire also to give an impulse to further discussion of the
methods to be adopted in the new determination. This is to
be done the more strictly and thoroughly, since the units,
having been once determined, ought not to be altered again
immediately in consequence of further investigations.
It is well known that W. Weber, to whom we owe the fun-
damental facts in this subject, has given four methods of ob-
taining a conductor of given resistance in electromagnetic
—units:—
I. A circle of wire of known dimensions is caused to revolve
through a certain angle about an axis (vertical) inclined to
the direction of the earth’s magnetism ; and the intensity of the
current thus induced is measured by means of a galvanometer
of known dimensions. The intensity of the current, under
similar conditions, is inversely proportional to the resistance
of the conductor.
II. Instead of measuring the dimensions of the galvano-
meter in the first method, the action of the unit current on the
magnetic needle of a multiplier is determined by the damp-
ing of its oscillations when the circuit is closed.
III. A magnetic needle is allowed to oscillate within a closed
multiplier of known dimensions, and the damping of its oscil-
lations is determined.
IV. A circle of wire is put into uniform rotation about a
horizontal or vertical diameter; and we observe the deflection
which takes place in a magnetic needle swinging at the centre
of the circle, in consequence of the current induced in the
reyolving circle by the earth’s magnetism. Since in carrying
out these methods each separate measurement is of necessity
attended with error, that method appears at the outset the most
reliable which involves the determination of the fewest con-
_ stants, and in which these determinations can be made with
most accuracy. Hence methods III. and IV. appear at the
outset to offer special advantages.
We will consider the fourth method first, in order to dis-
cuss at once a number of sources of error which partly affect
also the other methods. This method is in fact that employed
S2
—
260 Prof. G. Wiedemann on the Methods
by the Committee of the British Association appointed for the
purpose in 1863.
A wire coil is put into rotation about a vertical axis, in
consequence of which currents are induced in it, whose inten-
sity in unit time is, on the one hand, directly proportional to
the horizontal component of the earth’s magnetism and to the
change of the projection of the plane of the coil on the ver-
tical plane at right angles to the direction of that component,
and, on the other hand, inversely proportional to the resistance
of the coil.
But, then, the induced currents which traverse the coils act
upon the neighbouring coils, and induce in them extra currents
whose electromotive force is proportional to the change in the
directly induced current, in the unit time; hence the inductive
action in the spiralis diminished. The deflection of the needle
is determined by the total action of all the induced currents.
The following investigations are therefore necessary to deter-
mine the absolute resistance of the coil.
1. The measurement of the space enclosed by the windings
of the coil, to which the induction is, ceteris paribus, propor-
tional, as well as its form, upon which the extra currents in-
duced in it depend, and the moment of rotation exerted on
the magnetic needle at its centre.
These determinations offer very considerable difficulty.
If thick wire is employed for winding the coil, its diameter,
together with the insulating covering, must be exactly an —
aliquot part of the interior width of the frame on which the
wire is to be wound, or else the outer layers of wire will be
squeezed more or less between the wires of the inner layers, —
and so cause displacement. Moreover, as W. Siemens* has
shown, the wire is stretched in winding, the more the thinner
the wire is; and this extension may be as much as 6 per cent.
Again, the insulating covering of the wire becomes pressed
together; this takes place less when the covering consists of solid
gutta-percha or similar substance than when the wire is covered
with silk or cotton. The thinner the wire is, the more im-
portant do these errors become, of displacement of the wire, of
extension on winding, and of the squeezing together of more
of the insulating covering in proportion to the diameter of the
wire. It is therefore not correct to calculate the space enclosed
by the coils from the length of the wire before winding or
after unwinding, and from the dimensions of the coil.
On this account, as W. Siemens rightly remarks, the accu-
rate measurement of the length of the wire of about 1*1 milli-
* Poggendorff’s Annalen, 1866, vol. cxxvii. p. 327.
employed for determining the Ohm. 261
metre thickness to the tenth of a millimetre, as in the older
experiments of the British Association, was useless.
It is not difficult to determine the internal diameter, in
various directions, of the coils of wire (that is, the diameter of
the frame on which they are wound), either by means of a
kathetometer, or with an inextensible steel tape of constant
temperature; but, on the other hand, the measurement of the
external diameter or circumference is much more difficult, in
consequence of the inequality of the covering of the wire and
the unevenness of the surface.
If the error in the determination of the mean diameter
only amounted to 0°5 millim., which, in view of the circum-
stances mentioned, is certainly not an extreme estimate, then
in the case of the coil of 314 millim. diameter employed by the
Committee of the British Association the estimate of the space
enclosed by the coils would be wrong by 34;=0°32 per cent.
In order to reduce this error as much as possible, it is neces-
sary, as both W. Weber* and Lord Rayleight recommended,
to take the diameter of the coil as great as possible consistently
with accuracy of rotation. Also the wire should be wound with
a tension as uniform as possible; and the exterior diameter
should be controlled after each layer has been wound.
A much more important source of error lies in the uncer-
tainty of determining the mutual position of the separate coils,
depending upon the conditions explained above, upon which
the intensity of the extra current induced in the coil when put
into rotation depends. Since the inductive action of the coils
upon each other takes place at very small distances, a very
small error in measuring the distance apart is of great im-
portance.
A further source of inaccuracy is introduced by making the
coil of two parts parallel to each other, but with a space between
in order to admit the thread by which the magnet is sus-
pended; so that here also the parallelism and distance apart of
the two portions must be very exactly determined. That the
data may be greatly altered by the extra currents is seen from
the fact that, in an experiment of a Committee of the British
Association, the position of maximum induction of the coil in
rapid rotation was displaced by not less than 20°; and the
correction for this amounted to some 8 per cent.
If we seek to determine the self-induction by opposing the coil
to another of known coefficient as a Wheatstone’s bridge f,
ernie der Kéniglich Stichsischen Gesellschaft der Wissenschaften,
Bik.
+ Proceedings of the Royal Socisty, 1881, vol. xxxii. p. 192.
¢ Compare Maxwell’s ‘Treatise,’ vol. ii. p. 357; Brillouin, Comptes
Rendus, vol. xciii. p. 1010 (1881); Beibldtter, vol. vi. p. 39. -
262 Prof. G. Wiedemann on the Methods
then we have, besides the sources of error of the original
apparatus, a number of other sources of error which need to
be specially examined; so that it is possible the accuracy of
the results might be seriously prejudiced. In any case the
difficulty of accurately determining the self-induction is the
most suspicious part of the method under consideration.
' 2. The temperature of the coil must be determined with the
greatest accuracy, since the conductivity of the wire decreases
about 0°3 per cent. for a rise of temperature of 1° C. The
corresponding change of length, and ccnsequently of surface
embraced, amounts only to z5)¢o55, and may therefore be
neglected.
3. We have further to inquire whether there may not be
secondary currents induced in the supports of the apparatus,
if these are of metal, by the currents circulating in the spiral,
which may act upon the magnetic needle*.
This point may be determined by interrupting the conti-
nuity of the metallic supports by means of insulating material.
According to experiments of this nature, made by Lord Ray-
leigh and Dr. Schusterf, this source of error was not important
in the experiments of the British Association, the error amount-
ing only to 0°16 per cent. It would be better, however, to
construct the supports of insulating material. .
4, The testing of the instrument to determine if the coils le
symmetrically with reference to the axis of rotation offers no
particular difficulty, if we observe by means of a telescope cor-
responding points of the frame on both sides of the axis in
different positions of the coils, making with each other an
angle of 180°.
5. In the same way it is easy to ascertain by known optical
methods whether the axis of rotation is really vertical, and
remains so; deviation from the vertical position may exert a
considerable effect.
If the angle of dip were about Z=70°, an inclination of the
axis towards north or south of 0°°2 would cause an alteration
in the inductive action of the earth in the proportion of
cos 70°: cos (70°+0°2)—that is, not less than 1 per cent. An
inclination of this amount in the case of the British-Association
coil would correspond to a displacement of 0°5 millim. in the —
ends of the axis. An exact determination is therefore very
necessary. Small displacements of the axis towards east or
west have only an insignificant influence.
6. The counting of the number of revolutions of the coil in —
, Compare F. Kohlrausch, in Pogg. Ann. 1874, Ergainzungsband vi.
p- 9.
+ Loe, cit.
employed for determining the Ohm. 263
unit time by known methods offers no special difficulty; nor
does the maintaining of a constant velocity of rotation by
mechanical means*.
7. The adjustment of the magnet in the centre of the rota-
ting coil should also not be dificult to effect. Moreover a
small deviation from exact adjustment causes no important
error.
8. The moment of the magnet may be determined by vibra-
tion-experiments after determining its moment of inertia and
the horizonal component of the earth’s magnetism; or it may
be determined from experiments on deflection. If, in order
to render the inductive action of the magnet on the rotating
coil imperceptible, we employ magnets of very small moment,
then these methods offer many sources of error, on account of
the very perceptible influence of the friction of the air in the
vibration-experiments, or of the small distance at which the
deflecting magnet must be placed.
If the moment of the magnet is very small, it and the dis-
tribution of magnetism in the magnet (which is very difficult
to determine) have both very small effect upon the results.
If the poles of the magnet are at a distance from the cen-
tral point in the median plane of the coils which is less than
1 of their radius, and if the distance of the poles from the
plane is not greater than 0°84 of the length of the magnet,
then the force exerted upon it by a current in the coil is con-
stant to within 0°0005, under conditions otherwise similar,
up to a deflection of 56°.
9. The adjustment of the telescope and scale required for
reading-off the position of the magnet, and the correction of
the readings, may be made in the usual way; and the divisions
of the scale must be compared with an accurate measure. The
accurate measurement of the distance of the scale from the
central point about which rotation of the magnet takes place,
or from the reflecting surface of the mirror, offers a certain
amount of difficulty. .
10. The force of torsion of the suspension-thread of the
magnet may easily be compared with the directive force of
the magnet by turning the thread fastened to a torsion-circle
through a certain angle, and observing the deviation of the
magnet. Unavoidable changes of considerable magnitude
may result from the variable moisture of the air, if weak mag-
nets are employed.
11. We have, further, to inquire what influence currents of
air and the vibration of the apparatus caused by the motion
* Compare the ingenious arrangement adopted by Lord Rayleigh,
264 Prof. G. Wiedemann on the Methods
exert upon the needle when the coil is put into rotation with
circuit open. In the first experiments of the Committee of
the British Association, in which attention had not yet been —
paid to the separate conditions of the experiment in the way
which will be necessary for a final determination of the ohm,
these last-mentioned sources of error made themselves in a
high degree perceptible.
Thus F. Kohlrausch, in a discussion of these experiments,
has justly pointed out that, in order to avoid inductive action
on the coil of wire, the magnet (a magnetized steel ball of _
8 millim. diameter), in spite of its great mass, had onlya —
moment equal to that possessed by an extremely fine magnetic
needle weighing 0°025 gramme. The magnet was attached
by means of a wire 0°25 metre long to a mirror of 30 millim.
diameter suspended by a simple silk fibre of 2 metres length.
The currents of air produced by the rotating coil only 0°31
metre distant acting upon the relatively large surface of
the mirror and magnet, as well as the variable torsion of the
thread, become much too considerable in comparison with the
directive force of the magnet.
Further, the vibration of the apparatus produced by the
rotation may propagate itself to the case surrounding the
mirror, and so put the air, and with it the mirror, into rota-
tion. It might thus happen that the deflections obtained by
rotating the coil in one or the other direction might vary by
as much as 8°5 per cent. If the mean results obtained in dif-
ferent series of observations should differ amongst each other
by only 2°3 per cent., yet even this is not a guarantee of
greater accuracy, but can only be regarded as a proof that
the apparatus always acts in nearly the same way.
Moreover the supplementary elimination of sources of error,
e. g. by more exactly calculating the effect of self-induction,
as attempted in the memoir of Lord Rayleigh and Dr. Schuster,
can in no way free the results from the influence of sources of
error shown to exist by the deviations cited above. Aboveall
things, observations of this kind ought never to be arbitrarily
corrected on the ground of probability only without haying
perfectly definite numerical data; or else all secure experi-
mental ground is lost.
Hence we may consider it shown that the results of these
experiments are not to be themselves taken as a final determi-
nation of the ohm, but rather as extremely valuable prelimi-
nary experiments by which we have become acquainted with
the precautions to be observed.
By means of new experiments made by Lord Rayleigh and
Dr. Schuster with the apparatus of the British Association,
:
:
employed for determining the Ohm. 265
altered in some points, the difficulties mentioned above under
(1) remained unaltered; the magnet, however, was replaced by
four magnetized needles, each 0°5 centim. long, fastened on the
parallel horizontal edges of a cube of cork. The mirror was
attached directly to the cork. But here also the directive
force of the magnet is small in comparison with the somewhat
powerful influence of currents of air acting on the large sur-
face and small moment of inertia.
Further, the case protecting the suspended portions of the
apparatus is attached to the glass tube which surrounds the
suspension-thread. Perfect stability could hardly be obtained
with such an arrangement ; since with rapid rotation vibration
of the mirror would certainly be experienced. These experi-
ments also are to be regarded more as preparatory for later and
final measurements, and as such have been excellently carried
out. On this account no doubt the more exact data for ver-
tical adjustment of the axis &c. have not yet been given
throughout. Lord Rayleigh, as already mentioned, lays
emphasis on the necessity for new coils for the final experi-
ments, and raises the question whether these should not be
arranged as in the Helmholtz-Gaugain galvanometer, so that
the directive action of the current on the needle is independent
of any small excentricity or deviation of the needle.
In the final experiments, whether they are made according
to this method or according to one of the other methods,
it is in any case necessary that as complete a statement should
be given of each separate proceeding in arranging and using
the apparatus. Also the experiments should not be made
with an apparatus set up and adjusted once for all, since then
the errors of the arrangement will repeat themselves with each
new determination undertaken with the apparatus. On the
contrary, the apparatus itself must be frequently altered in
various ways. Only so can we obtain results independent of
each other, which can be used for mutual control.
The sources of error which are so difficult to avoid in using
method IV., more particularly in consequence of the extra
currents, have induced W. Weber* himself, in conjunction
with the late F. Zollner, to again take up the first method
(which had been employed by the first-mentioned so long ago as
1846 in preliminary experiments) with the most perfect experi-
mental means. Of two equal coils, weighing some 207 kilog.,
most carefully and very regularly wound upon mahogany
rings, as shown by measurement of different diameters, the
* W. Weber and F, Zollner, loc. cit.
266 Prof. G. Wiedemann on the Methods
coils consisting of cotton-covered copper wire about 34 millim.
in thickness, and having a resistance of about 5 ohms—one, the
multiplier, surrounds a cylindrical magnetic needle about
100 millim. long and 10 millim. thick, fixed in the magnetic
east and west plane. The diameter of the coils (interior about
960 millim., exterior 1040 millim., and breadth of coils about
254 millim.) is so large that the magnetic forces acting on the
needle may be supposed, without perceptible error, to be con-
centrated at their centre. The other coil, connected with the
first by conducting-wires, the inductor, is capable of rotation
about a vertical axis, out of the east and west position through
an angle of 180°. This displacement of the inductor takes place
suddenly at such times that the currents induced in it and
transmitted through the multiplier render the deflections of
the needle constant according to the “ method of multiplica-
tion’ or the “ method of recoil.” ji
In carrying out the experiments, the displacement of the
inductor by means of clockwork was not found to be practi-
cable, and it was therefore effected by hand. The time required
for the displacement (some 2 seconds) must only be a small
fraction of the time of vibration of the magnet hanging in the
multiplier. For this purpose the time of vibration of the
needle is increased (up to 30 seconds) by placing the needle
in a stirrup to which a tube of brass 272 millim. long was
fastened in a horizontal position and at right angles to the
needle, the ends of which carried plane mirrors. ‘Telescopes
with parallel scales are placed before both mirrors, each at a
distance of 4 millim. By this double reading the difficult
measurement of the scales from the mirrors is replaced by the
easier measurement of the distance of the scales from each
other, and of the distance of the mirrors apart. An exami-
nation of the point whether, and how far, the instants of dis-
placement of the inducing coil may differ from those indicated
by calculation, and how far these possible deviations may affect,
might be easily made*. In any case, according to the expe-
riments which have been made, this influence cannot be of
importance, since the results obtained at different times by use
of a magnet 100 millim. long agree with each other to within
0-06 per cent., and those obtained with a magnet 200 millim.
long do not differ at all from the mean result. This shows at
the same time that the instrument had not altered in any im-
_ portant respect in the interval. The inductor must be so far
removed from the multiplier that the currents in the first
cannot directly deflect the needle.
* Compare Chwolson, Bulletin de St. Pétersbourg, vol. ii. p. 403 ; Bes-
blatter, vol. v. p. 450.
employed for determining the Ohm. 267
It is a point of very great importance in the employment of
this method that self-induction in the inductor is without in-
fluence, and that, further, the intensity of the earth’s mag-
netism does not enter into the calculation, provided that it is
of equal intensity in the positions occupied by inductor and
multiplier. It may not be allowable to assume that this is
the case in ordinary rooms, because of iron hooks let into the
walls; but in a building constructed for the purpose this con-
dition might easily be fulfilled. This point may also easily be
controlled by oscillation-experiments ; the ratio of the directive
force of the earth may be determined at the two places.
li is true that we have to set against this advantage that we
have two coils to measure, and are so liable to a double error.
(This, however, is also the case in the experiments of the Bri-
tish Association described above, where the revolving coil con-
sists of two separated halves.) This disadvantage may be
considered small in comparison with the error resulting in
the fourth method from the measurement of the self-induction
of the coil. It is further reduced by the large dimensions of
the coils. At the same time stability of the apparatus, and
consequent freedom from disturbances resulting from vibration
and from currents of air, is much more easily obtained than
with the rapidly-rotating coil employed in the former method.
Previous communications on experiments with this appa-
ratus are only preliminary, on which account we are not yet
in possession of details of adjustment ; for which, however,
not only the name of W. Weber, but also that of Repsold, the
instrument-maker intrusted with the work, give us full gua-
rantee that such points as the verticality of the axis of rotation,
the adjustment of the coil magnetic east and west, the arrange-
ment for displacing the coil through exactly 180°, and so on,
will be attended to. The preliminary method of measuring
the circumference of the mahogany rings on which the coils
are wound and of their exterior circumference by means of
strips of paper, which were then compared with a divided
wooden rule, will no doubt give place to more exact methods
in the actual experiments.
A special advantage of this method is that the wires may
be unwound from the rings and wound again without any
great difficulty; and so repeated observations independent of
each other can be obtained.
This method is therefore to be recommended for the final
determinations.
If we employ Weber’s second method, we have no need to
determine the dimensions of the multiplier; but we determine
268 Prof. G. Wiedemann on the Methods
the damping of the oscillations of the needle, once with open
circuit and again with closed circuit. Hence, by determining
the deviation of the needle when the inductor is displaced,
the resistance of the circuit in electromagnetic measure may
be calculated. For this purpose the multiplier must enclose
the needle more closely, so that the damping may be sufficient.
We have to determine, besides the dimensions of the inductor,
the period of oscillation and moment of inertia of the needle
and the intensity of the horizontal component of the earth’s
magnetism. ‘The sources of error of this method have been
carefully examined by F. Kohlrausch*; the error in measure=
ment of the inductor may, however, have been scarcely esti-
mated high enough. (Compare also the following method.)
If proper experimental means and a suitable observatory
are availablet for accurate determination of the earth’s mag-
netism, this method may very well be employed together with
Weber’s first method.
In Weber’s third method, which is apparently so simple, we
have, in order to determine the absolute resistance of a multi-
plier, to observe only the damping of the oscillations of a
needle suspended in the coil when the ends of the coil are
united, and again when the circuit is open. In order to be
able to calculate the electromotive force due to the oscillations
of the needle and its action upon the needle, which is directly
proportional to that electromotive force, and inversely propor-
tional to the resistance to be measured, we must know in
general the dimensions of the multiplier and the position of
the needle relative to it, as well as the distribution of the
magnetism in the needle.
The former determinations are difficult to carry out exactly,
since, in order that there may be sufficient damping, no very
large dimensions can be given to the coil; the latter determi-
nations can only be made inexactly by observation of the
currents induced in a short coil at different points of the
magnet, or by numerous oscillation- and deflection-experiments
with a magnetic needle swinging at different distances from
various points of the magnet. We have also to satisfy our-
selves that the damping is not dependent upon the angle of
deflection of the needle.
This method has been employed by Fr. Weber f, in Ziirich,
* Loe. cit.
+ Compare also the new methods by F. Kohlrausch, Géttinger Nach-
richten, March 4, 1882.
t F. Weber, Elektromagnetische und kalorimetrische Messungen (Ziir-
cher und Furrer, Ziirich, 1878); Betbldtter, vol. ii. p. 499.
employed for determining the Ohm. 269
employing a magnet of 80 millim. length, 20-1 millim. breadth,
and 21-1 millim. depth, suspended by a silk thread between
two conical coils very regularly wound, of 144-43 millim. in-
ternal, 184-46 millim. external radius, and 51°64 millim.
breadth.
The mean distance of the spirals from each other was either
very small, or the distance of their median planes was made
164-4 millim., or very nearly equal to the mean radius of the
coils. In this last case the distance of the poles from each other
has no important influence, although it has in the first, where
also the distribution of moments in the magnet must not be
neglected. We must, however, always take into account
inevitable differences in measurement in consequence of the
mutual pressure of the coils and certain unavoidable irregu-
larity in the winding, which are more important in consequence
of the small dimensions of the coils, as in the fourth method
which we have already considered. Nevertheless it was shown,
by comparison with a standard resistance of Siemens’s, with
which the resistance of the coils was compared by means of a
Wheatstone’s bridge, in both the cases mentioned, and after
rewinding of the coils, that the standard resistance expressed
in absolute measure varied in three series of experiments only
from 0°9532 to 0°9570, from 0-9528 to 0:9555, and from 0°9527
to 0°9551— that is, not more than 0°5 per cent. The mean is
0°95451.
In further experiments according to another method, Fr.
Weber placed the coils mentioned above at a definite distance
from each other, connected the one, “ the inducing coil,” with
a very constant Daniell’s cell and a simple ring of 168°7
millim. radius; the other, “ the induced coil,” with a multi-
plier, which was composed of a coil consisting of two equal
conical halves placed close together, of 154:2 millim. inner
radius and 172-2 external radius, between which was suspended
a magnet 40 millim. long provided witha mirror. The simple
ring of the inducing circuit lay between these coils. The
deviation of the needle whilst a constant current passed through
the inducing circle measured its intensity J, which was to be
measured in absolute measure from the known dimensions of
the ring; the deviation on breaking the inducing circuit after
disconnecting the ring gave the intensity 7 of the induced cur-
rent. Since the induced electromotive force e=JP (where P
is the mutual potential of the coils) may be calculated in abso-
lute measure from the dimensions of the coil by putting the
constant of induction equal to unity, we obtain the resistance of
the induced circuit 7 from the formula r= =
270 Prof. G. Wiedemann on the Methods
We have therefore for these determinations to ascertain
the dimensions (1) of the wire ring, (2) of the inducing coil,
(3) of the induced coil, (4) of the multiplier, (5) of the dis-
tance of the separate layers of the inducing and induced coils
from each other, (6) the determination of the position of the
magnetic poles, to which are to be added the manipulations
required for the other methods, the adjustment of the needle
in the centre, and of the coils of the multiplier and of the
wire ring between them with reference to the meridian &e.
Since the intensities of the primary and secondary currents
are measured by the deflection of the same magnet, the hori-
zontal component of the earth’s magnetism does not enter into
the calculation. There are in this method many more sources
of error to be taken into account than in the other methods,
by which its accuracy may be seriously impaired.
Notwithstanding, Weber finds, by determining the resist-
ance of the inductive circuit by this method, and comparing
it with the Siemens standard which he employed, that at two
different distances of the inducing and induced coils, and with
two different intensities of the inducing current, a mean result
of 0°9554 (0°9589 to 0°9516)*.
This method has also been employed by Rowlandf, only that
he employed a tangent-galvanometer to determine the inten-
sity of the inducing current, but a special galvanometer to
determine the induced current; it was necessary also to deter-
mine the ratio of the intensities of horizontal force at the posi-
tion of the two pieces of apparatus. His three induction-
coils had a diameter of about 27°4 centim., and were wound
on frames having a thick brass rim on each side. They could
be combined in pairs, so that the one which served as inductor,
through which a constant current flowed which could be in-
terrupted, might be placed at four different distances from
the others (6°5 up to 11:47 millim.). Very thin-covered
copper wire (no. 22) was taken for the coils; so that the
sources of error mentioned on p. 260, caused by displacement
of the covering, the mutual compression of the coils, and ex-
pansion of the wire, become very prominent. Since the in-
* An indirect method employed by Fr. Weber to determine the resist-
ance of a zigzag platinum wire placed in a calorimeter, from the heat pro-
duced by a current whose strength in absolute measure was determined
by means of a tangent-galvanometer of known dimensions, can hardly be
placed by the side of the more direct methods, on account of the difficulty
-of all calorimetric measurements. Nevertheless Fr. Weber finds by this
method, by comparison with his Siemens standard, aresistance for the latter
of 0:9560, which again differs only 0:1 per cent. from the other determi-
nations.
+ Rowland, ‘ Silliman’s Journal,’ 1878 (3), pp. 325, 430.
employed for determining the Ohm. 271
duction-coils are so close together, a small error in measuring
their distance apart is of great influence—the more so since,
from what has been said, it follows that the position of the
separate coils could not be accurately controlled. That the
distance of the coils apart at various points was measured to
the =5 millim., and that the mean distance apart is given to
millim., and the mean radius to the y 5455 millim., can
ardly be regarded, in view of the above-mentioned disturbing
causes, as a guarantee of the actual exactitude of the results.
Since the length of the needle of the tangent-galvanometer
(2:7 centim.) amounted to only 7/5 of the diameter of the coil
(50 centim.), the deviation from the law of tangents is imper-
ceptible ; but, on the other hand, there is an important source
of error in the fact that the needle turned upon a point.
Rowland asserts that the needle, which was provided with a
pointer playing over a circle of 20 centim. diameter, always
took up its position accurately to 1 or 2 minutes (1 minute
corresponds to only 0:03 millim. upon the circle). Since this
_ does not at all agree with previous experience, an exact ex-
planation how so great sensitiveness was obtained is indis-
pensably necessary.
The needle of the galvanometer was 1:25 centim. long ;
the coils, which were brought up to it-from the east and west,
had an internal diameter of 3 centim. and an outer diameter
of 5:6 centim. ; their inner end-surfaces were at a distance of
0°935565 centim. (thus given to zoqgo5 millim.) from the
point on which the needle turned. Whether the law of tan-
gents is altogether applicable here must remain uncertain.
Since the intensity of the inducing and induced currents is
measured at different places, Rowland introduces a further
complication by determining the ratio of the horizontal com-
ponent of the earth’s magnetism at the position of the tangent-
circle and of the galvanometer by surrounding the galvano-
meter with a larger coil, sending the same current through it |
and the tangent-circle, and comparing the deflections. The
radius of the new circle (some 4 centim.) is again given.to
topoo Millim.
The values of the different dimensions given to so many
decimal places are probably not regarded by the author him-
self as accurate in the same degree, the last decimals (obtained
by interpolation) being added for the sake of completeness.
It is, however, always advisable to give exact account how far
actual observation goes, since the mean values can never be
accurate beyond the limit of possible observation, or else with
the roughest measures it would he possible by repeating mea-
surements to obtain any required degree of minuteness.
272 Prof. G. Wiedemann on the Methods
Since, moreover, the sources of error mentioned above may
undoubtedly cause considerable deviations, such a one-sided
accuracy cannot be a guarantee for the exactitude of the final
results *,
On account of the much larger number of determinations
which this method requires, I consider it much less suitable
for the final construction of a definite resistance than the
fourth and first of Weber’s methods, of which again I give
the preference to the latter.
After a conductor A of known absolute resistance has been
constructed, by the one method or the other, it has to be com-
pared with the resistance B of a mercury column of known
dimensions in order to determine the length of such a column
of 1 square millimetre section which possesses 1 ohm resistance.
If we employ Weber’s first method, we may introduce the
mercury column Bdirectly between the inductor and multiplier,
and calculate the resistance of B from the decrease of inten-
sity; otherwise the resistances A and B may be compared by
means of the differential galvanometer, or more conveniently
by means of the Wheatstone’s bridge, according to the accurate
method already employed by W. Siemens in constructing
copies of his mercury unit. Since we already know the length
of mercury corresponding to 1 ohm very nearly, we take care
to arrange the resistance B so as to be as nearly as possible
equal to the resistance A.
It is highly important, after calibration of the measuring-
wire, to secure perfect contacts by using freshly-amalgamated
thick copper connecting-pieces and cups full of pure mercury,
the resistance of which is previously determined by including
several in a circuit. Plug-contacts are not sufficiently accu-
rate. Also the temperature must be carefully kept constant
throughout at the right point, as was the case in the construc-
tion of Siemens’s copies.
* If we employ in this and other methods a coil wound uniformly on a
closed ring, a neutral solenoid, as inductor, but as induced coil a coil
surrounding the former at one point, the conditions are so far simpler
that the current due to opening or closing the current in the solenoid, only
the linear dimensions of the solenoid, its interior and exterior diameters
d and d,, the number of coils of the induction-coil and of the solenoid, or in
the case of a solenoid of rectangular section the height a, are concerned
(compare Roiti, Atti di Torino, vol. xvii., 30th April 1882). Nevertheless
the employment of such a solenoid is attended with the great bare!
of winding the wire exactly upon it, and of measuring its dimensions wit
sufficient accuracy. The latter is the more difficult, since the section of
the solenoid can only be taken relatively small, and the formula contains
; = os Venere t d
the expressions Vd— Vd, for a solenoid with circular section, a log |
for a solenoid with rectangular section.
.
|
employed for determining the Ohm. 275
A difiiculty presents itself here, since induced currents are
produced in A on opening and closing the current which
flows through the combination of wires. We must therefore
either employ a constant current of such feeble intensity that
the heating of the circuit shall be imperceptible, or, according
to the method of Kohlrausch*, who has also worked out the
necessary calculations, we must employ an induction-appa-
ratus which sends alternating currents through the circuit.
A special source of error is found in making contact with the
mercury column contained in an accurately -calibrated care-
fully cleaned glass tube. The ends of the tube terminate in
glass vessels of diameter relatively large. The apparatus is
best filled with mercury by pouring mercury into one of the
vessels and inclining the apparatus tow ards the same side,
then, after closing the openings, repeatedly exhausting the
apparatus as completely as possible, gently warming the tube,
then allowing pure air which has passed over phosphoric
anhydride and wadding to enter, and finally, after exhausting
again, allowing the mercury to flow into the tube by placing
it in a horizontal position. If the electrodes are immersed in
the vessels containing mercury, then the resistance of the mer-
eury in the tube is increased by that of the mercury contained
in the vessels up to the ends of the electrodes. This resistance
may be calculated on the assumption that the vessels are infi-
nitely large. It might perhaps be advantageous to determine
it directly by compensating the resistance of a tube filled with
mercury with two contact-vessels by a nearly equal resistance
on Wheatstone’s bridge, and then to cut the tube at one or
more points and to introduce wider mercury vessels of suitable
form, and then again determine the resistance. We might
also introduce two tubes, of lengths m and nm and of equal sec-
tion, between the same contact-vessels, and compare their
resistances, and from the data so obtained calculate the resist-
ance of the vessels.
In order to avoid this separate comparison of the resistance
of the coil determined in absolute measure with a mercury
column, Carey Foster t and Lippmann { have almost simul-
taneously suggested (L.) or carried out (© F’.) the ingenious
plan of employing Weber’s fourth method, as adopted | by the
British Association, and Poggendorfi’s compensation-method
* Poggendorff’s Annalen, 1871, vol. cxlii. p. 418.
tT Carey Foster, ‘ Electrician,’ issl, vol. vii. p. 266 ; Betblatter, vol. vi.
p. 133.
{ oe Comptes Rendus, 1881, vol. xcill. p. 715; Beiblatter,
vol, vi. p.
Phil. tha. S. 5. Vol. 14. No. 88. Oct. 1882. T
974 Prof. G. Wiedemann on the Methods
for determining electromotive force without having previously
determined the resistance of the rotating coil.
Let the resistance R to be investigated and a tangent com-
pass be included in the circuit of a constant pile, e. g. a thermo-
pile. Let the ends of the resistance be connected also by a
second circuit, into which a delicate galvanometer and the
coil rotating about a vertical axis are introduced during a
particular phase of its motion by means of a commutator
revolving with the coil. The velocity of rotation is so regu-
lated, or the resistance in the branch containing the constant
pile is so altered, while the velocity of rotation of the coil
remains constant, that the galvanometer is not affected. Then,
at the moment that the coil is introduced, the induced electro-
motive force in it is equal to the difference of potential at the
ends of the conductor R caused by the thermopile. If the
current-intensity in it, and also in the circuit of the thermo-
pile and of the tangent-galvanometer, be equal to J, then
E=JR. ‘The factor of reduction of the tangent-galvano-
meter is to be determined from its dimensions and the hori-
zontal component of the earth’s magnetism at the place, and
in the same way the electromotive force induced by the rota-
tion of the inductor. In most cases we may assume the hori-
zontal component of the earth’s magnetism to be the same at
both places, as in Weber’s first method, which thus disappears
from the calculation. In this method, therefore, we have the
same determinations to make as in Weber’s fourth method.
The uncertainty of contact in the commutator is without in-
fluence, since when the galvanometer is not affected there is
no current in the inductor-cireuit. If we adjust the commu-
tator so that it makes contact with the coil at the time of
maximum induction, just at the moment when it varies least,
then, if the ratios are in other respects properly chosen, the
influence of self-induction in the rotating coil is reduced to a
minimum. <A certain amount of care, however, is required
in order to avoid thermo-electric disturbances, resulting from
the heating of the points of contact; and the determination of
the exact phase during which the commutator makes contact
offers a certain amount of difficulty.
The results so far obtained by the different methods are,
some of them, tolerably far apart, although the investigations
have been carried out with great care, if not in all points with
the most perfect experimental means which a final determi-
nation of the ohm demands. Thus the resistance of a mereury
column 1 metre long of 1 square millim. section at 0° C. was
found by the first experiments of the British Association to
employed for determining the Ohin. 279
be 0°9830; according to F. Kohlrausch it is 0°9717:; accord-
ing to F. Weber 0°9550; and according to Lord Rayleigh and
Mrs. Sidgwick 0°9413 (20° om) The first ohm con-
structed by the British Association, according to F. Kohl-
rausch is 10196; according to Rowland 0-9910, and according
to Rayleigh and Schuster 0°9893 of the true ohm (10! 7
Hence at any rate it is indicated that the final determina-
tion of the ohm must not rest alone on experiments made only
according to one method and carried out at one place. Fur-
ther, the results of each separate method (as I have already
mentioned) offer security against possible constant errors only
if they are obtained from entirely independent series of ex-
periments, made with apparatus varied in all possible ways.
Since investigations are already in progress in different places,
with excellent apparatus and according to different methods,
we may shortly expect to be in a position to compare together
the data which they yield, and so to attain as reliable a final
result as possible.
In such important and permanent determinations as those of
the electrical units, a delay of a few months is of no import-
ance whatever in comparison with the reliability of the result to
be obtained. Any introduction of the ohm as given by detached
series of observations and distribution of copies for practical
use would therefore be premature and without authority.
The Commission appointed for the determination of the
electrical units does not complete its task by simply deter-
mining the ohm. It is further necessary to construct at
least one of the two remaining units, e.g. the volt. Since it
is at present impossible to construct this in a form capable of
reproduction, it will be necessary first to compare electro-
motive forces with those of a constant element whose electro-
motive force is known in volts. Weare therefore in the same
ease as if, wishing to measure a length in metres, we were
obliged to employ a yard measure whose ratio to the metre
was known. So much the more thoroughly are we obliged
to investigate the electromotive forces of the galvanic cells to
be employed as intermediate measures, and their dependence
upon external conditions. The cell invented by Latimer
Clark has indeed been shown to be capable of reconstruction
of exactly the same electromotive force ; at the same time it
can only be employed for electrostatic measurements, since it
becomes polarized when used to produce a current. Obser-
T2
oo
276 Mr. L. Fletcher’s Crystallographic Notes.
vations with reference to Daniell’s and other cells do not
appear to me to lead to any certain conclusion.
Similar indirect methods have to be employed for measuring
the intensity of a current in absolute measure; the factor of
reduction of the tangent-galvanometer employed, for example,
has to be determined. ‘This problem has been considerably
facilitated by the recent investigations of F. Kohlrausch and
Mascart on the electrochemical equivalent of silver, which,
however, exhibit small deviations among themselves. There
is here consequently a rich field for accurate investigation, for
which we have already a series of valuable preliminary inves-
tigations. All these labours, however, can only give a final
result sufficient for our present purpose when they are exe-
cuted upon some common and well organized plan, and are
carried out with the most perfect experimental means.
XXXII. Crystallographic Notes. By L. Furrcuer, J0A., of
the Mineral Department, British Museum; late Fellow of
University College, Oxford”.
[Plate VI. |
X. On Twins of Copper Pyrites.
HE memoir of Haidingert on the Crystallisations of
Copper Pyrites, published so long ago as the year 1822,
was so exhaustive and withal so simple in its character that
little seemed to be left to tempt the crystallographer to devote
further study to this mineral; and in fact, with the exception
of the papers of Sadebeck, whose early death all interested in
the progress of mineralogy must so deeply deplore, and the
confirmatory data in Groth’s Catalogue of the Collection of
the University of Strassburg, we have still no other informa-
tion at our disposal. A study of these memoirs and of the
various text-books of mineralogy leaves upon one’s mind such
a feeling of doubt as to the true statement of one of the laws
of twin-growth, and that (as will be explained later) a law
almost, if not quite, unique in the domain of crystallography,
that, at the suggestion of Professor Maskelyne, the collection
of copper pyrites in this Museum has been examined with a
view to a possible settlement of the difficulty,
To geta clear idea of the present position, it is necessary to
trace the history of this particular law from its first statement
- down to the present time.
In the above memoir of 1822, the twin-growths of copper
* Read before the Crystallological Society, June 5, 1882.
+ Memoirs of the Wernerian Eanicty, vol, iv. p. 1, 1822.
Mr. L. Fletcher’s Crystallographic Notes. 277
pyzites were assigned by Haidinger to three distinct laws. In
the first kind, the twin-plane, or plane of rotation, is a face of
the octahedron {111!, and the composition-plane, or plane
of junction, is generally parallel, but sometimes perpendicular,
to the twin-plane: these growths correspond to the blende
twins of the Cubic system. In the second, the twin-plane is a
face of the octahedron {101!, and the composition-plane is
perpendicular to the twin-plane. In the third, the twin-plane is
a face of the prism {110}, and the individuals are interpene-
trant. The second law is that with respect to which uncer-
tainty has arisen; and it is with this law that we have now to
deal.
In the original memoir of 1822 the growth is so clearly
described, and the law so distinctly expressed, that it 1s impos-
sible to read the memoir and to mistake its meaning. Three
years later, however, Haidinger published in the ‘ Edinburgh
Journal of Science’ a series of papers “ On the Regular Com-
_ position of Crystallised Bodies,’”’ copiously illustrated with
figures which have since found their way into almost every
manual of the science ; and in its natural place in the tetra-
-gonai (or pyramidal) system he describes once more, though
briefly, the particular growth of copper pyrites which we are
about to consider. There is little doubt that this secondary
description has been the cause of serious misunderstanding.
On page 68 of vol. iii. (1825) we read as follows :—“ Regular
composition often also takes place in this species parallel to a
plane of P—1{10 1}, or perpendicular to the terminal edges
of P {111}. There are particularly two varieties of this case
which in the present place deserve our attention. The indi-
viduals are either joined in pairs, or one central individual is
surrounded by four others, added in the direction of all the
edges of P. The product of the first, in the fundamental
pyramid, would be fig. 30 [similar to fig. 6]. This has not
yet been observed; but it will serve for explaining fig. 31, a
variety of the form P—x» {001}, P—2{112!, P{111},
yoy P 1302}, and ae P+1{33 23; from the mines of the
district of Siegen in Prussia. This and several other interest-
ing varieties of forms from the same locality I have described
on another occasion (Jem. Wern. Soe. vol. iv. part 1, p. 1,
1822), from specimens in the possession of Mr. Sack, of Bonn.”
Taken by itself, this explanation might at first sight suggest
the interpretation which seems to have been placed upon it by
some crystallographers—namely, that there are twin-growths
of copper pyrites in which the plane of composition is parallel
to a plane of the octahedron {101}.
278 Mr. L. Fletcher’s Crystallographic Notes.
This interpretation can never have been intended by Haidinger,
At the beginning of the series he had remarked that, for the
precise definition of a twin-growth, two planes must be given:—
first, the twin-plane, or plane of rotation, to indicate the
relative directions of corresponding faces of the two individuals ;
and, secondly, the composition-plane, or plane of junction, to
indicate their relative positions. Haidinger’s initial sentence,
“regular composition takes place parallel toa plane of {101},
or perpendicular to the terminal edges of {11 1},’’ may there-
fore refer either to the plane of twinning or to that of com-
position, and to this extent is indefinite. But seeing that
no plane of {101} is perpendicular to a terminal edge of
{111}, the above sentence must indicate two distinct cases
if the reference be to a composition-plane, while if the refer-
ence be to a twin-plane, only a single case is indicated ; for,
as will be shown later, a rotation through two right angles
in a plane of the octahedron {101} is crystallographically
identical in its results with a rotation through two right
angles perpendicular to (or round) a terminal edge of the octa-
hedron {111}. That Haidinger only recognizes a single case
is evident from the italics in the next line of the above quotation.
As a matter of fact, the figure of the twinned octahedron,
repeated from his first paper, shows the plane of composition
as perpendicular to the twin plane, though this is only evident
after careful inspection. His final reference to the original
memoir without calling attention to any deviation therefrom,
shows that he was still in accord with the explanation there
riven.
é From this we conclude that either a careful study of this
later paper of Haidinger on the regular composition of erys-
tallised bodies, or a simple reference to his original memoir
on the crystallisations of copper pyrites, would haye made
clear the fact that Haidinger regarded the composition-plane
as perpendicular to the twin-plane (101), though we grant
that at first glance his second paper might suggest that the
composition-plane is, in some cases at least, parallel to the
plane of twinning (101).
In 1830, Naumann’s well-known work* did in fact state
the law differently from Haidinger, and assumed the plane of
composition to be parallel to that of rotation. In his preface
Naumann makes special mention of the help he had derived
from Haidinger’s series of papers on regular composition, and
in his description of these particular growths adopts some of
the figures there given. It seems quite impossible for this
deviation from Haidinger to have been introduced wittingly;
* Lehrbuch der reinen und angewandten Krystallographie, 1830,
|
:
Mr. L. Fletcher’s Crystallographic Notes. 279
for attention is not directed to the difference in the explana-
tions, and, further, it is unlikely that Naumann had been able,
so soon after the publication of Haidinger’s work, to under-
take a special and minute study of this particular law.
We feel that the above reasoning shows clearly enough that
Naumann’s statement is a simple misinterpretation of that of
Haidinger, and that this can only have resulted from the fact
that Naumann referred to the secondary, and not to the ori-
ginal, explanation given by the author of the law.
As Naumann’s ‘ Crystallography’ became the recognized
and universal text-book on the subject, this statement, though
a mistaken one, has been extensively circulated, and appears
probably in every text-book of the present day, though, as
might have been expected, the explanation of 1822 is repeated
in Haidinger’s own manual of 1845.
In 1868* Sadebeck published the results of his study of
specimens of copper pyrites (belonging chiefly to the Berlin
collection), and in the explanation of the twins assumed the
_ correctness of Naumann’s statement of the law. In a second
paper, published in the following year+, he gives an explana-
tion of his position, so very brief and so clearly illustrative of
the present difficulties that a translation is given here:
“In my memoir on copper pyrites I have wrongly stated the
law of twinning; for I have supposed the twin-plane to be also
the composition-plane. According to this, one pair of tetra-
hedron-faces should meet in a salient angle of 1° 24’, and the
opposite pair in a reentrant angle of the same magnitude.
After I had published the memoir, Haidinger informed me
by letter that this was not the explanation he himself had
given, as may be seen from his statement in the ‘ Edinburgh
Journal of Science,’ which runs thus:—‘ Composition takes
place perpendicular to the terminal edges of P.’ In conse-
quence of this friendly private communication from so famed
a Nestor of the science, I subjected the crystals again to a
careful study. The result was that I found it impossible to
say whether the tetrahedron-faces actually coincided, or formed
an angle of 1° 24’. This led me to retain my old view, since
that law seemed to me a simpler one which regarded a plane
of the form {101} as at once twin-plane and composition-
plane. But if I now apply the general law for tetrahedral
twins to this case, it follows that, as faces of the positive
tetrahedron of the one individual are adjacent to faces of the
* “Ueber die Krystallformen des Kupferkieses,” Zert. d. deutsch. geolog.
Gesellsch. p. 605, vol. xx. 1868.
+ “Alloemeines Gesetz fiir tetraédrische Zwillingshildung,” Zert. d.
deutsch, geolog. Gesellsch, p. 642, vol. xxi, 1869,
280 Mr. L. Fletcher’s Crystallographic Notes.
positive tetrahedron of the other, the composition-plane is
perpendicular to the twin-plane. The tetrahedron-faces there-
fore must really fall into a plane; and I hope that crystals
may yet be found which will leave the matter beyond doubt.”
From this we conclude :—first, that Sadebeck had followed
Naumann, assuming his explanation to be that of Haidinger ;
secondly, that, owing to the practical difficulty of distinguish-
ing between growths according to the two laws, he could come
to no decision from simple examination of the specimens ;
and, thirdly, that he declared in favour of Haidinger’s view
merely that the law might not be at variance with a second
law, which was true in certain cases, but of which the general
application had not been proved.
Apparently before 1876 there was another change of view
on the part of Sadebeck ; for on page 82 of Rose and Sade-
beck’s ‘ Crystallography **, where this law is briefly referred
to, we read that ‘‘the individuals have a face of the form
{101} for composition-plane ;”’ and a footnote gives a refer-
ence to the first paper of Sadebeck, without stating whether
or not he had since obtained that evidence of the incorrect-
ness of Haidinger’s explanation which was confessedly want-
ing so late as the time of publication of the second. The
omission of any reference to the difficulty may have arisen
from unwillingness to perplex the student of an elementary
text-book.
The next mention of the law is made in Groth’s Catalogue of
the Strassburg Collection (1878). We there find that, “as for
the regular growths of copper pyrites, the results of Sadebeck
are quite confirmed by the specimens in the Strassburg collee-
tion ;”’ and further on we read that these particular growths
are symmetric twins about a plane of the form {101}. In
other words, Sadebeck’s first explanation, or that of Naumann,
is accepted. There is no reference to the difficulty in which
Sadebeck had found himself placed; indeed it is quite possible
that the later explanation of Sadebeck, agreeing with that of
Haidinger, had escaped notice owing to its having appeared
in a paper dealing with a more general subject and haying no
reference to copper pyrites in its title: in any case no mea-
surements are recorded which render it possible to distinguish
between the two statements of the law.
In the latter part of the same year, according to a paper on
_ haplohedral hemihedry f, either Sadebeck was in a state of
doubt as to which is the correct explanation, or else he con-—
sidered both correct; for we read as follows:—“ If, on the
* Rose and Sadebeck’s Elemente der Krystallographie, 1876,
+ “Ueber geneigtflachige Hemiédrie,” Zeit, d, deutsch, geolog. Gesellsch,
p. 601, vol, xxx, 1878,
Mr. L. Fletcher’s Crystallographic Notes. 281
one hand, a face of {1 0 1} be both twin-plane and composition-
plane, the adjacent tetrahedron-faces form small salient or re-
entrant angles ; if, on the other hand, the composition-plane
be perpendicular to the twin-plane, the tetrahedron-faces of
the one are coincident with the adjacent faces of the other.”
The probability is that both are mentioned, not because Sade-
beck believed them to be both true, but merely to show that
in either case the position then being contended for was a
tenable one; and in fact the position of the composition-plane
has no further bearing on the argument of that paper.
It would at first sight appear that a difference of a right
angle in the position of the plane of composition would mani-
fest itself by angular differences in the twin sufficient to render
any difficulty of distinction impossible; we shall therefore
attempt to make quite clear what differences would be ob-
served in growths characterized by such different laws.
Fig. 2 represents an octahedron {111} of copper pyrites in
equipoise, a 6 c d being one set of similar alternate faces, and
a 8 y 5 the other set respectively parallel to the first. This figure
approaches very nearly to the regular octahedron of geometry
and of the Cubic system, of which the faces are all equilateral
triangles and the sections through the edges all squares: the
difference therefrom was first made known by Haidinger in the
memoir of 1822. Though ABA B, the basal section of an
octahedron of copper pyrites, is a square, the sections CA C A,
CB CB through the terminal edges are merely rhombs, the
angles in the vertical axis being 90° 51’, and in the horizontal
axes 89°9’; the triangular faces are only isosceles, the vertical
angle of each being 60° 29’ and the basal angles 59° 454.
In fig. 1, abcd and a8y6 are the stereographic projec-
tions of the points in which lines drawn through the centre
parallel to the normals of the faces of the octahedron of fig. 2
would meet the sphere.
The faces of the form {101} truncate the terminal edges
of the octahedron {111}; TT QQ, four of the poles of this
form, are shown in fig. 1.
According to Haidinger’s measurement, 2Cqa is 108° 40’,
whence tay QC = tan Cacos Q Ca = tan Ca cos 45°.
Thus
QC = 44° 342’, QT =90° 51’, and Qa=35° 32’;
also
cos Ta = cos Qacos QT,
and
Ta = TB=90° 412,
while
Tz = Tb =180°—90° 412/=89° 18),
j
282 Mr. L. Fletcher’s Crystallographic Notes.
Fig. 3 represents a second crystal, with its faces a,b,¢d,
a1 Bt 71, parallel respectively to the faces abedaByé5d of
2
Both versions of the law assume that the plane of rotation
or the twin-plane is a face of the form {101}. Let us take
for the particular plane of rotation the plane (101) which
truncates the edge 6, ¢,, or the edge 6c, and is represented in
the stereographic projection by its pole T.
On rotating the crystal represented in fig. 3 through two
right angles round the normal TT to the plane (101), its
faces will take up positions represented in fig. 4; and the poles
of the faces in this new arrangement are introduced in fig. 1
as a,b, ¢,d,a,P,75,. In the first place we may remark that
as each of the pairs of faces 6, ¢, and y, d, is diagonally sym-
metrical to the line T T about which the rotation takes place,
e, will after the rotation have a direction parallel to that belong-
ing previously to the face 6), and still belonging to the face 6;
and similarly the face d, will after the rotation have a direction
parallel to that belonging previously to the face y, and still
belonging to y. In other words, the faces cd,,6, of the
rotated octahedron shown in fig. 4 are respectively parallel to
the faces Sydc of the octahedron of fig. 2. If the octahe-
dron had been the regular one of geometry, not only these
faces, but all the remaining faces and all the edges of the octa-
hedron of fig. 4 would have been parallel to taces and edges
of the octahedron shown in fig. 2. As the line T T bisecting
CC is perpendicular to the edge CA, and therefore not
parallel to the edge CA, the point T will not be midway
between A and C; and thus, although the edge A C would
be unchanged in direction by a rotation through two right
angles about T T, while B would be rotated to B and B to B,
yet C would not be rotated exactly to A nor A exactly to C;
and the edge C A of fig. 2 will thus not be parallel to A, C,
of fig. 4, nor the edge B A to the edge B, C,. In fact, while
the edge A, C, is parallel to the edge C A, the angle A, C, A,
is, as stated above, 90°51’, and the angle CAC is 89° 9;
whence the edges C, A, CA must have a mutual inclination —
of 1° 42’, Similarly, although the edge A, C, is parallel to ~
the edge C A, and the plane C A B to the plane A, O, B,, the
angle A, C, B,, as stated above, is 60° 29/ , and the angle
CAB is 59° 453’, whence the edges BA B, C, are mutually
inclined at an angle of 43).
The same results will follow, perhaps more simply, from
i,
Mr. L. Fletcher’s Crystallographic Notes. 283
a study of the stereographic projection of fig. 1; for as
Te=T6, ¢ will. be rotated into the position of 6, and 6,
into the position of ¢, while y, will be rotated to d, and d,
to y. With the other poles it will be different: thus e will
rotate into the position a, where Te=Ta,=89° 181’, and
ae, = Ta—T a, = 90° 419 — 89°18) = 19232’ = 8b, =aa,=08,.
Also TQ,=T Q = 89° 9’, whence Q Q,= 90° 51’— 89° 9 =
- 42’; and TC=T ©, = 44° 34), whence C C,=90° 51’.
Next, let M be a point bisecting the arc Q Q,; the poles of the
two octahedra will be symmetrically disposed to the twin-plane,
represented in the projection by the line MBM; for TM=
TB =90°, and the arcs Tb, Te, Te Tb Ta T8 Ta, Th, are
allequal. From this it will follow that Ma=M6=Ma,=M4;;
also that Ma,=M6,=Mb = Ma, and that My My, Md Md,
Me Mc, Mé Mé,, being all right angles, are equal to each
other. The poles of the two individuals are thus not only
symmetrical to the twin-plane M B M, but also to the plane
TBT at right angles with it, represented by an irrational
symbol approximating to (100 0 99), and thus not a crys-
talloid plane. The same arrangement of poles might therefore
be obtained by rotating the original octahedron about the line
M M parallel to the tangent of the circle at T, and therefore
to a “ terminal edge ”’ of the octahedron. {111!. It may be
remarked that, although the same arrangement of poles will
be obtained by rotation about the lines TT M M, the lettering
will not be identical in the two cases; but as in both cases the
planes which are quite or nearly coincident in direction are
always represented in the one individual by italic letters and
in the other by greek, there will be no crystallographic dif-
ference in the results of these two methods of derivation.
This proves that, as has been mentioned aboye, Haidinger’s
statement, “‘regular composition often takes place parallel to
a plane of {101} or perpendicular to the terminal edges of
4111,” indicates only a single case if the reference be to
the plane of rotation.
Haidinger’s law might therefore be equally well expressed
in the two following ways :—
I. Twin-plane a face of the form {101}; composition-plane
perpendicular to the twin-plane.
Il. Twin-axis a terminal edge of {111}; composition-plane
parallel to the twin-plane.
We are now in a position to discuss the difference of growth
which will be produced by a variation in the position of the
plane of composition. As the line TT is perpendicular to the
~
284 Mr. L. Fletcher’s Crystallographic Notes. —
edgesA GC CA and passes through the centre of the crystal,
the rhombs TB TB TB,T B, of figs. 2 and 3 will be per-
pendicular to the twin-plane, and will each represent the com-
position-plane of Haidinger. If, now, by simple translation,
without rotation the half TB TB AC above the rhomb of
fig. 2 be associated with the half TB, TB, A,C, below the
rhomb of fig. 4 in such a way that the two rhombs coincide,
we get the composition represented in fig. 5. This figure
will therefore be that of a growth according to the law of
Haidinger. For convenience of direct comparison with the
results following from the law as given by Naumann and
Sadebeck, the same growth as fig. 5 is shown in fig. 6 as it
would be seen either after a rotation of the whole figure
through two right angles about the vertical axis, or by an eye
placed at the back of the paper.
Again, let the rhombs MBMB M B\M B, of figs. 2 and 3
be the traces on the octahedron-faces of a plane parallel to the
twin-plane, and therefore the composition-plane of Naumann.
If now, just as before, the half MBM BC A above the rhomb
of fig. 2 be associated with the half M B, M B, A, C, below the
rhomb of fig. 4 in such a way that the rhombs coincide, we
get the composition represented in fig. 7. This figure will
therefore be that of a growth according to the law of Naumann. —
With the help of the stereographic projection of fig. 1 we
can now investigate the differences of the growths represented
respectively in figs. 6 and 7.
Fig. 6. Fig. 7.
Haidinger’s law. Naumann’s law.
dy,=yd,=0, aa, = b,=salient iS 234,
cd; = 6c; =0. bB,=«a,=reentrant 1° 233,
Edges C T TC, coincident, |Angle CM.MC,=salient 1° 42’,
mea ed sj » AM.MA,=reentrant 1° 4
Angle between the trunca- Angle between the trunca-
ting planes of C and C, ting planes of C and C,
= 89° 9. ""=90° 5,
The faces a B a; By are not The faces dy ¢, 8; are
in a zone. in a zone.
We have seen that in the projection the plane of composi-
tion isa plane of symmetry to the poles of the two individuals;
and we further perceive that in each case the plane of compo-
sition is a plane of symmetry to the faces actually shown by
®
; Mr. L. Fletcher’s Crystallographic Notes. 285
the twin-growths; and the angles of the upper half of fig. 6
are exactly equal to the similarly disposed angles of the upper
half of fig. 7, and the angles of the lower half of fig. 6 to the
similarly disposed angles of the lower half of fig. 7, the only
difference in the growths being the relation of the upper to
the lower half.
Of the specimens of copper pyrites in this collection, one
figured by Haidinger himself in the ‘ Catalogue of the Allan-
Greg Collection’ (now in the possession of the British
Museum), though probably not one of the original specimens
of the memoir of 1822, offered itself as the most likely to
afford a satisfactory solution of the difficulty. In this speci-
men, which comes from Freiberg, the twin-growths are dis-
posed parallel to each other on galena, and are associated with
quartz, chalybite, and calcite. The length of a side of the
triangular faces is about 1°5 millim. Haidinger’s drawing to
illustrate this specimen is virtually the same as fig. 9 (copied
from his paper of 1825), the only difference being that the
faces of e {101} being almost linear are not shown in the Cata-
logue. This figure represents the rotation as taking place about
each of the normals to the four upper faces of {101} of the
central individual, of which both the upper and the lower halves
are present. We may remark that a complex growth of this
perfect kind would be explained by the law of Naumann equally
with that of Haidinger, seeing that in the lower half of the
regular composition the various planes of junction are repre-
sented as parallel to the corresponding twin-planes, and in the
upper half as perpendicular to them. As none of the growths
have an all-round development, the figure represents the
growth in theoretical perfection rather than as actually ex-
istent; in fact the actual habit is more nearly shown in fig. 10,
which at the same time will serve to give an idea of the stria-
tion to be observed on the faces.
A crystal from this specimen appeared to show that the triad of
octahedron-faces 0 0; 0, did not quite coincide, as according to
Haidinger’s explanation’ should be the case; but still no satis-
factory measurement of the angle could be obtained. The re-
entrant angle lying in the zone cg at the junction of two
individuals could, however, be determined with very fair pre-
cision, although the faces are finely striated parallel to their
edge of intersection with each other. These planes were sup-
posed by Haidinger to belong to the common form 2{2 0 1}; and
as the angle made by a plane of this octahedron with the adja-
cent face of the form {101} is 18° 31’, the reentrant angle
according to his theory should be 37° 2’. Actual measurement,
286 Mr. L. Fletcher’s Crystallographic Notes.
however, gave 20° 9’; and closer examination rendered it clear
that on the crystal measured the faces belonged not to the —
form z{201}, but to another less common form {302}, |
whilst smaller almost linear faces of z {201} were to be seen —
lower down in the reentrantangle. The angle between (3 0 2)
and (101) being 11° 203’, the reentrant angle for this form
should be, according to Haidinger’s law, 22° 41’; on the
other hand, according to Naumann’s law, it should be 20° 59/
—that is, the difference of the inclinations of (302) and its
parallel (3 0 2) to the plane (101). The measured angle was
thus 50’ less than the angle calculated from Naumann’s law;
and the latter angle was itself 1° 42’ less than the one caleu-
lated according to that of Haidinger.
The difference between the calculated and measured angles
is large, and in fact is so considerable that it can only be
attributed either to the growth being not strictly a regular
twin, or to a deviation from the fundamental angle as deter-
mined by Haidinger. As the extreme accuracy of Haidinger’s
measurement of the fundamental angle of copper pyrites had
been confirmed both in the memoir of Sadebeck and in the
Catalogue of the Strassburg collection, and also by Kokscha-
row*, and as, further, this particular crystal did not lend
itself to a precise determination of any other angle than the
reentrant one above mentioned, the result seemed very unsatis-
factory, and for some time the examination was discon-
tinued. Two years later it was resumed ; and, happily, another
crystal from the same specimen was found to give reflections
so good that a precise measurement of the angle between two
octahedron-planes belonging to the same individual and on
opposite sides of « could be obtained. This was found to be
108° 173’, a deviation of 223’ from the angle as determined
from the specimens previously measured. A less precise deter-
mination of the angle of a terminal edge gave as mean
69°592’, the limiting values being 69° 542’ and 70° 03. From
the same crystal the angle o 0; was found by help of the 6 eye-
piece of a Fuess’s goniometer (as improved by Websky) to be
2° 3’, instead of zero according to Haidinger, and 1° 23)
according to Naumann and Sadebeck.
The whole difficulty had, however, now disappeared, as is
shown by the following table of calculated and observed
angles:—
* Bull. Soc. St. Pét, 1874, xix. p. 562.
Mr. L. Fletcher’s Crystallographic Notes. 287
|
t }
Tf001.101—|44° 343" 44° 24") 44° 221 44 214!
i
=a Observed.
| Calculated. | eye
| ° i me) 1 Onl | Ong ihe |
Pees de... 108 40 | 108 173} 108 163) 108 153) 108° 173"
1 © RABI oq
iota | 70 73] 69.56 | 69 553) 69 55 | be resin
Naum....|| 1 233 De 2 44 2 6 ;
Pg {iid itor ror 0/0) onl! ono \ ae
np, { Naum | 20 59 | 20 123) 20 10% 20 88) ago
1 Haid : | 22, 4 22 423 aa 493 92 423) J
From a third crystal not quite so perfect, but still giving
very good images, the angle a)’, was determined to be
HOS? 182,
There can thus be no doubt that:—
1st. The growth is strictly regular.
2nd. The parametral angle differs from that determined from
other specimens by previous observers, and is very nearly
44° 22,
ord.» The twin-plane is a face of the form {101}. And
‘4th. The composition-plane is parallel (and not perpendicu-
lar) to the twin-plane.
At the suggestion of Prof. Maskelyne, a careful analysis of
this specimen was made in the departmental laboratory, with
the view of ascertaining to what extent this variation in the
fundamental angle is attended by a difference from the che-
mical composition of ordinary copper pyrites. The following
results were obtained by Dr. Walter Flight:—
Py aaa Calculated,
Ip Il. Cu FeS.,,.
Copper... -. 25°78 30°66 — 84°45
MoM ovis rss’). O16 d4-11 30°57
Sulphur ... 37%°52 [35°23 by diff. ] 34°98
Arsenic . ._ traces
@uartz fou.) 0:28
: 98°74 100-00 100-00
No other metals were discovered, although carefully searched
for. The specimen is thus found to contain a considerable
and variable excess of FeS, over that of typical copper
pyrites—the first analysis corresponding very nearly to
Cu FeS,+4FeS8,, and the second to CuFeS,+}$FeS,. As
close examination of the specimen reveals the presence of
included minute crystals of iron pyrites (and mispickel), it is
possible that even in the second fragment, which was specially
288 Mr. L. Fletcher’s Crystallographic Notes.
chosen for its approximate homogeneity, this excess of FeS,
may be almost wholly due to mere admixture of iron pyrites.
Since the above determinations were made, the collection
has been enriched by the acquisition of a superb Freiberg
specimen of very much the same character as the one just
described, but on a relatively colossal scale; for the length of
side of the triangular face 0 0, 0, (and this is the smallest) is
here not 1°5 but 24 millim. Owing to the absence of reentrant
angles, the growth very much resembles a regular octahedron
truncated by the faces of a cube, one of the octahedron-faces,
however, showing in a very marked way the threefold com-
position of that part of the crystal.
A further examination of the collection has resulted in the
finding of a specimen (from Pool mines near Redruth) which
confirms the parallelism of the planes of composition and of
twinning in the most satisfactory way. The crystals of copper
pyrites have been here deposited on quartz crystals which they
partly enclose: they thus have not an all-round development;
in fact, there is a practical difficulty in determining more of the
growth than is shown in fig. 11; but this, so far as it goes, falls
little short of perfection (the dotted lines indicate the twin
in theoretical completeness). The images from @@, were so
well defined that the largest magnifier, «, of Fuess’s instru-
ment could be used, three different measurements at nearly
normal incidence giving respectively for the value of this angle
1° 23’, 1° 231’, and 1° 23’, while a measurement at almost
grazing incidence, when the images were broader, gave 1° 23.
The faces o 0, were not so perfect; but still, with the 6
eyepiece, good images were seen, from which two consecutive
measurements of the angle gave 1° 23’ and 1° 232’. Two
measurements of oo’ gaye respectively 108° 39’ 30” and
108° 39’ 45”. The following table renders more evident the
close correspondence of the observed and calculated angles.
Observed,
ooo — Calculated
Angles of Symmetrically disposed from
one individual. angles of the other. 001.101
=44° 342’,
ODA vine 70° 7H Die sbi 70° 7 WT ae
CP sass 35° «38l Wo Cg eeeees 35° 4! 35° 3/46”
@0' ... T0° 43! @o 0'g «0. 10° 12’, 70° 4°
He aS Ie 35° 3/46!
0.0! see 108° B98! 0g. 0%guovee01 08° 37’ 108° 40! 4”
Also @ @y.sse.. 1°28’, 1° 23Y, 1°23’, 19231" 1° 23/30"
O 09 secree 1° 23’, 1° 233’ 1° 23’ 30”
The linear faces {101} and the minute faces of another
-
Mr. L. Fletcher’s Crystallographic Notes. 289
octahedron g {20 3}, although present on the crystal, are not
shown in the figure.
A chemical examination made by Dr. Flight shows that this
specimen has a composition very nearly represented by the
typical formula CuFeS,. The following results were ob-
eed — Observed. Bere.”
Popper, Joos <+- 34:37 34°45
HOW) ssc sxs-escie 1x; 90:03 30°57
pulphur sscccs.. 31:92 34:98
OIaTED, -caceay co 4-19
100°51 100°00
Up to this point, for the sake of simplicity, a very important
property of copper pyrites, its hemihedral structure, has been
left as much as possible out of sight. It is found, however,
that the faces of the octahedron {111} of this mineral are not
all similar, but must be regarded as belonging to two di-
stinct tetrahedra: in the case of the first tetrahedron, for con-
venience of distinction termed the positive or o tetrahedron, the
faces are rough or striated, and are sometimes coated with oxide
of iron; on the cther hand, the faces of the second or negative
or » tetrahedron are smooth, bright, free from this coating, and
in general smaller than the former. From this it follows
that the set of faces denoted above by the italic letters
_abed, though similar to each other, are distinct in physical
character from those denoted by the greek letters « By 6;
whence we infer that in such a growth as would be represented
by fig. 7, where there has been a simple rotation of one indi-
vidual through two right angles from a position of identical
orientation with the other, and adjacent faces of the two indi-
viduals thus bear respectively italic and greek letters, the com-
position-plane will be a plane of geometrical, but not of physical
symmetry. As, however, the correlative tetrahedra and also
the correlative hemiscalenohedra are independent of each
other, not only in surface-characteristics, but also in their pre-=
sence on the crystal, even this geometrical symmetry could
scarcely be expected in the actual twin-growth.
Now Sadebeck states that in the actual twin-growth the
composition-plane is really a plane of symmetry not only to
the geometrical, but to the physical peculiarities—the regular
composition thus belonging to the class called by Groth
“symmetric twins ;” that instead of the faces of the octahe-
dron which are parallel, or nearly so, in the two individuals
belonging in one to the positive, and in the other to the nega-
tive, they really belong either both to the positive or both
to the negative tetrahedron. To pass, therefore, to the actual
Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. U
290 Mr. L. Fletcher’s Crystallographic Notes.
twin from parallel orientation of the individuals, there must be,
in addition to the rotation through two right angles round a
normal to (101), a further rotation of one of the two erystals
either through two right angles about a normal to one of the
faces of the prism {110}, or through a single right angle
about the vertical axis parallel to the edges of this prism.
Though this double rotation may be compounded into a single
rotation round the normal to a face of the octahedron {111},
the angle of this single rotation will not be 180°, as is the case
in other twins, but 119° 31’.
If this statement of Sadebeck be accepted as having a satis-
factory foundation, the growth must be regarded as up to the
present unique in character; for no other regular composi-
tion appears to have yet been discovered in which, starting
from a parallel orientation, a double rotation is absolutely
necessary for the representation of the relative disposition of
the two individuals. There exist twin-growths of tetartohedral
crystals, it is true, such as those of sodium chlorate and certain
regular compositions of quartz, described by Prof. Groth, which
are somewhat analogous in character; but they are capable of
a more or less satisfactory representation by a simple rotation
of one of the indiyiduals through two right angles from a
position where corresponding crystallographic lines of the
right and left individuals are identical in direction; they are
moreover intimately related to the directions of the erystallo-
graphic axes. As, however, it had been impossible for Sade-
beck to convince himself, from simple examination of the spe-
cimens, that certain faces assumed by Haidinger to be parallel
might not be inclined to each other at an angle of 1° 234’, it was
possible to entertain a doubt as to the specimens being suffi-
ciently well crystallised to allow of an absolute certainty in the
distinction of the two tetrahedra; and as the law is so curious
from its extreme rarity and simplicity, and so important in
its bearing on the general question of twin-growth, about
which there has lately been much discussion, it seemed desi-
rable to place the law, if possible, beyond all suspicion.
The accuracy of Sadebeck’s inference as to the disposi-
tion of the two tetrahedra in this twin-growth is confirmed in
the most satisfactory manner by the specimens in this col-
lection.
The Freiberg specimen of fig. 10 shows not only that the
individuals are symmetrical to the plane of composition, but
also that the differences of the two tetrahedra of each indi-
vidual are too marked to allow of this symmetry of physical
peculiarities being an accident of the growth.
The specimen from Pool mines (fig. 11) is even more satis-
factory still; for the faces w@, which give such excellent
:
Mr. L. Fletcher’s Crystallographic Notes. 291
images are perfectly smooth and bright, and remarkably dif-
ferent in aspect from the two dull and striated faces 0 05.
A further example is presented by a specimen (probably
from the Trevannance mine, St. Agnes) shown in fig. 12,
which the symmetry to the combination-plane and the extreme
difference between the smooth and the deeply-striated tetra-
hedra render most convincing. The angle between these
striations is so very definite that it can be measured with fair
accuracy by means of a microscope; it was determined to be
1202°, the angle calculated according to Naumann’s law
being 120° 28’, and according to Haidinger’s law 119° 31’.
Finally, we may refer to fig. 8, representing a Cornwall
specimen (now in the Museum) figured in 1825 by Haidinger
himself in his memoir on the Regular Composition of Crys-
tallised Bodies. Here the predominant form of each individual
is a hemiscalenohedron; and this in each pair is symmetrically
disposed to the plane of composition. Although this speci-
men is symmetrical in its habit, the planes s are so striated
and rounded that it was found impossible to assign to them
a definite symbol; they lie, however, in the zone defined by
the symbol [112], and approximate to {312}.
We conclude, therefore, that there is no doubt of the actual
existence of a kind of twin-growth which it is not possible to
represent by a single rotation through two right angles from a
position of parallel orientation of one of the individuals to the
other—that for the representation of this growth an additional
rotation is requisite, but that the simplest mode of represen-
tation is the one which regards the two individuals as symme-
trical to a plane.
EXPLANATION OF PLATE VI.
(To accentuate the differences in twin-growths according to the laws of
Haidinger and Naumann, fies. 1-7 are drawn for a parametral angle 423°
instead of 44° 343'.)
Fig. 1. Stereographic projection of the poles of {111}, and of the same
twinned about T T, the normal to (101).
Fig. 2. The octahedronabedaByé {111}.
Fig. 3. The octahedron a, 6, ¢, d, #, 8, y, 5, {111}, parallel to the last.
Fig. 4. The same turned through two right angles round T T the normal
to (101).
Fig. 5. Twin-srowth of {111}, according to Haidinger’s law.
Fig. 6. The same, viewed from the opposite side.
ix. 7. Twin-growth of {111}, according to Naumann’s law.
8. Twin-growth, with faces s of a hemiscalenohedron or disphenoid
(Haidinger, Edin. J. of Sc. 1825).
Fig. 9. Twin-growth of {111} {001} {101} {201} (Haidinger,
Edin. J. of Sc. 1825).
Fig. 10. A similar twin-growth.
Fig, 11. A twin-crystal from Pool mines, near Redruth.
Fig. 12, A twin-crystal, probably ae Trevannance mine, St, Agnes.
a
f 292 J
XXXII. The Tails of Comets.
By BE. Vawsittart NEALE.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN, Le
| VENTURE to offer an explanation of the remarkable
phenomena presented by the tails of comets, so simple
that, considering the number of eminent astronomers who
have turned their attention to this subject, and to whom it has
remained a mystery, | am almost afraid to suggest my expla-
nation, lest it should prove a sort of scientific mare’s nest.
Still, since I cannot see where it fails, while the subject is one
of considerable interest, I have determined to run the risk of
some eye more penetrating than my own discovering my error,
if there is one.
My explanation rests on the interaction of three forces, of
which two are known to exist, while the existence of the third
may, | think, be reasonably assumed. These forces are:—
(1) the force which urges the comet towards the sun; (2) the
expansive force of the heat of the sun; (3) the resistance of an
atmosphere surrounding the sun.
That there is such an atmosphere extending many hundred
thousand miles from the sun’s centre we know, because it can
be seen. How much further it may extend in a condition in
which it is invisible we do not know; but, considering the dis-
tance to which the atmosphere surrounding the earth is known
to extend by its action on meteoric bodies, we may, I think,
reasonably assume the existence of an invisible solar atmo-
sphere, extending far beyond the limits of the visible atmo-
sphere; and if this is assumed, we obtain an easy explanation
of the phenomena of comets’ tails.
The changes in a comet which give rise to its tail begin,
according to the account given by Mr. Higgins in his excel-
lent article on Comets in the current number of the ‘ Nineteenth
Century, by jets of a gaseous nature ejected towards the sun,
i. é. in the direction determined by the expansive force of the
sun’s heat, acting on the comet, combined with the moving
force of the comet. But soon, he says, these jets bend round,
as if they were carried back by a strong wind, and form an
envelope round the body of the comet and a cone behind it.
-Just so. Itis what would happen to a man dressed in a loose
robe and running rapidly through the air. His dress, though
cutee with him, would stream behind him, because it expe-
rienced more resistance than his body from the air. The jets
Mr, E. V. Neale on the Tails of Comets. 293
of gas which escape from the body of the comet and expand
when they leave it are more resisted by the sun’s atmosphere
than its more solid head, which therefore gradually overtakes
them ; so that they seem to fall back, till they constitute an
envelope round it, and then spread in a conical form behind
the head , through the joint operation of their own lateral move-
ments, of the i increasing expansive force of the sun’s heat as
the comet approaches the sun, of the increasing resistance of
the sun’s atmosphere (whence the head must continually gain
more and more on the parts of the tail at first thrown off), and
of the pressure of fresh envelopes continually forming round
the nucleus as it advances. The body of the comet is con-
stantly moving through the gases or vapours which it throws
off, and thus produces the appearance of a tail, by leaving
each successive part thrown off more and more behind it.
The central line of these successive envelopes would ob-
viously tend to be a straight line from the sun’s centre through
the head of the comet; though the continual change of direc-
tion in this line, as the comet approaches its perihelion, must
be liable to produce an apparent curvature in the tail, because
the parts first emitted, and therefore most distant from the
body, if they retain luminosity enough to be visible, must fall
more and more behind the advance of this central line in its
sweep round the sun.
The phenomena of divided tails, of bright streaks, &c., find
a ready explanation in the accidental variety of pressures to
be expected among jets of gas or vapour emitted under such
circumstances, and the effect of perspective, according as we
happen to look through the edges or across the more “central
parts of the envelopes forming “the comet’s tail—possibly com-
bined with actual variations of pressure in the sun’s invisible
atmosphere, arising out of the enormous changes which can
be observed in its visible atmosphere. But what as to the
change in the direction of the tail when a comet has passed its
perihelion? Why do comets then carry their tails before instead
of behind their heads? Because the direction of the pressures
which produce the tail has changed. Given an invisible solar
atmosphere, a comet moving towards the sun will be perpe-
tually passing from a rarer into a denser medium, while a
comet moving from the sun will be perpetually passing from
a denser into a rarer medium. At the same time the jets of
gases or vapours which it will continue to emit from the ex-
pansive force of the sun’s heat will then consist of particles
moving from the sun. Thus the two tendencies—the move-
ment of these particles due to the action of gravity, and the
tendency of the expansive force to exert itself in the line of
294 Mr. 8. W. Holman on a Simple Method
least: resistance—will combine to carry the luminous particles
emitted from the comet in advance of the mass.
That the change in the direction of a comet’s tail should
take place with the rapidity and to the extent observed in the
case of the enormous appendages of some of these bodies may
still appear surprising. But it must be remembered that, in
these cases, we can speak only of what we see. The conical
mass of gases or vapours extending behind the nucleus of a
comet may attain, in the case of the largest of these bodies,
to an expansion much greater than the part visible, which may
consist only of the parts that receive the strongest impulses
from the centre of force; so that when the tail seems to have
swung round through an enormous arc in the sky, what has
really happened may be only that the line along which the
substances forming it become visible may have shifted, in con-
sequence of the direction of the impulses proceeding from the
head having altered.
As the time when the most rapid alteration in the direction
of the tail of a comet takes place necessarily coincides with
that when the expansive action of the sun on the substances
emitted from the comet is at its maximum, there must be the
less difficulty in admitting the last hypothesis as an explana-
tion of this phenomenon. It is the only one, so far as I see,
that offers any difficulty in the way of the theory now proposed
respecting the tails of comets, which may be summed up in
the proposition that, as the incandescence of meteoric bodies
proves to us the existence of a widely diffused atmosphere
surrounding the earth, so the development of the tails of
Comets proves to us the existence of a much more widely dif-
fused atmosphere surrounding the sun—both sets of pheno-
mena being due to the same cause, namely the resistance of
these atmospheres to bodies rapidly passing through them.
T am yours &c.,
E. Vansittart NEALE.
15 Portsmouth Street, Manchester,
August 21, 1882.
XXXII. Simple Method for Calibrating Thermometers.
By Stuas W. Horman*.
f lisse calibration of a thermometer by most of the methods
in ordinary use is a tedious and somewhat difficult opera-
‘tion, and hence often neglected even in important work. For
the purpose of supplying a method simple both in observation
and computation, and at the same time accurate, the following
* From Silliman’s American Journal, No, 136, p. 278,
for Calibrating Thermometers. 295
process is described, which, although involving little that is
novel, has not to my knowledge ean used before.
First, however, it is necessary to recall to the attention
of observers the fact that, without calibration-correction, the
readings of a thermometer having a scale of equal linear parts
eannot be relied upon within one or more divisions of this
scale, and that thermometer-makers, knowing this, almost
universally space the graduation upon the tube to correspond
more or less closely with the shape of the bore, as determined
by previous calibration, or by comparison with a standard (1!)
instrument. This practice is much more general than is ordi-
narily supposed, and has an important bearing upon the accu-
racy of the work done with such instruments. For the scale
thus made is merely approximate, the dividing-engine or other
tool being usually changed only at such intervals as to make
the average error less than some specified amount. An inspec-
tion of these conditions will show that the calibration of such
a tube and scale can be only approximate, except with correc-
tions for the inequalities of the spacing, involving an amount
of labour disproportionate to the result obtained. The best
makers, such as Fastré, Baudin, and others, have produced
satisfactory thermometers graduated to equal volumes; but
eyen these are not as reliable as instruments of less cost with
a scale of equal linear parts, say of millimetres, supplemented
by a calibration by the observer. The best form of tube for
almost all work is one backed with white enamel, with an
inverted pear-shaped bulb at the upper end of the capillary
(a very important feature), and with a scale of equal arbitrary
linear parts (0°7 to 1 millim. is a suitable length for estimation
of tenths) or of approximate degrees, for convenience, etched
or engraved upon it.
Without reviewing here the methods proposed by various
writers, it may be said that it has been the general plan to
select beforehand upon the scale two poms between which to
make the calibration, this space being the “ calibration unit,”
the errors of these points being, of course, zero. This plan
has led to unnecessary complexity. Such an assumption is no
more requisite in calibration after a scale has been put upon
the tube, than in calibrating by the dividing-engine or micro-
meter before making the scale. It is obvious that the selec-
tion of these points is wholly arbitrary, and, if used at all, one
or both of them may, if desirable, be chosen after the observa-
tions with the calibrating-thread have been made. The choice
should be made with a view to facilitating the work. Hence
the use of the observed freezing- and boiling-points, upon
5 .
which some methods are based, is most undesirable.
oF
pe!
296 Mr. 8. W. Holman on a Simple Method
In the method which will now be given, either one or both
of these points may be left to be selected, according to the
combined conditions of length of thread employed, shape of
the tube, and numerical convenience, after the observations
with the thread have been made.
Let it be desired to find the calibration-corrections for a
given tube. Determinations which will give the errors of
every 3 centim. of length will ordinarily be sufficient ; but this
must depend on the result sought. Separate a thread of mer-
cury of about that length. The actual length of the thread
within two or three millimetres is of no consequence whatever;
and hence a suitable thread can be obtained in a very short
time.
Set the thread with its lower end at or near the beginning
of the graduation: call the reading* of the lower end of the
thread /,, and that of the upper end w,. Move the thread less
than 1 millim. and read again, finding thus /, and uw. Move the
thread about 1 centim., and read /; and w3. Move the thread less
than 1 millim., and readd,and w,. So continue throughout the
whole length of graduation, increasing the number of settings
or repeating the whole series in reverse order and several
times, if the highest attainable precision is desired. This
alternation between 1 millim. and 1 centim. in setting tends
towards the better elimination of errors in estimation. It is
not, however, essential, nor even always as well as an equal
number of distributed readings. This must depend upon the
skill of the observer. Avoid, as far as convenient, taking
readings with an end of the thread apparently just at the line
of the scale, as the width of the line, even in the best scales,
is a source of considerable errorf. If any point (e. g. the
zero-point of the graduation) has for any reason been selected
as the first of which the error should be assumed zero, the
settings may to adyantage, though not necessarily, be made
to extend each way from this.
Then 7%44—,, ug—ly, &e. will give a series of lengths of the
calibrating-thread in all parts of the tube. Before reuniting
this thread to the rest of the mercury, plot points with abscissas
1, lo, &e., and ordinates u;—h, u.—/,, &e., the corresponding
lengths of thread, and draw a smooth curve through the
points thus obtained. This line will give a general idea of the
form of the capillary bore ; and should any parts of it show
considerable irregularities, the corresponding portions of the
tube should at once be reexplored with the thread.
If not already done, the point A upon the scale, to be used
* Tenths of a division are supposed to be read by estimation.
+ Some of the advantages of Neumann’s method are offset by this error.
for Calibrating Thermometers. 297
as the starting- or reference-point of the computation, should
now be selected. In general the extreme ends of the tube are
to be avoided, as more likely to have been rendered irregular
or rapidly tapering in the process of making or joining on the
bulbs. If the zero of the numbering is placed one or two
centimetres from the bottom of the tube, it forms a desirable
starting-point.
Find upon the curve the ordinate w’ corresponding to the
abscissa A ; then with abscissa A+w’ find the corresponding
ordinate w’, with abscissa A+ u’+w” find the corresponding
ordinate w’”, continuing to the upper limit of the graduation.
Tf A is at a sufficient distance from the lower end of the gra-
duation, find a similar series below the point A. These points,
A, A+u’, A+u'+w", &., upon the graduation are separated
by equal volumes of the capillary. Select any one of these
as the second point of which the error is to be arbitrarily
assumed as zero, and call this B. Then
Atul +u’+...+unth=B.
There are thus 1 spaces of equal volume between A and B ;
1 :
and these correspond each to th of the interval B—A. Hence
the true reading (which, however, it is not necessary to com-
pute numerically) at the point
A is A,
} : P
A+u is A (BA),
A+u'+u" is ope (B—A),
B is B.
And the error obtained by subtracting the true readings, as
given in the right-hand column, from the corresponding actual
readings, given in the left-hand column, at ;
A is 0,
2 fi 1
Atul is At) A+ 2(B—A) baal! (B—A),
Asta tu" is uu!’ — + 2 (BA),
n
B is 0.
In selecting B it might have been assumed equal to A +1 %
thus making »=1, This would somewhat simplify the caleu-
298 Ona Simple Method for Calibrating Thermometers.
lation, and would be of equal accuracy, but is objectionable
from the fact that, in general, this volume would differ con-
siderably from the average volume obtained when 7 has a
greater value (always an integer), and the resulting series of
errors would assume larger numerical values.
The errors or corrections are, for purposes of interpolation,
most conveniently represented graphically by a smooth curve
through points with abscissas proportional to the direct
readings A, A+w, A+u'+u", &e.,
and ordinates to the corresponding corrections.
Should it be necessary to increase the accuracy by a second
calibration with a thread of different length, it is only neces-
sary to take one of approximately an integral part of (B—A),
and when the final curve of error is drawn make the error at
B equal to zero, distributing the difference at that point pro-
portionally to the scale-readings among the errors at the
intermediate points—in other words, to shift the axis of the
second curve of error so that it shall make the error at B
zeY0,
This method requires for each calibration the use of but
a single thread. The computation is simple, and involves a
minimum of approximation. Hrrors of observation are largely
eliminated by the number of settings made in all parts of the
tube, and by the inspection of the curve of lengths; both of
which operations tend in an unusual degree to detect mistakes
or any minor irregularities of the capillary. It avoids the
common requirements of setting the thread exactly at certain
definite points in the tube, or any approximate correction for
slight errors in such setting—two sources of considerable
error and inconvenience, especially when the thread must be
set near or under a line of the graduation. And, lastly, the
total time of calibration for a result of given accuracy is
reduced to one half or one third of that required by Neumann’s
method, the quickest and most satisfactory with which I am
acquainted except that given by Pickering. ‘The latter,
described with some slight inaccuracies, at the reference noted
below, is a neat application of the graphical method ; and the
curve of lengths of thread adopted in the method which I
have described is identical with the corresponding one given
by Professor Pickering, while the whole process is fully one
third shorter and somewhat more accurate. From a series of
calibrations executed upon the same thermometer (one with
a millimetre-scale, by Baudin, of Paris), using a variety of
methods, I have obtained slightly more concordant results
with the proposed method than with Neumann’s or Pickering’s
Distribution of Energy in a System of Material Points. 299
(all those possessing, however, nearly the same degree of pre-
cision), and decidedly better results with these than with any
of the other existing simple methods.
Considerable aid in eliminating errors of parallax in such
work is sometimes found by looking down upon the horizontal
thermometer through a vertical tube having a small hole at
each end. One of the cheap French microscopes with its
lenses removed, and inverted in its stand, answers this pur-
pose well.
With such a device two calibrations of the above-described
thermometer with threads of 3 and 5 centim. respectively, each
with only one series of observations, and requiring not more
than one hour and a half each for completion, gave results
whose average difference from each other at nine points was
0-04 millim., and the arithmetical sum of the extreme differ-
ences was 0:12 millim., a result of sufficient accuracy for any
class of work of which such an instrument is capable.
For brief descriptions of methods of separating threads of
mercury for calibration, reference may be made to the paper
by Russell, and the text-book by Pickering, noted below.
These processes are in general use, and are safe and convenient.
References upon Calibration of Closed Thermometer-Tubes.
Bessel, Pogg. Ann. vi. p. 287 (1826).
Rudberg, Poge. Ann. ix. pp. 355, 566; xxxvil. p. 376 (1836); xl,
pp. 39, 562 (1837).
Kohlrausch, ‘ Physical Measurements,’ p. 59 (English translation).
Pickering, ‘ Physical Manipulation, ii. p. 75 (1876).
Thiesen (Neumann’s Meth.), Carl’s Rep. xv. p. 285 (1879).
Russell (Neumann’s Meth., transl. from Thiesen), Amer. Journ. Sci.
xxi. p. 873 (1881).
Marek, Carl’s Repertorium, xy. p. 300 (1879). (Solution by least
squares. )
yon Oettingen, Inaug. Diss., Dorpat, 1865. (This I have been unable
to obtain.—S. W. H.)
XXXIV. On Boltzmann’s Theorem on the average Distribu-
tion of Energy in a System of Material Points*.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN, Graz, April 6, 1882.
ely you may feel disposed to have the accom-
panying notice of a paper of Maxwell’s transiated for
your valuable ‘ Philosophical Magazine.’ So far as I know,
this excellent paper of Maxwell’s has not been reprinted in
your Magazine; it may not, therefore, be without interest to
your readers that some notice of it should appear, if only as
* Translated from Wiedemann’s Bezbliitter.
+
300 On Boltzmann’s Theorem on the average Distribution
an abstract; and, further, my notice contains one on two new
things, amongst which a remark on Watson’s excellent book
may be interesting to English physicists.
With highest esteem,
Yours &e.,
Bo.LTzMANn.
MaxweEtu (Camb. Phil. Trans. vol. xii. part 3, pp. 547-
570, 1879) shows that this theorem may be easily proved
by means of Hamilton’s principle. The theorem is also
extended, since it is shown to hold good for any systems
determined by generalized coordinates, if only they satisfy the
principle of conservation of energy. ‘There is a difference in
method between Maxwell and Boltzmann, inasmuchas Boltz-
mann measures the probability of a condition by the time
during which the system possesses this condition on the aye-
rage, whereas Maxwell considers innumerable similarly con-
stituted systems with all possible initial conditions. The ratio
of the number of systems which are in that condition to the
total number of systems determines the probability in ques-
tion. In conclusion, Maxwell finds, further, that also for any
unstable system of very many.atoms in rotation under the
action of no external forces the mean energy of internal mo-
tion is the same for each atom, and that a mixture of gases in
a rotating tube behaves exactly as if each gas were present by
itself,
Maxwell’s proof mentioned above is as follows :—Let there
be given avy system 8 obeying the principle of energy. Let
its configuration be determined by 7 generalized coordinates
9i+++Qn; let the corresponding momenta be p,...p,- (For the
sake of clearness I will take occasionally the simplest example,
a system of material points acted on by any forces. q;... Gp will
then denote rectangular coordinates, p,...p, the products of
the component velocity into the corresponding masses.)
Let the law of the forces acting in the first system be such
that the potential energy V isa given function of the coordinates.
Then the motion of the system is completely determined when
we know the values g/;...p’, of the coordinates and momenta
at the commencement of motion and the time 7 which has
elapsed. (In the example this means that the coordinates and
component yeilocities at the commencement of motion must be
known.) It is then most natural to take the 2n+1 quantities
(+++ pny T a8 so-called independent variables. Since the law
of action of the forces is given, all other quantities relating to
the motion (¢. g. the values of the coordinates and momenta
after the lapse of the time 7, which Maxwell denotes by
of Energy in a System of Material Points. 301
g1++-p” without index) may be calculated as functions of these
2n+1 independent variables. If T be the kinetic energy at
the time T, then V+ T=E is the whole energy of the system.
These quantities may, of course, also be expressed as functions
of the 2n +1 independent variables*.
If we imagine each of the 2n+1 quantities g,...p,Hi actu-
ally expressed as a function of the 2 + 1 independent variables,
we obtain 2n+1 equations between 4n+2 variables. Hamil-
ton’s method consists in introducing in place of the indepen-
dents hitherto chosen, which we may call the “ old indepen-
dents,” other independents (the Hamiltonian independents).
We may, in fact, from the 2n +1 equations express any 2n +1
variables out of the 4n+2 variables occurring as func-
tions of the remaining 2n+1. Hamilton supposes the vari-
ables py... Pny P'1+++ Pn, T expressed as functions of g,.--Qny
q’\--+@ nH; so that the last-named variables play the part of
independents. Hach of the first-named variables is therefore
now to be regarded as a known function of these 2n +1 inde-
pendent variables. Starting from these Hamiltonian indepen-
dents, we easily find
Dg ES cla
Ce a, AEN i sit-dgie .) Ogos Oh”
where r and s are any equal or unequal numbers.
Just as the product of the differentials of three rectangular
coordinates da, dy, dz may be expressed by the product of the
differentials of polar coordinates and then becomes equal to
7 sin 0dr d0 dd, so if any m variables v,, v2...Um are func-
tions of m other w,, Ww... %m, the product of the differentials
of the first variables may be expressed by the product of the
differentials of the latter, by means of the well-known func-
tional determinant
dv dy dm | (1)
ey di, diy) datas
dv, dvz.. dm =duy dug. «+ Am 5
* EK will not contain 7, and will therefore simply be a function of
g',-+-p'n; Since it remains constant during the whole motion.
+ This follows thus:—If the magnitude A=2 is T dt be expressed as a
function of the Hamiltonian independents, then Hamilton shows (Thom-
son and Tait’s ‘Natural Philosophy,’ new ed. § 330, equation 18) that
‘ dA dA dA.
do cme dee Lane
whence it follows at once that
dp'y__ dps_—s PA
dqs dq’, dq dq's’
and so on.
302 On Boltzmann’s Theorem on the average Distribution
We have a special case if some of the v’s are identical with
some of the u’s—if, for example, we retain the z-coordinates
and transform only « and y into polar coordinates. Suppose
that v=, ¥,=U2,...Vk=U, but that vz41...Um are given
functions of w1, %2,..+%m3 then the functional determinant is
simplified to
dv, dv... dtm=aduy dug... dtm 4 dees) : at an §
Um
— Gia f
We may now apply this general formula to the former one.
Instead of u,;...um let us put the 2n+1 Hamiltonian inde-
pendents q...qn, 7)+++d/n EH; for vy... rz let us put q--- ns
but for v%%41...Um let us put p,...p,7. Then equation (2)
becomes
dq, .+»dqn dpy...dpn dt=
dp dp, dt
Dg 1g AGF. oe dy, dBy+ ae 7 idl, 7K (3)
Let us now in the generally-applicable formula.(2) intro-
duce other special values, viz. for u,...%m the Hamiltonian
independents again, but substitute q’;...9/n for v,... Uz, Whilst
for vy41+++Um We substitute the variables p’,...p/n7; which
indeed, according to Hamilton’s method, are also functions
of the independents introduced by him ; consequently equa-
tion (2) is applicable to this case just as much as to the
former. Hquation (2) becomes by this substitution,
71+ 2s) np OP aie 2-0 » OT =
dq’, ..+dq/n dyy..-dgn TH+
dp', dp'n dt
dj "dn di: «hs (4)
The reader is advised to write down the functional determi-
nants of equations (3) and (4) at length, and then for each
member of the functional determinant of equation (4) to sub-
stitute the value which it would have according to equa-
tion (1). We shall then have, except for sign and for an
exchange of horizontal and vertical lines, exactly the functional
determinant of equation(3). The two functional determinants
have therefore the same numerical value ; and since we are
here concerned simply with this, and in the equations (3) and
(4) the products of the differentials of the right sides are iden-
tical, it follows from these equations that
dq,.++dqn dpi... dpradt=dq'y...dqn dp'y.+. dp',dt.
Dividing each side by dz, we obtain
dgi +++ dn dpy+»» pad... dq'n dpy-<.dp'n, +k
of Energy in a System of Material Points. 303
which equation expresses Boltzmann’s theorem in its fullest
generality*.
In this equation the old independents 9/)...¢/n, p/1-++P'nT
appear again. Since we divided by dr, and consequently dr
appears no more in the equation, this is equivalent to saying
that the time of the whoie motion is to be regarded as a con-
stant. On the other hand, all the coordinates and momenta
holding good for the instant of commencement of motion (i. e.
all the quantities ’,...p’,) are to be increased by infinitely
small amounts. The values q,...p, of the coordinates and
momenta at the time 7 will therefore also undergo infinitely
small increase; and, according to equation (5), the product of
the first must be put equal to the product of the latter incre-
ments; consequently, if we choose the old independents, we
must have
dn pn =
SS aT ae oma se
dg, dp'n
For the sake of a clear view of the meaning of equation (5),
let us imagine, instead of one system S, an infinitely large
number of exactly similar systems 8. Let the law of action
of the forces be precisely the same for all the systems (of
course without any two systems having any action upon each
other). Let the duration of motion 7 be exactly the same for
all the systems—but the conditions of the systems at the in-
stant of commencement of motion not the same for all the
systems, but having at the instant of commencement of motion
the values of coordinates and momenta between the limits 9’;
and g'j+dq‘1...p’, and p’,+dp’» for all the systems. Then
also at the instant at which the motion ends the conditions of
all the systems will not be the same, and coordinates and mo-
menta may lie between the limits y, and q,+dq,...pp, and
* In Watson’s excellent book, ‘A Treatise on the Kinetic Theory of
Gases’ (Clarendon Press, 1876), p. 15, there is an error, or at least an
inaccuracy of expression, in the derivation of this equation. In the partial
differential quotients of the functional determinant, at the head of that
page, besides p and P, the time + of the motion is to be regarded as an
independent variable; but the equation following from this,
qr _ _ aA ale dQs
dP, dp,dP, dp,’
only holds good when E is variable independently of p and P. Conse-
quently, in forming the partial differential quotients of this equation, E is
to be regarded as constant; in forming those of the functional determi-
nant, 7 is to be regarded as constant ; and the applicability of an equation
holding good between the first partial differential quotients to the latter
requires still to be proved.
304 On Boltzmann’s Theorem on the average Distribution
Putdp, Then equation (5) holds good between the products
of differentials.
V is a function of the coordinates determined by the con-
stitution of the system; so also T isa function of the momenta —
or of the momenta and coordinates determined by the consti-
tution of the system. Therefore also H=V-+T is a function
of coordinates and momenta F(q,...p”) given by the consti-
tution of the system. If we imagine the variables replaced
by their values at the time 7, then EH appears also as a function
of these values, which we have also denoted by q...gn. HE
may therefore be introduced in the product dq,...dp, of
equation (5) in the place of one of the variables, e. g. p;; so
that we obtain
oe
dg, ++. dpy=dqy...dqy apg... dp,dE= ie
This magnitude E, the total energy of the system, is obtained —
also by substituting i in the function F for q,...p, their values
g/1++»p’, at the commencement of the time. “Then E appears
expressed as a function of g’;...’,, aud may be introduced
in the product dq’;...dp’, of equation (5) instead of p/;,
which gives us
a
Pal -(6a)
TE Gi e+ + Pn) (6)
dq’... dp'n=dq',...dq/ndp',... dp’, di
If g; be expressed as a function of the old Hee
g'1.+.Q'n7, then is the differential quotient of g, in the
usual sense, by atlein the time to increase without altering
otherwise the initial conditions CES ao: Maxwell denotes
itby g,. Itis of course also a function of Q'1--- Dat. Letts
value when t=0 be g’,; then, according to Hamilton,
dS dE (Gy. = Da) dB’, . Pn)
~ dp, dp; ; oa 7
Substituting the values (6) and (6a) in equation (5) and
dividing by di, we obtain
dq, +++ 1gn dpa +++ dpn _ dg'y +++ dq'n apes g++. Opn (7)
q1 q1 a
(dE does not occur here). The equation admits of the following
interpretation. Let there be given an infinite number of simi-
larly constituted systems 8. Let the time of the entire
motion have for all exactly the same value 7, and the total
energy exactly the same value E. Let the values of the
* Compare Thomson and Tait, new edition, § 318, equation (30).
.
of Energy in a System of Material Points. 305
variables g).-. Qn; P2++-Pn at the beginning of the times be
between the limits
gq’, and q',;+dq‘;..-g', and g,+dq'n, \ (8)
p’z and p’yt+dp's... p/n and p'n+dp'nI
for all the systems, while p, is determined by the equation of
energy. If, further, we denote the limits between which
coordinates and momenta lie at the moment at which motion
ends by
g, and gi, +dq,.+-q» and tet (9)
po and pot+dpy...Pn and pr+dpnr —
then again equation (7) must hold between the products of
differentials.
Maxwell employs now a method which he calls the statistical.
He assumes we have a large number N of systems such as §
given, having all exactly the same energy HE, but whose coor-
dinates and momenta at the commencement of motion have all
possible values. He proposes to himself the problem to inves-
tigate, not how coordinates and momenta change for each of
these systems with the time, but how many systems at a given
time ‘‘ have the phase (pq)’’—. e. for how many the coordi-
nates and momenta lie between the limits (9).
pi is always determined by the equation of energy. The
number of systems which at the time 7 “ have the phase ( pq)”
Maxwell denotes in general by
MQ A 05 5 Pat) AG, > .-AdnAps..-dpa . . (10)
The number of systems which, at time 0, have the phase (p’q’),
2. €. for which the variables at this time lie between the limits
(8), will consequently be denoted by
ON G6. On, P'o> > p'n0) dq'y...dqndp's..adp'n. + (I)
But, in accordance with the signification already given to
Qi---Pn and g’;..- p/n, exactly the same systems have the phase
(pq) at the time t which had the phase (p’q’) at the time 0.
The expressions (10) and (11) are therefore equal; whence,
referring to equation (7), we have
GF (Ga+ + + Yns Pa ++ Pat )= VF's ++ U'ny p'a + ++ Pad). » (12)
Maxwell calls the distribution of the system stationary when
the number of systems having any given phase, e. g. (p’q'),
does not change with the time—when, therefore, for any
Bee 9 iP a- > - Pn,
FQ 1-6 Om Pla + + PuT)=LD 1 F'n p'g+ + p'nO) (18)
Since in equation (12) g’,...p’ are also any initial values
Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. x
« ah
306 On Boltzmann’s Theorem on the average Distribution
of the variables whatever, equations (12) and (13) may be at
once combined with each other, and give
UAC oss Qny Po +++PunT =F (7 1-+- Yn, Po-+-f nt)
Since f no longer contains the time 7, it is better to omit 7
from under the functional sign and to write
DFG ++ Gry Pa ++ Pr) =D SPs ++ Pn; p'2+++P'n)» « (1A)
Here g/;..-Qnjp’o...p' are any initial values whatever ;
Qi +++Qn; P2-++pn are the values of coordinates and momenta
which a system starting from these initial values attains after
a time 7, in other respects unfixed.
Let us therefore imagine a system starting from any initial
values of coordinates and momenta; then in course of the
motion it will assume continually new and new values of co-
ordinates and momenta. The coordinates and momenta are
therefore functions of the initial values and of the time. But
there will be in general certain functions of coordinates and
momenta which have constant values during the whole motion,
as in a free system the component velocities of the centre of gra-
vity, or the sums of angular momenta, are invariable. Let us
therefore imagine in the expression g; f (41 .-+ ny Po+++Pn) first
of all those optional initial values from which each system
started, then continuously the values in order which coordi-
nates and momenta assume for that system as the time
increases; then for the existence of stationary distribution it
is necessary and sufficient that the value g,f shall remain
unaltered, or, in other words, ¢,;/ must contain only such
functions of 7,...p, as remain constant during the whole
motion of a system from any initial values whatever, and con-
sequently are dependent on the initial values, but not on the
time which has elapsed. Ifthe system is so constituted that its
coordinates and momenta, starting from given initial values,
assume in the course of a sufficiently long time all possible
values consistent with the equation of energy, then g,/ must
in general have the same value for all coordinates and momenta
consistent with the equation of energy—must therefore be a
constant.
I will now mention some other terms employed by Max-
well. If one of the systems 8 starting from a given initial
condition moyes, all the conditions through which it passes in
consequence of its motion as time increases, constitute the
* This or the identical equation (14) is necessary that the distribution
may be stationary. It is also sufficient; for from it and equation (12)
equation (15) follows at once for any g',...p'n whatever, which is exactly
the mathematical expression for a stationary distribution.
of Energy in a System of Material Points. 507
path of the system, each separate condition of motion a phase
of this path. All the functions of coordinates and momenta
which remain constant during the whole path he calls the
parameter characteristic of the nature of the path, whilst all
other functions of coordinates and momenta depend also on
the phase. In order that the distribution of the systems shall
be a stationary one, it is necessary and sufficient that / shall
be equal to z , multiplied by an arbitrary function of the para-
meters characteristic of the nature of the paths.
Maxwell considers the simplest case when this function isa
constant, and therefore /= 7 then
if
NCdq, ...ddn Ups « x3 dpn (15)
a em nat ates
is always the number of systems for which coordinates and
momenta lie between the limits (9), whilst p,; is determined
by the equation of energy.
This is, then, the simplest possible stationary distribution.
If the g’s denote the rectangular coordinates of material
points, then the products of the component velocities into the
corresponding masses my, 1v,... are the corresponding
momenta; then the kinetic energy
2 2
Dy p2
T= bm t...)= ei + eee...
tai ) 2m, 2m, ;
2
: myth « ae J
where evidently —-— is the kinetic energy resulting from the
motion of the first atom in the direction of the axis of x, and
soon. In like manner, generalized coordinates can always
be so transformed that
2 2
Ts +...
where the ys contain simply the coordinates. Maxwell calls
2
ue the “ kinetic energy resulting from the 7th momentum,”
or simply the “kinetic energy of the rth momentum” The
mean kinetic energy of any one of the momenta, say of the 7th
momentum, is therefore expressed by
il Yr Dr AQr +» -dpn . \J- : a a Dn
21 71
x 2
308 On Boltzmann’s Theorem on the average Distribution
Here the integration is effected with reference to all the other
p's before that with reference to p,.
I will here show only how the integration with reference to
pn is to be effected when 7 is not equal ton. For gq, is to be
substituted its value
. 2 2
o =nn=ViA/ B-V— Pa (16)
dp, 2 2
If we consider that, in the integration with reference to p,,
the quantities g,...Qn;2-+-Pn—1, and therefore also y--- Yn;
V, and p, are to be considered as constant, we may put
2
InP
2
E-V— vate a ae =a, and
then, in integrating with reference to pp, all up to g comes
before the sign of the integral, and ae reduces to
1
1 +a dx *
Jato: Baten
which, as is well known, can be easily calculated. The inte-
gration can be equally easily performed with reference to the
remaining p’s, and lastly to p,. Since V is a given function of
the coordinates, the mean kinetic energy may be found simply
by repeated integration.
The symmetry of the formula (16) shows at once that it has
the same value for all momenta, consequently also for all
atoms in the case of material points. The number Z, of the
systems for which the values of coordinates lie between q, and
Atdq...d, and gn+dqn, and the kinetic energy of the mo-
mentum p,between £ and k+dk, whilst all the other momenta
have all possible values, is found by integrating the expression
(15) with reference to those other momenta, but putting / 2k
dh 7
WV Qhey
which, whilst keeping the conditions for the coordinates, the
last momentum may be any we like, by integrating also with
reference to p, or k over all possible values.
The integration, after using the substitution (16), offers no
difficulty, and gives
and
for p, and dp,; the number Z, of the systems for
of Energy in a System of Material Points. 309
n—2
Zp= NC [TGV 1192 «+ Yn(QH—2V) ? dq... ddn «
nv 4
rG
yz, (-V-HFar(;
2
(@e-v)? ver@r(s)
This number, and consequently the law of distribution of kinetic
energy, has the same value for all momenta. For large values
of n, :
Z, __e@ dk
Le e kW/ 9
is the mean value of the kinetic energy of a
nearly,
where K=
momentum corresponding to these values of coordinates, and
the same for all momenta.
In order to apply these equations to the theory of Heat,
Maxwell imagines amongst the systems § precisely similarly
constituted warm bodies enclosed in absolutely rigid envelopes
impermeable to heat, which are completely mdependent of
each other, and all possess the same energy H. The systems
S therefore now represent to us very many similarly consti-
tuted real bodies of equal temperature and under equal external
conditions. The condition of motion of each of these bodies
is to be determined by the coordinates and momenta q,.../n
formerly employed. ‘The different bodies are to have started
from very different initial conditions; and the number of
systems for which, at the commencement of the time, coordi-
nates and momenta lay between the limits (9), is to be given
by the formula (15). We know that then the distribution is
a stationary one. The systems which had the phase (pq) at
the commencement of the time, it is true, soon pass out of this
phase; but exactly as many systems enter on this phase to
replace them, and thus it continues for all times. The equa- -
tions obtained above hold, therefore, for all bodies. The mean
kinetic energy must have the same value for each of the
momenta, viz. the value calculated above. The case might, of
course, occur that the equations should not hold good for each
n—2
* When V is small with reference to E, and n is large, (H—Y) 2
u—2
approaches to the limit E 2 e 2) andthe hydrostatic differential equa-
tion for polyatomic gases follows from the equation in the text.
310 On Boltzmann’s Theorem on the average Distribution
single body—that, for example, the mean kinetic energy of a
momentum should be greater in one body than that calculated
above, in which case it must of course be smaller again in other
bodies, so that we may have the true mean value for all bodies.
But it is to be remembered that all our bodies are found
similarly constituted, of equal temperature, and under similar
external conditions. In the case just spoken of, therefore, the
behaviour of bodies of that kind would be different according
to the initial condition from which they started. But this is
not confirmed by experience. As often as one and the same
body is left to itself with the same energy of motion and under
the same external conditions, it assumes with time the same
thermal condition, the stationary condition corresponding to
that temperature and those external conditions. We are
therefore justified in maintaining that our equations hold not
simply for the above-defined conceptions of bodies, but also
for the stationary final condition of each single warm body.
That the condition of equality of temperature between warm
bodies has a very simple mechanical meaning independent
of their initial conditions, follows also from the fact that
it is not influenced by the compression, turning, or displace-
ment of particular parts.
If we substitute for the system § two different gases sepa-
rated by a solid division-wall permeable to heat, then there
follows the equality of the mean kinetic energy of progressive
motion of the molecules of both gases, or Avogadro’s law ;
the proof of which, hitherto resting on the equality of this
mean kinetic energy in mixtures of gases, is unreliable, since
we are not able to show that the mean kinetic energy of pro-
gressive motion is the same in mixtures as in separate gases
at the same temperature.
The second case discussed by Maxwell is very interesting,
but cannot be here reproduced in full. In this g,...qn are
the rectangular coordinates 2,...2,, therefore p,...p, the
velocity-components multiplied by the masses my ...77n Wn of
a free system of atoms 8’ with any internal forces but without
external forces. Maxwell introduces into equation (5), instead of
duty dvy dw, duz dvzdw dug, the product dU dV dW dF d6dH dB;
where U, V, and W are the velocity-components of the centre
of gravity, F', G, and H the constant sums of angular momenta
of the elements of motion of the system S’. Equation (5),
dU dV dW dF dG dH dE
therefore, after dividing by ) assumes
33
ee eed m3 m3 m,
da’, ... den dv'3...dw'n _ day... din Avg... dwn
LT Gal
a 7! 4 arr &
of Energy in a System of Material Points. all
; é SEH a hee
where 7 is the distance of the atoms m, and m., r= gs #18
ad
the double of the projection of the triangle m,m,m 3 on the
yz-plane. If we have again an infinitely great number of
similarly constituted systems 8’ given for which the magni-
iudes E, U, V, W, F, G, H have equal values throughout, we
find, exactly as before, that the distribution of these systems is
stationary when the number of those for which a, ... zn, v3.-- Wn
lie between the limits x, and #,+dx,...w, and watdwn, is
Cdx,...dw”
arr
former case, the number of systems for which, with any velo-
cities, the coordinates of the atoms lie between infinitely close
limits, and, further, the number of those for which the
velocity-components of an atom also lie between infinitely
close limits, the mean kinetic energy of an atom, &e. I quote
two only of the results.
1. If &,, € be the velocity-components of an atom of mass m
referred to new axes of coordinates, of which, at the instant in
question, the z-axis passes through the atom, but the two
others are axes of the section of the momental ellipsoid by their
plane, whose origin at each instant is the centre of gravity of
the system, and which revolve with the angular velocities
which the system acquired in suddenly becoming solid through
the operation of internal forces, then the mean values of the
2, 2
m m
g 5) a , are the same for all atoms.
—aye” 1—byz"
In particular, the law according to which these magnitudes are
distributed amongst the atoms is the same as that accordin
pees ares ote 8
to which mz”, mv’, mw? were distributed in the former case.
equal to Maxwell calculates, exactly as in the
magnitudes m6”, i
/
/
a if M is the total mass of the
system, < is the distance of the centre of gravity of the system
from a straight line passing through the atoms whose direc-
tion-cosine, with reference to the new axes of coordinates, are
BC-—L? , AC—M’
1 ae ies ne 2.
if A, B, C are the moments of inertia of the system with refer-
ence to the new axes of coordinates, L, M, N the sums 2myz,
=mez, Sme«y with reference to the system of coordinates, and
At the same time y=
proportional to &,7,andé. Lastly, a=
ee ow
Deseo N ted
SA Bela a 8
If the number of atoms is very large, then still le Rane),
312 Mr. W. Le Conte Stevens’s Wotes
consequently the mean kinetic energy of internal motion (7. e.
of that relative to the new axes of coordinates), is the same
for the atoms.
2. A gaseous mixture distributes itself in a horizontal tube
rotating about a vertical axis, exactly as if each of its consti-
tuents were present alone in equilibrium under the action of
gravity and of centrifugal force. A tube 1 metre (/) long,
with one end in the axis of rotation, must make about ten (7)
revolutions per second in order that a mixture of hydrogen
and carbon dioxide shall contain at one end 1 per cent. ( p)
carbon dioxide more than at the other. The rotation must
last about two hours in order that the previous deviations from
a stationary distribution shall become about one hundred
times smaller ; p is proportional to the square of the velocity
of the moving end of the tube, and therefore to Pn’.
XXXV. Notes on Physiological Optics.
By W. Le Conte StEvEns*.
N the ‘ Philosophical Magazine’ for May 1882 the present
writer discussed certain phenomena of vision under yari-
able physiological conditions. Among these was stereoscopy,
attained from a pair of perfectly similar diagrams, with paral-
lelism or slight divergence of visual lines, the binocular re-
sultant image being caused to appear concave, convex, or plane
at will, by properly adjusting the cards in position so that the
two retinal images from them could be made either slightly
dissimilar or alike. A geometric discussion of this was given
in connexion with the record of other experiments that illus-
trated the important effect of muscular action in modifying
our unconscious interpretation of retinal sensations. This
discussion was preceded by a consideration of the current
theory of corresponding retinal points, which was accepted
only in a modified sense, and not mathematically. It was
assumed that, in examining the binocular resultant, freedom of
motion is allowed the eyes—a condition that has usually been
found necessary when stereoscopy by this method is performed
for the first time by any one who is not skilled in binocular
experiments. Hven at that date the writer was convinced that
play of the eyes was not indispensable, however effective it
might be in confirming the visual judgment. The geometric
discussion, though correct so far as it extends, was not deemed
capable of covering all the facts; but to test the extent to
* An Abstract from two Papers read before the American Association
for the Advancement of Science at the Montreal meeting in August 1882,
Communicated by the Author,
on Physiological Opties. 313
which it was possible to attain such results without motion of
the eyes, it was important to employ the electric spark as a
means of illumination. The opportunity of doing so was then
wanting, but has since been secured.
Vision by the Light of the Electric Spark.
The apparatus employed for the production of momentary
illumination was a large induction-coil belonging to the Phy-
sical Laboratory of Columbia College (New York), and loaned
for the purpose by Professor O. N. Rood. The stereoscope
used was the reflecting instrument described in a former
paper *, which had been so constructed as to give for registra-
tion the angle, positive or negative, between the observer’s
visual lines, the distance of each card from the eye that receives
its image, and the angle which the plane of this card makes
with the visual line, assuming the latter to be horizontal and
the axis of rotation of the card to be vertical. The writer was
fortunate in securing the cooperation of Mr. W. W. Share,
Assistant in Physics in Columbia College, who soon acquired
more than usual skill in the control of his eyes for binocular
experiments.
In the dark room the stereoscope was first so arranged that
parallelism between the two visual lines was necessitated, in
obtaining binocular vision of the pair of pictures at the moment
these were equally illuminated by the passing of a spark The
plane of each card being perpendicularly across the support-
ing arm of the reflector, the binocular resultant presented the
appearance of a series of concentric circles on a flat surface.
By rotating each card through a known angle on its vertical
axis, the binocular resultant couid be made to assume at will
the form of a convex or concave elliptic shield. The observer
was seated with closed eyes in front of the stereoscope while
the manipulator of the apparatus arranged the cards. The
observer, not knowing whether this arrangement would pro-
duce planeness, convexity, or concavity, was then invited to
open his eyes and interpret the binocular retinal sensation
attained by the illumination of the cards with a single spark.
It was found possible, nearly always, to make a correct inter-
pretation at the first trial. Mr. Share and the writer acted
each alternately as observer and manipulator; and the result
attained was confirmed by the experience of Professor Rood,
who tried the same experiments independently.
The distance and diameter of the circle on each card being
known, and also the angle of rotation on its vertical axis, it
becomes possible to calculate the maximum retinal displace-
* Philosophical Magazine, Decemher 1881,
314 Mr. W. Le Conte Stevens’s Votes
ment of images which would have corresponded retinally if
the angle of rotation, ¢, were zero. The attention being spe-
cially given to the centre of the binocular concave or convex
resultant, the illusion of binocular unity and depth in the pic-
ture remained possible when the retinal displacement cor-
responding to marginal portions of the combined image was
as great as ‘39 millim., or more than 80 times the diameter
corresponding to what has been estimated to be the minimum
visibile. By giving attention, through indirect vision, to the
marginal portions, the illusion of binocular unity was easily
destroyed, and double images at once became detectable. The
result was confusion and loss of the third dimension in space
at these marginal portions, while the perception remained clear
for central portions where no duplication could be perceived.
These effects were noticed by both Mr. Share and the writer.
The pictures found best in these experiments were concen-
tric circles consisting of broad black bands on a white ground,
or of white bands on a black ground. Various other stereo-
graphs were employed, many of them constructed for the pro-
duction of stereoscopic relief, which could be reversed or
totally suppressed by appropriate arrangement of the cards on
the arms of the stereoscope. The peculiar nature of the relief,
whether direct or reversed, was what the observer was re-
quested to ascertain, and with satisfactory results, usually
without delay. The most difficult case was that in which one
picture consisted of a red diagram ona green ground, the
other a green diagram of the same size on a red ground.
A series of experiments, continued through many days, was
tried under illumination with the electric spark, by Mr. Share
and the writer jointly, to test still further the effect of mus-
cular strain in modifying the unconscious interpretation of the
binocular retinal image as discussed ina former papert. The
optic angle was varied from 3° of divergence to 50° of con-
vergence of visual lines, while the stereograph of the moon
was again employed, being kept ata fixed distance on the
arms of the stereoscope while the observer, under the abnor-
mal conditions imposed, was requested to form an estimate of
apparent distance and diameter. Hach acted as manipulator
and recorder for the other, the observer being kept ignorant
of his own record until the whole series of experiments was
completed. The result was in each case quite similar to that
formerly obtained with vision by continuous light; but the
limit of error was much wider, showing that under such un-
usual conditions no single visual judgment is worthy of any
confidence. The general effect on each, however, was that
* Philosophical Magazine, December 1881,
on Physiological Optics. 315
strain of the internal rectus and ciliary muscles produces the
illusion that the object perceived is smaller and nearer.
The above is a mere statement of facts. Any discussion
they may suggest is reserved for a future paragraph.
The Binocular Union of Spectral Images.
If a sharply defined object be momentarily illuminated by
the intense light of the electric spark, a positive after-image -
is perceived and quickly followed by a negative image of short
duration. If the gaze be very steadily fixed upon one point
of an object that is strongly illuminated by the direct rays of
the sun, the eyes being at the same time protected from the
glare proceeding from surrounding objects, a negative after-
image is obtained that lasts several minutes. Since its exist-
ence is due to fatigue of the retina in certain parts while others
remain unfatigued, such an image appears always in the direc-
tion of the visual line, changing in apparent position with
every motion of the eye.
The late Professor W. B. Rogers, of Boston, published in
1860* some experiments on the binocular union of after-
images from illuminated lines so arranged as to produce the
appearance of relief. Perspective after-images were likewise
obtained by Wheatstone and by Wundt ; but an objection to
conclusions drawn from such perceptions as these consists in
the fact that the observer knows what effects would result in
direct vision under the conditions imposed; indeed he simply
retains a subjective perception of what he has just seen binocu-
larly. It is difficult to determine how far the perception may
be due to imagination rather than to immediate retinal sensa-
tion. Professor Rogers succeeded in attaining perspective
after-images even when the luminous lines were regarded suc-
cessively instead of together; but thus far no one else seems to
have confirmed this result; and the experiment is still liable
to the objection that the visual judgment is warped by antici-
pation and association. Hxperiments therefore have lately
been made with a view to testing these results, and at the
same time to ascertain whether any modification would be im-
posed by varying the muscular conditions under which the
spectral images are seen.
1. Across the median plane of vision was held a card with
the upper edge more remote than the centre, so that a white
band from top to bottom on a dark background was inclined
about 40°. This was fixedly regarded with each eye sepa-
* Proceedings of the American Association for the Advancement of
Science, 1860, p. 187 et seg.
316 Mr. W. Le Conte Stevens’s Votes
rately in succession, while held in direct sunlight, until both
retinas were fatigued. On going then into aslightly darkened
room, the inclined spectral image was easily perceived, appa-
rently in mid-air, On making the visual lines parallel, it
became projected on the wall, but without losing its obliquity.
On strongly contracting the internal rectus muscles, it ap-
peared still directly in front, but much smaller and nearer.
The experiment was repeated many times, and varied, but with
uniform results.
2. On separate cards a pair of diagrams were constructed
in such a manner as to produce an image in relief when bin-
ocularly viewed, in the stereoscope or otherwise. These were
separately and successively regarded in sunlight, each with
the appropriate eye. In the dark room the resultant after-
image appeared in mid-air in clear relief. On shutting one
eye, the component image that remained visible to the other
was at once projected upon the wall as a flat picture. Strongly
contracting the ciliary muscle of the eye remaining open, with-
out sensibly contracting the rectus muscles, the picture was
made to approach and grow apparently smaller, in almost as
marked a degree as by the previous experiment.
3. A series of concentric black and white circular bands
was constructed on a card, which was held in a vertical plane
obliquely crossing the horizontal visual line of the left eye.
After the retina had become fatigued, the same card was held
across that of the right eye, but with opposite obliquity, so
that the distortions of the elliptic images on the two retinas
should be opposite in sense. Hach eye was closed while the
other was receiving light from the card. The resultant spec-
tral image was concave instead of plane, and presented the
same variations with change of muscular conditions as in pre-
vious experiments.
4, To ascertain whether these perspective stereoscopic effects
were due to imagination and association, or whether they were
the immediate outcome of retinal sensation, from the existence
of dissimilar images remaining through fatigue in the two
eyes, it was necessary to test some one whose eyes were normal,
but who was ignorant regarding the nature of the visual effects
to be produced, and who therefore could not be influenced by
anticipation. It was found possible to enlist the interest of a
youth of good general intelligence, who was entirely unac-
quainted with even the elementary principles of binocular
vision. He submitted to be trained until he could secure
monocular after-images successfully with either eye at will.
Without granting him the slightest clue by which results
could be anticipated, the writer employed a pair of cards on
on Physiological Optics. 317
which were diagrams so arranged that the binocular resultant
could be made either a raised cone, a flat picture, or a hollow
cone, according to the mode of combination selected. These
cards were viewed in sunlight, never binocularly, but always
separately and in succession, the relation between the pictures
being varied in successive experiments. As soon as the retinas
were fatigued, the observer was led into a perfectly dark room,
and requested to describe the resultant spectral images per-
ceived. Without allowing him ever to know whether his
visual judgments were right or wrong, these experiments were
repeated day after day, until the youth’s own conclusions
were definitely formed by repeated interpretation of his retinal
sensations. His judgments were in the majority of cases cor-
rect, during the latter part of the time invariably so; and by
spectral images alone he learned what should be the proper
arrangement of pictures to produce a binocular resultant that
was concave or convex at will. The cards with concentric
circular bands were then substituted ; and in like manner he
soon learned what kind of obliquity should be given the plane
of each card in order to produce a concave or convex spectral
binocular image immediately afterwards. His eyes were not
sufficiently trained to enable him to test the effect of varying
the tension in either ciliary or rectus muscles, nor was he able
to perceive duplication in any part of any binocular spectral
image.
5. A pair of diagrams were constructed in such manner as
to show very plainly the binocular duplication of central parts
in the background when the foreground was regarded and the
gaze was monocularly directed to the centre of each in suc-
cession, with the usual precautions. The spectral image pre-
sented the appearance of relief. By an effort of special
attention the duplication of the background became percep-
tible; but at the same moment the appearance of relief was
lost.
Results from the Haperiments just described.
These experiments, in conjunction with those made by the
light of the electric spark, show that in the new mode of ste-
reoscopy play of the eyes is by no means necessary, although
it constitutes an important aid in all cases where a clear visual
judgment is not attainable at the first glance. They show
also very conclusively that the conscious perception of double
images in the binocular field of view, on which so much stress
was laid by Sir David Brewster”, far from being conducive to
clearness of binocular perception, tends rather to interfere
* Brewster, ‘The Stereoscope,’ p. 76 et seg.
318 Notes on Physiological Optics.
with it. If it be said that we unconsciously perceive them
and intuitively distinguish between the two kinds, homony-
mous and heteronymous, this conclusion cannot be confirmed
or disproven, except so far as experiments like those just
detailed may be accepted as having some bearing upon the
subject. The writer’s disposition is to discard intuition
entirely, and, with Helmholtz*, to regard the degree of atten-
tion bestowed upon objects pictured at the same moment on
different parts of the two retinas as an element of more import-
ance than either play of the eyes or the perception of double
images. The point in the field of view to which most atten-
tion is habitually given is that pictured upon corresponding —
retinal parts; but the attention is at the same moment divided,
being given in less degree to many other parts of the field of
view as simultaneously perceived with each eye. The mental
suggestion due to the impression of non-corresponding parts
is that of the third dimension in space. If this be called the
perception of double images, their effect seems to be dependent
upon their not emerging into consciousness. Add to this the
fact that the gradation between single and double vision is
wholly imperceptible, and hence that for infinitesimal depar-
tures from single vision there can be no demonstrable distine-
tion between the two kinds of double images. In the inter-
pretation of our sensations we are certain that experience is
our habitual guide, though by no means always a reliable one.
Whether intuition can be accepted as an additional guide at
all, it is not easy to pronounce. The debate between the
advocates of the empiristic and nativistic theories is doubtless
like the well-known quarrel about a certain shield, and may be
continued indefinitely. The domain of intuition is certainly
far more limited than was thought a few generations ago ;
whether it can be reduced to zero may perhaps be decided a
few generations hence. In all ordinary cases of binocular
vision the effect is cumulative. The judgment quickly reached
is a product not only of difference in the degree of attention
given at the same moment to objects seen by direct and by
indirect vision respectively, but also of variation in attention
to different points directly viewed in succession, of the mus-
cular sense while free play is given to the eyes, and of all the
elements available in monocular vision, which have been
grouped together under the name of physical in contrast with
physiological perspective.
* Helmholtz, Optique Physiologique, p. 1009.
weer chag
XXXVI. Notices respecting New Books.
A Treatise on the Transit Instrument as applied to the Determination
of Time. For the use of Country Gentlemen. By Latimer CLARK,
M.TI.C.E. §¢. (Published by the author, 6 Westminster Chambers,
London.) 72 pages text, with 29 pages Transit Tables.
= object of this little work is to popularize the use of the
portable Transit for finding correct time among amateurs of
small means. About half the work, describing the instrument and
its use, is written in a thoroughly popular style, as free as is possible
from technical terms. Simple modes of adjusting in position are
given; and the instrument is supposed to be used only in correct
position, so that no “corrections” have to be computed. This is
an admirable mode of use for a beginner: some preliminary personal
instruction would, however, be required; the detail given is not
enough for a person quite unused to instruments. The second part
is intended for more advanced amateurs. In this some astrono-
mical terms and usages are explained, and the mode of computing
the “corrections” to transits observed with an instrument not in
perfect adjustment are fully entered into.
The Tables (72 pages) contain the data for transits of the sun
and certain stars for six months in a simple form very suitable for
beginners ; they form an appendix to the text, and are to be pub-
lished anew yearly, thus saving the need of mastering the Nautical
Almanac (itself rather a formidable work).
There is a misprint of 8° 46’ 28” for 88 46™ 28° on p. 42, which
may confuse a beginner. The accounts of the Polestar on p. 26
and p. 48 do not agree: on p. 26 it is said that it “is very close to
the North Pole, and revolves round it daily at a distance of about
13 degree ;” whilst on p. 48 it is said, ‘let us imagine ourselves at
the North Pole. We should see the Polestar directly overhead
remaining motionless.” On the whole, however, the work may be
said to fulfil well the purpose for which it was written, and will
help to supply an amateur’s wants. To meet the case of amateurs
of small means, it is stated (in an advertisement) that an excellent
portable transit with 14” telescope and 13” aperture can now be had
for £8. ALLAN CunnineHamM, Major RE.
Geology of Wisconsin. Survey of 1873-79. Vol. III. Large 8vo,
763 pages. With numerous Plates and other Illustrations, and
an Atlas of Maps. Published under the Direction of the Chief
Geologist [T. C. Chamberlin] by the Commissioners of Public
Printing, in accordance with Legislative Enactment. { Madison. ]
1880.
Votume II. of this excellent Survey, published in 1877, and
noticed in this Journal for April 1880, p. 302, treated of the geo-
logy of the eastern, central, and south-western portions of the
State of Wisconsin. In the volume before us the extreme north-
western and north-eastern portions of the State are described. The
520 Notices respecting New Books.
former area is bordered by Lake Superior, between Minnesota and
Michigan ; the latter, with a part of the iron district of Michigan
annexed, is traversed by the Menoninee River and some of its
affluents.
Part I. of this volume consists of valuable observations by Pro-
fessor Roland D. Irving on the “General Geology of the Lake-
Superior Region,” which is estimated at 70,000 square miles in area,
with strata, probably more than 100,000 feet in thickness, including
four great unconformable systems; and the whole is coated with
enormous deposits of glacial drift, besides lake-alluviums. I. The
Laurentian. gneiss forms the crystalline nucleus of the region,
and is continuous with that of Canada. With some associated
and often gneissoid granite, these altered strata are greatly folded,
and have a general southerly dip, with an EW. strike, and an
enormous thickness. II. The Huronian rocks are 12,800 feet
thick, and consist of (from below upwards) :—1. crystalline tremo-
litic limestone and a partial quartzite, 130 feet; 2. quartz-schist,
mica-schist, and some noyaculite, 410 feet; 3. tremolitic magnetite-
schists and irony quartzites (Penokee fron Range), 780 feet; 4. black
mica-slates, with diorite and schistose quartzites, &c., 3495 feet ;
5. dark-grey mica-schists, with intrusive granite, 7985 feet. The dip
is northward, and the strike is oblique to that of underlying Lau-
rentians. III. The Keweenawan or Copper-bearing series succeeds,
seven miles in thickness, and consists of distinctly stratified igneous
rocks like great flows and ash-beds. The lower rocks, from 10,000
to 30,000 feet, are almost wholly augite-plagioclase—namely, dia~
base, melaphyr, and gabbro (Rosenbusch). Shales, sandstones, and
conglomerates then come in, and, becoming more and more frequent,
nearly exclude the igneous rocks for the uppermost 15,000 feet of
the series. IV. Lying on the eroded surface of the Keweenawan
strata is a great horizontal set of sandstones, defined as the “ Lake-
Superior Sandstone,” and regarded as equivalent to the Potsdam
Sandstone of the Mississippi valley.
In Part I. Professor Raphael Pumpelly gives the “ Lithology
of the Keweenawan System,” specimens of which were sent to him,
and represented Diabase, Melaphyr, Gabbro, Uralitie Gabbro,
Uralitic Diabase, Augite-diorite, and Felsitic Porphyries.
Part IIL., by Prof. R. D. Irving, describes the ‘‘ Geology of the
Eastern Lake-Superior District” of Wisconsin, premising its Topo-
graphy, with Altitudes, Drainage-system, Vegetation, and Soils.
The lithology, stratification, and economics of each of the great
systems are given in detail according to locality; also an account —
of the Glacial Drift and Lacustrine Clays (Champlain Series).
Part IV., by Mr. C. E. Wright, treats of the “ Huronian Series
West of Penokee Gap.” The Penokee Iron Range is here espe-
cially described, with the details of method of examination. The
magnetic bands being covered by Drift, their breadth and extent
were defined by the use of the solar dial-compass and the dipping
needle, both of which are succinctly described. The iron-ores are,
it seems, nearly all poor or “lean,” the good ore being probably
high up in the series.
Notices respecting New Books. 321
Part V., by Mr. E. T. Sweet, gives the topography, natural-
history, geology, lithology, and economics of the ‘“‘ Western Lake-
Superior District” of the State. Among the Quaternary deposits
occur the Moraines and Pot-holes of the Kettle Range, similar to
that of Eastern Wisconsin, described in the previous volume. In
the Glacial Drift occur not unfrequently nuggets and boulders of
native copper. Some of the granitic and gneissic boulders must
haye crossed Lake Superior and travelled at least 200 miles.
Part VI. consists of an account of the ‘Geology of the Upper
Saint-Croix District,” based on the Notes of the late Mr. Moses
Strong, edited by Mr. C. T. Chamberlin. It treats of the Surface-
features, the Quaternary formations, and the Older formations, both
generally and in detail. This area is inland and south of the
“Western Lake-Superior District.”
The Menominee Region, including parts of both Wisconsin and
Michigan, is described geologically and lithologically in Parts VII.
and VIII. by Major Thomas Benton Brooks and Mr. E. T. Street.
This being an important iron-district, overrunning the boundary
of the two contiguous States, and Wisconsin not supplying any
money for the Survey beyond its own border, Major Brooks com-
pleted the work at his own expense, and suffered serious illness also
from his labours. Besides the Superficial Deposits of Drift &c., the
country has:—1. The Caiciferous sand-rock and limestone and
the Saint-Mary’s (Potsdam) sandstone, of the Lower Silurian;
2. None of the Copper-series; 3. The Upper-Huronian granite,
gneiss, schists (hornblende, actinolite, mica, chlorite, and quartz),
iron-ores, clay-slate, carbonaceous slate or graphitic shale, quartzite,
and conglomerate. 4. Middle-Huronian clay-slate and quartzite.
5. Lower-Huronian dolomite, iron-ore, and quartzite. 6. Lauren-
tian granite, gneiss, and crystalline schists. Three elaborate Tables
of the rocks and their component minerals in the Menominee
and Marquette Regions present a summary of the lithological
characters of the several systems and series of rocks and of their
relative abundance and stratigraphical order. The descriptive
lithology of the Menominee rocks and of the Huronian rocks
south of Lake Superior form two interesting chapters (Chapters 3
and 4) of Part VII.; and are followed by Dr. Arthur Wichmann’s
microscopical investigations in the Huronian rocks, prefaced with
a technical account of the minerals composing the said rocks.
Besides this eminent lithologist of Leipsic, others have aided in
the microscopical lithology of Wisconsin as treated in this volume,
namely HE. Tornebohm, F. Zirkel, Herr Wapler, 8. Allport, Frank
Rutley, G. J. Brush, J. D. Dana, G. W. Hawes, A. A. Julien,
T. Sterry Hunt, Prof. R. Pumpelly, T. B. Brooks, and C. E. Wright.
Nine coloured plates of microscopic sections of rocks occur in the
volume, and enhance the value of the lithological descriptions. The
lithographic and chromolithographic views, maps, and sections,
illustrating the topography, geology, and mining, are numerous (44);
there are also 23 woodcuts, chiefly sections of strata. Above all,
the magnficent Atlas of Plates XVII. to XXX. inclusive, giving
Phil. Mag. 8. 5. Vol. 14. No. 88. Oct. 1882. Vi
322 Intelligence and Miscellaneous Articles.
many sections besides the coloured geological maps, is to be noticed
as a most useful adjunct to this liberally published Report on the
geological structure and capabilities of important parts of the great
State of Wisconsin.
The Life of Immanuel Kant. By J. H. W. Sruckenpere, D.D.,
late Professor in Wittenberg College, Ohio. London: Macmillan
and Co. 1882.
Tue work before us does not answer completely to its title. Our
notion of a Life involves in its essence the being written chrono-
logically. To put every thing in its proper place with respect to
time may be difficult in the case of a philosopher who flourished
one hundred years ago and whose life was remarkably uniform ; but
the task so accomplished would be more interesting to the general
reader and more valuable toa philosopher. For example, at the end
of Chap. XI. we are landed in the “return” to Kant’s philosophy,
while in Chap. XIII. we are led back to consider the old age and death
of the philosopher himself. Our author is in consequence apt to
fall into redundancy, a danger of which he is himself conscious ;
for he says at the beginning of Chap. XII., devoted to Correspond-
ence and Correspondents, “ Kant’s letters have already been so
extensively used in this biography, that little more need be said of
them.” In all other respects the workmanship of the volume
seems to us most praiseworthy.
Our author in his Preface says, “If Kant’s works throw light
on his life, it will also be found that his life aids materially in
understanding his works.” In the thirteen following chapters he
aims at giving all the data which can by any possibility throw light
on the views of the philosopher—scientific, moral, and religious.
There are data given, however, which one would think cannot
throw much light; for example, an account given of his method of
retiring (p. 435), the nature of which may be inferred from the
following specimen : :—‘‘ In summer one, in winter two nightcaps
were worn.’
With this book before him, the sciéntific man will be able to
appreciate the qualifications, natural and acquired, which Kant
brought to the task undertaken in the ‘ Critique of Pure Reason.’
XXXVII. Lntelligence and Miscellaneous Articles.
CONSERVATION OF SOLAR ENERGY.
BY PLINY EARLE CHASE, LL.D.*
LL forms of solar energy are due to solar radiation. The main-~—
tenance of the energy depends on the maintenance of the
radiations. In investigating the relations of centripetal and centri-
fugal action and reaction, it seems desirable to consider the following —
hypotheses and conclusions :—
* Abstract of a Paper read before the Americau Association at —_ '
treal, August 25, 1882, Communicated by the Author.
Intelligence and Miscellaneous Articles. 523
1. Laplace’s estimate that the velocity of transmission, in gravi-
tating acceleration, if finite, must be at least 100,000,¢ 100 times as
creat as the velocity of light.
2. Le Sage’s hypothesis that gravitation and luminous radiation
represent equal actions and reactions.
3. Faraday’s search for a gravitating constant.
4, Herschel’s comparison of the mean vis viva of light with that
of sound.
5. Weber’s identification of the velocity of light (v,) with the
“ electromagnetic ratio” (v,).
6. Berthelot’s “explosive waves,” and their action upon sound-
waves.
7. The inquiries of Siemens into the combined influence of rota-
tion, centrifugal action, gravitating fall, and chemical affinity.
a these considerations the following may be added :—
. Lf there is a natural unit of force, we may look for a natural
his of velocity.
9. Oscillations may be orbital, pendulous, or wave.
10. Different transformations of similar oscillations are harmonic.
11. Rotation may be regarded as a pendulous motion, due to
retarded and modified revolution.
12. The resemblance of Le Sage’s theory to the kinetic theory
of gases points to a probability that the natural unit of velocity is
oscillatory. This probability is strengthened if we assume the ex-
istence ot molecular and intermolecular elasticity.
13. In looking to the activities of the principal mass in our
system for indications of a natural unit of velocity, we find that
erayitating velocities may be represented by gt.
14. In order that gi may be constant, ¢ must vary inversely as g,
and therefore directly as r*. This variation is found in the rotation
of a nebulous sphere, where it holds good for all stages of expansion
or contraction which are not affected by external influence.
15. Gravitating acceleration should do its whole work in stellar
rotation as well as in planetary revolution.
16. Particles exposed to solar superficial gravitating acceleration,
during a single oscillation of half-rotation, would acquire a velocity
which is equivalent to the velocity of light. If we designate this
acquired velocity by v,, we have v,=gt=v, as a gravitating con-
stant, which gives the following extension to Weber’s analogy:
V,=vU.=vy. In other words, the unit of velocity which is indicated
by solar gravitation is the same as is indicated by light and by
electricity.
17. The velocity of light, like the velocity of sound, thus repre-
sents an elastic atmosphere whose height, if homogeneous, would
be twice the virtual fall which would give the velocity in question,
and whose elasticity is in harmonic accordance with solar rotation
and planetary revolution.
18. Subsidence, from Laplace’s limit of synchronous rotation and
revolution to the poles, gives a mechanical equivalent of 76,000,000 J
for each pound of subsiding matter. The spiral character of the
524 Intelligence and Miscellaneous Articles.
subsidence produces solenoidal currents, which may help to explain
the equality of v,, v., and v,.
ON THE APPEARANCES OF THE ELECTRIC ARC IN THE VAPOUR OF
BISULPHIDE OF CARBON. BY M. JAMIN, WITH THE ASSISTANCE
OF M, G. MANEUVRIER. ;
At the meeting of the 19th June I made known to the Academy
the modifications undergone by the electrie are in the vacuum of
an air-pump when the arc is produced by a Gramme machine with
alternating currents of high tension. I soon perceived that the
appearances are modified if gases or vapours are introduced into
the glass vessel in which the experiment is made. In the vapour
of bisulphide of carbon they are very remarkable.
The burner is formed by two parallel vertical carbons fixed at
their bases; the upper extremities, which face each other, can by a
simple mechanisin be joined or separated. The apparatus is placed
under a large receiver of an air-pump, in which a vacuum as com-
plete as possible is produced. It is known that then the arc is not —
formed ; it is replaced by the gleams of a Geissler tube; but when
a few drops of bisulphide of carbon are introduced, so as to obtain
an increase of pressure of 5 or 6 centim., the arc is seen to kindle
between the points when they touch, and to persist after they are
separated.
At that moment there is as it were an explosion of light, so vivid
as to be insupportable, incomparably superior to the usual bright-
ness of the arc. On looking at it through a dark-coloured glass,
one sees a brilliant arc 5 or 6 centim. in height, resembling a horse-
shoe or a capital omega. The two extremities are at the two
carbon points. Besides this a long flame is seen like that of a
hearth, which overhangs the arc, escapes from it, and ascends yer-
tically.
The points of the carbons appear red and very brilliant; but the
arc is pale green; and as its light dominates that of the carbons,
the whole room is illuminated with that tint, as it would be by a
Bengal light with copper. The brightness increases with the
increase of tension of the vapour, until it becomes intolerable; but
as the resistance of the medium is augmented at the same time, the
arc often goes out, and it is necessary to relight it every moment
by joining the two carbons.
Examined with the spectroscope this light presents all the lines
of carburetted gases in combustion, but more complete and sharper.
They are those described by M. Thollon at the meeting on August 1,
1881. The spectrum is very discontinuous. At its red end a
grooved region was seen—first a very bright line followed by several
others thinner and close, then a broader line a repetition of the
first and likewise followed by fine lines; these appearances were
repeated in going towards the orange, but growing weaker till they _
disappeared. After a dark interval the same appearances were
seen again in the yellow and the beginning of the green; then there
Intelligence and Miscellaneous Articles. 325
was a dark interval, then the repetition of the same effects in the
green, and finally in the violet.
In brief, the spectrum is composed of four grooved portions, in
the red, yellow, green, and violet, so identical that they might be
taken, except the colouring, for one and the same design which had
travelled from the red to the violet. It is quite probable that they
obey one and the same harmonic law, which remains to be discovered.
Of these four regions the green is the most luminous; it is that
which gives the special tint taken by the are and colouring all
objects green.
During the manifestation of these appearances a chemical action
takes place. If any air has been left in the receiver, or if the appa-
ratus is not quite closed, the bisulphide of carbon undergoes incom-
plete combustion, a mist of sulphur fills the space and is deposited
on the sides; the carbon burns alone. If the air has been well
purified, the mist does not form; a brown deposit settles on the
sides, becomes black, sticks to the glass, and tarnishes it. This
deposit is volatile; its odour reminds one of that of sulphur.
It is evidently a compound of sulphur and carbon, perhaps a
protosulphide corresponding to the oxide of carbon, perhaps an
isomeric modification of the ordinary sulphide. In fact, neither a
deposit of sulphur nor one of carbon is seen, and the carbons of the
burner have neither lost nor gained any thing. It is probable that
the bisulphide of carbon is dissociated, the sulphur volatilized, the
carbon in vapour disseminated in the arc, and that this carbon and
this sulphur recombine in the flame to reconstitute a combination
under different conditions. But this is only a conjecture, no ana-
lysis having yet been made.
To recapitulate, this experiment is remarkable for the extraordi-
nary quantity of light produced, the magnitude of the are, its
colour, the composition of its spectrum, and the chemical actions
which take place. It is not likely that it can ever be turned to
account for lighting, on account of its colour, unless perhaps for
light-houses or distant signals.—Comptes Rendus de UV Académie
des Sciences, July 3, 1882, t. xcv. pp. 6, 7.
ON THE ELECTRIC RESISTANCE OF GLASS AT LOW TEMPERATURES.
BY G. FOUSSEREAU.
The method employed consists in passing the electricity supplied
by a Volta’s pile of from 1 to 100 elements across a reaction-tube
of 1-2 centim. diameter and very regular thickness, closed at one
end. The electricity is collected in a condenser of known capacity,
the two armatures of which are connected with the two mercuries
of a Lippmann electrometer of measured capacity. The time ne-
cessary for communicating to the mercurial column of the electro-
meter a displacement corresponding to a determined difference of
potential is observed. :
The reaction-tube dips into a wider test-tube; and its two faces
326 Intelligence and Miscellaneous Articles.
are bathed, up to a known height, by two conducting masses of
concentrated sulphuric acid, into which dip some platinum wires
carefully insulated from the sides above the level of the liquid.
This apparatus is surrounded by a glass “ muff,” the air of which
is dried by sulphuric acid before commencing the experiments.
In order to obtain a uniform and slowly variable temperature,
the base of the apparatus is inserted, up to a level considerably
above that of the acid, in an oil-bath, which is itself surrounded by
a sand-bath which can be heated progressively. or the sand-bath
a refrigerating mixture can be substituted. The observations were
extended to —17° C.
If E designates the electromotive force of the pile, p, and p, the
internal and external radii of the tube, / the height of the liquid,
7 the specific resistance of glass per cubic centimetre, C the sum of
the capacities of the condenser and electrometer, and e the differ-
ence of potential communicated to the electrometer (always very
small in proportion to E), we have, expressing that the quantity of
electricity transmitted through the glass in the time @ has been
employed in charging the condenser,
jm _2chE x @.
Celogn 2
Pr
Several experiments, made with different heights of sulphuric
acid, permit the elimination of the influence of the bottom of the
tube, the thickness of which is not the same as that of the sides.
At the instant of the completion of the circuit the glass tube is
at first charged like a condenser. Its interior layers afterwards
gradually absorb a certain charge of electricity, necessary for bring-
ing them into the definitive state corresponding to the fall of poten-
tial established between the surfaces. During this variable state,
more or less prolonged according to the nature of the glass, the
effects of the charge of the glass are superposed to those of the
conductivity. The observations are commenced when the time
occupied in charging the glass has assumed a constant value.
I have also observed that rapid heating determines an apparent
increase of conductivity greater than the normal increase; in like
manner a rapid lowering of the temperature gives rise to an exag-
gerated resistance: but these phenomena quickly disappear, to give
place to the normal resistance; and they are not again produced
when the variations of temperature are slow *.
My observations have hitherto been made on three kinds of glass
—common glass (with a base of soda and lime), Bohemian glass,
and crystal.
In all three, raising the temperature produces a rapid increase of
conductivity ; the resistance can be expressed by exponential func-
* These phenomena appear to be due to variations in the dielectric
power of glass under the influence of temperature,
Intelligence and Miscellaneous Articles. 327
tions of the form
log x=a—bt+ct’.
(1) For common glass, of density 2°539, expressing the resist-
ances per cubic centim. in millions of megohms, we get the following
results :—
Temperatures. Resistances.
=EiGHEs re Die Ny os Suan Wek. £4). 0°705
shit tits Acie. AEC al ats te 91:0
1 ae PSE Pee arses ee 7970-0
In order to form an idea of the magnitude of this last resistance,
it may be remarked that it represents nearly twice the resistance of
a copper wire, of 1 square millim. section, reaching from the earth
to Sirius.
The whole of the results obtained upon common glass are ex-
pressed by the formula
log #=3'00507 — 0052664 x ¢+0:00000373 x f°...
The term of the second order being very small, the values of
logw are represented by a line which differs but little from a
straight line. The resistance varies nearly 4 of its value for each
degree of temperature.
(2) Bohemian glass of density 2°431, upon which I worked, has
from 10 to 15 times the conductivity of common glass at the same
temperatures. Its resistance is given by the formula
log e=1°78300—0°049530 x ¢4+ 0-0000711 x #.
(8) The crystal tried has for its density 2-933; and it, contrary
to Bohemian glass, has from 1000 to 1500 times the insulating-
power of ordinary glass at the same temperatures. Its conductivity
only begins to be manifest at above 40°.
At 40°-2 its resistance is equal to...... 6182
At 105° - S50 Mt ish tere oe 11°6
The results are represented by the formula
log 4 = 7-22370—0:088014 x t+ 0:00028072 x ¢*.
—Oomptes Rendus de? Académie des Scrences, July 31, 1882, t. xev.
pp. 216-818.
ON THE SURFACE-TENSION OF SOME LIQUIDS IN CONTACT WITH
CARBONIC ACID}. NOTE BY S. WROBLEWSEIf.
Tf instead of water we take a liquid which mixes in all propor-
tions with liquid carbonic acid—for instance, alcohol, essential oil
* The experiments were made in M. Jamin’s laboratory at the Sor-
bonne.
+ Abstract by the Author.
{ See the preceding Note, Phil. Mag. Sept. 1882, p. 236.
328 Intelligence and Miscellaneous Articles.
of turpentine, ether, chloroform—the phenomena assume the fol-
lowing form :— :
The surface-tension also diminishes with the increase of the
pressure under which the gas is placed; the velocity of the dimi-
nution is also much greater at a low than at a higher temperature ;
but the surface-tension, instead of stopping at a minimum which
would be something characteristic of the liquid, falls rapidly; and
at 0° C., under the pressure at which carbonic acid is liquefied, all
the liquids above mentioned, without distinction, have the aie
yne
centimetre”
But can they in this state be regarded as the same liquids? Not
atall. Let us take water as anexample. When it is saturated with
carbonic acid under the pressure of one atmosphere only, has it the
properties of pure water? It has a different density, a different
coefficient of expansion by heat; even the temperature of its
maximum density is changed. The changes which take place in
the liquids mentioned are much more considerable: we need only
observe what takes place with ether when it absorbs carbonic
acid under pressure. Its volume increases with such rapidity that,
although my method enables me to measure the surface-tension of
a liquid in a much shorter time than a minute, it is almost impos-
sible to take exact measurements in this case.
It follows from all these facts that the phenomena described in
these Notes have absolutely nothing to do with pressure. The
diminution of the surface-tension of the liquids depends solely on
the circumstance that the surface-tension of carbonic acid, with
which they are compressed, is parr slight. While the surface-
yne
centimetre
other liquids examined, with the exception of ether, lie between 32
~ dyne : a ee, 3 .@ dyne
and 25 ge the tension of carbonic acid is only 4-6 ae
Capillary phenomena depend only on the molecular forces acting
at the surface of the liquid. Therefore it is not surprising that the
presence of a body which possesses so feeble a tension among the
particles of the liquid of which that surface-layer is composed
exerts an influence upon the resultant of all those forces—that is to
say, upon the surface-tension.
The same mode of reasoning applies to the case of a liquid being
compressed with a much less liquefiable gas than carbonic acid—
such as oxygen, nitrogen, or hydrogen; for the more difficult it is
to liquefy those gases the less must be their surface-tension. The
effect of the compression will depend only on the value of that ten-
sion and on that of the solubility of the gas.—Comptes Rendus de
PAcadémie des Sciences, August 14, 1882, t. xcv. pp. 342, 343.
‘tension of carbonic acid—that is, a tension equal to 4-6
tension of water is equal to 80 nearly, and those of the
4
THE
LONDON, EDINBURGH, ano DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIBS.]
NOVEMBER 1882.
XXXVIII. Comparison of Methods for the Determination of
Resistances in Absolute Measure. By Lorp RAYLEIGH,
F.RS., Professor of Experimental Physics in the University
of Cambridge*.
pA. the present time, and in view of the projected confer-
ence at Paris, the subject of the present paper is enga-
ging a large share of attention; and Prof. G. Wiedemann {
has published an interesting discussion of some of the methods
that have been employed. Ihave thought it might be of ser-
vice if I also were to place upon record the views that I have
been led to entertain, and which are the result of a good deal
of experience.
Resistance being of the dimensions of velocity, its absolute
measurement involves the absolute measurement of a length
and of atime. ‘The latter is usually the time of a vibration of
a suspended magnet, and can be determined without much
difficulty. In the B.A. method it is the time of rotation of
the revolving coil, and can be obtained with all desirable accu-
racy. In this respect there is not much to choose between one
method and another; but when we come to consider the man-
ner in which the linear measurement enters, important differ-
ences reveal themselves. These will be discussed in detail
presently; but for the moment it will be sufficient to say that
* Communicated by the Author.
+ “ Ueber die bisherigen Methoden zur Feststellung des Ohm.” Se-
paratabdruck aus der Electrotechnischen Zeitschrift, July 1882. [Phil.
Mag. for October, p. 258. ]
Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. Z
330 = Lord Rayleigh’s Comparison of Methods for the
the presumption is in favour of any method which requires
only a single linear measurement. It is true that this ques-
tion cannot be decided without regard to the subject of the
measurement; but, with scarcely an exception, it is necessary
to know the mean radius of a coil of several layers of insulated
wire. This is apparently the measurement which fixes the
limit of final accuracy; and, in comparison with it, determi-
nations of the distances of mirrors and scales &e. are of
secondary difficulty.
It will be convenient now to enumerate the principal
methods which have been proposed for determining absolute
resistances. Minor details, which are not likely to influence
the final value of the results, will in general be passed over.
I. Kirchhoft’s Method, Maxwell’s Electricity and Magnetism,
§ 759.
The magnitude of a continuous battery-current in a pri-
mary coil-is compared with that of the transient current
induced in a secondary coil when the primary circuit is re-
moved. Rowland* effected an important improvement by
simply reversing the battery-current without motion of the
primary coil. The time of vibration of the ballistic galvano-
meter employed for the transient current is the principal time-
measurement. In Rowland’s investigation a second galvano-
meter was employed for the battery-current, and the ratio of
constants had to be found by auxiliary experiments. In Glaze~
brook’st recent determination by this method only one galva-
nometer was used, the battery-current being reduced in a
known manner by shunting. It is shown that the evaluation
of the resistance-ratios presents no serious difficulty.
Let / denote the ratio in which the primary current is re-
duced when it produces a deflection « upon the galvanometer,
@ the throw from rest due to the induction-current when the
battery is reversed, T the time of vibration of the needle mea-
sured from rest to rest, M the coefficient of induction; then
the resistance of the secondary circuit in absolute measure is
given by
_mtanaM _ ,
TO emee
Whenever, as in this method, the conductor whose resistance
in absolute measure is first determined is composed of copper,
frequent comparisons are necessary with standards of German
silver or platinum-silver. Otherwise a variation of tempera-
ture of about ¢ of a degree Cent., which can hardly be detected
* American Journal, xy. 1878.
+ Proc. Roy. Soc. June 1882.
Determination of Resistances in Absolute Measure. 331
with certainty by thermometers, would influence the result by
as much as one part in a thousand.
If it be granted that the comparison of currents and the
reference to the standard of resistance can be effected satis-
factorily, we have only to consider the amount of error involved
in the determination of M, the coefficient of mutual induction
between the two circuits, which is the fundamental linear
measurement. If the two coils are of very nearly the same
size, it appears from symmetry that the result is practically a
function of the mean of the mean radii only, and not of the
two mean radii separately. It is also of course a function of
the distance between the mean planes 6. Leaving out of con-
sideration the small corrections necessary for the finite size of
the sections, we consider M as equal to 474/ Aa multiplied by
the function of y, given in tables appended to the second
edition of Maxwell’s ‘ Electricity,’ where
2/ Aa
J Atar rey
or, if we identify A and a with their mean (Ag),
sin y=
tan y= ze
The error in M will depend upon the errors committed in the
estimates of A,and 0. If we write
dM dAy db
> Sh, sed
a Aaa
then, since M is linear,
A+p= +1.
Thus, if 6 were great relatively to Ag,
A=4, p=—3,
a very unfavourable arrangement, even if it did not involve a
great loss of sensitiveness. The object must be so to arrange
matters that the errors in A, and 6 do not multiply themselves
unnecessarily in M. But since pw is always negative, \ must
inevitably be greater than unity.
The other extreme case, in which 0 is very small relatively
to A,, may also be considered independently of the general
tables; for we may then take approximately (Maxwell’s ‘ Hlec-
tricity,’ § 705)
8A
M=4rA, log] ot 2 ,
whence 1
te ~ Tog (8A,/B) —2”
Z2
332 Lord Rayleigh’s Comparison of Methods for the
showing that as b diminishes ~ approaches zero, and accord=
ingly \ approaches unity, as is indeed otherwise evident. But
when 0 is small, it is the absolute error db which we must
regard as given rather than the relative error db/b; and thus
we are directed to stop at a moderate value of b, even if the in-
creased correction necessary for the size of the section were not
an argument in the same direction.
The following intermediate cases, calculated by the tables,
will give an idea of the actual conditions suitable for a deter-
mination by this method:—
y: b/2A,. A. [ M.
60 ‘577 9:61. |-t-6i 316
70 364 2-18 | —1-18 597
75 -268 1:98 | — -98 +829
80 176 1-76 | — -76 | sae
We may say that the error in the distance of mean planes will
reproduce itself something like proportionally in the final result,
and that the error of mean radius will be doubled.
Any uncertainty in the actual position of the mean planes
relatively to the rings on which the wire is wound may be
eliminated, as Glazebrook has shown, by reversing the rings
relatively to the distance-pieces.
This method is subject to whatever uncertainty attaches to
the use of a ballistic galvanometer*. In its favour it may be
said that the apparatus and adjustments are simple, and that
no measurements of distances between mirrors and scales is
necessary for the principal elements. It should be noticed
also that the error due to faulty determination of the distance
of mean planes can be eliminated in great measure by varying
this quantity, which can be done over a considerable range
without much difficulty or expense.
With reference to the capabilities of the method for giving
results of the highest accuracy when carried out in the most
ambitious manner, it is important to consider the effect of in-
creasing the size of the coils. The coils used by Glazebrook
have a mean radius of about 26 centim.; the axial and radial
breadths of the section are each about 2 centim. If we sup-
pose the mean radius and the sides of the section to be doubled,
the number of turns (about 800) remaining unaltered, the
sensitiveness would be increased both by the doubling of M
and by the diminished resistances of the coils, while at the
* See Phil. Trans. 1882, p. 669.
eae
yw? ~
=
Determination of Resistances in Absolute Measure. 333
same time the subjects of the linear measurements would be
of more favourable magnitudes. To enhance the latter advan-
tage, it would probably be an improvement to diminish the
radial breadth of the section, on which much of the uncertainty
of mean radius depends. In either case it is clear that the
limit of accuracy obtainable by this method has not yet been
reached.
Il. Weber’s Method by Transient Currents, Maxwell § 760.
“A coil of considerable size is mounted on an axle so as to
be capable of revolving about a vertical diameter. The wire
of this coil is connected with that of a tangent-galvanometer
so as to form a single circuit. Let the resistance of this
circuit be R. Let the large coil be placed with its positive
face perpendicular to the magnetic meridian, and let it be
quickly turned round half a revolution. There will be an
induced current due to the earth’s magnetic force; and the
total quantity of electricity in this current in electro-magnetic
measure will be
o= eu
where g, is the magnetic moment of the coil for unit current,
which in the case of a large coil may be determined directly
by measuring the dimensions. of the coil and calculating the
sum of the areas of its windings; His the horizontal compo-
nent of terrestrial magnetism; and R is the resistance of the
circuit formed by the coil and galvanometer together. This
current sets the magnet of the galvanometer in motion.”
“‘ If the magnet is. originally at rest, and if the motion of.
the coil occupies but a small fraction of the time of a vibra=
tion of the magnet, then, if we neglect the resistance to the,
motion of the magnet, we have, by § 748,,
soy 2 ell
Ges
where G is the constant of the galvanometer, T is the time of*
vibration of the magnet, and @ is the observed elongation.
From these equations we obtain
R
Sem IL
2 sin: 48,
=7Gq Tango
The value of H does not appear in this result, provided it is
the same at the’ position of the coil and at that of the galva-
nometer. This should not be assumed to be the case, but
should be tested by comparing the time of vibration of the
334 Lord Rayleigh’s Comparison of Methods for the
¢
same magnet, first at one of these places, and then at the
other.”
If a be the mean radius of the coil of the inductor and A
that of the galvanometer, we may write, neglecting the cor-
rections for the finite sizes of the sections,
=a" =
I= bf A s
so that
— 2 a
gG=2n"--
This is the linear quantity of the method. With respect to
the chances of error in determining it, we see that the error
of the mean radius of the inductor enters doubly, and that of
the mean radius of the galvanometer enters singly. Probably
in this respect there is not much to choose between this method
and the use in method I. of the same coils placed at a mode-
rate distance apart.
A colossal apparatus for the use of the present method has
been constructed and tested by MM. W. Weber and F. Zollner*,
the coils of which are as much as 1 metre in diameter. The
principal difficulty arises in connexion with the galyanometer-
magnet. Two magnets were used whose lengths were respec-
tively 200 millim. and 100 millim.; and the results obtained
in the two cases differed by as much as 2 per cent. The dis-
crepancy is doubtless due to the influence of the finite length
of the magnets causing the magnetic poles to be sensibly dis-
tant from the centre of the coil, for which point the effects are
calculated ; and the disturbance will be proportional to the
square of the distance between the poles, or more properly to
the “ radius of gyration” of the ideal magnetic matter about
the axis of rotation. But to assume that the disturbance from
this source was exactly four times as great in the one case as
in the other, and thence to deduce the result corresponding to
an infinitely short magnet, appears to me to be a procedure
scarcely consistent with the degree of accuracy aimed at. If
this method is to give results capable of competing with those
obtainable in other ways, it will be necessary to use a much
shorter magnet; or, if that is not practicable, to devise some
method by which the distance of the poles can be determined
and a suitable correction calculated.
In carrying out the observations in the usual manner, it is
necessary to measure the distance between a mirror and a
scale. By using a double mirror with two scales and tele-
scopes, MM. Weber and Zéllner avoid the principal cause of
* Ber. d. Kon. Sachs, Ges, zu Leipzig, 1880, ii. p. 77.
o
Determination of Resistances in Absolute Measure. 385
difficulty, 7. e. the unsteadiness of the suspended mirror, all
that is then necessary to know with accuracy being the dis-
tance between the two scales.
In using this and the three following methods great pains
must be taken with the levelling of the earth inductor, since
the deviation of the axis of rotation from the vertical (at least
in the plane of the meridian) gives rise to an error of the first
order with (in these latitudes) a high coefficient. In this
respect it would be a decided advantage to carry out the
experiments in a locality nearer to the magnetic equator (see
“Account of Experiments to determine the value of the B.A.
Unit in Absolute Measure,” Phil. Trans. for 1882, p. 684). It
is to be hoped that the measurements commenced by Weber
and Zéllner will be carried to a successful issue, as it is only
by the coincidence of results obtained by various methods that
the question can be satisfactorily settled. At present no value
in absolute measure of the B.A. unit or of the Siemens unit
has been published as the result of their work.
Ill. Method of Revolving Coil.
This method, first, it would appear, suggested by Weber,
was carried into execution by the celebrated Hlectrical Com-
mittee of the British Association*, and more recently by
myself with the assistance of Dr. Schuster and others+. The
greater part of what I have to say upon this subject has been
put forward already in the papers referred to, from which
alone the reader can form a complete opinion on the merits
or demerits of the method as hitherto practised. On the pre-
sent occasion I must take many of the conclusions there arrived
at for granted, or at most give a mere indication of the nature
of the arguments by which they may be supported.
Method III. differs from II. mainly in the fact that in III.
the earth-inductor is, so to speak, its own galvanometer, the
needle whose deflections measure the currents being suspended
at the centre of the revolving coil itself instead of at the centre
of another galvanometer-coil forming part of the same circuit.
If, asin Il., the inductor-coil were simply twisted through
180° when the needle passes its position of equilibrium, the
disadvantages of the simplification would probably prepon-
derate over the advantages. The diminution of effect due to
the oblique position of the coil relatively to the needle (except
at the moment of passing the magnetic meridian) would indeed
be compensated by the diminished resistance of the complete
circuit, and, as will presently appear, considerable advantage
* Brit. Assoc. Reports, 1862-1867. Reprint, Spon, 1873.
+ Proc, Roy. Soc, May 1881, Feb. 1882; Phil. Trans. 1882.
336 Lord Rayleigh’s Comparison of Methods for the
would arise in respect of errors in the measurement of the coil ;_
but an almost fatal uncertainty would be introduced from the
influence of self-induction. :
The important advantage of III., obtained, as I believe,
without any really important sacrifice, arises only when the
inductor is set into uniform rotation. In IL., if the connexions
were maintained without a commutator, the current in the
galvanometer-coil would be alternating, and therefore unsuit-
able for measurement with a magnetic needle; but in IIL,
although the current in the coil itself alternates, the reversal
of the coil relatively to the needle causes all the impulses to
operate finally in the same direction. When, therefore, the
coil is caused to revolve in a periodic time small relatively to
that of the free vibration of the needle, a steady deflection is
obtained which varies inversely with the absolute resistance
of the coil. 3
If we omit for the moment all secondary considerations,
although some of them may not be without importance, the
formula by which the resistance (R) of the revolving circuit
is given in terms of the mean radius (a), the number of turns
(7), the angular velocity of rotation (w), and the angle of
deflection (¢), runs
R=77°n’ao cot $;
from which it appears that, in respect of errors arising from
the measurements of the coil, this method is much superior to
those hitherto discussed. There is only one linear quantity
concerned; and the error committed in its determination enters
but singly into the final result. Indeed we may say that in
this respect no improvement is possible, unless it be in the
direction of substituting for the mean radius of a coil of
several layers some other kind of linear quantity more easy to
deal with.
In requiring the absolute measurement of angle, II. and
III. stand precisely upon a level.
The time of vibration in the experiments of MM. Weber
and Zéllner was 17 seconds or 80 seconds—none too long
relatively to the time (2 seconds) occupied in turning the
inductor. If we suppose the coil to be uniformly rotated at
the rate of, say, 2 revolutions per second, there would be 68
or 120 impulses upon the needle in the time of 1 vibration.
It would no doubt be a great exaggeration to represent the
increase of sensitiveness as being in any thing like this pro-
portion, since by the method of recoil it is possible to make
several observations of impulses during the time required for
one observation of steady deflection. Nevertheless it cannot
*
Determination of Resistances in Absolute Measure. 337
be doubted that the advantage of III. in respect of sensitive-
ness is very considerable.
Hxperience has shown that there is no difficulty in controlling
and measuring the rotation of the coil; but of course some
auxiliary apparatus is required for the purpose. Against this
may be set the escape from observations of the time of vibra-
tion, and from any uncertainty which may attach to the bal-
listic use of a galvanometer-needle. The suspended magnet
may easily be made of such dimensions that no appreciable
error can arise from supposing it to be infinitely small.
On the other hand, some new complications enter in method
III. which I desire to state in full. In the first place we have
to take account of the fact that the inductor moves in a field
of force due not only to the earth, but also to the suspended
magnet itself. Ido not think that the correction thus ren-
dered necessary (about 4 parts per thousand in my experi-
ments) adds in any appreciable degree to the uncertainty of
the final result; but we may take note of the fact that an
auxiliary determination must be made of the ratio of the mag-
netic moment of the suspended magnet to the earth’s hori-
zontal force.
If the metal ring on which the wire is wound be ona large
scale and sufficiently massive for strength, currents may be
developed in it, even although it is divided into two parts by
ebonite insulation. In my experiments the effect of these
currents was very sensible, and had to be allowed for by careful
observations of the deflection produced when the ring was
rotated with wire circuit open. In any future repetition it
will be worthy of consideration whether the ring should not
be formed of less conducting material. It does not appear,
however, that the final result can be prejudicially influenced ;
and the effect produced by secondary closed circuits allows us
to verify the insulation of contiguous layers or turns of the
wire by comparing the deflections obtained before the wire is
wound with those obtained after winding, but with main cir-
cuit open, any difference being due to leakage.
But the most serious complication in method III., and one
which in the eyes of some good judges weighs strongly against
it, is the disturbing influence of self-induction. With respect
to this, the first point to be noticed is that the action is per-
fectly regular, and that the only question which arises is
whether.its magnitude can be determined with such accuracy
that the final result does not suffer. Now the operation of
self-induction is readily submitted to calculation if a certain
coefficient (L) be known. We find
R=a'n’aw cot d{1—U tan’ ¢—U? tan* $},
338 Lord Rayleigh’s Comparison of Methods for the
where U is a numerical quantity dependent upon L, so that
the influence of self-induction is approximately proportional
to the square of the speed of rotation. The same law applies
also to any disturbances depending upon mutual induction
between the wire circuit and subordinate circuits in the ring.
It will be seen that, if the law of squares may be depended
upon, the influence of self-induction (and mutual induction)
can be satisfactorily eliminated by combining observations
taken at different speeds. In my experiments four speeds
were used, of which the greatest and the least were in the ratio
of 2:1. The effect of self-induction was therefore four times
as great at the high speed as at the low speed. In other words,
the quantity (about 1 per cent.) by which the low-speed result
is to be corrected in order to eliminate the influence of self-
induction is only one third of the discrepancy between the
uncorrected results of the extreme speeds. If, therefore, the
observations are good for any thing at all, they are good
enough to determine this correction with all desirable preci-
sion. If a check be considered necessary, it is supplied by
the results of the intermediate speeds. .
The above reasoning proceeds upon the supposition that we
have no independent knowledge of the magnitude of the coeffi-
cient U. In point of fact, this coefficient can be calculated
with considerable accuracy from the data of construction, so
that the empirical correction is applied only to a small outstand-
ing residue.
In considering the disadvantageous influence of self-induc-
tion as an argument in favour of II. as against ILL, we must
remember that the magnitude of the influence can be greatly
attenuated by simply diminishing the speed of rotation. At
half the lowest speed above spoken of, for which the correction
for self-induction would be reduced to + per cent., the deflee-
tion (over 100 millim. at a distance of 2670 millim.) would
probably correspond to a much greater sensitiveness than it is
possible to obtain under II. Ifwe prefer the higher speed,
it is because we estimate the advantage of doubled sensitive-
ness as outweighing the disadvantage of a fourfold correction
for self-induction.
The fourth objection which may be taken to this method,
and it is one from which II. is free, lies in the necessary crea-
tion of mechanical disturbance in the neighbourhood of the
suspended magnet.
How far these complications may be supposed to prejudice
the result of carefully conducted experiments must be left to
the estimation of the reader of my paper, in which yery full
data fora judgment are given. My own opinionis, that while
Determination of Resistances in Absolute Measure. 339
in the aggregate they must be allowed to have some weight,
they are far from preponderating over the advantages which
the method possesses in comparison with II.
If we take the view that the method itself is trustworthy,
the principal error will arise in connexion with the mean
radius of the coil; and it becomes an interesting question to
consider whether advantage may be expected from a further
increase in the dimensions of the apparatus. For this purpose
we may regard tang as given. The total resistance R will be
proportional to n’a/S, where 8 denotes the aggregate section
of the copper, from which it follows that oS may be regarded
as given, while a is left undetermined by the consideration of
sensitiveness. Thus, if we retain w and 8 unaltered in a mag-
nified apparatus, we shall have the same sensitiveness as before,
while the increased diameter of the coil and the relatively de-
creased dimensions of the section will conduce to amore accu-
rate determination of the mean radius.
The angular deflection being given, the correction for self-
induction is nearly constant whatever may be the proportions
of the coil.
If we are of opinion that there is danger in the operation of
self-induction, the case becomes strong for the introduction of
a second coil ina plane perpendicular to that of the first*. By
this means the relative correction for self-induction would be
reduced to one quarter, while the deflection remained unaltered.
It searcely needs to be remarked that this use of a second coil
would not, as in II., increase the uncertainty depending upon
the linear measurements, the two mean radii entering into the
result as parts, and not as factors. :
This combination would lend itself especially well to low
speeds of rotation; for the deflecting force, being uniform in
respect to time, would not give rise to forced vibrations of the
needle. The latter would have nothing further to do than to
indicate the direction of a constant field of force.
LV’.
This method, which was proposed by Foster t,and more re-
cently by Lippmann, and to a certain extent executed by the
former, is a modification of III., in which the electromotive
force generated during the rotation of the inductor is balanced
by an external electromotive force, and thus not allowed to
produce a current. The external electromotive force is due to
the passage of a battery-current through certain resistance-
coils; and the current is compared with the earth’s horizontal
* Proc. Roy. Soc. May 1881, p. 123.
+ Brit. Assoc. Report, 1881.
340 Lord Rayleigh’s Comparison of Methods for the
intensity (H) by an absolute tangent-galvanometer. The dif-
ference of potential at the two points of derivation is thus known
in terms of the included absolute resistance (R) and H. The
circuit is continued through a sensitive galvanometer and the
coil of the inductor, and is closed only when the latter coil is
nearly in the plane of the meridian. When balance is obtained,
the electromotive force of induction n.7a?.H .@ is equal to
RH tan «/G, where G is the constant of the tangent-galvano-
meter and « the angle of deflection, The result, from which
H disappears, if it may be assumed to be the same in the two
places, is thus
R=n7rd’G. w cota,
or, if A be the mean radius of the galvanometer-coil,
2
R=2nm7’o cot « =
from which the value of the resistance-coils is obtained in abso-
lute measure. One advantage of this method, which it shares
with VI. below, is that the resistance immediately expressed
may be that of well-constructed coils of German silver or of
platinum-silver at a known temperature.
This method is nearly free from the secondary objections to
III. discussed above. The self-induction of the revolving wire-
circuit does not enter, as no appreciable current is allowed to
form itself; but there would appear to be a possibility of dis-
turbance from mutual induction between the wire-circuit and
secondary circuits in the ring. It would certainly be neces-
sary to prevent the flow of currents round the ring by the
insertion of an insulating layer; and even with this precaution
some control in the way of a variation of speed would almost
be necessary. Again, it is a question whether disturbance,
from thermo-electricity for instance, may not arise at the place
where the contacts are made and broken.
_ It is to be hoped that a complete series of observations may
be made by this method, which certainly possesses considerable
merits; but at best it remains open to the objection mentioned
under II., with which in this respect it stands upon a level, 7. e.
that errors may enter from the measurements of both coils, the
error of A entering singly into the result, and that of a enter-
ing doubly.
In respect of requiring absolute measurements of angle,
there is nothing to choose between II., II]., IV., and V.
V. Weber’s Method by Damping.
This is the method followed by Kohlrausch * in his inyesti-
* Pogg. Ann. Erganzungsband vi.; Phil. Mag. 1874, April and May.
Determination of Resistances in Absolute Measure. 341
gations upon this subject. It is founded upon II.; but in order
to avoid the difficulty arising from the necessity of using a
magnet small relatively to the coil in which it is suspended, no
attempt is made to determine the constant from the data of
construction. The inductor is connected with a sensitive gal-
vyanometer, and the constant of the latter is deduced from
observations of the logarithmic decrement of the vibrations of
the magnet when ths circuit is closed (1), and when it is open
(A,). The result, however, involves H the horizontal inten-
sity, K the moment of inertia of the needle, as well as the time
of vibration T. Expressed roughly, in the notation previously
employed, it is
Free 32a*H?TX AB
ae Ke >? By?
where R is the resistance of the circuit composed of the in-
ductor and galvanometer, A and B are the arcs of vibration
in the method of recoil.
Interesting as this method is in some respects, I cannot but
agree with Rowland in thinking that the final formula is
enough to show that it cannot compete with others on equal
terms, if the object be to obtain a result of high accuracy.
The horizontal intensity itself is perhaps nearly as difficult to
determine as absolute resistance; and the error thence arising
doubles itself in the result. There is in addition the error
of K. But even if H and K were not subject to error at all,
I believe that the occurrence of the fourth power of the radius
of the inductor is a fatal defect, and tends to explain the dis-
erepant result obtained by Kohlrausch*. It is also worthy of
note that the error of levelling enters twice as much asin IL.,
IIl., and IV.
VI. Lorentz’s Method.
This method, which, with the introduction of certain modi-
fications not affecting its essential character, I am disposed to
consider the best of all, was proposed and executed by Lorentz,
of Copenhagen, in 18737. A circular disk of metal, main-
tained in rotation about an axis passing through its centre at
a uniform and known rate, is placed in the magnetic field due
* Oct. 1882.—It is very satisfactory to note that Kohlrausch (Gétt. Ges.
Sept. 1882) has recently detected an error in the value of the area of the
windings of the inductor assumed in his previous calculations. Introdu-
cing the new value, obtained by an electrical process analogous to that
described in Maxwell's ‘ Electricity,’ § 754, he finds
1 B.A. unit = -990x 10°.
Tt Poge. Ann. cxlix. p. 251,
342 Lord Rayleigh’s Comparison of Methods for the
to a battery-current which circulates through a coaxal coil of
many turns. The revolving disk is touched near its centre
and circumference by two wires. If the circuit were simply
closed through a galvanometer, the instrument would indicate
the current due to the electromotive force of induction acting
against the resistance of the circuit. The electromotive force
corresponding to each revolution is the same as would be
generated in a single turn of wire coincident with the cireum-
ference of the disk by the formation or cessation of the battery-
current. If this be called y, and M be the coefficient of induc-
tion between the coil and the cireumeference, m the number
of revolutions per second, the electromotive force is mMy.
For the present purpose, however, the circuit is not simply
closed, but its terminals are connected with the extremities of
a resistance R through which the battery-current flows, and
the variable quantities are so adjusted that the electromotive
force Ry exactly balances that of induction. When the gal-
vanometer indicates no current, the following relation, inde-
pendent, it will be observed, of the magnitude of the battery-
current, must be satisfied,
R=mM;
and from this, M being known from the data of construction,
the absolute resistance R of the conductor is determined.
Tt will be seen that this method has pretty close affinity to I.
The secondary circuit is here, in a sense, reduced to a single
turn, or rather to as many turns as the disk makes revolutions
in a time comparable with the time of swing of the ballistic
galvanometer; but the disadvantage of a reduced number of
turns is probably more than compensated for by the continuous
character of the induced current, which allows of its being
brought into direct opposition to that of the battery. During
the months from April to August of the present year I have
been occupied in carrying out a determination by this method.
Space will not permit of a detailed consideration of the various
questions which presented themselves; and I must content
myself with a brief statement of the procedure, and with such
a discussion of the sources of error as will allow a comparison
of this method with others. I hope shortly to communicate a
detailed paper upon the subject to the Royal Society.
One of the principal difficulties to be overcome arises from
the exceeding smallness of the resistance R, less than 3}, B.A.
in my experiments. Lorentz employed an actual column of
mercury of known dimensions, so that the result is given at
once in terms of mercury. I had intended to follow the same
course, but, after some trials, came to the conclusion that
there would be difficulties in the way of thus obtaining the
Determination of Resistances in Absolute Measure. 348
degree of accuracy aimed at, and ultimately adopted a method
of shunting. The main current from the battery was divided
into two parts, the larger of which passed through a resistance
of half a unit, formed by combining two singles in multiple
ares. ‘The resistance traversed by the other part of the main
current was much larger (from 10 to 20); and it was to two
points on this branch distant +15 that the wires of the derived
circuit were connected. With proper precautions this arrange-
ment was found satisfactory, and the equivalent resistance R
could be accurately expressed in terms of the standard B.A.
units. The adjustment for obtaining the balance was effected
by varying a large resistance placed in multiple arc with one
of the others ; or rather two effective resistances were used,
one on either side of that required for balance, the latter being
finally calculated by interpolation from the indications of the
galvanometer.
By observing only the effect of reversing the battery-cur-
rent the results are freed from the influence of terrestrial
magnetism, and from the very sensible thermoelectric force
having its seat at the slidmg contact. These contacts were
made by means of brushes of copper wire. One brush pressed
against the cylindrical edge of the disk, which was about
+ inch broad; and the other pressed against the shaft on which
the whole turned. The area included by the secondary circuit
was therefore not exactly that of the disk, but required a small
correction, as to which, however, there is no difficulty.
The arrangements for driving the disk and for observing
the speed were the same as for the revolving coil of method III.
The results, which in the same arrangement have not differed
- by so much as 7,495 on different days, show that the sensitive-
ness was sufficient.
After these explanations I come to the main subject of the
present remarks, viz. the degree of accuracy likely to be
attained in the fundamental linear measurement. In the pre-
sent case the quantity to be determined is M; and so far there is
no difference between this method and I. But the fact that
the secondary circuit is here represented’by a disk whose dia-
meter can be measured much more accurately than that of a
coil introduces a certain modification. It is necessary also that
the arrangements be symmetrical with respect to the middle
plane of the disk, as, on account of the width of the brush, the
place of contact cannot be considered as well defined. The
necessary condition can be satisfied with a single coil by placing
it so that its mean plane coincides with that of the disk. In
this position slight errors of adjustment produce effects of the
second order only, and every thing depends upon the radii.
344 Lord Rayleigh’s Comparison of Methods for the
Preparatory to the design of the apparatus for my experi-
ments, I made some calculations of the values of the induction-
coefficient and of its rates of variation for various ratios of the
radius of the coil (A) to that of the disk (a). The angle y
(see method I.) is here (b=0) determined by tan?}-y=a/A.
If we write
éM _ 2 5A oa
iN aes a ae
the sum of % and vy will be unity. The following are the
values found. Those under M are proportional only, and
relate to the case in which A is constant.
a/A. r. v M
az) —12 4+2°2 4°37
6 —1°36 | +2°36 6°65
a, —15 +2°9 9°80
8 —2:0 +3°0 14:4
In Lorentz’s apparatus the value of a/A was even larger than
the last in the table, and the radial dimension of the coil was
no small fraction of (A—a). On this account, as has already
been pointed out by Rowland, no very accurate result could
be expected.
In my experiments two similar coils were used whose radius
(A) = about 26 centim., and in two distinct arrangements.
In the first arrangement the two cells were placed close
together; so that the case corresponded pretty closely with that
just spoken of. The radius of the disk is about 16 centim.; _
and thus the proportions are nearly those of the second ex-
ample in the table. It will be seen that the circumstances are
not unfavourable to accuracy, the error of mean radius of the
coil entering into the result to a less extent than in any of the
methods hitherto described, except III. and IV. The disk is
so much more easily measured, that the larger coefficient 2°36,
applicable to it, should not lead to much error in the result.
This arrangement was worked at two speeds of rotation in
the proportion of 10: 16, and gave with close accordance
1 B.A. unit =°9867 x 10° C.G.8.
In the other arrangement the two coils were separated to a
considerable distance, and the induction-coefficient depended
not only upon the mean radii of the coils (and of the disk),
but also upon the distance of their mean planes. The pecu-
liarity of this arrangement, to which I wish to draw special
Determination of Resistances in Absolute Measures. 345
attention, is that it is possible so to proportion the quantities
that the error of mean radius of the coil does not affect the result,
which accordingly depends only upon the diameter of the disk
and the distance of the coil’s mean planes. How this may
come about will be readily understood by considering the de-
pendence of M upon A when a and bare given. It is clear
that M vanishes, both when A is very small and when it is
very large ; from which it follows that there must be some
value of A for which the effect is a maximum and therefore
independent of small variations of A.
In carrying out this idea it is not necessary to approach the
above-defined state of things very closely; for of course we
have in reality a good approximate knowledge of the value
of A. In my apparatus the distance of mean planes was about
30 centim., so that 6 = about 15 centim. With the actual
proportions a calculation of the effects of the various errors
shows that
oM oA ob on ,
M7 a 967-+18— 3
so that the error of A enters in quite a subordinate degree.
The positive coefficient of 5A shows that with the given coils
and disk the separation was somewhat too great to secure the
greatest independence of 6A.
The success of this arrangement depends principally upon
the degree of accuracy with which } can be determined. The
two rings on which the wire is coiled are separated by distance-
pieces; and, as in I., by reversing the rings relatively to the
distance-pieces the result may be made to depend upon the
mean length of these pieces and the mean thicknesses of the
rings at the places of contact. The three distance-pieces were
held together in one length and measured under microscopes;
and the thicknesses of the rings were taken with verified cal-
lipers. There can hardly be a doubt but that this determina-
tion is much more accurate than that of the mean radius of a
coil; and, what is also of some importance, it admits of repe-
tition at pleasure with comparatively little trouble.
The value of the B.A. unit resulting from the measurement
with this arrangement was 9869 x 10° C.G.S.*
There seems no reason why a further increase of accuracy
should not be obtainable by enlarging the scale of the appa-
ratus. If we suppose the scale doubled, the number of turns
in the coil and the angular speed of the disk being unaltered,
the value of M would be doubled; and thus with the same
* The reductions not being yet finally completed, these numbers are
liable to a change of one or two units in the fourth place of decimals.
Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2A
346 Messrs. Cross and Bevan on the Correlation of
battery-current the sensitiveness would be improved. Or, if
we suppose the circumferential linear speed of the disk rather
than its angular speed to be constant, the sensitiveness would
be unchanged. If the larger coil were made of the same kind
of wire as the smaller, its resistance would be augmented; but
if the dimensions of the section were also doubled, so as to
keep the proportions throughout, the advantage in this respect
would lie with the larger apparatus.
On the whole, I am of opinion that if it is desirable at the
present time to construct apparatus on the most favourable
scale, so as to reach the highest attainable accuracy, the modi-
fication of Lorentz’s method last described is the one which
offers the best prospect of success. Before this is done, how-
ever, it appears to me important that the value now three
times obtained in the Cavendish Laboratory by distinct me-
thods should be approximately verified (or disproved) by other
physicists. To distinguish between this value and those ob-
tained, for instance, by Kohlrausch, by Lorentz, or by the
first B.A. Committee, should not require the construction of
unusually costly apparatus. Until the larger question is dis-
posed of, it appears premature to discuss the details of arrange-
ments from which the highest degree of precision is to be
expected.
XXXIX. On the Correlation of the Chemistry of the Carbon
Compounds with the Phenomena of Life. By C. F. Cross
and K. J. BEvAN*.
T is not for us to dilate upon the marvellous progress of
Organic Chemistry during this century, nor to find fault
with the inevitably specializing tendency of research in the
province of the carbon compounds ; and we certainly owe an
apology for entering upon a subject of such magnitude as the
correlations of chemical with biological science. That which
we offer is derived not so much from the consciousness of being
able to originate views of these correlations which shall be more
productive than certain which appear to prevail, as from the
practical necessities of the investigations in which we find
ourselves engaged, the paucity of the landmarks to which
we have to look for guidance, and the misleading character
of certain of the recognized principles and methods which has
become manifest in the results of their application. In fine,
there are numerous points in that portion of Biochemical
Science the study of which we are prosecuting which call
for critical discussion; and the existence of the imperfections
* Communicated by the Authors. ~
.
Curbon Chemastry with Vital Phenomena. 347
which it shall be our aim to expose we can only account for
by the influence of the specializing tendency preventing che-
mists generally from following up the science in its wider
relations.
Ii is certainly the ideal issue of organic chemistry to co-or-
dinate the multitudinous facts already and to be amassed con-
cerning the carbon compounds, with the genesis, changes, and
ultimate fate of the substances which go to build up the tissues
of living organisms. Beyond this, indeed, many chemists do
not hesitate to indulge in expectations as to the possible
achievements of synthesis, which know no limits short of the.
inconceivable. The special “vital force” of a previous age
they dismiss as an ancient cloke of ignorance long since dis-
earded, under the genial influence of the sun of knowledge,
even by those who most tenaciously opposed its sheltering
folds to the stormy blast of “‘ unbelief ;’’ and thus by removing
the great barrier, the whole universe of matter and force is
opened out to the “conquering progress of man.” In the
words of an authoritative modern text-book, ‘At the present
day the belief in a special vital force has ceased to encumber
scientific progress. We now know that the same laws of com-
bination regulate the formation of chemical compounds in
animate and inanimate nature’”*. The authors of this mani-
festo, however, leave us in doubtas to whether they regard the
belief in question as itself obsolete, or, by being modified in
accordance with the invincible array of facts by which their
second dogma has been established, as brought within the
pale of natural truth, and thus to have become an aid, and not
an encumbrance, to scientific progress. The two propositions
are certainly not equivalent unless this latter interpretation be
allowed ; and as equivalence is evidently intended, we take it
that the authors, leaving the mystery of life to vindicate itself,
also intended this interpretation, and would allow the chemical
phenomena of life to be as special, say, as the phenomena of heat.
But it is difficult to rest satisfied with the isolated and phy-
sical interpretation of the passage; the generalizing tendency
of modern physical science impels us to give it a wider con-
sideration. Thus, to develop our parallel, we have long ceased
to regard heat as having any special objective existence ; and
although its phenomena are, in relation to our perceptions,
still sufficiently special to admit of classification apart, we no
longer allow the exigencies of science to impede our progress
towards a better understanding of the unity of nature, but
recognize in heat ‘a manifestation of energy as a mode of
molecular motion,” a definition which is sufficiently exclusive
* Roscoe and Schorlemmer, ‘ Treatise on Chemistry,’ iii. p. 10.
348 Messrs. Cross and Bevan on the Correlation of
of subjective impressions. Further, chemists are in the habit
of referring the phenomena of their science to the existence of
a force of chemical affinity, and that without any justification
more or less elaborate, in deference to its conditional character
or to the metaphysical questionings which underlie all our
natural science. And when we examine into the grounds
upon which our belief in a vital force may be said to be dis-
missed, we find that we have in them only the basis of a truer
knowledge than heretofore of what the vital force is and what
it is not. Since the dismissal of the hypothesis of spontaneous
generation, the distinction of matter into animate and inani-
mate has assumed a very sharp character. In the animate
world we have a province of distinct phenomena ; into this -
world, matter is coerced and is made to manifest properties
distinct from those which it otherwise possesses ; and in this
world force is distributed and co-ordinated in such a way as to
compel the acknowledgment of agency. Speaking physically,
we admit that life is one of the narrowest—i. e. most exten-
sively conditioned of phenomena; but this does not lessen our
belief in the working, under these conditions, of a special
agency. The minutely intimate correlation of life with its
chemical phenomena doubtless leaves in the minds of many
but a very narrow margin for the operation of the special
agency in question, and makes its assumption appear propor-
tionately gratuitous. At the same time we have no proof that
the science of “‘energy”’ affords the ultimate criterion of
natural truth; and we cannot recognize that it has done more
than modify the belief in a special vital force, though the
modification has been so deep as to convert it from being an
encumbrance to an effective aid to scientific progress.
How far our progress, thus emancipated from a serious
impediment, may be expected to go, is a question which must
be relegated to metaphysics ; at the same time we hold that
the results of physical inquiry have as yet given no warrant
for anticipating, as the realizable ideal, that our science will
ever overleap the barrier of structural organization. The limi-
tation herein expressed seems to us so obviously to define the
natural attitude of the chemist towards living matter, that not
without the strongest proofs will he change it for the extreme
of conceivable ideals; and in the practical work of investiga-
ting the products of life and growth he will find such abun-
dant confirmation of his natural impressions as to remain
convinced that the distinction of the material universe into
animate and inanimate is real and transcendental*.
* This subject will be found exhaustively discussed in ‘ Chemical Ditti-
culties of Evolution,’ by J. J. McLaren (1877).
|
|
|
a tt i
vo, a
Carbon Chemistry with Vital Phenomena. 349
Chemistry and biology occupy to one another an antithetic
relation as_regards their subject-matter : the goal of the one
is the starting-point of the other; the protoplasm as yet undif-
ferentiated, to which the biologist complacently refers the
origin of life, is to the chemist a perfect microcosm, and its syn-
thesis perhaps the highest possible achievement of his science.
With regard to the supervening phenomenon of organization
—the entrance of life—there is also a distinction of attitude.
To the biologist it is axiomatic—beyond that, a fact without
the range of observation, and one of which we venture to say,
therefore, he can give no account. Now the chemist finds his
attention challenged, and his work of speculative investigation
begin, at an earlier point in the history of the planet, when
as yet life was impossible ; his speculations moreover have a
certain basis in observation and analogy; and having initiated
his career, why break off and affect to view with veiled eyes
a change merely in the disposition of the matter and force
already existent and active? Why, further, should we attach
to the entrance of structural organization a mystic signifi-
cance, when not only are we familiar with the inverse change
from the organized to the amorphous condition, but find it in
many cases to involve no change in the inner subsensible
molecular structure, or at least no deeper change than can be
included within the province of isomerism? Cellulose, for
instance (in the form of cotton), is dissolved by the ammonio-
cupric reagent, and on adding excess of acid is reprecipitated,
and may be recovered without loss of weight; the change
undergone cannot, therefore, be more than morphological.
Furthei, the amorphous cellulose behaves towards reagents so
similarly to the original, that the change in question appears
to have affected merely the external structure. Add to these
considerations many others of a similar character, which need
not be here specified, togecher with the numerous syntheses of
the products of life and growth which have been achieved in
the laboratory, and lastly the narrow range of physical con-
ditions under which life is possible, and we have a fair con-
ception of the intellectual position from which might emanate
the dogma, “we have ceased to believe in a special vital force.”
We, speaking personally, see no more reason, in these teach-
ings of molecular philosophy, for ceasing to believe in life as
resulting from special agency, than for ceasing to recognize
the living individuality of our English language or constitu-
tion, and the agency of Englishmen in their establishment
and development, because they are originally a rearrangement
of materials and forces once the possession of now obsolete or
effete nationalities. We are not aware that in any philosophy,
350 Messrs. Cross and Bevan on the Correlation of
worthy the name, life was or is regarded as any thing more
than a rearrangement and special disposition of the preex-
isting: it cannot be doubted that life, as known on this planet,
had a beginning ; nor, further, that the whole analogy of the
origin of subsequently derived life points to it as an indivyi-
dual and special phenomenon. In a word, the doctrine of
Spontaneous Generation has been expunged from biological
science; and a revival of its analogue from the point of view
of chemical science we hold to be groundless. Not only so,
but, to give a more practical expression to these views, a
loose adoption of the non-belief in a special vital force will
materially impede progress in the domain of biological che-
mistry. We cannot find a stronger proof of the want of
recognition of the special and peculiar nature of the chemical
phenomena of life than in the prevalence of empirical methods
for the resolution of plant substances, their empiricism con-
sisting chiefly in their unreasoned foundations upon the me-
thods of separation of inorganic substances. To this portion
of the science our attention has been specially directed; and
we proceed to discuss it in certain of its bearings upon the
main subject of this paper.
The work of the plant, considered in its intrinsic results, is
to grow, to form tissues and organs ; a side issue of growth
is the elaboration of substances which subserve future growth;
and a subsidiary result is the formation of certain substances
which we may regard as excreta, as unavailable for the main
end. These excreta are often bodies of well-defined physical
properties, of more or less simple molecular structure, whose
constitution is so far comprehended as to allow of their syn-
thetical production in the laboratory. For the isolation of
such bodies, methods founded upon the fixity of their consti-
tution are general and satisfactory. But, on the other hand,
substances whose essential condition is that of continual dif-
ferentiation, whose constitution is but little understood even
when viewed statically, whose relationship to the former group
is probably of a parental character, should be treated with
due regard to these distinctions : indeed it seems hopeless to
attempt to comprehend their chemical functions in disregard
of these their special biological correlations. The neglect of
these considerations has led to the adoption of empirical and,
to that extent, arbitrary methods of analysis and classification;
names have been multiplied to individualize bodies which,
occurring in a developmental series, should have received a
corresponding general or group definition; and much time and
capability have been spent in establishing facts before their
probable and relative value had been taken into consideration,
:
es! AD
Carbon Chemistry with Vital Phenomena. dol
The chemistry of cellulose is a case in point. This substance
will be found, even to this day, treated by chemists as a well-
defined body, of intrinsically fixed characteristics ; whereas
physiologists, with special regard to its functions in the living
plant, have long since observed it to be capable of many modi-
fications, more or Jess profound, and have not hesitated to
regard it as the parent substance of that large class of aro-
matic bodies of which tannin is the type.
Geology had made us acquainted with the very profound
modification of cellulosic structures which are seen in coal; and
the chemical study of coal in its various forms had revealed a
progressive increase in aromatic potentiality ; and yet the
obvious generalization of these several results has been widely
ignored, the genetic connexion suggested by this large group
of naturally occurring substances has been practically neglected,
and chemists have remained satisfied with a purely empirical
treatment. Taking this connexion as a working hypothesis
and investigating the essential relations therein suggested, we
feel assured that a much more productive field of inquiry is
opened out. The essential difference between coal and cellu-
lose is measured by the difference of their products of decom-
position by dry distillation: in coal we have the source of the
vast series of aromatic compounds which constitute the sub-
ject matter of the most important development of our science.
Although the constitution of coal is still unsolved, and we
cannot yet say to what extent it might be made to yield
aromatic bodies by less drastic processes of resolution than
that of destructive distillation, yet the general fact that in
relation to cellulose it possesses an increased (immediate)
aromatic potentiality has been sufficiently established.. The
nitrogen, further, derived from the proteid matters of the
parent tissues exhibits a progressive diminution; and the che-
mistry of the formation and decomposition of coal may be
considered independently of this element*. It remains there-
fore to investigate the conversion of cellulose into substances
of the aromatic group of compounds.
The first link in the chain of development would appear,
from the researches of physiologists, to be contained in the
phenomenon of the lignification of cellulose structures. In
the life of the plant, extreme processes of reduction and oxi-
dation, of synthesis and resolution occur simultaneously and
continuously. The formation of cellulose and its lignification
have been ranged by physiologists on the basis of this anti-
thesis. The connexion between lignin and the great group of
* W. A. Miller, ‘Elements of Chemistry,’ iii. p. 145, by whom this
subject appears to be developed more consequently than by most writers.
352 Messrs. Cross and Bevan on the Correlation of
astringent substances has been already established*; and the
latter have been assumed by physiologists to be residues of
the oxidation of carbohydrates. In regard to the lignifica-
tion of structures originally consisting of pure cellulose, we
have two alternative hypotheses to account for the change:—
(1) that it results from an intrinsic modification of the cellu-
lose itself effected in situ; and (2) that it is the result of com-
bination of cellulose with aromatic bodies formed elsewhere
in the plant, and probably as residues from the oxidation of
carbohydrates. There is perhaps more negative evidence on
the subject of the second than there is positive in favour of
the first hypothesis; and the difficulties which beset the eluci-
dation of the question are an apt illustration of the limitations
which impede the solution of the chemical phenomena of life.
If the cellulose combine with astringent substances presented
in solution, to form insoluble products, these may be assumed
to resemble those compounds which form the basis of the
dyeing of the cellulose fibres. A superficial study of any of
the non-cellulose or lignified fibres will satisfy the observer
that they behave rather as modified celluloses than as a com-
pound of the above weak order. In the first place, the reso-
lution vf the fibre-substance of lignified fibres can only be
effected by means of drastic reagents, whereas a compound of
cellulose with a body that it has merely removed from solution
(that is to say, in what we may term adhesive combination)
is always easily decomposed. We have further made a series
of observations upon seedlings, which show that the astringent
substances formed during germination are present in the
juices and yet absent from the substance of the fibro-vascular
bundles. Again, if lignification followed the course in ques-
tion, it is difficult to account for the comparatively invariable
composition of bast-fibres. Not only are they remarkably
uniform in composition from end to end, but they may be
obtained white and lustrous by a process of bleaching which
occasions a minimum loss of weight ; they may be converted
into explosive nitro-compounds, an examination of which
shows them to be homogeneous; they are soluble in the
ammonio-cupric reagent, a property which has been denied to
them by certain observers; and the precipitate obtained on
adding an acid is simply the amorphous modification of the
originally organized fibre-substance. The characteristic yel-
low coloration moreover which lignified fibres give when
treated with a solution of aniline sulphate, and upon which
much stress has been laid as distinguishing them from the
* Sachs, Handb. der exper. Phys. (1865) pp. 361-369 ; Sachse, Farbstoffe
&e. (1877), p. 113; Cross and Bevan, Chem. Soc, Journ. xli. p. 90,
Carbon Chemistry with Vital Phenomena. 353
cellulose fibres, we have found to be so considerably weakened
by previously boiling the fibre in a solution of acid sodium
sulphite as to be afterwards in many cases quite undistinguish-
able. As the loss in weight due to this treatment is imper-
ceptible, and the lignin substance remains practically un-
changed, the colour-reaction in question is referable to the
presence of some body resulting from a superficial decompo-
sition (oxidation) of the lignin substance. These observations
are a strong confirmation of the view enunciated with much
emphasis by Sachs* many years ago, that the only inference
to be drawn from the biochemical facts then established is that
lignin and cellulose are genetically connected.
In our early work on bast-fibres, we were led to regard
the jute-fibre as typical of a class of bodies analogous to the
glucosides, and which we termed cellulides, a name which suffi-
ciently explains our views. Subsequently to this, we found
that Hlasiwetzt had arrived at similar conclusions in discussing
the chemico-physiological relationships of the tannins, phloba-
phenes, resins, and glucosides. He not only regards cellu-
lose, tannins, and resins as genetically connected, but is con-
vineed of the a priori probability of the existence of series of
gummides and mannides parallel with the glucosides. We
take this as an additional warrant for the correctness of our
view; and in conformity with these conclusions and subse-
quent experience, we may state our hypothesis with more
emphasis to be, that the fibre substance of lignified fibres is, in
its chemical constitution, dominated by the cellulose mole-
eule, upon which aromatic molecules, resulting from intrinsic
modification of the cellulose itself, have been built. Whether
the aromatic molecule is of the nature of a quinone, as would
seem to be indicated by the products of the action of chlorine,
we have some hesitation in affirming, recognizing more clearly
than we then did the difficulty of reasoning from the pro-
ducts of decomposition of once living substances back to the
condition under which they are formed.
The celluloses, which constitute the framework upon which
the plant world is developed, being regarded thus as capable
of modification, and lignification as the first of the series of
changes through which they pass from the group of carbo-
hydrates, to which they originally belong, to the extended
yrange of naturally occurring substances of aromatic character
included in the large group of astringents, in the several
varieties of coal, and probably also of other important groups,
* Sachs, ibid. Cf Koroll, Quant. Chem., unters. Zstg. Kork, Bast
&e.: Diss., Dorpat (1880).
+ Chem. Soc. Journ. xxxviii. p. 666; Ann. Chem. Pharm. cxliii. p. 40,
354 Messrs. Cross and Bevan on the Correlation of
such as the resins, it is surely incumbent upon chemists to
recognize the call to investigate the natural origin and history
of the carbon compounds, and first of all in their relation to
cellulose. We know the objection in the minds of many to
forsake the familiar landmarks of positive physical definition,
such as crystallization and molecular volume, for a province
where the absence of the criteria hitherto regarded as al] im-
portant makes the results to be obtained appear to that extent
conjectural; we know indeed that the objection in many cases
takes the more active form of almost refusing credence to any
results obtained with substances that are amorphous and essen-
tially transitional; and against this attitude a most emphatic
protest is to be lodged. Arithmetic cannot cope with the
physics of living matter; and we shall need to promote our
equations and constants several degrees before we can include
its chemical phenomena. Moreover the purity of substances,
as the only condition in which to be approached by the che-
mist, will need a very elastic interpretation in presence of
matter undergoing differentiation; and such properties as have
hitherto been regarded as affording the only guarantees of
purity will have no place in a vast amount of research that
requires to be done. We clearly recognize the large amount
of work already accomplished by isolated effort in this depart-
ment of chemical science ; but these remain for the most part
uncorrelated, and, as a glance at the text-books will show, in
a great measure unrecognized.
Not only have the suggestions of physiologists in regard to
the probable origin of aromatic substances in the plant been
but little developed by chemists, but the equally important
correlation of the carbohydrates with the fats, which follows
from their physiological equivalence, still lies without our
science. Here also a transformation in series is suggested,
the intermediate terms of which are probably to be found in
cutin and analogous bodies, constituents of cork structures.
The changes through which the transition is accomplished are
probably very profound, more so than in the conversion of
cellulose into lignin. Of the mechanism of the conversion we
are as yet entirely ignorant; but we have the conviction, in
this as in every other case, that the vital force of the plant
operates through the same materials and forces which lie at
our disposition, and that its results can therefore be studied
and in some measure reproduced.
The study of these transformations must, in the first
instance, of course be analytical; and most important correla-
tions will follow from a comparative examination of the pro-
ducts of resolution of plant-substances, Take, for instance,
Carbon Chemistry with Vital Phenomena. 355
mucic acid, and represent its connexions by a diagram, and we
find a large number of very important correlations implicated,
thus:—
Cellulose.
Gums.
Mucic acid.
We SS
(Dichloro-muconic acid) (Pyromucic acid).
Adipic acid. Furfuraldehyde.
aS ee ee
—_—, rm
! pitas ;
Cork tissues. Fats. Lignin. Astringents.
A quantification of these relationships, and a multiplication
of investigations according tv such a priori correlations, could
not fail to establish important truths concerning the genetic
connexions of the carbon compounds.
A further illustration of the want of correlation of chemical
with biological investigation is to be found in the prevalence
of empirical and statistical analyses of plant-substances in
agricultural work. To a certain extent it is evident that
statistical must prevail over molecular methods where the
complex substances and mixtures of substances which are
elaborated in the plant world are the subject of inquiry; but we
contend that these may be ordered on a much more rational
basis than is at present adopted.
The somewhat arbitrary choice of reagents, such as Schulze’s
for the isolation of cellulose, of boiling dilute sulphuric acid
and alkali successively applied to plant-substances for the
determination of their so-called crude fibre, the dismissal of
whole groups of bodies as ‘extractive matters”? or as “ in-
crusting and intercellular substances,” and the general absence
of the recognition of the genetic connexion of these substances
with those from which they are separated—in fine, the almost
exclusive choice of the indirect and statistical before direct
methods of observation, argues a certain misapplication of
time and capability, and sufficiently accounts for the indiffer-
ent, if not critical, attitude of the greater number of chemists
towards Biochemical science. We may cite the literature on
the subject of chlorophyll, the proteids, the carbohydrates,
including cellulose, the group of pectous substances, and, until
the recent work of O’Sullivan and Brown and Heron, starch. A
more special illustration is to be found in the work of Meissner
and Shephard on the origin of hippuric acid in the urine of
Herbivora. In order to identify the parent substance—that
constituent of grasses which could yield the necessary benzoic
356 Correlation of Carbon Chemistry with Vital Phenomena.
residue—the authors, adopting the statistical method of exclu~
sive separation, arrived at length at the substance in question
—a body which Foster*, in quoting their work, terms a form
of cellulose. This substance was found to differ from cellulose,
on the result of an aggregate elementary analysis, by a some-
what higher carbon percentage, such as, according to the
reasoning of these authors, would be due to the presence of a
body of the composition of quinic acid; and this they regard
as a constituent of this substance, and as converted. during
the process of digestion, into hippuric acid. Pushing then
the statistical method of inquiry beyond its limits, and evi-
dently for the purpose of confirming @ priori views, the authors
appear to us to have missed the most important development
of their otherwise valuable work. Had they examined the
“form of cellulose ”’ at which they arrived by a direct method
of proximate resolution, they would have obtained the aromatic
substances, allied to the astringents and phenols, which we have
obtained from lignified fibres. That they are digested by the
Herbivora has been established by numerous observerst; that
they are the source of the benzoic residue necessary to form
hippuric acid is &@ priori very probable: in fact it must be
regarded as first in the order of the probabilities to be inves-
tigated. As such, indeed, it is occupying our attention ; and
whatever be the result it will be more valuable, because more
definite, than any conclusion arrived at by means of the in-
direct method.
We refrain from extending our discussion of these subjects
in anticipation of the more detailed publication of our re-
searches. We think we have shown grounds for our state-
ment that there is a general want of correlation of chemical
with biological research, especially in the hesitation on the
part of chemists to adopt, as working hypotheses, the wider-
reaching conclusions of physiologists as to the natural origin
and history of the carbon compounds. We have also endea-
voured to show that, while our conception of the vital force
has been modified so as to have entirely lost the significance
that belonged to it in a previous age, we have no ground for
dismissing it for the alternative view of life as immanent in
the universe of matter and force. We have expunged an error
that was partial, and are in danger of generalizing the nega-
tive by which it needed to be met.
Postscript.—Since writing the above, our researches have
* Die Hippursdure (Hannover, 1866) ; ‘Text-book of Physiology,’ 2nd
edit. p. 354. Cf. Weiske, Zeitschr. Biol. xii. p. 241.
+ Weende, Berichte.
established a connexion of the closest order between the aro-
matic portion of the molecule of lignin (bastose) and the tri-
atomic phenols—a fact which considerably strengthens the
views advanced by physiologists as to the correlations of the
carbohydrates with the aromatic group, and the reasoning by
. which we have sought to emphasize them. The researches in
question, on this point, will be published in due course.
On the Dimensions of a Magnetic Pole. 357
XL. On the Dimensions of a Magnetic Pole in the Electrostatic
System of Units. By Outver J. Lopez, D.Sc.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
VHE discussion which has been carried on in your pages*
respecting the dimensions of a magnetic pole serves to
illustrate the divergency of thought between those in this
country who have been brought up, “electrically, ander Faraday
and Maxwell, and the continental philosophers so eminently
represented by Prof. Clausius. From one point of view the
discussion may be said to have been roused by a simple mare’s
nest constructed by dropping a factor out of one side of an
equation (as was pointed out at once by Prof. Fitzgerald and
by Mr. J. J. Thomson); but from another point of view it is
the natural and inevitable consequence of the different aspects
from which these matters can be regarded:—the English
standpoint, in which the medium is recognized as the active
agent, and is continually present both in the mind and in the
formule; and the continental standpoint, from which the
medium is perceived as so much empty space, and is taken
account of as such in the formule. Both these aspects of the
subject are worth consideration; and it may be conducive to
future clearness to discuss them at moderate length.
Coulomb’s measurements provisionally established the fact
that in air the mechanical force between two electrically
charged bodies was proportional to ee’/r?; but the subsequent
researches of Faraday proved that this proportionality only
holds so long as the medium enveloping the bodies is un-
changed, and that the above quotient must be multiplied by
different factors in order to give the force exerted in different
media. Thus if the same two charged bodies were immersed
in bisulphide of carbon, they would repel one another with
much less vigour than they do in air.
Introducing therefore as a factor the electric inductive
* Phil. Mag. [5] vol. xiii. pp. 376, 381, 427, 429, 431, 530; and vol. xiv.
pp. 124 & 225.
358 Dr. O. J. Lodge on the Dimensions of a Magnetic a
capacity K, we have the general equation
ee
Now all that is solemnly essential with respect to the dimen-
sions of the quantities here involved is that e?/K must be a
force into an area, or that
(e]=[L][KF}’.
If we proceed to define the unit of electricity so as to make K
of no dimensions and to equal 1 for air, that is a convention,
and it is the basis of the electrostatic system ; but the above
statement is no convention, but a natural truth.
Precisely the same kind of thing is true in magnetism; and
we now know that the force between two magnetic poles is not
independent of the medium surrounding them, but that if the
torsion-balance were full of, say, ferric chloride, the force
between the two poles would be measurably less than if it
were full of mere air. Thus we again need a factor for com-
pleteness ; and the real law is that
mim’
or that
[m]=(L] [pF }.
The conventional magnetic system of units is based on the
definition of m in such a way that w, the magnetic inductive
capacity of the medium, shall be of no dimensions, and shall
for air be simply 1.
All then that is objectively and physically fixed about the
matter is that the dimensions of ¢/./K and of m//p are
absolutely and mechanically definite, being each of them a
length into the square root of a force, or
MLiT”.
But observe that the two system of units, the electrostatic
and the magnetic, the arbitrary definition of e and the arbi-
trary definition of m, are in their origin utterly independent ;
not that they are wnrelated, but their relation must be a matter
for future and experimental investigation. All we can so far
say about them is, that,in every possible consistent system that
can be adopted,
[eK7*] = [mp] =[LF**]= [Me-4). . . (1)
(The last term of this triple identity is added for the sake of |
completeness, though it does not directly belong to the present
Pole in the Electrostatic System of Units. 309
subject : the letter & is intended for the gravitation-constant
as determined by the Cavendish experiment. Jam not aware
whether the question of the possible dependence of this con-
stant on the optical density of the medium surrounding the
attracting masses has ever been considered; but I feel sure
that a direct experimental attack on this question would not
be uninteresting, and it might lead to important results. )
We now come to the Cirsted-Ampeére discovery of the con-
nexion between m and e—the form of the connexion being
that an electric current flowing in a closed circuit can pro-
duce a magnetic potential, and therefore of course can act on
magnets, precisely as if it itself were a magnet of a certain
strength and form. The potential so caused at any point in
air is found to be simply proportional to the strength of the
current and to the solid angle which the circuit subtends as
seen from that point; or, in other words, the moment of the
magnet which is equivalent to the current is simply pro-
portional to the strength of the current and to the area of the
contour round which it flows.
The unit of current most simply and directly applicable to
these electromagnetic phenomena is not the old electrostatic ©
unit at all, but a new unit which may be defined in many
ways—as, for instance, these :—-
The electromagnetic unit of current is that which produces
unit magnetic potential at a point whence its circuit
subtends unit solid angle;
Ii is also that which produces unit magnetic intensity, in a
given direction, at a point whence the solid angle sub-
tended by its circuit is changing at unit rate, per unit
displacement, in that direction;
And, again, it is that current which when flowing round a
contour of unit area is equivalent to a magnet of unit
moment,—
all these statements being derived directly from the unit mag-
netic pole thus :—
Unit magnetic potential is defined to exist wherever a soli-
tary and stationary unit pole would possess unit energy ;
Unit magnetic intensity exists wherever unit pole would
experience unit force ; and
Unit magnetic moment is that possessed by two unit poles
of opposite sign rigidly connected by a bar of unit length.
(The connexion between the old electrostatic unit and this
new electrical unit thus magnetically defined may be ex-
pressed, if | am not mistaken, by saying that a ring charged
with the electrostatic unit of electricity would have to revolve
in its own plane with an angular velocity of about 3x 10"
360 Dr. O. J. Lodge on the Dimensions of a Magnetic
radians per second in order to produce the same magnetic
effects as the electromagnetic unit of current flowing in the
same ring.
Or, conversely, the electrostatic unit magnetic pole would
be that which would experience unit force if placed at the
centre of a circle of unit radius in which the electrostatic unit
of electricity was moving with unit velocity.
This definition I believe to hold equally well in any homo-
geneous medium; for it is pointed out below that the electro-
magnetic effect of a current is independent of w; while as
regards K, a quantity which we might perhaps think would
be likely to affect the result, we must remember that electric
displacement is totally independent of any such circumstance.
So, corresponding to the common electrokinetic equation,
Cds
Force =f =?
Ye
we shall have, for a moving charge,
mev
Force = 7?
whence
[me]=[ML’T""}. . 2 ow
If statements like these are in the main correct, and after
the experiments of Rowland we are bound, I suppose, to
believe in the truth of something of the kind, they ought to
remove Dr. Everett’s objection (Phil. Mag. June 1882, p. 481)
as to the introduction of electrostatic units into magnetism ;
unless indeed he maintains the thesis—no doubt a tenable one
—that directly you begin to carry a charged body about, the
discussion of its performances no longer belongs to electro-
statics.
Bonen from this digression, we have now to ask whether
the statements above made are really definite and independent
of the magnetic properties of the mecium surrounding the
circuits, or must we introduce a factor to express the influ-
ence of this medium when it is other than air?
Mr. J. J. Thomson has instructively raised this question
(Phil. Mag. for June); and he and others at Cambridge consider
it a matter to be settled by experiment; and they further con-
sider that, in order to agree with Maxwell’s view, experiment
ought to make the magnetic effect of a solenoid and its air-
equivalent magnetic shell differ, as soon as they are both intro-
duced into some medium for which w is not unity. Now,
though agreeing with this as far as it goes, | venture with
diffidence to think that Maxwell would have drawn a distine-
‘?
Pole in the Electrostatic System of Units. 361
tion between the medium inside the region of the solenoid
corresponding to the substance of the magnetic shell, and that
outside. He over and over again lays stress upon the fact that
artificial solenoids can only be compared with magnetic shells
for the space outside the shells, and that the line of integration
must never be allowed to thread the circuits. Let us follow this
out and see what it means when applied to the above question.
I will assume it possible (for it certainly is theoretically
possible) to imitate any steel magnet whatever by a proper
arrangement of electric circuits, both being at present im-
mersed in a non-magnetic (7. e. non-magnetizable or w=1)
medium. The two arrangements are completely equivalent
for all the region outside both—the region outside both being
defined by the shape of the steel. For the comparison is not to
be urged within the steel, because of the magnetized surfaces,
which would have to be cut through, a circumstance which
would completely alter all the conditions ; and it is not to be
urged within the region of space near the solenoid which is the
counterpart of the steel-occupied region, simply because here
there are no magnetized surfaces to be cut through, and there-
‘fore the conditions will be continuous.
Now take some non-magnetic medium, which for shortness
T will call “clay,” mould it into the shape of the steel, and
place it in or around the solenoid so as to mechanically define
the limits of the “‘outer region.”” And now immerse both
magnet and solidified solenoid in any medium for which yu
differs from unity: I venture to assert that the equivalence
which existed in air will be entirely maintained in the mag-
netic medium—even though that medium be iron or bismuth,
—and that, for both, the magnetic intensity at any point will
be its air-value divided by pu.
Still keeping both the things in the magnetic medium,
remove the clay from the solenoid and permit the medium to.
flow into the space it occupied. If what I said before is true,
the solenoid will now be too strong for the magnet, for the mag-
netic permeability of the interior will increase its effect u times,
while that of the exterior will, as before, diminish it wth 3 SO
that the effect of the solenoid completely immersed in the
medium is precisely the same as it was when in air, while the
effect of the magnet, from whose interior the magnetic sub-
stance is of necessity excluded, is still 1h of what it was in
air. This latter seems to be the kind of experiment which
Mr. J. J. Thomson suggests in his June letter (p. 429), and
Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2B
362 Dr. O. J. Lodge on the Dimensions of a Magnetic
which, he says, Mr. Sargant then intended (and I hope still
intends) to carry out.
The solenoid being now completely surrounded with homo-
geneous magnetic substance, wall a portion of it in with paper
or glass to the shape of the steel of the magnet, and then pull
both magnet and solenoid out into the air again. Naturally
the solenoid will still be ~ times too strong for the magnet,
but no further discrepancy need be expected; and if the cur-
rent of the solenoid has been weakened when inside the mag-
netic medium so as to restore the disturbed equivalence, they
will remain equivalent when the region external to both is
again filled with common air.
These statements, if in their essence granted, require to
make them complete certain provisos about the boundary of
the vessel containing the magnetic medium, unless it be infi-
nitely large, and also a discussion of what happens in the case
of more than one magnetic medium, But the magnetization
of bounding surfaces, and the accidents which happen to lines
cutting surfaces of discontinuity, are perfectly understood and
need not be here entered into.
Moreover, in making these statements I am merely saying
what one would expect to happen without evidence to the con-
trary; but Iam not for an instant implying that direct experi-
mental investigation is unnecessary and would not be highly
desirable. On the contrary, I think it would be most desirable
and satisfactory to have the matter thoroughly sifted.
Supposing, then, that I have so far made no mistake, we
can make the general statement of the equivalence of a cur-
rent and a magnet thus—
The magnetic moment of a circuit is equal to the strength of
its current multiplied by tts effectwe area and again multiplied
by the magnetic inductive capacity (or permeability) of the medium
in the interior of the region enclosed by the contour (which region
for a simple plane circuit is a mere shell), but is wholly inde-
pendent of the magnetic properties of all the rest of the sur-
rounding medium.
The corresponding dimensional equation is
[m]=[LpeT~}.
Substituting in this the value of [m] from (1), we obtain the
relation
ib
[-K]=5, - Mer
whence
nl=L Jose
a
4
_
;
Pole in the Electrostatic System of Units. 363
These relations must all hold in any consistent system of
units, since they express physical truths ; but of course they
are not all independent. The number of independent relations
must be limited by the number of fundamental experiments,
viz. three—Coulomb, Coulomb, and Oersted ; and the short-
est way of writing the independent relations is this :—
[we? |=[Km?]=[ML] i
[wKe?]=1. ;
and
(5)
The electrostatic convention makes [K]=1; the electromag-
netic convention makes [w|=1.
So far every thing being pretty clear and straightforward,
we have now to ask how it was that Prof. Clausius should
have jumped to the conclusion that Maxwell had fallen into
error™, or else that he held a theory of magnetism different
from (and not merely an amplification of) Ampére’s and
Weber’st. With this latter horn of the dilemma, by the way,
he is half allowed by Mr. J. J. Thomson (September) to have
succeeded in transfixing Maxwell; and Dr. Hverett (June) is
not extremely energetic in his repudiation even of the alterna-
tive of the first.
Now itis perfectly true that Maxwell, in stating the current
theory of magnetism, says without any kind of retraction or
hesitation that “the magnetic action of a small plane circuit
at distances which are great compared with the dimensions of
the circuit is the same as that of a magnet whose axis is normal
to the plane of the circuit, and whose magnetic moment is
equal to the area of the circuit multiplied by the strength of
the current..... and if a magnetic shell.... &. be substi-
tuted .... then the magnetic action of the shell on all distant
points will be identical with that of the current.”’ And in dis-
cussing Ampére’s theory, he ignores the existence of magnetic
media whose u does not equal 1 as completely as Prof. Clausius
could wish.
But then, according to Weber’s extension of Ampére’s
theory (an extension I suppose universally accepted), the pro-
perties of magnetic substances of all kinds are explained by
molecular electric currents, and no magnets or magnetic sub-
stances other than those consisting of current-conveying
molecules exist. [And with reference to a remark of Mr.
* Phil. Mag. June, pp. 3887 & 392. + Ibid. August, p. 126.
2B 2
364 Dr. O. J. Lodge on the Dimensions of a Magnetic
Thomson’s in the September number, p. 225, I may say in pass-
ing that it seems to me that Maxwell held, though no doubt
tentatively and hypothetically, the view that electric currents
and small magnets are identical and not only equivalent. |
The coefficient » is thus foreign to Ampére’s theory applied
universally; and this is how it has happened that Prof. Clausius
has failed to recognize its existence and has been led intoerror*.
A system dealing with Ampérian magnets in media for which
» does not equal 1 is a mongrel combination which may no
doubt be occasionally convenient but which never can be
thoroughly satisfactory.
We may accept then without hesitation Clausius’s presen-
tation of Maxwell’s views, viz. both that a small magnet zs an
electric current, and that magnetic moment ALWAYS equals
simply integral current x area—remembering, however, that
there exist currents in molecules besides the gross and arti-
ficial currents in our copper wires, that these are directed by
our artificial currents and add to their effects, and that in all
cases they are most distinctly to be taken into account.
In air, so far as it is non-magnetic, these molecular currents
are zero, and the magnetic induction and the magnetic force
are everywhere equal ; but in media consisting of Amperian
* Very many errors,I now find; for he has also ignored K, Faraday’s simple
old electrostatic constant; and accordingly his equations (1), (2), (4), &c.
express mere conventions (if they were any thing more, then truly m,
would have to equal m4, and e,=ea, as he begins to perceive in his August
letter); while his general equation (3), which is the foundation of his
reasoning, is quite wrong, and is indeed at the bottom of the whole con-
fusion. In using the term “error” here, I would be understood to mean
rather “divergency from opinions commonly held in this country” than
absolute incorrectness as to matter of fact. For it would not be becomi
to apply the latter term to views held by Prof. Clausius when the experi-
mental foundation of opposing views is confessedly incomplete. The
views held by Prof. Clausius are no doubt perfectly consistent, and would
probably be in accord with fact if only the medium produced no effect
such as it is here commonly supposed to produce; and whether the me-
dium does or does not produce such an effect appears to some extent at
present a subject of legitimate debate and a matter for experimental
investigation. It will be understood therefore, that in stating one side
strongly I have been influenced by the wish to be clear, rather than with
the desire to dogmatize.
Since the above letter was in type Dr. Francis has kindly called my
attention to a paper by Prof. Helmholtz in Wiedemann’s Annalen, No. 9,
1882, to which I might have further referred if I had known of it in
time. As far as I can hurriedly understand his position, Prof. Helmholtz
in part endeavours to reconcile the views of Maxwell and of Clausius b
throwing a doubt upon the Weber-Ampére theory ; and in fact he pat:
to pure physicists not to abandon the old electrostatic for the more cum-
brous and less surely founded electromagnetic system.
[A translation of Professor Helmholtz’s paper will appear in our next
number.—Ep. Phil. Mag. ]
¢
Pole in the Electrostatic System of Units. 365
molecules there is an extra magnetic induction, due to the
pointing of these along the lines of force, which is 47 times
the magnetization, and which has to be added to the other,
thus making the total magnetic induction at any point pu times
the magnetic force there.
The effect of the medium is a physical fact; and no theory
can presume really to dispense with the constant wu. All that
the Ampérian theory does is to give a physical interpretation
to it, and to render one independent of it so soon as one takes
account of every current-conveying circuit, whether molecular
or other, existing in the field, and does not arbitrarily elect to
deal only with those gross solenoids which we can excite and
immediately control by batteries.
There can be no doubt, I think, that the mind of Maxwell
on this subject, as on most others, was as clear as daylight ;
and so far from falling into the least suspicion of an error, he
expresses himself in art. 615 (1st edit.) almost as if he were
joining in the present discussion, saying :—
“There is one result . . . . whichis of very great importance.
If we suppose that no magnets exist in the field except in the
form of electric circuits, the distinction which we have hitherto
maintained between the magnetic force and the magnetic
induction [and therefore also the difference ~—1] vanishes,
because it is only in magnetized matter that these quantities
differ from each other. According to Ampére’s hypothesis
ee the properties of what we call magnetized matter are
due to molecular electric currents, so that it is only when we
regard the substance in large masses that our theory of mag-
netization is applicable ; and if our mathematical methods are
supposed! capable of taking account of what goes on within
the individual molecules they will discover nothing but elec-
tric circuits, and we shall find the magnetic force and the
magnetic induction everywhere identical. In order, however,
[N.B.] to be able to make use of the electrostatic or of the
electromagnetic system of measurement at pleasure we shall
retain the coefficient u, remembering that its value is unity
in the electromagnetic system.”
I am, Gentlemen,
Your obedient servant,
University College, Liverpool, OxtvER J. Lopes,
September 28, 1882.
[ 366 ]
XLI. On the Electric Discharge in Rarefied Gases.
By Dr. EucEN GOLDSTEIN*.
|
HAVE shown in two former papers{, and more com-
pletely in my book ‘A New Form of Electrical Repul-
sion’ (published by Springer, Berlin), that the discharge
cannot be effected by the actual projection of gas-particles.
The same considerations which oppose the theory of the pro-
pagation of electricity by projected gas-particles, also at once
exclude the assumption that other ponderable particles, having
access to the space in which the discharge takes place, play
any essential part as carriers of electricity in the discharge.
Such particles might consist of disintegrated portions of the
substance of the electrodes, particles of the wall of the vessel,
or of dust.
The theory that the kathode-rays at any rate are produced
by projected particles of the substance of the electrodes has
been recently defended by Gintl§ and Puluj||. Numerous
arguments] may be urged against it, over and above those
which are at the same time opposed to a special convection by
the particles of the gas. I will briefly mention one or two
points. I have mentioned on a former occasion** that a system
of pores in an insulator, or a single opening of relatively small
dimensions, sends out rays whose properties are equivalent to
those of the rays which issue from a metallic kathode. The
rays of narrow openings, for example, possess the property of
rectilinear radiation, and of exciting phosphorescence, which
cannot here be explained by a projection of the substance of
the pole.
Kathodes imitated by systems of pores represent special
cases of the phenomenon of secondary negative light, which is
* Translated from the Annalen der Physik und Chemie, 1881, new
series, vol. xiii. Communicated by the Author.
+ The readers of this Magazine will find that some observations and
conclusions in the first chapter of the above paper, concerning the conduc-
tivity of vacuum, do not differ from the views expressed by Prof. Edlund
in a paper reprinted in the January number of the Philosophical Magazine
for 1882. I beg to mention therefore, that my paper appeared in print
in the February number (1881) of Wiedemann’s Annalen, and that Prof.
Edlund presented his to the Royal Swedish Academy, April 23, 1881.
¢ Phil. Mag. [5] x. pp. 173 & 234.
§ Gintl, ‘Studies of ‘ene Radiant Matter’ (Prague, 1880).
|| Puluj, Sitzungsberichte Wien. Akad. 1880, p. 864.
| E.Wiedemann( Wied. Ann. x. p. 252, 1880, Phil. Mag. x. p. 418) thinks
it possible to conclude from Zahn’s experiments (Wied. Ann. viii. p. 675,
1879) that the view of Gintl and Puluj is untenable.
= *4P tl. Mag, xp. 1/5.
On the Electric Discharge in Rarefied Gases. 367
produced with the properties of rectilinear propagation, exci-
tation of phosphorescence, &c., at openings of any width, if
these openings occur in diaphragms or in tubes connecting
vessels or introduced into them, the area of which is consider-
able in comparison with the diameter of the opening. A con-
sideration of these bundles of rays possessing the properties of
the kathode-light issuing from wide openings also protects the
experiments on narrow openings against the objection that the
coincidence of their rays with the kathode-rays depends on a
conductive action of particles of the insulating substance
which might possibly be torn off from the edges of the opening.
It has further been shown* that the positive light also pos-
sesses the property of rectilinear propagation, and of exciting
phosphorescence when the exhaustion has been carried far ;
it does not seem to be reasonable to adopt an explanation for
the phenomena of the kathode-light the principle of which is
not applicable to the exactly similar properties of the positive
light.
“The most convincing proof, however, is given by the fol-
lowing observation, which I have made in experiments on the
kathodic deflection. This last name was proposed in the
book referred to above for the deflection of the electric rays
there described, of which I have made usef in determining
the velocity with which the electricity propagates itself. I
may assume it to be known that a kathode of aluminium pro-
duces no deposit on the walls of the tube even after several
hours’ use, whilst a kathode of platinum of no great thickness
soon produces a completely opaque metallic deposit on the
part of the tube played upon by the kathode-light. Two
straight smooth wire electrodes, a and b, are inserted in the
end of a cylindrical discharge-tube parallel to the axis of the
tube. If both are made at the same time kathodes of the same
discharge, then each of the two wires causes a deflection, in the
rays of the other which pass by near to it, of the nature of a
repulsion. We have then, as already described, two sharply-
bounded surfaces, of which the one receives no rays from a,
whilst none of the electric rays emitted by 0 fall upon the
other. At the density of gas favourable to the production of
phosphorescence, both surfaces are distinctly seen upon the
surrounding brilliantly phosphorescing surface. This pheno-
menon is also observed when one of the kathodes a is of pla-
tinum, until the increasing thickness .of the platinum-deposit
prevents the phosphorescence of the wall.
According to the-view of Gintl and Puluj, that portion of
the glass wall on which no rays fell from the platinum elec-
* Phil. Mag. x. p. 236. + Ibid. p. 246.
368 Dr. E. Goldstein on the Electric
trode ought evidently to remain free from the platinum deposit.
If, however, we examine the glass wall, we find that the sur-
face from which the kathode-rays are deflected—as determined
at high pressures by the visibility of the blue rays themselves,
_and at low pressures by means of the phosphorescence which
they excite—is just as thickly covered with the platinum as the
surrounding portion of the wall, and exactly as we observe to
be the case in cylinders where the platinum wire alone acts
as kathode while } is not excited. It follows that the rays of
the kathode-light are deflected, but not the projected particles
of the electrode ; the two cannot therefore be essentially con-
nected.
The discharge is therefore not to be explained by a projec-
tion of material particles, either of the substance of the elec-
trodes or of the gas. It follows from the experiments on the
order of magnitude of the velocity of propagation of electricity,
taken together with the views held on the constitution of gases,
that the assumption of oscillations of these particles does not
afford a satisfactory explanation, and the assumption of motions
of rotation remains equally unfruitful. The wall of the con-
taining vessel is not altogether neutral in the passage of elec-
tricity through the space enclosed by it; it shows itself
phenomena of charge and discharge which appear to be not
altogether without influence upon the main discharge between
the metallic electrodes. If we wish to go so far as to ascribe
to particles possibly torn off from the walls of the vessel when
they are discharged the same function which, in the view just
considered, gas-particles or electrode-particles were unable to
perform, this assumption, quite apart from all new objections,
is open to all the objections urged against the previous hypo-
thesis.
Recent investigations have shown that the dust suspended
in gases plays an important and previously unsuspected part
in the loss of electricity suffered by feebly-charged conductors
in the open air, or in gases not specially purified. In almost
all cases in which we have hitherto regarded a mass of gas as
a carrier of statical electricity, we must now regard the dust
suspended in the gas, in cases where drops of liquid cannot he
present, as the only vehicle of the electricity. We might
easily imagine an hypothesis ascribing a similar essential func-
tion to the dust in gases in the case of current electricity as
in the case of statical electricity, but that the objections we
have previously considered might easily be employed to refute
an assumption of the kind.
The discharge cannot then in general be explained by the
motions of ponderable particles ; it follows therefore directly
CC
Discharge in Rarejied Gases. © 369
from the experiments which prove this, that that medium
must be essentially concerned in the discharge which, accord-
ing to our present views, together with the gas-molecules, the
particles of the electrodes of the walls, and any other solid
substances which may be present, occupies the space in which
the discharge takes place—that is to say, the ether.
According to my view, the discharge is a process which
takes place in the free ether. I have already indicated this
view in the work already several times mentioned, and will
now give other evidence supporting the observation made
there.
Hittorf* found that the resistance of the positive light
always decreased as the exhaustion of the gas increased ; on
the other hand, he thinks he has shown that the resistance
increases with the exhaustion in the kathode-light and at the
surface of the kathode. Changes in the form and magnitude
of the anode have no influence on the resistance. The great
resistance which offers itself to the discharge at an extreme
exhaustion, and finally leads to its extinction in a vacuum as
perfect as possible, depends therefore altogether upon the
resistance at the surface of the kathode and in the space filled
by the kathede-light. After I had recognized that the pecu-
liarities of the negative light might be produced at any point
whatever of the column of positive light by simple changes in
the cross section of the discharge-tube, and that each separate
stratification of positive light is nothing else than a modified
bundle of negative light, this opposition between kathode-
light and positive light appeared to me just as doubtful as
already a number of other supposed differences between the
two, which I had found not to exist.
I found in fact that, exactly as with the positive light, the
resistance of the kathode-light at small pressures becomes vanish-
ingly small in comparison with the total resistance of the dis-
charge. Hence, since no specific resistance exists at the anode,
and since further, as already mentioned, the resistance of the
positive light vanishes in comparison with the total resistance
of the discharge, it follows that the resistance to the discharge
at very small pressures takes place entirely at the surface of the
kathode.
My experiments on this subject were not made by means of
a galvanometer, like those of Hittorf, but by means of the
spark-micrometer, which is here much more efficient. The
spark-micrometer was included in a second circuit connecting
the electrodes, and the distances of the poles of the micrometer
compared for the different densities of gas and lengths of
* Hittorf, Poge. Ann, cxxxvi. p. 1 (1869).
370 Dr. E. Goldstein on the Electric
kathode-light at which the currents of the inductorium either
cease to pass through the exhausted tube or else pass no longer
through the micrometer*.
* The distances of the balls of the spark-micrometer corresponding to
these two alternatives are not exactly identical. The discharges do not
pass exclusively through the exhausted tube up to a certain distance of
the balls, and then with a certain small decrease of this distance exclu-
sively across the air-space between the balls; but between the distances
of the balls at which the spark takes one only of the two courses open to it
are to be found positions of the micrometer at which both paths are taken
—sometimes the one, sometimes the other—and the one path the less fre-
quently the nearer we come to the distance at which the other is taken
alone. This apparently unstable character of the resistance in the tube
does not affect the accuracy of the measurements here in question; we
may compare the resistances by comparing the distances of the balls
apart at which for a certain fixed time, say two minutes, no spark passes
in the tube or between the poles of the micrometer. The distances so
measured agree upon repetition to ;'; millim.—that is to say, toa fraction
of 1 per cent. of the distance measured. The alternation of the discharges
with certain distances of the balls no doubt depends, partly at least, upon
the same cause as the following phenomenon, which I have observed in
the same experiments, and which, as far as I know, has not been pre-
viously described.
If we include the spark-micrometer in a branch circuit of an exhausted
tube which transmits both the discharge at ‘‘ make” and that at “ break,”
then, if the distance between the balls of the micrometer be gradually
diminished, the current at “break ” completely leaves the tube and passes
altogether in the free air, whilst that at “make” continues to traverse the
tube with undiminished light. Consequently we are able to study the
discharge of the “ make” current in the exhausted gas separate from that
of the “ break” current; whereas hitherto a separation of the two currents
has been effected by introducing an air-break in the direct cireuit inclu-
ding the tube, with which arrangement the tube is traversed only by the
discharge due to the “break” current. The reason of this phenomenon
may lie in the different maximum tension of the current on “making”
and “breaking” contact, and may correspond to the observation of tele-
graphists, that discharges of great tension (as observed in electrical
storms) will sooner traverse a short distance through air in the form of a
spark than traverse a long metallic circuit in the form of a current.
Such phenomena show that in the case of discharge through gases, the
division of currents cannot be calculated according to Ohm’s law. This
we see from the so-called Holtz’s “funnel-tubes.” If two similar tubes
are placed opposite to each other side by side in the same induced currrent,
then at suitable pressure of gas the current does not subdivide itself be-
tween the two in any definite ratio to the resistances of the tubes, but
the one tube remains entirely dark, the current goes altogether through
the other.
The law according to which currents divide when the discharge takes
place in gas must therefore be investigated empirically in the first place.
I take this opportunity of remarking that I have made an erroneous
assumption on this subject in a series of experiments in my book pre-
viously referred to, which, however, does not actually affect the result
obtained. I believed myself justified in assuming as the evidence of
certain phenomena (p. 146), that if a part of the discharge traverse a me-
tallic circuit from the kathode a to an electrode 6, and then the resistance
of a moistened thread be introduced between 4 and a wire c, that then the
Discharge in Rarefied Gases. 371
One of the experimental tubes is represented in fig. 1.
A cylindrical tube is provided with a flat kathode placed
at right angles to the axis of the tube, and nearly as large
as the section of the tube. The anode is placed close in
front of it, or in other cases consists of a very short wire
in the plane of the kathode itself. Inside the cylinder is
a movable partition c, consisting of a short glass cylinder ter-
minated by a plane surface at the end turned towards the
kathode. In accordance with what I have noted on former
occasions”, the positive light disappears for such an arrange-
ment of the electrodes when the exhaustion has reached a
certain limit, or it is confined to the immediate neighbourhood
of the anode ; the kathode-light, on the other hand, expands
to any extent if the exhaustion is sufficient, and the expansion
of its rays is limited only by their striking upon a solid wall.
Hence, when a sufficient exhaustion has been reached, we can
vary the expansion of the kathode-rays within wide limits by
sliding the piece ¢ (by inclining the discharge-tube and tap-
ping it) along the tube; since its length is always equal to the
distance between the kathode and the end-surface of the
movable cylinder, which can be moved right up to the anodeft.
If now the expansion of the kathode-light is made to vary
in the ratio 1 : 30, the total resistance of the discharge at low
pressures does not alter so much as in the ratio 1: 1-05.
Hence the resistance of the kathode is a vanishing quantity in
comparison with the resistance at the surface of the kathode.
Hence we see that the resistance of the whole quantity of
gas contained in a discharge-tube becomes smaller the more
density of the discharge at ais not changed. ‘There is in fact a certain
change; but its influence upon the phenomena considered in the place
referred to is so small that, upon repetition of these experiments with
actual constancy of density at a, results were obtained partly exactly cor-
responding, partly nearly corresponding.
The examples given on p. 149 for the magnitude of the deflective
power in a particular case consequently represent these values at least
very nearly. The same method was employed (p. 181) to confirm a result
obtained by two other methods; so that the result given there is not
affected by the failure of the experiment in question.
* Goldstein, Phil. Mag. iv. p. 362; ‘A new Form of Repulsion,’ p. 8.
+ In order to resist blows without deformation, the anode in these cases
was made of strong iron or steel wire. ;
372 Dr. E. Goldstein on the Electric
the density of the gas is diminished ; the space in which the
discharge takes place conducts better the less gas it contains ;
and since this change is always in the same direction while
the density is continuously reduced, so far as the experiments
can be extended, we must conclude that the greatest conduc-
tivity would be obtained after complete removal of the gas.
But after complete removal of the gas the discharge-space
contains only free ether; and I therefore regard this as the
true medium of the discharge. Any gas present seems to act
only as a hindrance to the ether.
Detailed speculations on the concrete form of the motion of
the free zther to which the discharge is due are, in my
opinion, premature.
We are not justified in regarding the discharge as essen-
tially a progressive motion of the ether so long as, on the one
hand, we regard Doppler’s principle as valid in optics, and, on
the other hand, refuse to attach any considerable value to the
progressive motion of gas-particles in the discharge. We
must’ then ascribe to the motion of the ether amongst the
relatively stationary gas-molecules an optical effect precisely
similar to that produced by the motion of gas-molecules in
ether at rest. Experiments on the constancy of gaseous
spectra when observed in directions parallel and at right
angles to that of the electric rays, show at once the absence
of progressive motion of the ether (of velocity comparable
with the velocity of propagation of the ray-discharge), after
we have shown by other experiments* the relatively stationary
condition of the gas-molecules.
It appears to me safest to characterize the motion of the
eetber in discharge as radiant, in accordance with what has
been previously statedt. Every particle concerned ina pencil
of negative light assumes the same form of motion which is
excited at the point of origin of the pencil.
The behaviour of the discharge towards magnetic forces has
frequently been brought forward in support of the view that
the gas-mass forms the medium of the discharge, since this
behaviour may obviously be explained by regarding the gas-
molecules as carriers of electricity. If the magnet acts upon
the positive light of an equatorially-placed cylindrical tube
with electrodes at the end, and finally compresses the light
which at first filled the width of the tube into a thin thread
lying in the equatorial plane against the wall of the tube, itis
generally assumed that the gas-molecules are compressed
together with the electricity; Ihave not found this confirmed.
* Goldstein, ‘A New Form of Electric Repulsion,’ Chap. IV.
+ Phil. Mag. x. p. 184.
Discharge in Rarefied Gases. 373
A piece of metallic sodium was introduced into a cylindrical
vessel 4 centim. in width and more than 20 centim. long, having
the electrodes at its ends; and the tube was then quickly filled
with dry nitrogen. After the tube had been so far exhausted
that its positive light filled the section of the tube, the sodium
was brought upon a part of the wall of the cylinder, in a hori-
zontal position, played upon by the positive light. The sodium
was next warmed until no more hydrogen was evolved, the tube
was refilled with fresh nitrogen, and exhausted again to the
same density as before. The sodium is then heated strongly
until it begins to volatilize, and the discharge, which was
reddish purple before, assumes a golden-yellow colour in its
neighbourhood. If the heating be carefully managed, it is seen
that the sodium vapour diffuses itself very slowly; so that the
discharge in the upper part of the tube still shows the red
colour due to the nitrogen, whilst it is of a golden yellow in
the lower part of the tube. If the tube be brought in a hori-
zontal and equatorial position near to a strong magnet, whose
poles are so placed that the positive light is drawn upwards,
the discharge, which at first filled the whole width of the tube,
is concentrated into a thread of greater or less tenuity against
the upper surface of the tube. But this thread possesses the
pure purple colour of the nitrogen discharge without any trace
of the sodium-yellow. The sodium vapour is consequently not
displaced by the magnet, together with the current, as we are
accustomed to see with movable carriers of electricity; the
current seems to obey the magnet with-
out affecting the gas-molecules. The
result is exactly the same in experi-
ments ‘made with the Holtz machine
instead of the induction-coil.
I have further examined whether it
is possible to recognize a transport of
gas-molecules by means of the magnet,
in the local increase of density which
must result from the assumed transport
in a closed space traversed by the dis-
charge. Two discharge-tubes, A and B,
fig. 2, were joined together in the man-
ner shown by means of a tube in which
a stopcock was inserted. A second stop-
cock at the end of a short tube shuts B
off from the pump during the time oc-
cupied by an experiment. The cylin-
drical portions of A were sufficiently long to show stratified
positive light, at least in the cylinder containing the anode,
374 Dr. E. Goldstein on the Electric
when pure dry air was employed. The distance between the
similar boundaries of the different layers, or the number of
layers in a given distance, is a very delicate test for change of
density in the gas. Changes in the residual gas which corre-
spond to less than ;4, millim. mercury are shown by very
marked changes in the interval between the layers*.
The current of a coil was first sent through A, the number of
layers in the anode-cylinder determined, and the boundary of
each on the kathode-side marked on the tube with ink, thus
marking the size of eachlayer. The current was regulated so
as to give perfectly steady stratifications. Opening and closing
the tap h, before or after turning on the current, did not affect
the position of the stratifications. The combination was now
brought near to an electromagnet while the current was pass-
ing and while the tap h was open, the poles of the magnet
being so placed that the discharge appeared compressed
towards the side of the tube B furthest from the tube A. If
this concentration of the discharge depended upon an increase
in density of the gas, then the gas in B outside the column
along which the discharge passes must be rarefied, and gas
from A would enter and rarefaction in A would result. After
a few seconds h was closed, the current of the magnet was
interrupted, the tube removed from the neighbourhood of the
magnet to guard against the effect of any residual magnetism,
and the discharge again sent through A. The number and
position of the layers were found to be exactly the same as
before the action of the magnet on the discharge.
The same result was obtained by operating as follows :—
The initial density of the stratified discharge of an induction-
coil through A was noted; then, after interrupting the current
of the coil, the rapidly following discharges of a powerful
Holtz machine were sent through B; and this discharge was
subjected to the action of the magnet. On now again pass-
ing the current of the coil through A, there was no sign of —
any change in density; any change which had taken place
must therefore have been less than 745 millim. mercury; on
the other hand, the change of density necessary to produce
(when possible) effects upon the discharge, similar to those
produced by the action of the magnet at constant density,
must be measured by centimetres of mercury. The theory
which makes the gas molecules the carriers of the current is
therefore in no way supported by experiments with the magnet.
The view which 1 take of the part played in the dis-
* By the interval between two consecutive layers I understand here
and elsewhere the distance between the bounding surfaces turned towards
the negative pole.
ia
Discharge in Rarefied Gases. | 375
charge by the free zether is commonly supposed to be refuted
(where it is mentioned at all as a possible case, e. g. in text-
books) by a reference to the experience of spectrum-analysis.
If the zther were the vehicle of the discharge, it is said, all
gases would give the same spectrum—the spectrum of zther—
when subjected to the discharge. But since each gas has a
special characteristic spectrum, the gass mass must be regarded
as the conductor of the electricity. But it is well known that
the zether itself has no power of emitting light. The fact that
it has no “ spectrum ”’ is therefore no evidence that it cannot
conduct electricity. With equal justice it might be argued
that the phenomena of light and heat due to a current can
only be produced in the molecules of the conducting substance;
every conductor in whose mass non-conducting particles are
embedded proves the contrary. The luminosity of a gas pro-
duced by the discharge depends entirely upon its molecules
possessing the form and period of oscillation which are neces-
sary for the emission of visible rays. That this vibrating
* motion is accompanied by motion due to electricity, executed
by the particles themselves or their zether-envelopes, does not
seem to be necessary; but, as the phenomena of fluorescence
and phosphorescence in sunlight show, the molecules of bodies
may execute motions of the form and period of the vibrations
of light by taking up the vibrations of the surrounding free
eether.
T assume that a similar process take place when a gas is
rendered luminous by the electric discharge. The discharge
itself represents a motion of the free ether, and is in itself
non-luminous. This motion of the ether disappears, being
communicated to the gas-molecules and their constituent
atoms; the particles of each molecule then vibrate in accord-
ance with their special structure and the conditions as to
elasticity of the molecule, and communicate again to the
zether the transversal vibrations so produced as such; thus the
original motion which the ether possessed as electricity is
converted into light, and of course into light whose oscilla-
tion-periods depend upon the specific nature of the gas-mole-
ecules. The difference in spectrum between chemically dif-
ferent gases thus in no way disproves the conduction of elec-
tricity by the ether. I thus regard the luminosity of gases
traversed by the electric current as a phenomenon of reson-
ance. Ishould not be disposed to regard it as a phenomenon
of fluorescence or phosphorescence, for two reasons :—(1)
Because in fluorescence and phosphorescence the vibrations
are transferred from the ether to the atoms, and back again to
the zther, without changing their character as transversal
376 Dr. E. Goldstein on the Electric
vibrations; here, on the contrary, a motion of the ether
which does not consist of transversal vibrations is converted
into transversal vibrations. We have, however, a phenome-
non analogous to this in acoustic resonance, where we see the
longitudinal motions of particles of air transformed into the
transverse vibrations of a resounding string. (2) lam dis-
posed to reject the name phosphorescence for the phenomena
under consideration, because, according to all the ideas which
we have so far associated with the name phosphorescence, an
hypothesis as to the temperature-conditions of the discharge
would be introduced by the choice of this name, since the
temperature of a gas is always supposed to be lower than that
of a gas of like emissive power rendered luminous by heat.
But this, even assuming that the conclusions of E. Wiode.
mann as to the temperature of the discharge should be con-
firmed by further experiments, is not yet accepted as the true
character of the light of the discharge; and my speculations
on the nature of the discharge do not in any way prejudice
the question of the temperature of the discharge. For the
present I leave this entirely out of the discussion.
The assumption that a vacuum conducts electricity has con-
sequences which are far-reaching, especially in the domain of
cosmical physics. The usual fate of attempts to found a
cosmo-physical theory upon experimental results is scarcely
such as to encourage imitators. At the same time I venture
to point out at least so much as this, that certain terrestrial
phenomena of an electric or magnetic nature which, because
of the coincidence of their periods or epochs with solar
changes, have been explained as due to the statical influence,
magnetic induction, &c. of the sun’s mass, might possibly be
more conveniently referred to electric currents radiating
through interplanetary space from the central body. Expe-
riment shows no limit to the expansion of that remarkable
motion which we observe in the kathode-rays as we eliminate
the ponderable medium more and more completely—it is
conceivable that the sun radiates electric rays as well as light-
rays through space. We see that even when the two poles
are placed close together, the kathode-rays stream out into
space without limit, without reference to the position of the
anode; consequently for electrical communication with the
sun, it would not be necessary that the earth should be the
source of electricity or pole of the current, but discharges for
which both poles are situated on the sun might produce rays
radiating from the sun into space.
a
:
|
Discharge in Rarefied Gases. 377
IL.
_ I consider two processes to be necessary for the production
of the discharge:—(1) A change in the condition of the ether,
preceding the discharge, which produces a certain condition
of unstable equilibrium in the arrangement of its parts: this
condition may be called, for shortness, tension of the ether.
(2) The restoration of equilibrium: this constitutes the dis-
charge itself.
The tension which precedes the discharge is not equally
great in all cross sections of a discharge-tube, even when the
- tube is of equal section throughout; it may even equal zero
in certain parts of the tube. ‘The tension has either finite or
maximum values at the surface of the metallic poles and at
those points which appear as points of issue of the separate
positive layers or of the secondary negative pencils. The
resultant of the opposing force produced by the tension on
each element of the kathode is directed away from it; at the
other points of issue also, it is directed at each point towards
the side turned away fromthe kathode. When the restoration
of equilibrium commences, a motion results in consequence
of the finite or maximal tension on the surfaces, which ad-
vances to the side of each surface of issue remote from the
kathode, and, originally excited in free ether, transforms itself
secondarily on its way into transversal vibrations of the ma-
terial atoms. The distances in which the tension before the
discharge was zero, and in which the, motion excited at the
surfaces of issue does not propagate itself, remain dark; such
places are the distances between the positive light, on the one
hand, and the kathode-light or secondary negative light, on the
other hand.
The greater the exhaustion becomes, the more do the dis-
tances between the surfaces of origin increase, and at the same
time also the distances to which the motion excited at the sur-
faces of issue extend. This latter increase, however, is com-
pleted more rapidly than the increase in the distances between
the surfaces of origin; hence it comes that one and the same
section of the space occupied by the discharge may be affected
by motions which radiate from two or more surfaces of origin.
(Penetration of the kathode-light into the positive light or of
the stratified pencils into each other.) Experience shows that
such motions penetrating each other do not sensibly alter each
other when their directions are the same; but when their
original directions are inclined to each other at a considerable
angle, they show marked phenomena of deviation *.
* Goldstein, Wien. Ber. 1876, 23 Nov.
Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2C
378 Dr. E. Goldstein on the Electric
That the so-called sether-envelopes of the gas-molecules or
atoms take part in the emission of light resulting from the dis-
charge is a matter of course ; but the part which they play in
the processes of charging and discharging must remain for
future discussion. The forces exerted by the material particles
upon which the formation of the zether-envelopes depends, tend
to produce a different disposition of the ether from that which
would result from the electrical forces only. Consequently
the more gas-molecules are included in the space occupied
by the discharge, the greater the electrical forces must be
in order to bring about the disposition of the ether which
must precede the discharge. Hence we understand how the
gas acts as a hindrance to the discharge, and why conduc-
tivity of the space occupied by the discharge continually im-
proves as the gas is more and more completely removed.
In any case, 1am unable to accept EH. Wiedemann’s view%,
according to which the zther-envelopes are the real medium
of the discharge. If, moreover, the ether-envelopes suffer
deformations without the free ether taking any part in the
process (and in the case of the kathode-discharge Wiedemann
excludes any such participation), then, as regards the velocity
of propagation of the discharge, Wiedemann must assume
a pure distance-action between the zther-envelopes, since in
highly rarefied gases we regard the times during which the
zether-envelope and the sphere of action of a molecule are in
contact with those of other molecules, or penetrate them, as
small in comparison with the times during which the sphere
of activity is isolated.
The assumption that the direction of the negative current
from the kathode is the direction in which the electric dis-
charge is propagated in the kathode-light, and also in the
secondary negative pencils and positive stratifications, con-
trary to the usual view, seems to be justified by numerous
experimental results. I would call attention, first of all, to
the phenomena of shadows, which, formerly observed only
with the kathode-light, have caused this phenomenon to be
represented as a motion from the kathode, even by the de-
fenders of the convection theory.
If a solid body be placed in a pencil of the kathode-light,
or of the secondary negative light, then, as may be observed
directly, that portion of the pencil falling upon the object which
lies between its end turned towards the kathode and the object
itself remains in every case intact, but that portion of the in-
cident pencil lying on the further side of the space occupied
by the object is wanting. The shadows previously described f,
* E. Wiedemann, Wied. Ann. x. p, 245, 1880; Phil. Mag. [5] x. p. 419.
+ Phil. Mag. [5] x. p. 236.
sta iat i i a rts
ae,
-
formed in the phosphorescent surfaces excited by the positive
light, and their position indicate similar behaviour. If the
electric rays in the kathode-light proceeded from its exterior
boundary towards the kathode, and in the secondary negative
and positive pencils from the side of the anode towards the
side of the kathode, then, on introducing an object, the pencil
of rays would, on the contrary, remain intact from the exte-
- rior boundary up to the object, and the shadows would appear
upon the wall upon the kathode side of the object.
Another argument for propagation in the direction of the
negative current is found in the phenomenon described above,
that the properties of secondary negative rays are, even for
considerable distances, such as correspond to the conditions
which exist at the negative boundary of the pencil of rays—
that is, the one nearest to the kathode. The pencil, which
with increasing evacuation radiates continually more and more
from the mouth of a narrow tube opening into a wider
vessel, contains rays possessing the properties of the light of
narrow tubes. If the pencil had its origin in the wider
vessel and propagated itself from it into the narrower tube,
we should expect to find its properties more in accordance
with the conditions of discharge offered by wide tubes. The
pencil between a narrow cylinder and a wider one following
upon this upon the side of the anode would show then the
same colour and spectrum as those pencils which have their
origin in the wide cylinder and compose the column of its
positive stratifications.
A further criterion for the direction in which the electric
rays propagate themselves is found in their magnetic behaviour
as described above for the kathode-rays, in accordance with
Hittorf’s conclusions.
It is characteristic of this behaviour that if a (sufficiently
weak) magnet is allowed to act upon the end of a long
kathode-pencil remote from the kathode, only this end is
affected by the magnet, whilst those portions of the pencil
near the kathode retain their form and position unaltered.
Ifthe magnet is brought into the neighbourhood of the kathode
itself so as to act upon the portions of the rays nearest the
kathode, then the whole pencil is deflected together with these
portions even toits furthest point, upon which, in consequence
of its great distance, the magnet could exert no action directly.
The electric particles (or ‘the electric motion) at the end of
the ray remote from the kathode therefore follows the direc-
tion impressed upon the particles at the kathode itself; but
the particles at the kathode are not influenced by action upon
the particles at the further end. Both phenomena agree with
2C 2
Discharge in Rarefied Gases. 379
380 Dr. E. Goldstein on the Electric
the theory that the particles at the outer end of the ray were
previously at the kathode, and are immediately opposed to the
view that the particles nearest to the kathode have already
passed through the place occupied by the remote ends; that is,
the motion in the kathode-light must propagate itself from the
kathode outwards.
Exactly correspondent are the phenomena of the rays of the
secondary negative pencils, and also of the rays of the sepa-
rate positive stratifications, when these are sufficiently expanded
by high exhaustion. Hence the discharge propagates itself
also in each separate stratification from the bounding surface
on the kathode side to the boundary on the side of the anode.
The often-mentioned phenomena of deflection are to be inter-
preted ina similar manner. If K (fig. 3) be the projection
of a plane kathode, K’ that ofa thin wire, quae
s the natural direction of an electric ray
issuing from K, then the ray through K’
takes the form s K’s’; at K’ it bends round
through a considerable angle, and beyond
K’ follows again a straight course, which,
however, deviates considerably from the
direction s K’; 7. e. the portion of the ray
beyond K’ obeys the deviation which was
exerted upon the electrical particles at K’.
Hence the forces which produce motion
between the first point and the kathode. This is very simply
explained by the hypothesis that the electrical motion in the
ray propagates itself from the kathode outwards (in the direc-
tion of the arrow).
ITI.
The velocity and direction of the discharge of a pencil of
electrical rays is to be distinguished, a priori, from the velo-
city and direction with which the tension that precedes the
discharge propagates itself. We are not here further con-
cerned with the velocity of this tension, but only with its
direction. I believe that the phenomena observed indicate
very plainly a propagation of the tension also in the direction
of the negative current; that is, the tensions for the separate
positive stratifications are developed in the same order of time
as that in which they follow each other in space from the
kathode towards the anode. I draw this conclusion from the
fact that the position and peculiarities of the separate com-
pletely formed stratifications, and in particular the position of
Discharge in Rarefied Gases. 381
the heads of the stratifications, 7. e. of the points from which
the separate discharges formed by the stratifications issue, de-
pend altogether upon the positien and peculiarities of the
kathode, and not at all upon the conditions of the anode*.
Let the discharges pass in a cylinder with terminal elec-
trodes which can be moved along the axis of the vessel towards
each other by means of an arrangement which need not at pre-
sent be further described.
If the anode in such a vessel is caused to approach the fixed
kathode, no displacement whatever of the stratifications in
front of the anode is observed; they remain altogether im-
movable and unchanged, so far at least as their continued
existence is consistent with the new position of the anode.
Since the positive light in every case reaches only to the anode,
the layers which were situated in the portion of the tube
* The experiments described in what follows are performed with stra-
tified discharges in pure dry air or in dry highly exhausted hydrogen,
produced from a sufficiently powerful induction-current by regular inter-
ruption of the primary current. Under these conditions we obtain thick
stratifications which do not vibrate to and fro like the so-called “ saucer”
stratifications, but, with a constant pressure of gas, preserve their position
unaltered. I think it necessary to mention this, because to many who are
still accustomed, upon mention of stratifications, to figure to themselves
only the “ saucer ” stratifications and their behaviour, the mention in the
following of motionless stratifications with constant intervals between
them may appear surprising. The thick stratifications, strange to say,
are always treated, sometimes as quasi-pathological developments, as phe-
nomena which are disturbances of the normal phenomena of stratification ;
sometimes as optical illusions, caused by rapid vibration to and fro of the
“saucer” stratifications assumed to exist alone. According to the evi-
dence I have given, the meaning and mutual relation of the different
forms of stratification are tolerably clear; each separate layer in a cylinder
is qualitatively analogous to the discharge at a kathode which occupies
the whole section of the cylinder. When the exhaustion is small this
kathode-light is only a thin layer, corresponding exactly to the thin
“saucer” stratification. If the exhaustion proceeds, the electric rays
which make up either structure lengthen and so increase its thickness;
and just as the kathode-rays finally lengthen so much as to completely
fill the dark space and reach to the first positive layer, so the rays of stra-
tifications extend so much as to completely occupy the dark spaces between
them. As the density of the gas decreases the thickening proceeds further,
the intervals between the heads of the layers continually increasing, and
the rays issuing from the heads continually occupying the increasing
intervals. When the stratifications appear most plainly in a cylinder with
dry air, their thickness is very nearly equal to the diameter of the cylinder,
so that with wide vessels they are of considerable thickness. As little as
a kathode-discharge with extended rays is a monstrosity or disturbi
phenomenon, or consists entirely of a luminous layer vibrating to and fro,
so little can we entertain similar views about the thick layers ; and as the
laws of the kathode-light may be studied most easily in the longest pen-
cils of it which can be obtained, so also it is just the thickest layers which
represent the phenomenon most completely developed, which are in the
first instance best suited for the study of the stratification.
382 Dr. E. Goldstein on the Electric
passed over by the anode in its approach to the kathode dis-
appear one after the other, presenting the appearance of the
layers being gradually absorbed by the anode. If the anode
is caused to move from its original position away from the
kathode, then all the layers originally present remain unaltered,
whilst new layers appear in the space left by the anode, of
which each immediately upon its formation remains completely
indifferent to the further motion of the anode.
Let us now move the kathode, and first let the motion be
an approach to the fixed anode; at once the whole of the
layers present begin to move, and are displaced each in the
same direction and exactly by the same amount as the kathode
itself. (In the distance occupied by the discharge, shortened
by the approach of the poles, there is consequently room only
for fewer layers than before ; each layer disappears as soon as
it is pushed up against the anode by the motion of the kathode.)
If the kathode is removed from any initial position whatever
further away from the anode, all the layers present follow
the kathode, and keep exact time with the motion of the
kathode itself; new layers appear in the space between the
last of the layers originally present and the anode as the
kathode moves further away, and each immediately after its
formation follows the motion of the kathode*. ~~
The interval between every two layers in a cylinder is so
little different in passing from one pair to another, that in a
cylindrical column of stratified light at given density of gas
and intensity of discharge, we may speak simply of the stra-
tification-interval of the column.
The number of layers present is therefore equal to the quo-
tient of the length of the column by the stratification-interval.
If the distance of the electrodes varies continuously, this
quotient will only be a whole number in particular cases. If
the division of the space occupied by the discharge into layers
advanced from the anode, then in the case when the length
of the positive light is not divisible by the stratification-interval
without remainder we should expect that the incomplete
and abbreviated layer corresponding to this remainder would
be found at the negative end of the positive light, whilst at
the anode there would be nothing but complete layers.
Observation shows exactly the contrary: the positive layer
nearest the negative end of the positive light, 7. e. nearest to
the kathode, preserves the same constant extension with every
distance of electrodes; so also the following layers, only the
one directly in contact with the anode shortens or lengthens
* Goldstein, Phil. Mag. [5] iv. p. 362.
F
:
|
Discharge in Rarefied Gases. 383
exactly in proportion as the excess of the above-mentioned
quotient above a whole number changes.
The changes of colour are also strikingly characteristic of
the influence of the kathode, as explained above. The conse-
cutive layers of a column of positive light may show very
striking differences of colour, even when no differences in
form and magnitude can be perceived; these differences are
very marked when hydrogen is employed.
The colour of a layer when the difference of electrodes changes
is always, ceteris paribus, dependent on its position with refer-
ence to the kathode. Suppose, for example, that we observe a
cylinder the positive light of which is divisible into five layers,
the one next the kathode being blue, and the following ones in
order being yellow, red, greyish red, and grey. Next to the
anode we have, therefore, a grey layer. If the distance of the
electrodes is now diminished by the length of one layer, whether
by the motion of the anode or of the kathode, it is the grey
layer which disappears, and we have a greyish-red layer next
the anode followed by the rose-coloured, yellow, and blue layers
in order. If the distance between the electrodes be further
diminished by the length of one layer, the greyish-red layer
disappears, and the rose-coloured layer is in contact with the
anode, followed by the yellow and blue layers in order.
When the poles are caused to approach further so as to leave
only two layers, the yellow layer is next the anode, and the
blue layer tollows it. If, therefore, we count the layers from
the anode, then with every change of distance between elec-
trodes, the first, second, and every layer change colour; but if
we count from the kathode, then the colour of the nth layer is
independent of the distance of the electrodes, and each layer
present possesses always the same colour.
Hence the colour of each layer is regulated by the position
of the kathode, and depends on its position in the series,
counting from the anode.
Lastly, we may vary the size of the anode indefinitely with-
out causing any change in the position of the layers present ;
but if the magnitude of the kathode be changed, the position
of all the positive layers changes. The smaller the kathode
becomes, under conditions otherwise similar, the larger becomes
the interval between the kathode and the first positive layer,
but the interval petween the positive layers is not altered ; so
that each single layer lies further from the kathode the smaller
the kathode is made.
We cannot, however, assume that the kathode, or the phy-
sical conditions which obtain at the kathode determine the
conditions of tension and discharge of the whole stratified
384 Dr. E. Goldstein on the Electric
column; but it appears that the position and properties of each
separate layer depend mainly or entirely upon the position
and properties of the layer preceding it on the side of the
kathode. The influence of the kathode on all the members of
a stratified column, which appears so markedly in the experi-
ments just described, would then be only an indirect one, inas-
much as the properties of the kathode determine the proper-
ties of the kathode-light ; this determines the position and
properties of the first positive layer, this the position and
properties of the second layer, and so on. This conclusion is
drawn from experiments on the secondary negative light.
We saw that in a cylinder where the kathode is moved, all
the layers move in the same direction as the kathode and
through an equal distance. If now we introduce into the
cylindrical tube C (fig. 4), with movable kathode K, a por-
tion of tube R fitting C closely and also movable in it, haying
a narrow opening at «, then, as already explained, « acts as a
secondary negative pole for the portions of the whole discharge
between and the anode A*.
If now, whilst R retains the same position in any portion
of the discharge-cylinder, the kathode K is moved, all the
layers between K and « move as in the previous experiments ;
but the layers between x and A remain immovable, in spite of
the displacement of the kathode.
If, on the other hand, K be fixed and R be displaced, so that
the secondary negative pole «© moves with the secondary nega-
tive light radiating from it, then all the layers between and
A are displaced exactly like the stratifications of a simple
cylinder haying a metallic kathode at z.
If the separate layers of the discharge show different colours,
then we observe further that, when K moves, the colours of
all the layers between K and « behave as previously described
* A may with advantage be made short, and placed somewhat excen-
trically but parallel to the axis of the tube, so that it may not be struck
by the movable piece R.
goueme bae.
Discharge in Rarefied Gases. 385
for the simple cylinder, but the colours of the layers between
z and A show no regular relationship to their position in order
from K; their colours remain the same however their position
in order varies. But if « be moved, the same law holds good
for these layers as if z were a metallic kathode—the colour of
each depending on its position in order from «, and the colour
of every nth layer, counting from 2, remaining the same for
every position of x.
The dependence of the stratifications upon their secondary
negative pole, and the complete analogy with the dependence
upon the metallic kathode, is seen, lastly, also in the influence
of the magnitude of the secondary pole. If its magnitude be
diminished the layers become further apart, as if from a dimi-
nished metallic kathode; and the displacement is in both
cases more marked when the surface of the pole is diminished
in a greater ratio”.
If we have now a tube (fig. 5) provided with
two secondary poles w and y of this kind, of which
only z is movable and y is fixed (the piece RY of
which y is the mouth may be conveniently united
with the wall of the large vessel by fusion when
* The diminution of a secondary negative pole- may
be effected in a variety of ways. Fig. 6 shows in one
diagram three different simple arrangements for effecting
this :—
In eylinder I. a glass diaphragm is arranged perforated
with two round openings of different sizes; a glass ball is
also enclosed in the tube, whose diameter exceeds that of
the largest opening. By allowing the glass ball to rest
upon the one or the other of the two openings, the dis-
charge issues from a larger or smaller secondary pole.
(Of course the opening acts on the side towards the ka-
thode as a secondary positive pole.)
In cylinder II. the opening x of the communicating
glass tube is the secondary negative pole; a glass rod,
provided at one end with a knob to prevent its falling
completely through, is movable to and froin 7». It is
clear that by this means the magnitude of the opening x
may be varied.
Cylinder IiI. shows the simplest arrangement, a glass
tap the perforation of which replaces the communicating
tube. The magnitude of the secondary pole is a maxi-
mum when the tap is completely open. If we gradually
turn the tap from this position, and so gradually reduce
the magnitude of the secondary negative pole, we see
the layers gradually recede from the pole. The adyan- }f
tage of this arrangement is found in the power of gradu-
ally altering the magnitude of the pole ; its disadvantage |j
in the gradual alteration of the quantity of gas contained
in the tube, by the evolution of gases produced by the
action of the discharge on the substance with which the tap is lubricated.
386 On the Electric Discharge in Rarefied Gases.
the apparatus is constructed), w lies between the kathode K and
y. Ifthe kathode K is movable, we observe first that its motions
only affect the stratifications between it and z, but, on the other
hand, all between « and y, as well as those between y and A,
are unaffected. If z is moved, we find that the motion of this
pole causes a motion only of the stratifications between # and
y; the stratifications between y and A remain unmoved. In
the same way, when the magnitude of the negative pole varies,
it is found that only changes in the pole y affect the position
of the stratifications between y and A.
Hence the position of each stratification depends on the
position and properties of the secondary negative pole, or
pencil of secondary negative light nearest to it. But since
each separate positive layer, even in a simple cylinder, is, as I
have shown%, only a form of the secondary negative pencil (the
section of its origin is itself a secondary negative pole), it fol-
lows that the position and properties of each separate layer,
even in a simple cylinder, do not depend so much upon the
kathode and kathode-light as upon the position and properties
of the layer immediately near it. If, then, in a simple cylinder
all the stratifications are put into motion by displacing the
kathode, it follows that the motion of the kathode itself properly
causes only a corresponding change in the position of the
kathode-light which issues from it; the displacement of the
point of origin of this last displaces the surface of origin of
the first positive layer; this change displaces the surface of
tension for the second layer, and so on.
I have mentioned that, in a simple cylinder, the consecutive
intervals between the stratified layers of the positive light
differ very little from each other; but if we observe also the
very stnall differences which present themselves, we find that
the intervals graduaily decrease from the kathode towards the
anode. If the space in which the discharge takes place be
contracted at any point whatever so as to produce a secondary
negative pole, then the intervals diminish only up to this pole;
beyond it the intervals suddenly increase and a new series of
decreasing intervals begins, again increasing beyond a new
secondary pole, and soon. We find, then, that the magni-
tude of each stratification-interval is determined by the ratio
of the secondary negative pencil produced by the change of
section which immediately precedes the interval under consi-
deration.
In passing to infinitely small changes in section when the
secondary negative pencil passes into a positive layer, we find
that the magnitude of the interval between any two layers
* Goldstein, Berl, Monatsber. 1876, p. 280; Phil. Mag. [5] iv. p. 361.
ee
Carbon Dioxide as a Constituent af the Atmosphere. 387
depends on the properties of the layer forming the component
of the pair nearest to the kathode ; or, shortly, each layer, or
the conditions existing at its point of origin, always influence
the layer following next to it, on the side of the anode, but
does not influence the preceding, on the side of the kathode.
The conditions under which the nth layer forms seem to
stand to the properties of the n+1th layer in the relation of
cause and effect ; and hence it seems to me only a verbally
different expression of the observed facts if we assume, as above,
that the propagation of the electrical tensions, or the produc-
tion of the separate layers, takes place in the direction of in-
creasing values of n, 2. e. advances from the kathode towards
the anode.
Berlin, Physical Institute of the University.
XLII. Carbon Dioxide as a Constituent ofthe Atmosphere. By
Hrnest H. Coox, B.Sc. (Lond.), A.R.C.S., Lecturer upon
Chemistry and Physics at the Bristol Mining School*.
(*® all the agents which have brought about geologic
changes and modified the surface of the earth from time
to time, the atmosphere seems to have been the least studied.
Nor is this very surprising when we remember the peculiarity
of its action. So general and cosmopolitan are its effects that
their very abundance causes us to overlook them—and, again,
so slowly acting that the changes effected require the employ-
ment of long periods of time. The two constituents of the
atmosphere which have been most active in producing these
changes are the oxygen and the carbon dioxide. The latter
substance occurs in the air in such a relatively small amount
that we are apt to underrate its influence. But when it is
remembered that, were it not for the presence of this sub-
stance in the air, no coal and very little limestone could have
been formed, we at once see its importance. In fact, to come
somewhat nearer home, without carbon dioxide in air no vege-
table growth could take place ; and without plant life very
little, if any, animal life would occur. Thus this substance,
although in itself inimical to most forms of animal life, is
absolutely necessary in the atmosphere in order that those
animals may exist. In the present paper an attempt is made
to consider some of the results arising from the presence of
this substance.
* Read before the American Association for the Advancement of Science
at Montreal, on August 25, 1882. Communicated by the Author,
388 Mr. E. H. Cook on Carbon Dioxide
Amount of Carbon Dioxide in the Atmosphere.
This question has been made the subject of experiment by
many of our leading chemists. In order to calculate the ab-
solute amount, we require to know two things—viz. the capa-
city or weight of the air, and the percentage of CO, which it
contains. Fortunately the data for doing this have been
determined with very great accuracy. The lengths of the
diameters of the earth have been determined to be very nearly
7899 miles for the polar and 79254 for the equatorial ; “and.
in these measures it is pretty certain that there is not an error
of a quarter of a mile”’*. Applying the ordinary rule for the
cubic content of an oblate spheroid, we obtain 259,026,554,299
cubic miles as the capacity of the earth. Now the height of
the homogeneous atmosphere is found to be 26,214 feett, or
very nearly 5 miles ; calculating the capacity of the spheroid
formed by adding this distance to the lengths of the diameters
given above and subtracting the capacity of the earth, we
obtain the cubic content of the atmosphere supposed homo-
geneous: this is found to be 591,647,337 cubic miles. With
regard to the amount of carbon dioxide present in the air,
the older experimenters, Dumas and Boussingault (Ann. Ch.
Phys. iii. pp. 257, 288), Lowy and Saussure (Pogg. Ann.
xix. p. 891), have published results which yield a mean of
4 vols. in 10,000 of air, or 43 parts in 10,000 by weight.
Thorpe (Journ. Chem. Soc. vol. xx. p. 189) has shown that
over the sea the average is 3 vols. in 10,000 ; while Saussure
states that at high altitudes the proportion of dioxide is greater
than at lower levels. Without deviating very far from the
truth we may take 4 vols. in 10,000 of air; and we thus find
(assuming capacity of air to be 592,000,000 cubic miles)
236,800 cubic miles as the amount of CQ, in the atmosphere.
Finally, calculating from the specific gravity, we find the
weight to be 4287 billions of pounds. Expressed on the
metric system these figures become:—
Cubic capacity of air... 2,439,987,200,000,000,000 kilolitres.
Weight of CO, in air... 1,913,685,903,480,000 kilogrammes.
I have given these calculations somewhat in detail because
of the great difference between my numbers and those hitherto
published. Thus, Dumas and Boussingault (op. cit.) say that the
air is equal in weight to 581,000 cubes of copper each havin
a side of 1 kilometre: this gives 4,200,000,000,000,000,000
kilolitres as the capacity of the air, or very nearly 40 per cent.
* Herschell, ‘ Familiar Lectures,’ p. 53.
t+ Maxwell, ‘Theory of Heat,’ p. 228,
NN EE EEEEeEeEeEEeEeEeEeEEEEE eG eee eS Sa r,l,l ee
as a Constituent of the Atmosphere. 389
too high. Again, Roscoe and Schorlemmer (‘ Chemistry,’
vol. i. p. 449) state that “the amount of CO, in the atmo-
sphere reaches to upwards of 3000 billions of kilogrammes,”
which is about 33 per cent. in excess of the truth*.
Sources whence the Air derives its Carbon Dioxide.
These are mostly natural ; but the progress of civilization
has added a large artificial supply to those already existing.
We may state them as follows:—
(1) Combustion of carbonaceous bodies.
(2) Respiration of animals.
(3) Decomposition of vegetable and animal substances.
(4) Volcanos and other subterranean supplies.
Under the first heading is included the amount produced
by the burning of coal, wood, peat, &c. From the most re-
cently issued statistics with regard to the amount of coal
raised in the world that I have been able to consultTt, I find
that for the last three years at least 280 millions of tons have
been raised annually. This is probably a slight underestimate.
Assuming that 75 per cent. of this consists of pure carbon,
which if completely burnt in air would produce CQ,, and
allowing a further 10 per cent. for the carbon thrown away
with the ash, we leave 182 millions of tons which are annually
converted into carbon dioxide. This will produce 1,800,000
tons per’day, or very nearly 1800 millions of kilogrammes
per day. Assuming that by the combustion of wood, peat,
oil, &c. there is added one third more, we produce a total of
2400 millions of kilogrammes daily.
In the case of the respiration of animals we can only form
an approximate estimate. The population of the world is at
present about 1500 millions; and it has been shown by experi-
ment that each individual produces on an average about a
kilogramme of CO, per day of 24 hours. Thus the human
race, in respiring, add to the air about 1500 millions of kilo-
grammes of carbon dioxide perday. Remembering the large
* The above calculations are made on the figures deduced from the
results of the experimenters cited above. Recent investigations have,
however, thrown some doubt on the correctness of these numbers, the
general opinion being that 4 vols. in 10,000 is much too high. Thus,
Fittbogen and Hasselbarth (Chem. Centr. 1875, p. 694) give 3:4 vols. in
10,000 as the average; Farsky (Chem. Centr. 1877, p. 198) found 3-4,
while more recently Reiset ( Comptes Rendus, lxxxviii. pp. 1007-1011) de-
duces 2:942, Taking the mean of these numbers, we have
Weight of CO, in air .... 1545 billions of ilogrammes nearly.
+ Mineral Statistics for Great Britain for 1881; and Smyth’s ‘Coal
and Coal-Mining,’ latest edition.
‘
390 Mr. E. H. Cook on Carbon Dioxide
amount of animal life existing on the globe, and also that
many of the larger species produce a greater quantity in a
given time, we may with asufficiently near approach to accu-
racy say that from the lower animals the air receives twice as
much daily as from man. Hence from the whole animal
kingdom we derive about 4500 millions of kilogrammes.
The amount of dioxide which the atmosphere receives from
decaying animal and vegetable substances is impossible to esti-
mate. Most of it is produced in regions far away from the
abode of man. That aconsiderable quantity is produced from
this source, however, is evident when we consider the vast
quantity of vegetable matter which year after year falls to the
ground and undergoes decomposition. In fact, if the estimate
of the amount of action exerted by plants given later on in
this paper is a correct one, we must conclude that a much
greater amount of dioxide is produced by this process than
has been hitherto supposed. Although it is evidently impos-
sible to give figures, yet, in order to arrive at a numerical
estimate, we may assume that the same quantity is yielded as
by man, viz. 1500 millions of kilogrammes daily.
The last source whence the air receives its supply of carbon
is from volcanos and the fumaroles and rents in the ground
in volcanic districts. The amount thus supplied is enormous,
both active and extinct voleanos joining in increasing the
quantity. Considering the area occupied by the volcanic dis-
tricts, and the immense quantities of gas which are given off
from the craters and fumaroles, we must readily come to the
conclusion that from this source by far the greater part of the
atmospheric carbon dioxide is derived. In fact Poggendorfft
has calculated that at least ten times as much is derived from
this source as from all others put together. The numbers
given above for the amount yielded by other sources are pro-
bably greater than similar numbers deduced by Poggendorff,
since the amount of coal used and the population have both
increased since his time. Instead, therefore, of taking ten
times, if we take five we shall perhaps approach very near to
the absolute amount given by Poggendorff. This will give
us about 40,000 million kilogrammes daily given to the atmo-
sphere from subterranean sources”.
Taking the whole of these results together, we have that
from all sources there is daily added to the atmosphere the
* Supposing this CO, produced according to the equation
CaCO,=Ca0+CoO,,
we shall have daily decomposed about 90,000 million kilogrammes of
limestone.
OO — ———— =~ eo
r
_ Area of Arctic and Antarctic land . 8,200,000
as a Constituent of the Atmosphere. 391
enormous amount of at least 50,000 millions of kilogrammes
of carbon dioxide. Dividing the absolute amount given above
by this number, we find that the amount of carbon dioxide in
the atmosphere would be double what i 1s at present in about
one hundred years if there were no means of compensation. In
arriving at this estimate no account has been taken of the
amount of oxygen used up in producing the dioxide. This
obviously affects the first three sources only; but by taking it
into account we should reduce the time somewhat; but practi-
cally this correction is so slight that it can be neglected.
Poggendorff made a similar calculation, and gave 386 years as
the period which it would take to double the amount of the
dioxide, supposing there were no compensating influences at
work. The discrepancy in the two numbers is explained,
first, by the absolute amount of CQ, in the air being much
less according to my calculations than that previously sup-
posed, and also by the circumstance that Poggendorff’s esti-
mate of the amount yielded by the combustion of carbonaceous
substances was much less, owing to the defective data at his
command.
Compensating Influences.
Having now arrived at an estimate of the amount of carbon
dioxide daily added to the atmosphere, let us examine the
causes which bring about its decomposition and removal from
the air. The known causes which are at work producing this
change may be considered under three heads, viz.:—
(1) Fixation of carbon by growing plants.
(2) Removal of dioxide by zoophytes.
(3) Absorption of dioxide by inorganic chemical actions.
The first cause here mentioned is one which is essential to
almost all forms of vegetable growth. In estimating its mag-
nitude we are met by the want of reliable experimental data,
making it almost impossible to arrive at any definite conclu-
sion. It is, however, the only one which restores the oxygen
to the atmosphere, in the other two actions the dioxide being
absorbed bodily without being decomposed. Also most, if
not all, the decomposition effected by plants will occur during
the spring and summer, the most active period of plant-growth.
The second and third causes act continuously. Certain expe-
riments have shown that a square metre of leaf will decompose
in sunlight about a litre of CO,. Also Mr. Trelawny Saun-
ders, some years ago, calculated for Sir Charles Lyell the area
of the land-surface of the globe. The figures he gives are* :—
Total area of land . . . + 97,600,000 square miles.
3 7
* Ansted’s ‘ Physical Geography,’ p. xxxviii.
392 Mr. E. H. Cook on Carbon Dioxide
Thus the land-surface bearing vegetation capable of decom-
posing carbon dioxide amounts to 49,400,000 square miles. A
large portion of this land, however, is uncovered by vegeta-
tion: cities are built on it; barren mountains rise out of it;
and large rivers run through it. Hstimating the absolute
area of leaf (7. e. chlorophyll-bearing organs) borne by the
plant-bearing land of the earth as 50 per cent. of the total
area, we find that 24,700,000 square miles of leaf are en-
gaged in purifying the atmosphere. This is equal to about
63,973,000,000,000 square metres, which gives the number of
litres of CO, decomposed per hour. But sunlight only lasts,
on an average, about ten hours a day; consequently the total
amount daily decomposed is equal to ten times this amount.
Finally, allowing 25 per cent. for the diminution of the action
which takes place in winter, we find that the enormous amount
of 479,000 millions of kilolitres, or over 900,000 millions of
kilogrammes of carbon dioxide are decomposed daily. ‘This
amount is much greater than that produced from all sources
taken together. Butit must be remembered that a large por-
tion of the carbon thus withdrawn by plants during the spring
and summer months is returned to the air again by the decom-
position of the leaf in autumn. Although we have allowed for
this above, yet if plant-action is anything like so powerful as
these calculations show, that allowance will have to be consi-
derably increased. Again, a reduction, and perhaps a consi-
derable one, will have to be made on account of the respiration
which has been proved to take place in some plants during
the hours of darkness; but I am unable to find an account of
any experiments upon this point. The magnitude of this
action given by these calculations is astonishing. This paper
was commenced under the idea that the action usually attri-
buted to plants was greatly overestimated, and that their
purifying effect was exaggerated. It will be seen that the
vegetable life on the globe is sufficient of itself to keep up
the purity of the air. ‘The author wishes this statement to be
received with caution, because of the unsatisfactory nature
of the fundamental experiment upon which the calculations
are based, and also of our total want of knowledge of the
amount of plant-respiration. This latter action may be much
greater than is usually supposed.
The second great action going on in nature is effected by
the interposition of animal life. It consists in the removal
from.sea-water of the carbon dioxide held by it in solution by
certain low forms of animal life. The most important of these
are Actinozoa and Foraminifera—the former being concerned
in the building of coral reefs, and the latter in forming those
as a Constituent of the Atmosphere. 393
immense masses of rock-material of which the chalk and
nummulitic limestone may be taken as examples. Certain other
forms of animal life, such as Brachiopoda &c., also add their
influence to that of these lower forms; but their effects, how-
ever, are comparatively insignificant. The immense influence
exerted by these minute creatures is evident when we re-
member the vast masses of limestone entirely of organic origin
occurring in geological formations of all ages. Millions of
tons of limestone formed in this way occur in the solid crust
of the earth; and every ton of limestone contains about nine
hundredweight of dioxide. Nor is this action confined to the
past. It is as active now, in all probability, as when engaged
in building up those immense deposits of white chalk so
abundant in some parts of Hurope. Recent deep-sea sound-
ings haye revealed the fact that Foraminiferal life still flou-
rishes in the depths of the ocean, while the coral-polypes are
still building reefs in the warmer seas. On the other hand,
we must not forget that Darwin has shown that these coral-
polypes can only exist in water of a certain temperature, which
is only;attained in the warmer seas, and at a certain depth below
the surface of this water. Their influence, therefore, is limited
and confined to a comparatively small area of the globe.
Another circumstance which seems to have been overlooked
by most writers upon the subject is, that this dioxide fixed in
the solid state in this way is contained in the water, and not
in the atmosphere. It is generally supposed that all of it has
been derived from the air; but a very large portion must have
been obtained from submarine volcanic eruptions, and never
formed part of the atmosphere at all. Taking all things into
consideration, this cause, although very powerful, seems rather
to be one whose influence is only felt after the lapse of many
years, and, for activity, cannot be equal to the first one.
The third action going on in nature effecting the purification
of the airis a strictly inorganic one. Included under this head
are such processes as the conversion of felspar into kaolin, the
decomposition of such silicates as hornblende, pyroxene, &c.
The large deposits of kaolin and decomposed felspar which are
met with in the earth sufficiently prove the magnitude of this
action. Calculations were made many years ago by Ebelmen
(see the Recewil des Trav. Scient. de M. Ebelmen, Paris, 1855),
and have recently been recalculated and very clearly stated in
an excellent paper by Dr. T. Sterry Hunt, F.R.S.* A glance
at the numbers given in these memoirs will show the vast and
important effect which these processes must have exerted.
* « Chemical and Geological Relations of the Atmosphere,” American
Journal of Science, May 1880,
Phil. Mag. 8. 5. Vol. 14. No. 89. Nov. 1882. 2D
394 Carbon Dioxide as a Constituent of the Atmosphere.
Thus, Dr. Hunt says “ that a weight of carbonic dioxide equal
to more than twenty-one times that of our present atmosphere
would be absorbed in the production from orthoclase of a layer
of kaolin extending over the earth’s surface with a thickness
of 500 metres, an amount which evidently represents but a
small proportion of the results of felspathie decay in the sedi-
mentary strata of the globe.”” Hvidently, then, here we have
a cause which has removed, and is removing, a vast amount of
carbon dioxide from the atmosphere. Any estimate of the
rate of its action is obviously impossible. It must not be for-
gotten, however, that subaerial felspathic decay is a very slow
process, and that therefore the large deposits of decomposed
felspar found in the earth seem to point rather to a compara-
tively slow process acting through an immense number of years
than to a rapid process such as that effected by plants.
General Conclusions.
It is of course evident that, if the compensating influences
are just equal in amount and in rate of action to the producing
ones, the amount of carbon dioxide in the air will remain con-
stant. Unfortunately an insufficiency of reliable data prevents
a definite answer being given to such a question. The fore-
going considerations, however, seem to show that in all pro-
bability the causes at work removing atmospheric dioxide are
more powerful than those producing it. As a consequence,
the atmosphere is being robbed of this constituent, the greater
part of which is becoming fixed in the solid-earth as carbonate
of lime. But this process has already gone on for so long a
time, that there is already fixed in this way an immense quan-
tity of CO, equal to many hundreds of times the amount con-
tained in the existing atmosphere. The question of the source
of this large amount naturally arises; but the answer to be
given must simply be.an admission of our want of knowledge.
The idea that it all at one time formed part of the atmosphere
of the globe has been suggested by Brongniart; and Dr.
Sterry Hunt considers (Joc. cit.) that a universal atmosphere
of the same quality as that of the earth exists, from which the
carbon dioxide now fixed in the earth’s crust has been derived.
There can be no doubt that, unless we accept the latter of
these theories, there must at some antecedent period have been
an atmosphere covering the globe much richer in this gas than
the present one; but whether such an atmosphere would
account for the luxuriant vegetation of the Coal Period is at
present an open question. If Dr. Hunt’s hypothesis be a cor-
rect one, it is interesting to remember that the carbon which
we contain in our bodies may have existed at one time as a |
my | Cot
On the Dimensions of the Magnetie Pole. 395
portion of the body of an inhabitant of the most distant
member of the universe. But whichever way we consider the
subject in the light of the facts which we have stated, it is full
of unusual difficulty, and is singularly devoid of accurate
experimental data.
XLII. On the Dimensions of the Magnetic Pole
in Electrostatic Measure.
To the Editors of the Philosophical Magazine and Journal.
GENTLEMEN,
HAVE had the honour of reading a letter upon the-di-
. mensions of the magnetic pole in electrostatic measure
which Dr. Lodge addresses to you this month. His sugges-
tion seems to me to reconcile the views of Prof. Clausius and
Mr. J. J. Thomson on this subject. A model of the magnetic
system must be made in a substance of the same magnetic
permeability as the medium that is to surround the current-
system, and must be substituted in the place of the magnets,
before any comparison can be effected: The two systems,
current- and magnetic, will then be always equivalent if once
equivalent.
Dr. Lodge treats this as a suggestion; but I think it is
almost susceptible of demonstration. According to Weber’s
law, a current flowing in a closed circuit can be replaced by a
sumple magnetic shell of which the edge coincides with the
eireuit. The shell may be as thin as we please; but its strength
must have a definite value. This law we only know to be true
for air. Consider any equipotential surface of the positive
magnetism on one face of the shell, at a distance from it infi-
nitely smaller than the thickness of the shell. It passes through
the substance of the shell, issuing at the edges, and covers the
positive face. Similarly such an equipotential surface of the
negative magnetism on the other face passes through the
substance without cutting the former surface, and covers the
negative face.
If on each of these surfaces we spread a surface-magnetism
of which the density is the quotient of the magnetic force by Ar,
then for all points outside the pair of surfaces and the shell we
may replace the latter, and therefore its equivalent current-
system, by the magnetic couts upon the equipotential surfaces.
Now consider any diaphragm, 8, completely enclosing these
surfaces and the shell. If instead of air we substitute a me-
dium of magnetic permeability » throughout space outside 8,
a surface-density o is developed upon 8. But the equipoten-
tial surfaces and the coats of magnetism thereon are not
- affected by this development; for they relate only to the en-
2
D2
396 Notices respecting New Books.
closed system. Hence the magnetic and current-systems, if
equivalent in air, are equivalent in a medium which does not
penetrate through any portion of the space occupied by the
magnetic substance. wpe
It is particularly to be noticed that, while in air any two of
the infinite number of magnetic shells equivalent to two closed
currents exercise the same attraction upon one another, this is
no longer true when they are immersed in the medium yp.
Then each pair exercises the same attraction as the two cur-
rents when the corresponding diaphragms S are drawn in the
shape of the magnetic shells.
An experiment made by me in the Cavendish Laboratory
last June confirms, as far as it goes, Dr. Lodge’s view ; but,
fearing to make my letter too long for insertion, I must post-
pone any account of it for the present.
I am, Gentlemen,
Your obedient servant,
October 20, 1882. ie B. SARGANT.
XLIV. Notices respecting New Books.
The Concepts and Theories of Modern Physics. By J. B. Svaxo.
London: Kegan Paul and Trench. 1882,
ope write an adequate criticism of this book would involve writing
a book of equal size. In the present review it is intended to
make clear the standpoint from which the author speaks, and the
general conclusions reached, rather than to enter into a detailed
criticism of these conclusions. The failure to appreciate the posi-
tion from which the author writes has already led to some mis-
understanding and not a little confusion. Itis stated in the preface
that the work is intended “as a contribution not to physics, nor
certainly to metaphysics, but to the theory of cognition.” There is
probably no word which is more quoted and less understood than
the word “metaphysics.” It is used by hardly any two writers in
the same sense; and it is not too much to say that in many cases
it is merely used as a term of abuse without any clear conception
of its meaning. As in the present work this word is constantly
used, and, moreover, as the author’s main purpose is to show that
certain scientific theories are in reality metaphysical, it will be im-
portant to understand precisely the signification which he puts
upon the word. It is abundantly evident from the whole book that
the subject which Mr. Stallo condemns, and rightly condemns, under
the name of metaphysics is that which is far better designated by
ontology ; and in fact he himself frequently uses these terms as
synonymous. The assumption of fictitious entities as causes, the
belief that “ the true nature of things can be discovered only by
divesting them of their relations—that to be truly known they
must be known as they are in themselves in their absolute essence,”
and in fact the whole procedure of ontology, is what is meant by
Notices respecting New Books. 397
“metaphysics.” Against metaphysics in this sense of the term the
author, in common with many other scientific writers, wages un-
ceasing war. Admitting the utter futility of the ontological method,
it is very questionable whether this has not been overdone, whether
this reiteration of abuse against ontology is not mere slaying of the
slain. It is far otherwise if, after a man has clearly understood
what ontology means and has been convinced of the falsity of its
method, he sets himself to see whether these same errors exist in
subjects non-metaphysical, and even in the reasoning of those who
were loudest with their revilmgs. This is action, not profession,
and indeed noble and useful work in the field of criticism. As
Prof. Huxley most truly has said, “ It is the business of criticism,
not only to keep watch over the vagaries of philosophy, but to do
the duty of police in the whole world of thought. Wherever it
espies sophistry or superstition they are to be bidden to stand, nay,
they are to be followed to their very dens and there apprehended and
exterminated, as Othello smothered Desdemona, ‘else she'll betray
more men.’” This in truth is the task which Mr. Stallo has un-
dertaken in the present volume, having chosen the field of science
for his beat.
Besides having critical value, it is stated that the work is “in-
tended as a contribution to the theory of cognition.” Now this
term, which is a translation of the German “ Erkenntniss-Theorie,”
is but seldom used in this country in precisely the same sense which
is here, in common with modern German usage, adopted. In the
present work it is used in a sense very similar, if not identical,
with what I have called the “ New Metaphysic” (Phil. Mag. xiv.
p- 7))—that is to say, in regard to method. The author, as we have
seen, entirely rejects the “old metaphysic,” or ontological method
of inquiry—“ all cognition being founded upon a recognition of
relations ;” and his theory of cognition seeks to discover these rela-
tions. The “thing per se,” the ‘ Ding an sich” or thing-in-itself of
Kant, and ‘“‘the absolute,” as well as the assumption of other fic-
titious entities as the “fountain and origin of all phenomenal
existence,” is distinctly repudiated; and hence these conceptions
form no part of his theory of cognition. From this standpoint the
author proceeds to examine the validity of the reasoning upon
which the mechanical theory and other scientific theories rest. It
may fairly be asked, what are the qualifications of the author for
this by no means easy undertaking? The title-page of the book
affords no information on this point. It will therefore be probably
unknown to most readers of the book in this country that the
author is an American judge of no small reputation, who (I believe
myself to be correct in saying) was formerly a professor of physical
science.
The book itself bears witness to the author’s wide acquaintance
with philosophical and scientific writings. The volume may be
divided into two parts. The first, consisting of eight chapters, is
devoted to a rigid examination of the atomictheory, the kinetic theory
of gases, and the doctrine of the conservation of energy. While ad-
mitting the value of the atomic theoryas a “ working hypothesis,” the
398 Notices respecting New Books.
author attempts to show that, as a scientific explanation of the con-
stitution of matter, it is of little or no value. The kinetic theory of
gases is condemned without reservation, as not even satisfying the
conditions of a scientific theory and as based upon ontological
assumptions. The doctrine of the conservation of energy is con-
sidered to be sound ; and the chapter which is devoted to its exami-
nation shows an intimate acquaintance at least with the history of
the subject. A detailed criticism of the validity of the author’s
conclusions (for there is much to be said against them) would be
impossible within the limits of a review; and therefore this will
not be attempted here; but one or two positive errors and miscon-
ceptions will be noticed. In the first place, it is mcorrect to say
(p. 23) ‘‘that with few exceptions scientific men of the present day
deem the validity of the mechanical explanation of the phenomena
of nature to be, not only unquestionable, but absolute, exclusive,
and final. They believe that this validity is not conditioned, either
by the present state of human intelligence, or by the nature and
extent of the phenomena which present themselves as objects of —
investigation.” The reverse of this is nearer to the truth. A man
of science, in the capacity of a scientific investigator, is logically
compelled to consider no explanation or theory as final, but to be
prepared at any moment to abandon an explanation which should
prove to be insufficient or at variance with facts, im favour of
another which more adequately accounts for them. This is what
all scientific men hold and are bound to hold, as Liebig expressed
it in a passage actually quoted by the author in another part of
the book, ‘‘The secret of all those who make discoveries is that
they regard nothing as impossible.” Throughout the book the
author seems to lose sight of the necessary tentativeness of all scien-
tific theories. Under the head of the Atomic Theory the author
discusses the doctrine of the indestructibility of matter. In Chap-
ter II. he states that the true correlate of motion is not matter, but
mass; and hence this term is used where ordinarily the word matter
is employed ; but when discussing the indestructibility of matter in
Chapter VII. we find that he uses this term,and not indestructibility
of mass, which is really what chemists mean. The current doc-
trine is first stated, ‘‘ That the constancy of mass is attested by the
balance, which shows that neither fusion nor sublimation, neither
generation lior corruption, can add to or detract from the weight
of a body subjected to experiment. When a pound of carbon is
burned, the balance demonstrates the continuing existence of this —
pound in the carbonic acid, which is the product of combustion, and
from which the original weight of carbou may be recovered. To
test the correctness of this interpretation we may be permitted
slightly to vary the method of verifyingit. Instead of burning the car-
bon, let us simply carry it to the summit of a mountain or remove it
to a lower latitude: is its weight still the same? Relatively it is:
it will still balance the original counterpoise. But the absolute
weight is no longer the same. This appears at once if we give
to the balance another form, taking a pendulum instead of a pair
of scales.” What the author means by talking about “ absolute
et
Notices respecting New Books. 399
weight,” when he so rigidly insists “that there is nothing abso-
lute or unconditioned in the world of reality,” is by no means clear,
especially as we find from the context that what he calls “absolute
weight ” is evidently and, indeed, necessarily based upon a relation.
In any sense the expression “absolute weight” is a contradiction
in terms. From this the author argues that “the ordinary state-
ment of the fact is crude and inadequate;” and adds that it is
“further necessary to remember that this weight may be infinitely
reduced, without any diminution in the mass of the body weighed,
by a mere change of its position in reference to the body between
which and the body weighed the relation subsists.” Itis this very
constancy of mass or quantity of matter amid all changes, of ne-
cessity relatively determined, which chemists mean to indicate
by the expression “ indestructibility of matter ;” and the author’s
criticism merely amounts to a quibble about words; he has mis-
taken the letter for the spirit. Of the second half of the volume,
Chapters IX. to XII. are devoted to the theory of Cognition, and
contain an analysis of scientific ultimates, Matter, Force, Time, and
Space—that is, a consideration of how we really know these, to
what realities these words correspond. This being not strictly a
scientific inquiry, although of much interest and importance, the
_results will not be considered here. In Chapters XIII. and XIV.
transcendental geometry receives most severe and lengthy treat-
ment. Lobatschewsky’s non-Euclidean geometry and Riemann’s doc-
trine of the manifoldness of space, which have occupied the attention
of the most eminent mathematicians during recent years, are consi-
dered to be absurd. The same ontological error “‘ which has given
rise to the atomo-mechanical theory in physics, has led to the doc-
trine of pangeometry in mathematics.” Even admitting the author’s
criticism as to the nature of space, it by no means follows that trans-
cendental geometry is not a legitimate department of mathematics.
The Nebular Hypothesis is considered in Chap. XV.as the cosmogony
of the atomo-mechanical theory. The author rejects the hypothesis,
first, because “all speculations respecting the universe as an unli-
mited whole” are fundamentally madmissible; and, secondly, the
hypothesis has proved to be at variance with a number of impor-
tant astronomical facts. The last chapter of the book consists of
a summary and forecast, the author concluding that ‘the atomo-
mechanical theory cannot be the true basis of modern physics,” and
looking to the Conservation of Energy as a basis for the future.
On the whole the book deserves careful consideration from all
physicists ; for although the author has more than once mistaken
the letter for the spirit, which gives some of the criticism a ludi-
crous aspect, and, further, has in many cases attributed to Science
speculative doctrines and opinions held by individual scientific men,
yet there is much acute and careful critical work in the volume.
Certainly Science ought to be the first to welcome and the last to
reject candid criticism of her methods and theories; for, perhaps
even more than other pursuits, Science maintains Magna est veritas
et preevalebit. Wynpuam R, Dunstan,
[ 400 ]
XLV. Intelligence and Miscellaneous Articles.
ON DR. C. W. SIEMENS’S NEW THEORY OF THE SUN.
BY M. FAYE.
[ would appear that this theory has greatly struck our physicists ;
for it had scarcely appeared in London when it was translated
and published in France in various forms, and especially in the last
number of the Annales de Chimie et de Physique. I suppose that
the principal object of this haste was the announcement of fresh
experiments which have been instituted by the author upon the
chemical action of light. It is well known that, under the action
of light and with the intervention of the chlorophyll of plants,
aqueous vapour and carbonic acid are decomposed at ordinary tem-
peratures, and brought back to the combustible form, carbon and
hydrogen variously associated. Dr. Siemens has tried whether the
action of the light of the Sun alone would not produce this decompo-
sition if we submit to it, without any other intermediary, aqueous va-
pour and carbonic-acid gas excessively rarefied, brought for example
to the vacuum of ;,,,;. His experiments, which, in my opinion,
only require a counter-test which it would be easy to institute,
have given perfectly affirmative results. Thus, the burnt gases
having been brought to such a rarefaction that they no longer
ermitted the passage of the induction-spark, a few hours’ exposure
to the light of the Sun sufficed to enable the mixture to allow this
spark to pass with the well-known coloration that it acquires in
hydrocarburetted media *.
Regarding these beautiful experiments as decisive, Dr. Siemens
has been led to inquire whether this phenomenon does not per-
form in the universe a part still more considerable than in yege-
table life. Supposing Space to be filled with analogous gases,
already burnt, the light of the Sun would revivify the combustibles
hydrogen and carbon, which would then be quite ready to furnish
the food of a fresh combustion.
By drawing them to himself and burning them afresh, the Sun
would recuperate a good portion of the enormous heat which one
is grieved to see him radiating in pure loss into celestial space.
Dr. Siemens has thus been led to put forward the following
hypothesis :—Space is filled with burnt gases, aqueous vapour
and carbonic acid, mixed with imert gases, nitrogen &c., pretty
nearly the same as those of our atmosphere, at a pressure of
suzy: These gases are partially converted into combustibles
under the action of the solar light; then, by a mechanism like that
of the fan of a blower, the Sun draws them to himself, burns them,
and sends them back again into space. This immense source of
heat would be continually resuscitated ; the only part of its radia-
tion lost would be that which is not absorbed by the cosmical
medium of a density of 5345.
* A vacuum produced in a bell-glass into which a drop of oil of
turpentine has previously been introduced, for example.
Intelligence and Miscellaneous Articles. 401
It is perfectly true that, for the physicist, air at 5,45) would be
an almost absolute vacuum, so much so indeed that in such a
vacuum the electric spark would no longer pass. But to the
astronomer such a medium would be very dense. When we
speak, in Astronomy, of the resistance of a medium or of the
wether, and when by the aid of the most delicate observations and
the most profound calculations, we seek for traces of this re-
sistance, we have to do with a very different thing.
Without entering upon these discusions, I will remark that the
trajectory of a cannon-ball with a velocity of 500 m. is sufficiently
altered at the end of a few seconds to compel artillerists to take
into account the resistance of the air in their tables.
Tf the air is reduced to 5,5, but the velocity of the projectile
becomes that of the celestial movements, 60 times as much for
example, these palpable effects will become, for a multitude of
celestial projectiles of dimensions comparable to those of our
cannon-balls, twice as great as in our firing-grounds, and this not
merely at the end of a few years or a few centuries, but at the
end of a few seconds.
In the second place, it seems to me that the celebrated English
physicist has somewhat neglected to examine into the quantity of
matter which he adds to the solar system. Under the influence of
attraction this matter would go to unite itself with the preexisting
stars, with the sun especially, and would continually augment their
mass. Nothingis easier than to form an idea of this. A litre of air
containing the required proportion of aqueous vapour weighs at least
1 gr. at the ordinary pressure. Ata pressure of 5>),, this will be
0-0005 gr., and a cubic metre will weigh 0-0005 kilog. This being
settled, if we restrict the solar system to a sphere including all
the planets as far as Neptune, the weight of the excessively rarefied
matter added by the hypothesis would be, in kilogrammes,
4 7 (6400000 x 24000 x 30)? x 0:0005 kilog. *
The actual weight of the Sun is, in kilogrammes,
4 (64000000)? x 5°6 x 324000 T.
The first is 100,000 times as great as the second. It is there-
fore 100,000 times the mass of the Sun that this hypothesis adds to
those of which celestial mechanics has hitherto kept so minute an
account.
It is not very probable that the astronomers will adopt such
hypotheses. No doubt they wouid be pleased to think that Nature
has provided the Sun with resources to make his heat last longer ;
but as his final refrigeration is still, under any circumstances, a
* The first number is the radius of the earth in metres; the second the
distance of our globe from the Sun in terrestrial radii; the third the
distance of Neptune in parts of the distance of the Sun.
+ The first number is the radius of the earth in decimetres; the second
the mean density of our globe referred to that of water ; the third the
mass of the Sun referred to that of the earth.
402 Intelligence and Miscellaneous Articles.
tolerably distant catastrophe, they will console themselves by the
thought that the things of this world, even the most beautiful, do
not appear to be made to last for ever.
As to the fundamental experiments of Dr. Siemens, they will
lose none of their importance in their eyes. The business is
to surprise a secret of living nature, one of the laws of the organic
world ; and their desire will be that Dr. Siemens may pursue the
course in which he has commenced so brilliantly, even though they
cannot hope to have a very bright light thrown by it upon their
own researches.— Comptes Rendus, October 9, 1882, p. 612.
ON THE CONNEXION BETWEEN THE GAS-DENSITY AND STRATUM-
INTERVAL IN GEISSLER TUBES. BY DR. E. GOLDSTEIN.
- Let the total length of a series of immediately consecutive strata
of the positive light, of which the first is that which is next to the
positive end of the tube, divided by the number of strata, be called
the mean interval. The following data respecting this quantity are
abstracted from experiments with dry air, hydrogen, and mixtures
of the two, under such conditions of the discharge that the strata
do not exhibit the to-and-fro vibrating saucer-shapes which escape
any precise measurements, but appear in the so-called nebulous
forms, which can be brought to a considerably greater degree of
stability. In opposition to the generally current view that these
clouds represent degenerations and derangements of the proper
stratification, I have already* called attention to the far greater
probability that they only represent the full development of that
phenomenon. The thick cloudy strata stand in precisely the same
relation to the thin saucer-like strata as a long-rayed tuft light at
the cathode to thin films at first mvesting the cathode, from which,
with diminishing density of the gas, the elongated rays are deve-
loped. In order to form a clear conception, I wished, further, to
be able to presuppose as known that in cylindrical tubes the
stratum-interval increases with increasing width of the tube+, so
that, in tubes filled with air, the intervals between the individual
strata, when the latter are most distinctly formed, are about equal
to the diameter of the tubet.
If, now, we determine, for cylindrical tubes of different widths
inserted in the current-circuit, from an equal number of strata the
mean stratum-interval J, J’, J",... for any two pressures of gas d
and ¢, we obtain constantly
in words :—For cylindrical tubes of different widths, the mean
stratum-interval constantly varies in the same ratio between the
same gas-pressures. Therefore, if, for example, in one of the tubes
* Wied. Ann. xii. p. 272.
+ Monatsb. der Akad, Berlin, 1876, p. 294; Phil. Mag. [5] iy. p. 853.
1 Wied. Ann. xii, p. 272.
Intelligence and Miscellaneous Articles. 403
the stratum-interval has by the rarefaction of the gas been raised
to twice or three times its first-measured value, then in all the
other tubes the intervals have been doubled or trebled.
The tube-diameters in my experiments varied between 2 millim.
and 4 centim. The above-mentioned regularity came out, indepen-
dently of whether the different cylinders formed separate vessels
with two metallic electrodes each, or whether, united into a single
‘tube, they were inserted in a line one behind another in the current.
The law is moreover found to hold good equally whether the
mean interval be taken from a large or a small number of strata,
provided the numbers in the different tubes be equal, although at
the same time the absolute value changes. From this it can be
concluded that each single interval also increases in accordance with
the above-mentioned law.
The value of the mean interval is found with great regularity to
be, in every tube, as much smaller as the number of strata from
which it is derived is greater. Yet the amplitude of the undulation,
multiplied by the greatest number of strata employed, never reaches
the value of the smallest of the single intervals. Consequently,
from the above law it follows that, if in any tube the magnitude of
the mean stratum-interval for a series of gas-densities D,, D,... Dn
is known, and also, for a number of other tubes, each value of the
mean interval that corresponds to any one of those densities, the
number of the strata which these tubes can show at all the densities
from D, to D, can be calculated.
The proportion 7° = a permits us to conclude that the func-
8
tion according to which the mean interval varies with the gas-
density is the same for tubes of different widths. Experiments
for the purpose of ascertaining that function gave the following
result :—
If the rarefactions of the gas increase in a geometrical series, the
stratum-intervals are augmented also, very nearly, in a geometrical
series. But the exponents of the two series are not identical ;
that is, the stratum-intervals are not (as was once maintained by
the other side) inversely proportional to the pressure of the gas.
On the contrary the measurements prove that the intervals increase
much more slowly than the rarefactions—approximately at the rate
of 4 when the rarefaction is 3. I will defer more definite state-
ments until I have determined the exponents with the greatest
possible exactness, for which I am at present experimenting ona
Toepler pump in the form described by von Hagen*.—Monatsbe-
richte der Kon. Akad. der Wissenschafteu zu Berlin, 1881, pp. 876—
878 (separate impression, communicatd by the Author).
ON THE ELASTICITY OF RAREFIED GASES. BY E. H. AMAGAT.
This subject has already been treated by Mendeleef, Kirpitchoff
and Hemilian, by Silgerstrom, and by myself. Those researches
* Wied, Ann. xii. p. 425,
404 Intelligence and Miscellaneous Articles,
having led to different results, I thought it necessary to resume
my experiments, considerably improving my apparatus, especially
in what concerns the measurement of the pressures, which is the
only difficulty peculiar to this investigation. The method employed
having been already described in the Annales de Chimie et de
Physique, t. viii. (1876), 1 shall only dwell on the modification
which the differential barometer has undergone ; it is the essentially
delicate part of the apparatus, all the other parts of which haye
also been considerably improved. This barometer consists of a
single glass tube bifurcating, at about 70 centim. above the level of
the mercury in the cistern, into two wider cylindrical branches, one
of which forms the barometric chamber, and the other is put into
communication with the space filled with the gas the pressure of
which is to be measured. The immediate result of this disposition
is that there is no need to attend to the difference of temperature
between the two mercurial columns, which are here joined into one
at a little distance below the meniscuses. The branches of the
bifurcation are prolonged upwards by stems of very small diameter,
having each a glass cock, and joining again to form a single stem.
The rest of the apparatus is disposed so that the manometer can be
charged in place by the process generally adopted nowadays, which
consists in first exhausting it with a Sprengel pump; this was
worked, moreover, during all the time of the filling, so as to main-
tain the vacuum continually dry by the intervention of a tube
containing phosphoric acid. All suction of air through the slender
point was avoided by covering the surface of the mercury with a
layer of sulphuric acid, which remained in the cistern during all
the experiments. Above the lower single branch was a glass cock,
by closing which the differential barometer could be transformed
into an ordinary truncated barometer, and thus the errors due to
variations of the atmospheric pressure be eliminated—which is
extremely important.
In order to avoid as far as possible the errors due to refraction
and capillarity, the two branches of the manometer, before being
soldered to the single stem, were rounded and polished inside with
the same copper mandrel, so as to be rendered perfectly cylindrical ;
a plane facet was then cut on the exterior, quite parallel to the
generating lines of the interior cylinder. This done, the pieces
were soldered, the necessary precautions being taken to keep the
plane facets rigorously i in the same plane.
These pieces are very difficult to obtain: a Jarge number of them
break or split, either during the rounding, or the soldering, or even
after these operations are finished. The cylinders were smoothed
and cut by M. Lutz; the manometers were afterwards finished by
M. Alvergniat ; that is to say, they were made with all the skill and
perfection that could be wished for.
To eliminate capillarity-errors, an internal diameter of 2 centim.
was given to the cylinders; and they were evidently perfectly
equal: it was easy to verify that the mercury in them was in per-
fect equilibrium under the thread of the cathetometer.
et
. ,
‘ )
Intelligence and Miscellaneous Articles. 405
T shall not dwell upon the precautions which I took with respect
to the illumination of the meniscus (by means of a pencil of elec-
trie light sifted by passing through a column of water coloured with
a little bichromate of potass) in order to be certain of viewing the
upper part of it. Here a cause of error exists which is much more
frequent than is generally thought, especially when the black sil-
houette of the meniscus is projected upon a bright ground.
The measurements were performed with a small cathetometer
of a peculiar construction, on which 5}, millim. could be read off,
and which I had made by M. Benevolo, in my private atelier, spe-
cially for these researches.
In my first investigation I descended only to 6°5 millim. pres-
sure ; this time I have often operated with pressures below 1 mil-
lim. I always arrived at the result that the deviation is of the
order of magnitude of unavoidable errors. Indeed, for initial
pressures of 12 millim. (in round numbers), two series composed of
ae
pv
being sensibly = 2v') the numbers 0-9986 and 1:0020 relative to
air; for the initial pressures comprised between 3 and 4 millim.
the results varied between 0-9999 and 1-0040; and for pressures
near 1 millim. the extremes are 0-999 and 1°015: this divergence
corresponds to an error of 15 millim. in the measurement of the
pressure. All these numbers are means.
In his experiments M. Mendeleef obtained a series of products pv.
This appears a more favourable condition for showing how those
products vary. According to him, they go on decreasing with the
pressure, starting from a certain pressure which would be 6 decim.
for air. In order to preyent any delusion in this respect, it is well
to observe that every sensibly constant cause of error in the esti-
mation of the pressures, taking effect upon smaller and smaller
pressures, and consequently giving a relatively greater and greater
error, will produce the illusion of a regular augmentation or dimi-
nution of the products pv. This is what must result, for example,
from the want of absolute vacuum in the barometric chamber, even
if it be only on account of the effect produced by the mercury
vapour.
In short, a minute examination of the possible errors has shown
me that, even if one could attain in the readings the precision
spoken of by M. Mendeleef (thousandths of a degree, and thou-
sandths of a millimetre), that pressure would be illusory in the
presence of errors proceeding from manifold causes—such as the
refraction- and capillarity-errors (which, even when the precautions
I have indicated are taken, are never absolutely cancelled), the
error due to the compelled imperfection of the barometric chamber
(which, causing all the pressures to appear a little too low, tends to
produce the illusion of a negative deviation), that due to condensa-
tion of gases on the sides of the vessels or even on the mercury,
&e. &e. ;
By admitting an error of one or two hundredths of a millimetre,
numerous fairly concordant results gave for the value of
406 Intelligence and Miscellaneous Articles.
which is no exaggeration, we arrive at divergences of the order of
magnitude of the deviations found; it is therefore impossible to
‘ pronounce a decision upon either the direction or even the existence
of those deviations. All that we can say is that at the lowest pres-
sures at which experiments have been made (1 millim. or even less ;
I have experimented at two tenths of a millimetre) no abrupt
change in the law of the compressibility of gases appears to be pro-
duced ; they still follow Mariotte’s law, with the exception of diver-
gences for which the experiments cannot be responsible. It is
certainly possible that sufficient rarefaction, acting like a great
elevation of temperature, would cause other gases to follow the
law p(vu—a)=c, as takes place for hydrogen; but there is a great
distance from this to the boundary state spoken of by Mendeleef
and Siljerstrém, in which the gases would become infinitely little
compressible—a mere hypothesis, to which the numerical results
of M. Siljerstro6m do not even appear to lead, as M. Petier has
already remarked in the Journal de Physique.
The study of carbonic acid has led me to analogous conclusions.
For hydrogen the deviations found have varied between —0-0010
and 0-0028 for initial pressures between 3 and 6 millim. in round
numbers.— Comptes Rendus de V Académie des Sciences, Aug. 7, 1882,
t. xcv. pp. 281-284.
ON THE INFLUENCE OF TEMPERATURE UPON THE SPECTRA OF
METALLOIDS. BY M. D. VAN MONCKHOVEN.
Kirchhoff and Bunsen have shown that the temperature of the
flame in which a substance is reduced to vapour has no influence
upon thé position of the bright lines of its spectrum. When, for
instance, sodium or lithium is volatilized in the flame of a spirit-
lamp, or in that of the oxyhydrogen blowpipe, the lines remain the
same, but their brilliancy increases with the temperature: most
frequently some new thin lines appear at the elevated temperatures ;
but it never happens that those which have already been emitted
at lower temperatures disappear. If this is always the case as
regards the metallic vapours, it is never so with the lines emitted
by the metalloids*. Pliicker has in fact shown that oxygen, ni-
trogen, sulphur, selenium, &c. give two different spectra which
have no line in common, according as the spectral tubes contain-
ing these substances are heated by the ordinary spark of the elec-
trical machine or by that of a Leyden jar. He admits there-
fore, and with him nearly every physicist, that certain elementary
bodies give, at a high temperature (Leyden jar), a spectrum different
from that given by the same body at a low temperature (ordinary
spark).
PBut numerous and varied experiments have proved that we
can obtain those spectra called those of high temperature at very
* Hydrogen is an exception; but this gas is known to be a true
metal, not only as to its chemical properties, but also as to its physical.
Hydrogen bears, as regards conductivity of heat and electricity, the same
relation to other gases as mercury to the other liquids.
Intelligence and Miscellaneous Articles. 407
low temperatures, and vice versd. Thus, at very feeble pressures
(0-001 metré), with tubes of oxygen or nitrogen and with very
small Leyden jars, we obtain the spectrum which Pliicker attributes
to high temperatures, while the tube is scarcely warm after the ex-
periment has last several minutes, and the brilliancy of the light
emitted by the incandescent gas is very feeble. The same tube,
traversed by the current of a very powerful induction-coil (without
the interposition of a Leyden jar), emits, on the contrary, an ex-
tremely bright light, becomes rapidly hot, and nevertheless gives
the spectrum which Plicker attributes to low temperatures.
But here is a still more decisive experiment. Let us take a tube
in the form of an H with four electrodes, and filled with nitrogen*,
oxygen, or one of those gases (or vapours) which give two spectra.
Through this tube let us pass at the same time the currents of
two inducticn-coils, of which one has a Leyden jar interposed.
We shall observe the two spectra superposed-—the spectrum assigned
to elevated temperatures (Leyden jar), and the spectrum assigned to
low temperatures (ordinary spark).
According to Pliicker’s hypothesis, the gas would have, at the
same physical instant, two different temperatures, which is inad-
missible.
It may perhaps be objected that, the interrupters of the two coils
not working strictly in unison, the perception of the two spectra is
due to the persistence of the images upon the retina. But this is not
the case, as some tubes, especially with oxygen, give forth light for
several tenths of a second after the current has been interrupted.
We attribute the change in the spectra given by these metalloids
to a vibratory state peculiar to their molecules, directly depending
upon the nature of the electricity employed. Thus, a tube of
highly rarefied hydrogen gas, submitted to the action of ordinary
sparks, presents quite a different aspect from the same tube submitted
to the action of the condensed spark.
Highly rarefied gases, traversed by the continuous current of the
battery, or by a current interrupted by sparks (induction-coil), pre-
sent a dynamical state well known under the name of stratification.
But this stratification differs entirely, according as we employ the
ordinary spark, the condensed spark, or the continuous current of
a battery of very high tension.
’ We shall see in further communications that with each different
behaviour of an incandescent gas (alteration in the stratification,
colour of the light emitted, &c.) there is always a corresponding
modification, and often an entire change, in its spectral lmes—an
effect assuredly independent of the temperature.— Comptes Rendus,
Sept. 18, 1882.
ON A THERMOSCOPIC METHOD FOR THE DETERMINATION OF
THE OHM. BY G. LIPPMANN.
It will be remembered-that Mr. Joulef employed a calorimetric
* Nitrogen in the electric are gives a different spectrum from that given
by Geissler’s tubes or the spark in air.
+ Reports of the Committee &c., pp. 175-190 (London, 1873).
rr”
’
408 Intelligence and Miscellaneous Artieles.
method for the determination of the ohm. The method which Iam
about to describe differs from that of the eminent physicist in not
requiring the quantities of heat to be measured or the mechanical
equivalent of heat E to be known. This last point is not unim-
portant ; for in Joule’s calorimetric method the final approximation
is limited by the uncertainty at present existing respecting the
exact value of the number E; that is to say, the possible error is
near ;1,.
The wire of which I wish to know the resistance is placed in the
middle of a vessel arranged as a calorimeter in the centre of an en-
closure with a constant temperature. An electric current is passed
into the wire, and its intensity 7 measured. I wait until, m con-
sequence of the heat liberated by the current, the vessel attains a
stationary temperature; I leisurely ascertain that it is so by em-
ploying a thermometer, or, rather, a sensitive thermoscope, placed
inside the vessel. This done, I interrupt the current, and then set
in action a motor which produces friction in the midst of the vessel
that already contains the wire. The heat evolved by the friction is
substituted for that just before evolved by the current. I manage
so that the stationary temperature resumes its former value ; I then
have r?=T, T being the work expended, whence the value of r.
It is scarcely necessary to add that the friction-apparatus must
remain in the vessel which contains it, even when it is not in ope-
ration, and be furnished with the known arrangements for measu-
ring T. It is also more convenient to commence by the friction-
experiment, and afterwards to regulate the intensity 7 so as to
recover the same stationary temperature. Lastly, it may be advan-
tageous, for apparatus of large capacity, to replace the observation
of the stationary temperature by that of the velocity of the heating.
In the form given to it by Joule in 1867, the calorimetric
method of the English physicist rests equally upon the measure-
ment of 7 and the measurement of a mechanical work, namely the
work done at the time of the determination of E. Moreover, it
involves two calorimetric measurements, which are to be mutually
eliminated from the final result—namely, the calorimetric measure-
ment which accompanies the determination of E, and that which
accompanies the passage of the electric current. These imterme-
diate determinations bring in their causes of error and their cor-
rections, owing to the imperfections of the calorimeters employed
in making them. I dispense with them by taking care to expend
the work T and the electric energy 777 in one and the same calo-
riscopic vessel. It becomes as needless to ascertain the quantity
of heat evolved in that vessel as to ascertain the weight of the
tare in a double weighing ; and the advantage obtained appears
analogous to that which there would be in replacing two successive
single weighings, made with different balances and different weights,
by a Borda’s double weighing.— Comptes Rendus de ? Académie des
Sciences, Oct. 9, 1882, t. xcv. pp. 634, 635.
THE
LONDON, EDINBURGH, anv DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIKS.]
DECEMBER 1882.
XLVI. On Variations in the Vertical due to Elasticity of the
Earth's Surface. By G. H. Darwin, F.R.S., formerly
Fellow of Trinity College, Cambridge*.
1. On the Mechanical Effects of Barometric Pressure on the
Earth’s Surface.
| ig remarks of Signore de Rossi, on the observed con-
nexion between barometric storms and the disturbance
of the vertical, have led me to make the following investiga-
tion of the mechanical effects which are caused by variations
of pressure acting on an elastic surface. The results seem to
show that the direct measurement of the lunar disturbance of
gravity must for ever remain impossible.
The practical question is to estimate the amount of distor-
tion to which the upper strata of the earth’s mass are sub-
jected, when a wave of barometric depression or elevation
passes over the surface. The solution of the following problem
should give us such an estimate.
Let an elastic solid be infinite in one direction, and be
bounded in the other direction by an infinite plane. Let the
surface of the plane be everywhere acted on by normal pres-
sures and tractions, which are expressible as a simple harmonic
function of distances measured in some fixed direction along
* Appendix to the Second Report of the Committee of the British
Association on the Lunar Disturbance of Gravity. Read at the Meeting
at Southampton, August 1882. Communicated by the Author.
Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 24h
410 Mr.G. H. Darwin on Variations wn the Vertical
the plane. It is required to find the form assumed by the
surface, and generally the condition of internal strain. :
This is clearly equivalent to the problem of finding the dis-
tortion of the earth’s surface produced by parallel undulations
of barometric elevation and depression. It is but a slight
objection to the correctness of a rough estimate of the kind
required, that barometric disturbances do not actually occur
in parallel bands, but rather in circles. And when we con-
sider the magnitude of actual terrestrial storms, it is obvious
that the curvature of the earth’s surface may be safely neg-
lected.
This problem is mathematically identical with that of finding
the state of stress produced in the earth by the weight of a
series of parallel mountains. ‘The solution of this problem has
recently been published in a paper by me in the ‘ Philosophical
Transactions’ (part ii. 1882, pp. 187-230); and the solution
there found may be adapted to the present case in a few
lines.
The problem only involves two dimensions. If the origin
be taken in the mean horizontal surface, which equally divides
the mountains and valleys, and if the axis of z be horizontal
and perpendicular to the mountain-chains, and if the axis of «
be drawn vertically downwards, then the equation to the
mountains and valleys is supposed to be
z
z= —hcos 3?
so that the wave-length from crest to crest of the mountain-
ranges is 27b.
The solution may easily be found from the analysis of sec-
tion 7 of the paper referred to. It is as follows:—
Let a, y be the displacements at the point «, < vertically
downwards and horizontally (a has here the opposite sign to
the « of (44)). Let w be the density of the rocks of which the
i are composed, g gravity, v modulus of rigidity ;
then
1 dW
== |e -W], ]
i. dW
Y= 5,be—s - 2
where a “Ss z
W= —guhe ? Coss J
From these we have at once
1
due to Elasticity of the Earth's Surface. 411
a= io + sea cos = |
2u b |
y= gemal sine, ( a EA
de _—gwh *) a ee
=~ (14 5) sing. J
The first of these gives the vertical displacement, the second
the horizontal, and the third the inclination to the horizon of
strata primitively plane.
Atthe surface,
Z— 7 Coss, y=0,
da gwh . z Ae ERO BRNO)
dz. 29° b
Hence the maximum vertical displacement of the surface is
+gwhb/2v, and-the maximum inclination of the surface to
the horizon is
+ cosec 1” x gwh/2vu seconds of arc.
Before proceeding further, I shall prove a very remarkable
relation between the slope of the surface of an elastic horizontal
plane and the deflection of the plumb-line caused by the direct
attraction of the weight producing that slope. This relation
was pointed out to me by Sir William Thomson, when I told
him of the investigation on which I was engaged; but I am
alone responsible for the proof as here given. He writes that
he finds that it is not confined simply to the case where the
solid is incompressible; but in this paper it will only be proved
for that case.
Let there be positive and negative matter distributed over
the horizontal plane according to the law whcos(z/b): this
* It is easy to verify that these values of 2 and y, together with the
yalue p=guwh e—/* cosz/b for the hydrostatic pressure, satisfy all the con-
ditions of the problem, by giving normal pressure gwhcosz/6 at the free
surface of the infinite plane, and satisfying the equations of internal equi-
librium throughout the solid. I take this opportunity of remarking that
the paper from which this investigation is taken contains an error, inas-
much as the hydrostatic pressure is erroneously determined in section 1.
The term —W should be added to the pressure as determined in (3).
This adds W to the normal stresses P,Q, R throughout the paper, but
leaves the difference of stresses (which was the thing to be determined)
unaffected. If the reader should compare the stresses as determined from
the values of «, y in the text above, and from the value of p given in this
note, with (38) of the paper referred to, he is warned to remember the
missing term W:
2H 2
412 Mr. G. H. Darwin on Variations in the Vertical
forms, in fact, harmonic mountains and valleys on the infinite
plane. We require to find the potential and attraction of such
a distribution of matter.
Now the potential of an infinite straight line, of line-density
p, at a point distant d from it, is well known to be —2yp log d,
where wp is the attraction between unit masses at unit distance
apart. Hence the potential V of the supposed distribution of
matter at the point 2, z Ai given by
V=—2uwh (~* cos? Plog VW {2 + (€—z)dé
= —pwhb { [sin : log {27+ (€— 23] avi aia ee dt
It is not hard to show that the first term vanishes when taken
between the limits.
Now put t= -— = * so that sin? = sin . coss + cos sings
and we have
eat “(sine cos> + cos — tf in’ a
b 6 b/14#
But it is known* that
** ¢ sin ct dt ae eee
ie ee 3 bd 142 i=
Therefore V =2arpwhbe-*" cos :
If g be gravity, a earth’s radius, and 6 earth’s mean density,
3g
2p =
A d 2a6
dqwh z
= a be" Coss. . « » « « (A)
The deflection of the plumb-line at any point on the surface
denoted by «=0, and z, is clearly dV /gdz, when e=0. There-
fore
i ds Sowhis ae
the deflection rig x 5 a5 0; -: nn
But from (2) the slope (ora &, when 2 is zero) is
* See Todhunter’s ‘ Integ. Cale.’ ; chapter on “ Definite Integrals.”
pif ie
due to Elasticity of the Earth’s Surface. 413
Therefore deflection bears to slope the same ratio as v/g to
4a0. This ratio is independent of the wave-length 27b of the
undulating surface, of the position of the origin, and of the
azimuth in the plane of the line normal to the ridges and val-
leys. Therefore the proposition is true of any combination
whatever of harmonic undulations ; and as any inequality may
be built up of harmonic undulations, it is generally true of
inequalities of any shape whatever.
Now a=6:37 x 10° centim., 8=52; and 4ad=12°03 x 10°
grammes per square centimetre. The rigidity of glass in
gravitation-units ranges from 1°5 x 10° to 2°-4x 10%. There-
fore the slope of a very thick slab of the rigidity of glass, due
to a weight placed on its surface, ranges from 8 to 5 times as
much as the deflection of the plumb-line due to the attraction
of that weight. Hven with rigidity as great as steel (viz.
about 8 x 10*), the slope is 14 times as great as the deflection.
A practical conclusion from this is that, in observations
with an artificial horizon, the disturbance due to the weight
of the observer’s body is very far greater than that due to the
attraction of his mass. ‘This is in perfect accordance with the
observations made by my brother and me with our pendulum
in 1881, when we concluded that the warping of the soil by
our weight when standing in the observing-room was a very
serious disturbance, whilst we were unable to assert positively
that the attraction of weights: placed near the pendulum was
perceptible. It also gives emphasis to the criticism we have
made on M. Plantamour’s observations—namely, that he does
not appear to take special precautions against the disturbance
due to the weight of the observer’s body.
We must now consider the probable numerical values of the
quantities involved in the barometric problem, and the mode
of transition from the problem of the mountains to that of
barometric inequalities.
The modulus of rigidity in gravitation-units (say grammes
weight per square centimetre) is v/g. In the problem of the
mountains, wh is the mass of a column of rock of one square
centimetre in section and of length equal to the height of the
crests of the mountains above the mean horizontal plane. In
the barometric problem, wh must be taken as the mass of a
column of mercury of a square centimetre in section and equal
in height to a half of the maximum range of the barometer.
This maximum range is, I believe, nearly two inches, or, let
us say, 9 centim.
The specific gravity of mercury is 13°6; and therefore
wh=34 grammes.
The rigidity of glass is from 150 to 240 million grammes
414 Mr. G.H. Darwin on Variations in the Vertical
per square centimetre, that of copper 540, and of steel 843
millions.
I will take v/g=3 x 10°; so that the superficial layers of
the earth are assuined to be more rigid than the most rigid
glass. It will be easy to adjust the results afterwards to any
other assumed rigidity.
With these data we have
fe iO ald
Gy a Ee
also 648,000 5:67
7 ~ 10
It seems not unreasonable to suppose that 1500 miles
(24x 10* centim.) is the distance from the place where the
barometer is high (the centre of the anti-cyclone) to that
where it is low (the centre of the cyclone). Accordingly the
wave-length of the barometric undulation is 4°8 x 10* centim.,
and b=4°8 x 10°+6-28 centim., or, say, b=*8 x 10* centim.
Thus, with these data,
ie
2v
We thus see that the ground is 9 centim. higher under the
barometric depression than under the elevation.
If the sea had time to attain its equilibrium slope, it would
stand 5 x 13:6, or 68 centim. lower under the high pressure
than under the low. Butas the land is itself depressed 9 cen-
tim., the sea would apparently only be depressed 59 centim.
under the high barometer.
It is probable that, in reality, the larger barometric inequa-
lities do not linger quite long enough over particular areas to
permit the sea to attain everywhere its due slope, and therefore
the full difference of water-level can only be attained occa-
sionally.
On the other hand, the elastic compression of the ground
must take place without any sensible delay. Thus it seems
probable that the elastic compression of the ground must exer-
cise a very sensible effect in modifying the apparent depres-
sion or elevation of the sea under high and low barometer.
It does not appear absolutely chimerical that at some future
time, when both tidal and barometric observations have attained
to great accuracy, an estimate might thus be made of the
average modulus of rigidity of the upper 500 miles of the
earth’s mass.
Kyen in the present condition of barometric and tidal infor-
=00117.
b=4°5 centim.
due to Elasticity of the Earth’s Surface. 415
mation, it might be interesting to make a comparison between
the computed height of tide and the observed height, in con-
nexion with the distribution of barometric pressure. It is
probable that India would be the best field for such an attempt,
because the knowledge of Indian tides is more complete than
that for any other part of the world. On the other hand, we
shall see in the following section that tidal observations on
coast-lines of continents are liable to disturbance, so that an
oceanic island would be a more favourable site.
Tt has already been shown that the maximum apparent
deflection of the plumb-line, consequent on the elastic com-
pression of the earth, amounts to 00117; and this is aug-
mented to 0’:0146, when we include the true deflection due
to the attraction of the air. It is worthy of remark that this
result is independent of the wave-length of the barometric
inequality, and thus we get rid of one of the conjectural data.
Thus, if we consider the two cases of high pressure to right
and low to left, and of low pressure to right and high to left,
we see that there will be a difference in the position of the
plumb-line relatively to the earth’s surface of 0/0292. Hvyen
if the rigidity of the upper strata of the earth were as great
as that of steel, there would still be a change of 0-011.
A deflection of magnitude such as 0/03 or 0-01 would
have been easily observable with our instrument of last year ;
for we concluded that a change of 51, of a second could be
detected when the change occurred rapidly.
It was stated in our previous Report that at Cambridge the
ealeulated amplitude of oscillation of the plumb-line due
directly to lunar disturbance of gravity amounts to 0/0216.
Now, as this is less than the amplitude due jointly to elastic
compression and attraction, with the assumed rigidity (3800
millions) of the earth’s strata, and only twice the result if the
rigidity be as great as that of steel, it follows almost certainly
that from this cause alone the measurement of the lunar dis-
turbance of gravity mnst be impossible with any instrument
on the earth’s surface.
Moreover the removal of the instrument to the bottom of
the deepest known mine would scarcely sensibly affect the
result, because the flexure of the strata at a depth so small,
compared with the wave-length of barometric inequalities, is
scarcely different from the flexure of the surface.
The diurnal and periodic oscillations of the vertical observed
by us were many times as great as those which have just been
computed; and therefore it must not be supposed that more
than a fraction, say perhaps a tenth, of those oscillations was
due to elastic compression of the earth.
416 Mr. G. H. Darwin on Variations in the Vertical
The Italian observers could scarcely with their instruments
detect deflections amounting to +4, of a second; so that the
observed connexion between barometric oscillation and seismic
disturbance must be of a different kind.
It is not surprising that in a volcanic region the equaliza-
tion of pressure, between imprisoned fluids and the external
atmosphere, should lead to earthquakes.
If there is any place on the earth’s surface free from seismic
forces, it might be possible (if the effect of tides as computed
in the following section could be eliminated) with some such
instrument as ours, placed in a deep mine, to detect the exist-
ence of barometric disturbance many hundreds of miles away.
It would of course for this purpose be necessary to note the
positions of the sun and moon at the times of observation, and
to allow for their attraction.
2. On the Disturbance of the Vertical near the Coasts of
Continents due to the Rise and Fall of the Tide.
Consider the following problem:—
On an infinite horizontal plane, which bounds in one direc-
tion an infinite incompressible elastic solid, let there be drawn
a series of parallel straight lines, distance J apart. Let one of
these be the axis of y, let the axis of z be drawn in the plane,
perpendicular to the parallel lines, and let the axis of z be
drawn vertically downwards through the solid.
At every point of the surface of the solid, from z=0 to J,
let a normal pressure gwh(1—2z/l) be applied; and from
z=( to —/ let the surface be free from forces. Let the same
distribution of force be repeated over all the pairs of strips
into which the surface is divided by the system of parallel
straight lines. It is required to determine the strains caused
by these forces.
Taking the average over the whole surface, there is neither
pressure nor traction, since the total traction on the half-strips
subject to traction is equal to the total pressure on the half-
strips subject to pressure.
The following is the analogy of this system with that which
we wish to discuss: the strips subject to no pressure are the
continents, the alternate ones are the oceans, g is gravity,
w the density of water, and / the height of tide above mean
water on the coast-line.
We require to find the slope of the surface at every point,
and the vertical displacement.
It is now necessary to bring this problem within the range
of the results used in the last section. In the first place, it is
convenient to consider the pressures and tractions as caused by
due to Elasticity of the Earth’s Surface. A17
mountains and valleys whose outline is given byz= —h(1—2z2/l)
from z=0 to /, and z=0 from z=0 to —/. To utilize the
analysis of the last section, it is necessary that the mountains
and valleys should present a simple-harmonic outline. Hence
the discontinuous function must be expanded by Fourier’s
method. Known results of that method render it unnecessary
to have recourse to the theorem itself. It is known that
+47—30= sin0+4 sin 20+4 sin 30+...
—t0=— sin 6+4sin 20—4 sin36+...
pea 1 1
37 + 0=— 4 cos@+ 55c0s 30+ =c0s 50+... ¢;
7 3° dD
the upper sign being taken for values of @ between the infi-
nitely small positive and +77, and the lower for values between
the infinitely small negative and —7.
Adding these three series together, we have
2{4sin20+4sin40+..} +24 cos @-+ 500s 30+ 200s 5O+.. \
equal to 7—20 from 6=0 to +7, and equal to zero from
@=0 to —7. Hence the required expansion of the disconti-
nuous function is
— = ty sin204+3sin40+...},
Ah 1 1 f a
—— cos 8+ 3300s 36+ <=cos50+... by |
where Te
Deepest ce? ols ty ZN
for it vanishes from z= —/ to 0, and is equal to —h(1—22/l)
from z=0 to +/.
Now, looking back to the analysis of the preceding section,
we see that, if the equation to the mountains and valleys had
been x= —/sin (z/b), « would have had the same form as in
(2), but of course with sine for cosine, and y would have
changed its sign and a cosine would have stood for the sine.
Applying then the solution (2) to each term of our expansion
separately, and only writing down the solution for the surface
at which z=0, we have at once that y=0, and
ax Uh TY 5 8in20 +7 sin 46+ asin 66+... },
Tt 2 4 6 (8)
+o =| cos 8+ $008 30+ 300s 50+...
TU 1
418 Mr. G. H. Darwin on Variations in the Vertical
. da «wda,
The slope of the surface is ET de thus
be mp Lz C08 28+ ¢ 608 46 + § cos BO +... .F |
gwh 2 1 bi | MR
— 22h 2 f in 6+ sin 30+ pysin 56+... }.|
The formule (8) and (9) are the required expressions for
the vertical depression of the surface and for the slope. _
It is interesting to determine the form of surface denoted
by these equations. Let us suppose, then, that the units are
so chosen that gwhl/m?v may be equal to one. Then (8)
and (9) become
= pain 20+ 4 sin40+...+24 5080+ 7008 30+... \ (
1A =400820+4c0s40+...—=4 Asin + psin 30+... }. 11)
When @ is zero or +77, da/d@ becomes infinite, which de-
notes that the tangent to the warped horizontal surface is
vertical at these points. The verticality of these tangents
will have no place in reality, because actual shores shelve, and
there is not a vertical wall of water when the tide rises, as is
supposed to be the case in the ideal problem. We shall, how-
ever, see that in practical numerical application, the strip of
sea-shore along which the solution shows a slope of more than
1” is only a small fraction of a millimetre. Thus this depar-
ture from reality is of no importance whatever.
When 6=0 or +7,
ee Ae da ee CS 2
a= ={ ptratpat-- } = 1-052 ="670, (12)
being + when 6=0, and — when 0=+7.
When 0= +47, « vanishes; and therefore midway in the
ocean and on the land there are nodal lines, which always
remain in the undisturbed surface, when the tide rises and
falls. At these nodal lines, defined by 0= +37,
da__ 4) ax 24 Sata }
Wis 7102 coh ig 38 ie
= — 3466 + °6168= —:9634 and +°2702.
Thus the slope is greater at mid-ocean than at mid-land.
By assuming @ successively as $7, 4a, 47, and summing
arithmetically the strange series which arise, we can, on pay-
due to Elasticity of the Earth’s Surface. 419
ing attention to the manner in which the signs of the series
occur, obtain the values of « corresponding to 0, +47, +147,
tem, +é7, +$7, +37, +82. The resulting values,
together with the slopes as obtained above, are amply suffi-
ient for drawing a figure, as shown annexed.
LOW TIDE.
HIGH TIDE,
LAND. SEA. LAND
SEA.
-~ LOW TIDE
SOOT TNE Te a aS aE I
The straight line is a section of the undisturbed level, the
shaded part being land, and the dotted sea. The curve shows
the distortion, when warped by high and low tide as indicated.
The scale of the figure is a quarter of an inch to }7 for the
abscissas, and a quarter of an inch to unity for the ordinates ;
it is of course an enormous exaggeration of the flexure actu-
ally possibly due to tides.
It is interesting to note that the land-regions remain very
nearly flat, rotating about the nodal line, but with slight cur-
vature near the coasts. It is this curvature, scarcely percep-
tible in the figure, which is of most interest for practical
application.
The series (8) and (9) are not convenient for practical cal-
culation in the neighbourhood of the coast, and they must be
reduced to other forms. It is easy, by writing the cosines in
their exponential form, to show that
cos 0+ 4c0s 20+4 0s 30+...=—log,(+2sin}0), . (13)
cos 0—£ cos 20+4.c0830—...= log.(2cos30), . . (14)
where the upper sign in (13) is to be taken for positive values
of 6 and the lower for negative.
For the small values of @ with which alone we are at present
concerned, the series (13) becomes — log, (+@) and the lower
loo; 2!
“ee half the difference and half the sum of the two
series, we have
Lcos20+icos40+..... =—tlog(+0@)—4log2, . (15)
cos 0+4 cos 30+4c0s50+ =—tlog(+0)+4log2. . (16)
Integrating (16) with regard to 0, and observing that the
420 Mr. G. H. Darwin on Variations in the Vertical
constant introduced on integration is zero, we have
sin 0+ Les 30+ Emnba: ...= —40[log( +0)—1] + d6log2.
2 La
Then, from (15) and (17),
1 cos 20-+4.00840+.. =f mee pein 30+...)
20 oe
T Tove
=—3(1- log (+0)—3(1 + = log 2—
Integrating (15), and observing that the constant is zero,
we have
& sin 20+ asin 46+...=—46[log( +0)—1] —40 log2. (19)
Integrating (17) , and putting in the proper constant to ~
make the left side vanish when 6=0, we have
1 1 1
ata B +.1.— (F005 0+ 5.008 30+...)
= —1@ log (+0)+i0 ($4 log2). . . (20)
For purposes of practical calculation, @ may be taken as so
small that the right-hand side of (18) reduces to —}log (+28),
and the right-hand sides of (19) and (20) to zero.
Hence, by (8) and (9), we have in the neighbourhood of
the coast,
_oek ANT)
AB Tet gaat ea |
wh tt
= x — x 21087, f » + (21)
da __—gwh Qarz |
re =>—_ ones log. 10 logyo T. J
I shall now proceed to compute from the formule (21) the
depression of the surface and the slope, corresponding to such
numerical data as seem most appropriate to the terrestrial
oceans and continents.
Considering that the tides are undoubtedly augmented by
kinetic action, we shall be within the mark in taking h as
the semi-range of equilibrium tide. At the equator the lunar
tide has a range of about 53 centim., and the solar tide is very
nearly half as much. Therefore at spring-tides we may take
h=40 centim. It must be noticed that the highness of the
tides (say 15 or 20 feet) near the coast is due to the shallow-
ing of the water, and it would not be just to take such values
due to Elasticity of the Earth's Surface. 421
as representing the tides over large areas ; w, the density of
the water, is of course unity.
If we suppose it is the Atlantic Ocean and the shores
of Hurope with Africa, and of North and South America,
which are under consideration, it is not unreasonable to take
Las 3900 miles, or 6°28 x 10° centim. Then 27z/l=z~x 10-8.
Taking v/g as 3 x 10° (that is to say, assuming a rigidity
greater than that of glass), we have for the slope in seconds of
are, at a distance z from the sea-shore,
40
Orx3x 108 x log. 10x (8— logyo z)
=07-01008 (8—logyz). . . . (22)
cosec 1’ x
From this the following table may be computed by simple
multiplication :—
Distance from
mean water-mark. Slope.
1 centim. =—elcenhin. eae 6260-0806
iS Aen a= 0): Sapa Maran parr ss 07 (05
Oe, == LMC. ot tty SOOUD
103°, = lOmetres. 25 4 6 o5 2.0504
HOE = OOP RO sare & stk OAMS
LO? ;, ae su kiloms she slat oe OS02
HOP, Se (hes 8 ee a at es Oa
PeaeOccentms— 20.0) 8k. OLTO
em ete DO A OLS
10’ centim. SS UD ea Me? ata el eames O80!
On considering the formula (22), it appears that z must be
a very small fraction of a millimetre before the slope becomes
even as great as 1’. This proves that the rounded nick in the
surface, which arises from the discontinuity of pressure at our
ideal mean water-mark, is excessively small; and the vertical
displacement of the surface is sensibly the same, when mea-
sured in centimetres, on each side of the nick, in accordance
with the first of (21).
The result (5) of section 1 shows that, with rigidity 3 x 108,
the true deflection of plumb-line due to attraction of the
water is a quarter of the slope. Hence an observer in a gra-
vitational observatory at distance z from mean water-mark,
would note deflections from the mean position of the vertical
13 times as great as those computed above ; and as high
water changes to low, there would be oscillations of the ver-
tical 24 times as great. We thus get the practical results in
the following table:—
422 Mr. G. H. Darwin on Variations in the Vertical q -
Distance of Amplitude of
observatory from apparent oscillation
mean water-mark. of the vertical.
10 metres’... 2 US. Oras
100) a0 3. 1 ea eo
Vkilom. isin 4S ee
10: ,, (5% 01,5 se) OP
90: of) wlezalon, Gea an
50. pe ajodaetes, gin eae”
100° "ee
It follows, from the calculations made for tracing the curve,
that halfway across the continent (that is to say, 3142 kilo-
metres from either coast) the slope is
648,000 gwh
vis TU
x ‘2708 second of are =0:00237,
and the range of apparent oscillation is 0/006.
In these calculations the width of the sea is taken as 6283
kilometres. If the sea be narrower, then, to obtain the same
deflections of the plumb-line, the observatory must be moved
nearer the sea in the same proportion as the sea is narrowed.
If, for example, the sea were 3142 kilometres wide, then
at 10 kilometres from the coast the apparent amplitude of
deflection would be 0-042. If the range of tide is greater than
that here assumed (viz. 80 centim.), the results must be aug-
mented in the same proportion. And, lastly, if the rigidity
of the rock be greater or less than the assumed value (viz.
3x 10°), the part of the apparent deflection depending on
slope must be diminished or increased in the inverse propor-
tion to the change in rigidity.
I think there can be little doubt that in narrow seas the
tides are generally much greater than those here assumed ;
and it is probable that at a gravitational observatory actually
on the sea-shore on the south coast of England, apart from
seismic changes, perceptible oscillations of the vertical would
be noted.
Sir William Thomson has made an entirely independent
estimate of the probable deflection of the plumb-line at a sea-
side gravitational observatory*. He estimates the attraction
of a slab of water 10 feet thick (the range of tide), 50 miles
broad perpendicular to the coast, and 100 miles long parallel
with coast, on a plummet 100 yards from the low-water mark,
and opposite the middle of the 100 miles oflength. He thinks
this estimate would very roughly represent the state of things _
* Thomson and Tait’s ‘ Natural Philosophy,’ § 818.
due to Elasticity of the Earth's Surface. 423
say at St. Alban’s Head. He finds, then, that the deflection
of the plumb-line as high tide changes to low would be
zoobo000 Of the unit angle, or 0/050. The general theorem
proved above, as to the proportionality of slope to attraction,
shows that, with rigidity 3x 10° for the rocks of which the
earth is formed, the apparent deflection of the plumb-line
would amount to 0°25.
Ii is just possible that a way may in this manner be opened
for determining the modulus of rigidity of the upper 100 or
200 miles of the earth’s surface, although the process would
be excessively laborious. The tides of the British Channel
_ are pretty well known; and therefore it would be possible by
very laborious quadratures to determine the deflection of the
plumb-line due to the attraction of the tide at any time at a-
chosen station. If, then, the defiection of the plumb-line could
be observed at that station (with corrections applied for the
positions of the sun and moon), the ratio of the calculated to
the observed and corrected deflection, together with the known
value of the earth’s radius and mean density, form the mate-
rials for computing the rigidity. But such a scheme would
be probably rendered abortive by just such comparatively
large and capricious oscillations of the vertical as we, M.
d’Abbadie, and others have observed.
It is interesting to draw attention to some observations of
M. d’Abbadie on the deflections of the vertical due to tides.
His observatory (of which an account was given in the Report
for 1881) is near Hendaye, in the Pyrenees, and stands 72
metres above and 400 metres distant from the sea. He
writes* :—
““ Jai réuni 359 comparaisons d’observations spéciales faites
lors du maximum du flot et du jusant ; 243 seulement sont
favorables a la théorie de l’attraction exercée par la masse des
eaux, et l’ensemble des résultats pour une différence moyenne
de marées égale a 2°9 metres donne un résultat moyen de
056 ou 0-18 pour le double de l’attraction angulaire vers le
Nord-Ouest. Ceci est conforme a la théorie, car les différences
observées doivent étre partagées par moitié, selon la loi de la
réflexion ; mais comme il y a toujours de l’inattendu dans les
experiences nouvelles, on doit ajouter que sur les 116 compa-
raisons restantes il y en a eu 57 ot le flot semble repousser
le mercure au lieu de Vattirer. Mes résultats ont été con-
firmés pendant Vhiver dernier par M. l’abbé Artus, qui a eu
la patience de comparer ainsi 71 flots et 73 jusants consécutifs,
de janvier 4 mars 1880. Lui aussi a trouvé un tiers environ
* “Recherches sur la Verticale,” Ann. de la Soc, Scient. de Bruxelles,
81.
424 Mr. G. H. Darwin on Variations in the Vertical
de cas défavorables 4 nos théories admises. On est done en
droit d’affirmer que si la mer haute attire le plus souvent le
pied du fil a plomb, il y a une, et peut-étre plusieurs, autres
forces en jeu pour faire varier sa position.”
We must now consider the vertical displacement of the
land near the coast. In (21) it is shown to be
_guh_ fl ,
a x 2°1037,
where a indicates the displacement corresponding to z=0.
With the assumed values, h=40, v=3 x 10°, 1=6°28 x 10%,
I find #,=5°684 centim. Hence the amplitude of vertical
displacement is 11°37 centim. As long as Al remains constant
this vertical displacement remains the same ; hence the high
tides of 10 or 15 feet which are actually observed on the coasts
of narrow seas must probably produce vertical oscillations of
quite the same order as that computed.
If the land falls, the tide of course rises higher on the coast-
line than it would do otherwise ; hence the apparent height of
tide would be h+a,. But this shows there is more water
resting on the earth than according to the estimated value h ;
hence the depression of the soil is greater in the proportion
1+4,/h to unity; this again causes more tide, which reacts and
causes more depression, and so on. Thus on the whole the
augmentation of tide due to elastic yielding is in the ratio of
ako Gg\ol! fan’ 1 :
1+ 2+ (2) +(?) = Me! 0) i. jk
This investigation is conducted on the equilibrium theory ;
and it neglects the curvature of the sea-bed, assuming that
there is a uniform slope from mid-ocean to the sea-coast. The
figure shows that this is not rigorously the case ; but it is quite
near enough for a rough approximation. The phenomena of
the short-period tides are so essentially kinetic that the value
of this augmentation must remain quite uncertain; but for the
long-period tides (the fortnightly and monthly elliptic) the
augmentation must correspond approximately with the ratio
ie (1- gu 21037).
TU
The augmentation in narrow seas will be small; but in the
Atlantic Ocean the augmenting factor must agree pretty well
with that which I now compute*.
* Sir William Thomson has pointed out to me, since the meeting of
the Association, that this augmentation will only hold true in the cases
of certain distributions of land.
due to Elasticity of the Earth's Surface. 425
With the previous numerical values we have a) // (which is
independent of h) equal to 1421, and 1—«,/h=:8579 =$ very
nearly. .
Thus the long-period tides may probably undergo an aug-
‘mentation at the coasts of the Atlantic in some such ratio as
6 to 7.
The influence of this kind of elastic yielding is antagonistic
to that reduction of apparent tide which must result from an
elastic vielding of the earth’s mass as a whole.
The reader will probably find it difficult to estimate what
degree of probability of correctness there is in the conjectural
value of the rigidity, which has been used in making the
numerical calculations in this paper. The rigidity has not
been experimentally determined for many substances; but a
great number of experiments have been made to find Young’s
modulus. Now, in the stretching of a bar or wire the com-
pressibility plays a much less important part than the rigidity;
and the formula for Young’s modulus shows that for an in-
compressible elastic solid the modulus is equal to three times
the rigidity*. Hence a third of Young’s modulus will forma
good standard of comparison with the assumed rigidity, namely
3x 10° grammes weight per square centimetre. The follow-
ing are a few values of a third of Young’s modulus and of
rigidity, taken from the tables in Sir William Thomson’s
article on Elasticity+ in the Encyclopedia Britannica:—
A third of Young’s modulus and
Material. rigidity in terms of 10° grammes
weight per square centimetre.
BONG. tears A OME L 2
Slate . . . . About 3 to 4.
Glass : . . - Rigidity 1°5 to 2°4.
Weer a ee AE
Copper. . . . 4, and rigidity 4°6 to 5-4.
Steel . . . . 7 to 10, and rigidity 8-4.
It will be observed that the assumed rigidity 3 is probably
a pretty high estimate in comparison with that of the mate-
rials of which we know the superficial strata to be formed.
It is shown, in another paper read before the Association at
this meeting, that the rigidity of the earth as a whole is pro-
bably as great as that of steel. That result is not at all incon-
sistent with the probability of the assumption that the upper
strata have only a rigidity a little greater than that of glass,
* Thomson and Tait’s ‘ Natural Philosophy,’ § 683.
+ Also published separately by Black (Edinburgh).
Phil. Mag. 8. 5. Vol. 14. No. 90. Dee. 1882. 2F
496 On Variations in the Vertical.
3. On Gravitational Observatories.
In the preceding sections estimates have been made of the
amount of distortion which the upper strata of the earth pro-
bably undergo from the shifting weights corresponding to
barometric and tidal oscillations. These results appear to me
to have an important bearing on the utility of gravitational
observatories.
It is not probable, at least for many years to come, that the
state of tidal and barometric pressure, for a radius of 500 miles
round any spot on the earth’s surface, will be known with
sufficient accuracy to make even a rough approximation to the
slope of the surface a possibility. And were these data known,
the heterogeneity of geological strata would form a serious
obstacle to the possibility of carrying out such a computation.
It would do little in relieving us from these difficulties to place
the observatory at the bottom of a mine.
Accordingly the prospect of determining experimentally
the lunar disturbance of gravity appears exceedingly remote;
and I am compelled reluctantly to conclude that continuous
observations with gravitational instruments of very great
delicacy are not likely to lead to results of any great interest.
It appears likely that such an instrument, even in the most
favourable site, would record incessant variations of which no
satisfactory account could be given. Although I do not
regard it as probable that such a delicate instrument should be
adopted for regular continuous observations, yet, by choosing
a site where the flexure of the earth’s surface is likely to be
great, it is conceivable that a rough estimate might be made
of the average modulus of elasticity of the upper strata of the
earth for one or two hundred miles from the surface.
These conclusions, which I express with much diffidence,
are by no means adverse to the utility of a coarser gravita-
tional instrument, capable, let us say, of recording variations
of level amounting to 1” or 2”. If barometric pressure, tidal
pressure, and the direct action of the sun and moon combine
together to make apparent slope in one direction, then, at an
observatory remote from the sea-shore, that slope might per-
haps amount to a quarter of a second of arc. Such a disturb-
ance of level would not be important compared with the
minimum deviations which could be recorded by the supposed
instrument.
It would then be of much value to obtain continuous syste-
matic observations, after the manner of the Italians, of the —
seismic and slower quasi-seismic variations of level.
On the Evolution of the Earth-Moon System. A27
I venture to predict that at some future time practical astro-
nomers will no longer be content to eliminate variations of
level merely by taking means of results, but will regard cor-
rections derived from a special instrument as necessary to each
astronomical observation.
XLVI. New Views of Mr. George H. Darwin’s Theory
of the Evolution of the Earth-Moon System, considered as to
its bearing on the question of the Duration of Geological Time.
By the Rey. Samurt Haveuton, ID., Fellow of Trinity
College, Dublin*.
a has- been tacitly assumed, even so far back as the times
of Newton and Clairaut, that the earth and planets have
passed through a liquid condition (owing to former great
heat) before assuming the solid condition which some, at least,
of them now possess.
Laplace, in his nebular hypothesis, also assumes the former
existence of this liquid condition; and it is openly asserted by
all geologists who believe that the earth consists of a solid
crust (more or less thick), reposing upon a fluid or viscous
nucleus.
It has been proved by Sir William Thomson, following out
the views of the late Mr. Hopkins, that the present condition
of the earth, taken as a whole, is such that it must be re-
garded as being more rigid than glass or steel, possibly more
rigid than any terrestrial substance under the surface-condi-
tions of pressure.
The following considerations show that it may be fairly
doubted whether the earth or any other planet ever existed in
a fluid condition.
1. The possibility of the equilibrium of the rings of Saturn,
on the supposition that they are either solid or liquid, has been
more than doubted, and the most probable hypothesis respect-
ing them is, that they consist of swarms of discrete meteoric
stones.
2. It is difficult to understand the low specific gravity of
Jupiter and the other outer planets, on the supposition that
they are either solid or liquid; for we know of no substance
light enough to form them f. If the outer planets consist of
* From the ‘ American Journal of Science ’ for November 1882. Read
before the Mathematical Section of the American Association for the
Advancement of Science, at Montreal, August 1882.
+ The force of this argument could not be felt before the revelations of
the spectroscope, because at that time there was no proof that the whole
universe was composed of the same simple substances, and those very
limited in number.
22
428 Rey. S. Haughton on Mr. G. H. Darwin’s Theory
discrete meteoric stones moving around a solid or liquid
nucleus, the difficulty respecting their specifie gravity would
disappear.
3. The recent researches connecting the November, the
August, and other periodic swarms of shooting-stars with
comets, tend in the direction of showing that comets in cooling
break up into discrete solid particles (each no doubt having
passed through the liquid condition), and that probably the
solar nebula cooled in like manner into separate fiery tears,
which soon solidified by radiation into the cold of space.
4, Mr. Huggins’s recent comparisons of the spectroscopic
appearances of comets and incandescent portions of meteoric
stones, showing the presence in both of hydrocarbon and
nitrogen compounds, confirm the conclusions drawn from the
identity of the paths of comets and meteoric periodic shooting-
stars.
5. Mr. H. A. Newton, in a remarkable paper read before
the Sheffield Meeting of the British Association (1879),
showed the possibility (if not probability) of the asteroids
being extinct comets, captured and brought into the solar
system by the attraction of some one or other of the outer
large planets, and permanently confined in the space between
Mars and Jupiter, which is the only prison-cell in the solar
system large enough to hold permanently such disorderly
wanderers.
In the same paper Professor Newton threw out the idea
that some of the satellites of the large planets might also be
of cometary origin.
From all these and other considerations it is therefore
allowable to suppose that the earth and moon, when they sepa-
rated from the solar nebula, did so as a swarm of solid
meteoric stones, each of them having the temperature of
interstellar space, 7. e. something not much warmer than
460° F. below the freezing-point of water.
Mr. George H. Darwin has shown admirably how the earth-
moon system may have been developed from the time when
the earth-moon formed one planet, revolving on its axis in a
few hours, to the present time, when the earth and moon (in
consequence of tidal friction) have pushed each other asunder
to a distance of sixty times the radius of the earth *.
In his paper on the tidal friction of a planet} (supposed
viscous and under the influence of bodily tides caused in
it by.an external body such as the moon), Mr. Darwin has
found a remarkable equation of condition, which may be thus
* Proceedings of the Royal Society, 19th June, 1879.
+ Phil. Trans. 1881, part ii. p. 494.
a
a
ba of the Evolution of the Earth-Moon System. 429
expressed :—
a Wdt
d(/r) « =e EP Sea eeaue (1)
where
r=distance between centres of earth and moon,
¢=time elapsed from a fixed point,
= p(n—Q) (2 )
1+ p20)” SWE hy PAG! etl are eaiG
n=angular velocity of earth’s rotation,
Q=angular velocity of moon’s orbital revolution,
p=quantity varying inversely as the viscosity of the planet.
The extreme interest of equation (1) consists in the appear-
ance of the inverse sixth power of the distance.
As the function W varies very slowly, we find by integra-
tion, for any portion of time during which VY may be regarded
as constant,
Ds
iN E es oa) i OU LE AO ey
a most unexpected and remarkable result.
Upon reading Mr. Darwin’s papers, my mind turned to a
problem with which I was familiar, viz. the retardation of the
earth’s rotation produced by the lunisolar tide exerted upon
the ocean supposed collected in an equatorial canal, the moon
and sun having no declination; and I readily found an equa-
tion to express the evolution of the earth-moon system, on the
foregoing hypothesis as to friction.
This equation is the following :—
HOE et eee Pere
where var
\n— G
o= f4V 2(n—O)? —P}./4n—- OP +7” Fin tee) Ale (5)
f=coeficient of friction supposed proportional to relative
velocity,
k varies inversely as 7°,
V,=velocity at earth’s equator.
This leads, as in Mr. Darwin’s hypothesis of viscous earth,
to the integral Li
ENS ae ge ere ae, re AF)
The form of the functions VY and © is similar, as both ascend
by odd powers of (n—2) and vanish when n=0—that is to
say, at the beginning and end of the evolution by friction of
the earth-moon_system.
=
430 Prof. H. Helmholtz on Systems of Absolute
It is quite clear, therefore, that the remarkable expression
(1) found by Mr. Darwin is not peculiar to his special hypo-
thesis of a viscous earth, but can be deduced equally well
from the totally distinct hypothesis of an absolutely rigid
earth retarded by the tidal action of a liquid ocean.
I was led by this result to consider the case of the earth-
moon, separating (as I believe they did) from the central
solar mass in the form of a swarm of discrete masses of mete-
oric iron and stone, each one having the temperature of the
cold of interstellar space, or not much aboveit. Translating
this conception into mathematical language, I find that the
equation of continuity belonging to the hydrodynamical
theory applies equally well to the meteoric theory, viz.
vy=y!, s.r
where v, v’ are the velocities at any two points, and y, y’ are
the depths of the ocean or meteoric swarm at the same points.
The depth of the swarm or ocean without jostling or friction
will be least under the moon and greatest at right angles to
the moon, and the velocities will be inversely. Hence the
chances of jostling among the meteorites when disturbed by
the moon’s tidal action will be proportional to the velocity,
being greatest where the velocity is greatest and the area of
passage least, and vice versd.
This consideration reduces the meteoric problem to that of
the hydrodynamical problem, with a friction proportional to the
velocity, and gives equations in all respects similar to those
derived by Mr. Darwin from the hypothesis of a viscous earth.
On the meteoric hypothesis, if the jostling of the stones be
slow they may cool almost as fast as they are heated, and the
result will be a cool earth and almost indefinite time at the
disposal of geologists.
XLVIII. On Systems of Absolute Measures for Electrie and
Magnetic Quantities. By Prof. H. Hetmuorrz*.
pa have hitherto been obliged to employ two
different systems of electrical absolute measures, the
electrostatic and electromagnetic ; while for magnetic quantities
only one has always been made use of—namely that introduced
by Gauss, in which only the parts of the metre and the gramme
employed as the units of length and mass have changed.
Indeed the employment of those two systems of electrical
measures could not be dispensed with, for practical reasons,
because the determination of the factor which had to be used
* Translated from Wiedemann’s Annalen, 1882, no.9, vol. xvii. pp. 42-54,
Measures for Electric and Magnetic Quantities. 431
for the reduction of electrostatic to electromagnetic measures,
namely Weber’s critical velocity, could not yet be effected
with the same degree of precision that could be attained within
the sphere of electromagnetic measurements on the one hand
and electrostatic measurements on the other. It was on this
account more advantageous to employ in each experimental
investigation that system of measures to which the quantities
measured could be referred with the greater exactness.
To this is to be added the consideration of avoiding excessively
large numbers, which will probably induce us to continue to
employ for electrostatic and galvanic phenomena two kinds of
measures, although reducible to one another. At present the
electromagnetic methods of measurement are the most perfect;
- they are unmistakably the most important practically for an
art that advances with giant strides; and I have therefore
considered that the International Congress that met in Paris
last year acted quite suitably in endeavouring to establish an
electromagnetic system of absolute measures. Had the aim
been purely scientific, I should have preferred the electrostatic
system hitherto employed, since this, I think, best represents
the essential analogies of the phenomena by analogous for-
mulz, and gives to them the clearest and most intelligible
expression. It was on this system, grounded on Gauss’s
principles, that most of the physical-mathematical treatises in
this department of science have hitherto been based.
Just on this account it would appear to me very undesirable
if this system should now entirely fall, and even its name give
place to a new one, as proposed by Clausius in his recently
published memoir*. I would not at all recommend the mul-
tiplication of systems of measures without very urgent reasons;
and certainly the transference of a name already in use and
frequently employed to a new system would inevitably pro-
duce needless and vexatious confusion in physical literature,
even apart from any estimate of the relinquished in compa-
rison with the new system.
Any determination of a new absolute measure must be based
on the measuring observation of a natural process or behaviour,
just as already, among the three fundamental units, the
gramme has been reduced to the two others by means of the
density of pure water at 4° C. The measure of magnetic
quanta which has hitherto been exclusively employed is
founded on the definition laid down by Gauss, according to
which the repellent force between two magnetic quanta, m,
and m,, which are situated at the distance r from one another,
* Clausius, Verhandl. des naturh. Vereims d. preuss. Rheil. u. Westfal.
March 6, 1882; Wied, Ann, xvi. p. 529; Phil, Mag. June 1882, xiii, p. 881.
432 Prof. H. Helmholtz on Systems of Absolute
is put not merely proportional, but equal to the value of
(m,.m,/r°). Since the force and the length r are to be mea-
sured by known methods, the value of the product (m, . mg)
is thereby determined in absolute measure ; and therefore, if
from other facts the ratio (m,/m;) can be determined, m, and
m, can each be separately determined.
Exactly the same principle is also applied by Gauss, at the
commencement of his memoir “ Allgemeine Lehrsatze in
Beziehung auf die im verkehrten Verhiltnisse des Quadrats
der Entfernung wirkenden Anziehungs- und Abstossungs-
kriifte”’*, to electrical quanta and gravitating masses. Al-
though he has not in the latter two cases carried the prin-
ciple into practical effect, it would be justifiable to designate
all three methods by his name as that of their mental author.
That which refers to electricity gives the electrostatic system
as»it has hitherto been employed. The third, referring to
gravitating masses, will probably in future play an important
part, when we have succeeded in accomplishing more exact
determinations of the force of gravitation. If, like Maxwell,
we denote by angular brackets the dimensions of the expres-
sion enclosed in them, by M a mass, by L a length, and by T
a time, according to Gauss the attraction between two heavy
masses m at the distance 7 is
‘i= ae pel fe =| al
aig re he TA)” | eee
On the left stands a density, on the right a function of the
time. If, therefore, as hitherto, we put the absolute density
of water equal to unity, while the unit of mass is determined
in gravitation-measure, a time-measure is thereby given which
is independent of the probably variable rotation of the earth,
and only a single measure, the metre, is left to be handed
down by tradition. But even this could be absolutely defined
if we availed ourselves of an invariable velocity, for instance
the velocity of light in free zether.
Thus, for example, the period of revolution T of a small
satellite revolving close to the surface of a sphere of pure
water of normal density D, would, independently of the radius
of the sphere, in gravitation-measure be
T= %,
and the velocity of light
foal, Whee af 2B
v= a= bh Sa
* Resultate aus den Beobachtungen des magnetischen Vereins 1839.
Measures for Electrie and Magnetic Quantities. 433
by which latter equation the length L would be given. This
system would therefore free us from the handing-down of any
traditional measure.
In Gauss’s magnetic and electrostatic measure the dimen-
sions of the magnetic quantum m and the electrostatic
quantum ¢ are determined by the equations
[m]=[e]=[M*L?T™”),
both based on the phenomenon of repulsion between resting
magnetic or resting electric quanta.
On the other hand, for electromagnetic determinations the
ponderomotive action of a closed electric current upon a pole
of a magnet was used, the laws of which have been mainly and
completely formulated by Ampere.
The components of the magnetic forces produced in its
vicinity by an electric current can, like those of a magnet, be
represented as differential quotients of a potential-function
which satisfies the same differential equations as those of mag-
nets, and only differs from those of the latter in that it periodi-
cally increases in value by the same quantity as often as only
one pole is caused to make a whole reyolution about the con-
ductor of the current. As the electromagnetic forces are pto-
portional to the current-intensity of the conductor, the period
of the potential is also proportional to that intensity, and inde-
pendent of the shape of the conductor. Maxwell on this
account employs the value of the period of the potential 0 as
a measure for the intensity of the current C, and therefore, in
§ 623 of his Treatise on Electricity and Magnetism, puts the
dimensions of the two equal:
[O]=[C].
The fixed numerical relation between the two follows from an
earlier passage of the above-mentioned work, § 479, where T
denotes the magnetic force of a very long straight current-
conductor at the small distance r from its axis, and J is put
for C:—
Tr=2J.
Since
O=T .2ar,
O=47J,
by which Maxwell’s determination becomes, when Gauss’s
magnetic measure is employed, equal to the electromagnetic
measure proposed by W. Weber.
In Ampere’s time a complete theory of potential-functions
did not yet exist. He has, however, represented quite accu-
434 Prof. H. Helmholtz on Systems of Absolute
rately what we can now, in the manner stated, express in con-
formity with nature, by a suitably chosen fiction; namely, he
imagined a surface bounded by the conductor, dividing the in
this case doubly connected space covered with a double mag-
netic layer. If the magnetic moment of each unit of surface
of the double layer is denoted by pw, according to well-known
principles the leap of potential between the two sides must be
O=47rp,
and therefore ~=J. With this form of expression of Ampére’s
law Prof. Clausius stops.
Both forms are perfectly equivalent and equally justified,
so long as we measure the magnetic quanta according to
Gauss’s rule. This Prof. Clausius also admits ; but he thinks
an extension of Maxwell’s expression to other systems of mea-
sures must be rejected ; he explains this as an oversight on
Maxwell’s part, and the equations and determinations of mea-
surements derived from it as erroneous.
The only reason which, in this respect, he alleges against
Maxwell’s definition is the following, in § 3 of the memoir
above cited:—“ The force, however, which a current exerts
upon a magnetic pole is electrodynamic ; and from this it fol-
lows that an equation of which the deduction is based upon
this force can be regarded as valid only in the dynamic system
founded upon the electrodynamic forces, and not in the static
system based on the electrostatic forces.”
But even if one, as an adherent of Ampére’s hypothesis,
entertained no doubt respecting the first part of this proposi-
tion, I do not see why the conclusion should be urged against
Maxwell only, and not against the interpretation of Ampére’s
law adopted by Clausius himself, since the latter is, after all,
nothing but another way of expressing the same facts. Both
quantities, Maxwell’s potential-period © as well as Ampére’s
magnetic momentum of unit surface, are, in Gauss’s system of
measurement, of the dimension [m/L]; both have a physical
meaning only in “ the representation of the force which a cur-
rent exerts upon a magnetic pole.”
The true reason of the difference moreover appears to me to
lie in quite another circumstance—namely, in Maxwell’s defi-
nition of the magnetic potential Q. This is with him not the
form of calculation 2[m/7], but he defines it in this case, as
also in the corresponding applications to electrostatics and
electrodynamics, by stating that Q.m is a work—which defi-
nition also underlies Gauss’s definition of m.
The differential quotient —dQ/dz is, corresponding to this,
the force which acts upon the unit of magnetism, and therefore
Measures for Electric and Magnetie Quantities. 435
(—Q) Jacoby’s force-function. If we introduce for m another
measuring unit, and measuring with it obtain m, Oy, J,
instead of m, 0, J, then must, according to Maxwell’s defi-
nition,
mOA=mO,,
and therefore
mJ =m,J3.
The unit of current therefore increases in the inverse propor-
tion of the newly chosen unit of magnetism to the old one;
but the force which the unit of current exerts upon the unit
of magnetism remains constant. With Prof. Clausius, on the
contrary, both m and J increase in the same, and not in the
inverse ratio, and the force increases as m” or J. According
to his determinations, the feigned surface of Ampere always
produces one more leap, equal to the momentum of unit of
surface, in the function =(m/r); but this function has then
no longer the signification of the force-function for the newly
chosen magnetic units.
In all this I cannot perceive any mistake of Maxwell’s; and
his equations, derived from the formulation chosen by him of
the fundamental phenomenon, are altogether as consistent with
each other and as correct, if understood in the sense of their
author, as those of Prof. Clausius. Rather, this case shows
that, if we abandon Gauss’s determination of the magnetic
unit, we again fall into at least two different and equally jus-
tifiable systems of measuring-units; and, for my part, I could,
with respect to both Maxwell and Clausius, draw from this
the practical conclusion that we ought by no means to forsake
the above-mentioned method of Gauss until we have particu-
larly important reasons and a definite purpose for such a pro-
ceeding, when the choice between the systems of Maxwell and
Clausius would probably be decided on positive grounds.
Now, although J must vindicate Maxwell from the charge
of having, in consequence of an oversight, set up incorrect
equations, yet it should be mentioned that in the w ording of
the text of § 623 of his work, where he reduces the dimensions
of all the rest of the electric and magnetic quantities to the
dimensions of any one chosen from among them, an omission
occurs which might easily lead the reader into error, if he
does not closely examine the connexion of the somewhat com-
plicated systems of equations of §§ 622 and 623, and which
seems to give to the propositions of § 623 a greater extension
than Maxwell himself would probably have given them. For
at the beginning of Chapter X., in § 620, he speaks of electro-
static and electromagnetic but not of magnetic units, and
436 Prof. H. Helmholtz on Systems of Absolute
moreover gives definitions according to which the electro- |
kinetic units are determined without any consideration of
magnetism. But in § 621 he introduces magnetic quantities
without in any way saying expressly that, in all his determi-
nations of the ratio between electric and magnetic quantities,
the electromagnetic determination discussed in the chapters in
question,
AnJ =O,
will be retained.
In this respect Maxwell’s intention in sketching different
systems was exactly the same, and as limited, as that more
recently carried out by Clausius, although, from the cause
above discussed, the manner of carrying it out by the two has
turned out different.
The matter being so important, I will take leave to give
here a summary of the connexion of the equations of the cor-
responding paragraphs (621-623) of Maxwell’s Treatise on
Electricity and Magnetism. In § 621 he arranges the quan-
tities for which the dimensions of the unit are to be determined.
I place them here in a somewhat different order, and with the
notation of their meaning which is more usual in Germany.
There are four electrostatic, namely :—
e, electric quantum ;
K, electrostatic potential-function ;
®, dielectric polarization, measured by the electric density
at the surface of the dielectric ;
©, the electric force in a point, acting upon the unit of s.
The four corresponding magnetic quantities he denotes, in
the same order, by m, 0, B, H. ;
To these are added four more corresponding quantities,
namely :—
C, the intensity of a current ;
©, current-density ;
p, the electrokinetic momentum of a current ;
9, the vector-potential of electric currents.
As regards the meaning of the last two quantities, p is
Neumann’s electrodynamic potential of the other currents
present, referred to the entire conductor (passed through b
the unit of current) for which it is calculated ; and %.ds is
the same potential referred to a conductor-element ds situated
at a determined place.
I remark further that the quantities denoted by German
capital letters are vectors, 7. e. quantities having direction and
resolvable into components according to the law of the paral-
lelogram of forces,—and that the selection of them resulted
from Maxwell’s endeavour to introduce, as far as possible, only
Measures for Electric and Magnetic Quantities. 437
directly observable quantities into the calculation, and to avoid
hypotheses.
In § 622 Maxwell sets forth dimension-determinations for
the products and quotients of these twelve quantities, as given
immediately by their meaning. There are fifteen of these
determinations, in which those quantities referable to elec-
tricity are kept quite separate from those which refer to mag-
netism, so that (which is certainly remarkable) from these
fifteen determinations no relation between electricity and mag-
_netism appears. I arrange them tabularly, retaining Max-
well’s above-employed notation of the dimensions.
No. | Dimension. Electric quantities. Ae ee
Mel tM | fe), [p. 0). [m0]
2 M/(LT’) |[D.€], [C.] [B.H]
3. p [e/C], [p/E}, [UAE]
4 L [E/E], [p/] | /9]
5 UE Le/D], [O/@] Lm/%]
The last series of determinations result from the first, if they
be divided by the product of the quantities in question of the
second and fourth series. The fifth series may therefore be
omitted as superfluous; then there remain the following iden-
tical equations between the quantities in the first four rows:—
fel (eat [eh
[el eee [6] al
Caan A
Lastly, there are left three independent determinations for
the four magnetic quantities m, 0, 8, , and seven for the
eight electric quantities e, H, p, C,D, ©, €, A. If, therefore,
of these two groups one quantity each be defined by other de-
-terminations—for example m and e, the quantum of magnetism
and the quantum of electricity—all the others are completely
defined, namely :—
438
Prof. H. Helmholtz on Systems of Absolute
Electric. Electrokinetic. Magnetic.
Forces: ...... [¢]= lees [a] = ea [Hl= [ae
Densities ...|[D]= ital TCj= al [B]= ka
[e]=[CT]
These are the determinations which, without any further
limiting equations, result from the above fifteen. These can
be applied to any definition of the units of m and e, and there-
fore also to the electrostatic-magnetic system of Gauss.
Now follows, in Maxwell, § 623, “These fifteen equations
are not independent of each other; and in order to deduce
from them the dimensions of all the twelve units they contain,
we require one more equation.” In fact we require two,
since e and m must be determined singly by recurring to two
facts of observation regarded as fundamental phenomena. The
one here wanting, not expressly mentioned by Maxwell, but
from the connexion self-evidently presupposed, we can write
as above:— [2]=[C].
Clausius has chosen for it the less perspicuous
[p]=[~].
But, since one of the fifteen determinations in § 622 reads
(m.O]=[p.C],
each of the two follows from the other.
Just on this account, however, the closing words of § 623,
“ All the above-given determinations are correct for any sys-
tem of units we may choose,” must be altered, and limited to
electromagnetic systems, and, indeed, to such only as are
derived from the meaning, as defined by Maxwell, of the fun-
damental law of electromagnetism. For that coucluding sen-
tence applies neither to the electrostatic system nor to the
system set up by Clausius. Of the possibility that another
conception of the electromagnetic fundamental law might here
lead to other consequences Maxwell probably did not think ;
and in this respect Clausius has indeed, in his most recent
memoir, given a thankworthy enrichment of our ideas.
Finally, we must speak of the reason why Prof. Clausius is
Measures for Electric and Magnetic Quantities. 439
willing to drop the electrostatic system, constructed according
to Gauss’s principles, hitherto employed. The only thing he
says on this subject is contained in § 1 of hismemoir. After
mentioning that the forces exerted upon each other by closed
electric currents may be regarded as indubitably known, he
continues:—* As, further, the small electric currents which
according to Ampere are to be assumed as existing in the
interior of a magnet are likewise closed, we have in magnetism
to do with forces of the same kind.” Thereupon follows an
analysis, according to which the forces of two magnetic quanta
are to be regarded as dynamic.
This reason, however, would be decisive only if it were cer-
tainly proved that Ampere’s hypothesis corresponds to the
reality, while up to the present it can hardly be said that it
has been clearly and consistently worked out for all sorts of
diamagnetic and ferromagnetic bodies. In particular, this
hypothesis would also require that the hypothetic molecular
eurrents of magnetized bodies should show the changes which
are to be generated by electrodynamic induction, as they are
in fact logically assumed to do by W. Weber in his well-
known explanation of diamagnetic polarization. How this
ean be reconciled with the properties of ferromagnetic bodies
I leave the adherents of this theory to explain. Meanwhile,
however interesting this theory may be, we may look upon it
as neither verified nor even completely worked out.
Among the electrodynamic theories which assume direct
action at a distance, its quantity and direction depending on
the absolute er relative motions of two electric quanta, stands
that of Faraday and Maxwell. It has at least this superiority
to those, that it does not violate either the principle of the
finiteness and constancy of energy or that of the equality of
action and reaction ; and moreover it bases a theory of light,
free from many difficulties of the hitherto received undulation
theory, upon the identical hypotheses which form the ground-
work of electrodynamics. In order to discover the essential
character of the forces of electricity and magnetism, Maxwell
excludes those processes in which, according to the sort of
friction, heat is generated and electric or magnetic energy
lost, and founds his theory upon conservative processes only.
In particular, he excludes the conduction of electricity in con-
ductors, and the coercive force in magnets. Then, however,
his fundamental equations present the most complete analogy,
not between magnets and moved electricity, but between
resting dielectric and resting magnetic polarization. It is
precisely to this analogy that Gauss’s electrostatic system of
measures perfectly accommodates itself.
440 Messrs. Trowbridge and Penrose on
I will make one more remark, that when one seeks to form,
after the analogy of Hamilton’s principle, that integral, taken
with respect to the time, whose variation gives the equations
of motion according to Maxwell in place of the electrodynamie
potential of Clausius (Maxwell’s electrokinetic energy), a bilinear
function of the components of the electric flow, on the one
hand, and of the components of the magnetic momenta, on the
other, arises in which the latter have to be dealt with, but not
as velocities. This last point I reserve to myself to treat soon
in another place.
For the present I need only remind physicists that the
ground on which Prof. Clausius is inclined to reject the hitherto
accepted electrostatic system is a hypothetical assumption,
contested between different theories ; and I would beg them
not to transfer the name of the electrostatic system pro-
ceeding from Gauss, and hitherto employed by preference in
mathematical works, to another. In this system the potentials
(m?/r) and (e?/r) are quantities of work; their entire physical
importance rests upon the fact that they are such. The theory
of the potential-functions forms one of the most complex and
interesting chapters of mathematical physics, corresponding to
well and perfectly known physical processes. If Gauss’s units
be changed, then must we accustom ourselves to add factors
to all potential-functions, in order that they may remain quan-
tities of work and their differential quotients give the forces,
On the contrary, whether J? is a force and mJ a work, or
whether we must write for them A’J? and AmJ, appears to
me much less important, especially as we know well and
accurately just a portion of the department of electromagnetic
actions, viz. that consisting of closed currents, but in the pro-
vince of unclosed currents the most luxuriant flora of hypo-
theses still flourishes.
XLIX. The Thomson Effect. By Joux TROWBRIDGE and
CHARLES BrncHAM PENROSE’.
IR WILLIAM THOMSON? first discovered that when
an electrical current passes through a piece of metal,
the ends of which are of different temperatures, it carries
heat with it; the direction depending upon the character of
the metal and the direction of the current. This pheno-
menon is known as the Thomson Effect. Le Rouxt subse-
quently verified Thomson’s results, and gave an incomplete
table of the effect in different metals. No especial pains have
* From Silliman’s American Journal of Science for November 1882.
+ Phil. Trans. 1856, vol. iii. p. 661.
t Ann. de Chim. et de Phys. 1867, [4] vol. x. p. 258.
eS eee ee Le ee
a eS ee ee ee es.
the Thomson Effect. 441
been taken hitherto in experimenting with pure metals. We
have thought it would be valuable to test the effect in as pure
a metal as we could obtain by electrolysis. We have also
extended Le Roux’s table by the addition of the effect in
nickel, which Thomson was unable to obtain, and also in
carbon. An endeavour has been made to ascertain if the
effect is reversible, and also to discover if it is modified in a
magnetic field.
The strip of nickel, 45 centim. long, 2°6 wide, and 2 mil-
lim. in thickness, was placed with its Hat surface horizontal.
One face of a thermopile was placed at a fixed point on the
surface of the nickel, separated from it by a thin piece of mica.
A weight pressed upon the other surface. The thermopile
was connected with a Thomson’s reflecting galvanometer of
six ohms resistance. The two extremities of the strip of
nickel were connected with a battery of six Grove cells, the
wires first passing through a key so that the direction of the
eurrent could be reversed. One end of the nickel was kept
at the temperature of the air, 15° C.; the other at a constant
red heat by means of a Bunsen burner. The metal was heated
in this way from 9 a.m. to 3 P.m., until it reached a condition
of thermal equilibrium, as shown by the galvanometer. The
scale of the galvanometer was then moved until the spot of
light came to 0. The current from the Grove cells was then
passed for one minute alternately in opposite directions, and
the deflections of the galvanometer were read every quarter of
a minute. Before the direction of the current was changed,
the circuit was each time broken, and the spot of light was
allowed to fall to 0. The following table gives the results.
The column marked “‘ C-H” gives the deflections when the
current was passing from cold to hot. The small numbers
show which deflections in each pair were taken first.
C-H. H-C.
Defiections taken every + minute. Deflections takez every ¢ minute.
1 Deeley e Tees | seo ae |ye ae wakes 2
4-1 42 | 40 | 43 | 44 SOP AON roiO ale oOubaceek
6:3 | 64 | 6:5 | 64.) 6-4 HOME G20 OA SO) 8 6:0
female tO =| 0-0) | 7:2 Hie Gils | OA Ge AO
ee | FO. es | ee. Gt | 73 | 65 | 68 | 72
From this table it is obvious that more heat is evolved by a
constant current per unit time in passing from the cold to the
hot end of the nickel than in passing in the opposite direction.
The Thomson Effect in pure nickel is consequently negative ;
Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 2G
442 Messrs. Trowbridge and Penrose on
i. e. heat is absorbed by a current in passing from hot to cold,
and evolved in passing from cold to hot. The above results
were confirmed by many similar experiments, as will be seen
later.
It was next determined to find whether the Thomson Effect
was reversible—that is, whether the heat absorbed by a current
in passing across a section of temperature ¢ was equal to the
heat evolved by the same current when passing in the opposite
direction across the same section. This subject has import-
ant bearings on the thermodynamical theory of thermoelec-
tricity.
The following method was pursued:—Both ends of the nickel
were at the temperature of the air, 15° C. The current from
six Grove cells was passed as before, and the deflections of the
galvanometer were observed every half-minute. The apparatus
was arranged exactly as before. Column I. of the accompany-
ing table gives the deflections. One end of the nickel was
now placed in melting ice. After one hour it reached a con-
dition of thermal equilibrium, and the current from the Grove
cells was passed alternately in opposite directions. The deflec-
tions are given in II. and III.
If the deflections in IL. and IIL. are subtracted from the cor-
responding deflections in I., we get the amount of deflection
due to the Thomson Effect. It will be observed that all the
deflections in II. are less than those in I., and those in ILI. are
greater, as they obviously should be. The only inaccuracy in
this determination is due to the fact that we neglected the
alteration in electrical resistance of the nickel due to the slight
change in temperature.
aes TI
7 ae H-CO: C-H. .
“ np | Deflections | Deflections Lat ) I.—III.
ie atte M every every |
2 ‘ | $ minute. % minute. | /
1:8 18 2:0 0-0 —02
26 2°4 2°8 0-2 —02
29 2°65 3°15 0:25 —0:25
3-1 2°75 3-95 0-35 015 |
The numbers in these tables are obviously too small to draw
any conclusions. They, however, confirm the preceding results
as to the direction of the Thomson Effect; and tend rather to
prove than disprove the reversibility of the effect. The experi-
ment was repeated several times, but with no better result.
Experiments were also made to test the influence of mag-
the Thomson Effect. 443
netism on the Thomson Effect. Nothing but negative results,
however, were obtained.
The strip of nickel was placed horizontally, with its flat sur-
face perpendicular to the axis of a large electromagnet, the
strip being between the two poles of the magnet. One surface
of the nickel was pressed against one pole; on the other sur-
face was placed one face of the thermopile, while the opposite
face was in contact with the second pole of the magnet. Mica
was used, as in the previous experiments, to protect the faces
of the pile. The whole was wedged and pressed tightly toge-
ther, and clamped by means of wire, the object being to pre-
vent any motion of the nickel when the magnet was made.
One end of the nickel was heated by a Bunsen burner ; the
other was at the temperature of the air. Six hours were re-
quired for the apparatus to reach a condition of thermal equi-
librium. The electromagnet was connected with thirty-eight
freshly set-up bichromate-of-potash cells, with plates of large
size. A current from eight Grove cells was now passed along
the nickel, with and without the circuit of the magnet being
made. The deflections of the galvanometer were exactly the
same in each case, showing that in a magnetic field (at least
of the strength in the experiment) the Thomson Effect was
unaltered.
It is unfortunate that the strength of the field could not be
accurately obtained, as the batteries had been running about
thirty minutes by the time the experiment was completed.
The field, however, was very much stronger (as shown by
rough tests) than in another experiment, where the minimum
value was found to be 184 times the vertical intensity of the
earth’s magnetism.
The determination of the relative value of the Thomson
Hiffect in nickel by the following method gives of course but
approximate results. The value, however, is probably as accu-
rate as those given by Le Roux for other metals.
A strip of copper, of about the same dimensions as the nickel
used before, was arranged exactly as the nickel had been. The
thermopile was insulated from the strip by the same piece of
mica, and the same weights were placed on the upper surface.
One end of the copper was heated in boiling water; and
when the apparatus had reached a condition of equilibrium,
the deflection of the galvanometer was 35 centim. A current
from four amalgamated Grove cells was now passed alternately
in opposite directions along the bar, the deflections of the spot
being taken, in each case, after one minute. The results are
given in the left-hand table :—
2G 2
444 Messrs. Trowbridge and Penrose on
| Differences Differences
C-H. H-O. | between | O-H. H-O. between
Deflections Deflections | oh: Deflections | Deflections the same
_|taken every | taken every| -condineg | taken every |taken every g ont
minute. minute. | Preece hh minute. minute. def jes
120 2 | 130 4 1-0 145) | 138 2 12
1235 (epee le 0-8 Icsh 13.0 10
pp Ee 13°42 30 1:3 14:3 } 1g'4, 2 8)
12:0 2 12-8. 1 | 08 148 ? iss Ib
Mean difference =0°97. Mean difference =1°15.
The strip of nickel was now substituted for the copper,.
every thing else remaining exactly the same. One end of the
nickel was heated, and the thermopile was placed on such a
spot that the galvanometer gave a deflection of 35 centim.
The same current was passed as above. The results are
given in the right-hand table. Let d= the mean difference
in the first table, and d’= that in the second, d and d’ are then
proportional to the elevation of temperature of the part of the
bars under the pile on account of the Thomson Effect. Let
o= coefficient of Thomson Effect; that is, o is such a quantity
that od@ represents the heat absorbed per unit current per unit
time in passing from section at temperature 9 to section at
temperature 0+d6. The heat evolved in unit section when
the temperature is increased by $d. K is }KdSD, where K
is a constant depending on the galvanometer, 8 is the specific
heat, and D the density of the metal. If we consider the
Thomson Effect to be constant under the pile, and @ and @& to
represent the temperature of the ends of the space covered by
the pile, we have :—
o(0—6/)=K SSD;
and the similar expression for nickel,
d!
o'(0—8')=K FSD.
eta aie ee » ou (hh)
Kiquation (1.) then gives the relative value of the coefficient of
the Thomson Effect at any temperature 0.
S=-095, §’=:108, D=8-9, D/=8:3, d=0-97, d’=115
o’
= 1°25; .*., o/ =]2ome
Co
the Thomson Effect. 445
In Le Roux’s table c=2; .*. of =2°50: cand o’, however,
are of opposite sign. Introducing nickel, Le Roux’s table
becomes :—
+ =
Sb 64 Fe 31
Cd 31 Bi 3l
im LE Arg 25
Ag 6 Pits
Cee 32 IN ey
Al O01
Sn 0-1
The Thomson Effect in carbon was next investigated. The
carbon used was the graphite of the common carpenter’s lead-
pencil. The pencils which gave the best results were Faber’s.
Attempts were first made to measure the direction of the
Thomson Effect in the same way as in the case of nickel—that
is, by placing a face of the thermopile on one surface of the
carbon, the two ends of the carbon being maintained at con-
stant temperatures, and passing the electric current alternately
in opposite directions. This method was unsuccessful from
the tact that one Grove cell heated the carbon to such a degree
that in one minute the spot of light was thrown off the gal-
vanometer-scale, thus rendering it impossible to measure,
with any accuracy, the rate at which the deflection increased.
The method of Le Roux was then tried, of using two strips
of carbon, each face of the pile being in contact with one strip.
This method not only doubles the deflection due to the Thom-
son Effect, but also greatly diminishes the deflection due to the
heat evolved on account of the electrical resistance of the car-
bon. Ifthe two strips of carbon were exactly the same in all
their physical properties, and the contacts with the faces of
the thermopile were the same on each side, the latter deflec-
tions would evidently be entirely eliminated.
Two carpenter’s pencils were split longitudinally, the lead
being left in one half of the wood. They were then tightly
bound, parallel, against each face of the thermopile, and insu-
lated from it by thin pieces of mica. Especial care was taken
to fasten the carbons firmly, so as to prevent any motion from
the passage of the current. The pencils were placed perpen-
dicularly, the lower ends in two vessels of mercury, surrounded
by melting ice; the upper ends were at the temperature of the
air. The upper ends were electrically connected; and the
‘wires from a battery of three Grove cells were placed in the
vessels of mercury. The thermopile was connected with a
reflecting galvanometer of six ohms resistance.
446 Messrs. Trowbridge and Penrose on
When the system had reached a condition of thermal equi-
librium, the current from the battery was passed, and the
observations were made. The vessels of mercury and the cor-
responding pencils are denoted by “a” and “6.” The cur-—
rent entered alternately in “a” and “ b,” the deflections of the
galvanometer being taken, in each case, every half minute.
The deflections showed that the pencil “a”’ was warmer than
“b;” but the difference of temperatures was greater in one case
than in the other.
The following table represents the results of two sets of ex-
periments. The smali numbers at top show which column of
each pair was taken first.
First experiment. | Second experiment. |
Current Current | Difference, || Current | Current . Difference,
enters enters | proportional enters | enters proportional
at “a.” at “5,” to47H. || ata.” at “8.” | to47 EB.
Pe (eR,
21-0 208 | 0-2 | 208 20-2 06
3845 324 21 | 347 32'8 19
2 1 | : 2
21:2 21°0 0-2 19-5 18-2 13
345 33°0 15 31:0 293 a r/
370 342 28
2 ; ry 2 |
21-4 206 | 08 19'8 iso | 18
34:3 32°8 15 318 292 | 26
| 373 340 33
2 ut / ao ie 2
21-7 216 01 20:0 188 12
36:0 34:3 17 382°6 30°4 2-2
42-4 40-0 2-4 38°7 35°7 30
2 1 eis, 2
23-0 21-7 | 13 21:0 19'8 1:2
38'2 350 | 3:2 33'8 Sis: 2-5
45°5 41-2 / 43 39°8 36°3 35
aot 1 / 1 2
23-5 230 | O85 20:0 1990 | 190
39:0 370 —s| 2-0 o22. |) 129 San 2-4
45°8 43°8 2-0 av4 | 343 . ok
From this table it appears that the Thomson Effect in ordi-
nary a is negative ; that is, heat is apparently evolved
when the current passes from cold to hot, or the negative cur-
rent carries heat with it. The difference in the last columns
are obviously proportional to four times the Thomson Effect,
the Thomson Effect. 447
assuming that the effect is reversible. It also appears from
the table that the effect increases as the temperature increases,
which is in accordance with Tait’s assumption.
These experiments were repeated with the graphite from
other kinds of pencils; but in no case was the effect nearly as
marked as in Faber’s. ven in the case of Faber’s pencils
many trials were made before satisfactory results were obtained.
Hquations representing the thermal condition of a bar when
acting as a conductor of heat and electricity may be deduced
as follows:—One end of the bar is supposed to be maintained
at-a constant temperature, the other at that of the air ; and the
electric current is supposed to be constant. For simplicity,
we will assume that the specific electrical resistance of the bar
is constant throughout, 7. e. is independent of slight differ-
ences of temperature.
The quantity of heat, H, evolved by the current in time 64,
in the section of the bar Sdwz (8 being the area of a section),
is represented by
HES PRS8e of, 8 le ea
x= distance of the section from heated end. If we assume
that the thermal conductivity is unaltered by the slight rise in
temperature due to the current, it can easily be seen that the
flow of heat due to conduction is unaltered by the current.
Hence we can consider that the heat evolved by the current is
partly used in raising the temperature of the section Séz, and
that all the rest escapes from the surface by radiation.
The Thomson Hffect is at present purposely neglected.
The bar is supposed to have reached a permanent condition
as regards conduction before the current was passed. Let 0
be the temperature of the section of the bar we are considering
before the current passes; let h= the exterior conductivity
or velocity of cooling ; let p= the rise of temperature above
@ when the current passes. Assuming Newton’s law of
cooling, the heat radiated on account of the rise of tempe-
rature p is proportional to ph; and the quantity radiated
from the section in time 6¢ from the same cause is
n= phidegoh cece ee oe CE)
[= the periphery of the bar.
In time 6¢ the increase of temperature p becomes p+ 6p;
and the heat developed in the section by this increment is
He=OSDSzt Sp. > 1) Ce)
As we saw that the heat of the current was expended only
448 On the Thomson Effect.
in the ways represented by (II.) and (III.), we have
H = H, + EG . . . . . . (IV.)
If we now consider the influence of the Thomson Effect, we
simply add that a certain quantity of heat is absorbed or
evolved by the current in the section Séz, distinct from that
represented by [’R.
If o = the coefficient of the Thomson Effect, the heat ab-
sorbed or evolved due to this effect is, in time 64,
H,=I080.5t..... |. Os ee
The effect being proportional to the current, and o being de-
fined as such a quantity that o6@ represents the heat absorbed
or evolved in passing from a point at temperature @ to +60,
per unit current per unit time, introducing this effectin (1V.),
H — H, + H, -- H,, . . e . Py (V2)
as the total value of the excess of heat (due to the current)
in the section can be considered as made up of these quantities.
Substituting the values in (VI.) from (I.), (II.), (IIL), (V.),
and transposing,
plhdx . bt= PRSéz . dt—CSD6z . 8p—1068 . dt;
dp 56
St —Ic 52’
. phl=PRS—CSD
or, at the limit,
apis ad : d
2 = capl! RS—phl—Io]. . (VIL)
This equation gives the rate at which the temperature rises
when the current passes, and will approximately apply to the
preceding experiments.
When the temperature of the bar becomes permanent,
apy:
di?
and (VII.) becomes
Te ede
PRS phl=lo— =();
. p= | PRS ie2”] 1
p= [1 RS Io | > so
giving the excess of temperature due to the current in the per-
manent condition of the bar.
The values in (VIII.) are all easily determined except o
and h, The differential coefficient a (the rate of change of
On the Reflection of Electrical Rays. 449
temperature due to conduction along the bar) can readily be
found by experiment; or deduced by analysis, as in the case
of an infinite square bar, where
6=aG-” and = —ak@G—™.
As p may easily be determined by experiment, the equation
can be used to determine o, as
PRS—pAhl
p= SS SS
(IX.)
If Tait’s assumption that o = MT (where M is some con-
stant and T the absolute temperature) is true, we might obtain
two values of o for two points of the bar, the temperature of
which was known, eliminate 4 from the two equations, and
thus obtain a value for M. If we performed the same opera-
tion for two other points, we should get another value for M,
and could verify Tait’s assumption if this value was equal to
the preceding.
The sources of error in the preceding investigation are due
to assuming Newton’s law of cooling, to neglecting the change
of electrical resistance due to a change of temperature, and to
partly neglecting the change of thermal conductivity due to the
same cause.
L. On the Reflection of Electrical Rays.
By Dr. HE. GOLDSTEIN *.
[Plate VII. figs. 1-8.]
[ has been usually assumed f that the (rectilinear) electrical
rays radiating from the kathode of the discharge of an
induction-coil terminate where they impinge upon a solid wall,
and that beyond the point in which they cut the wall they
cannot propagate themselves in any direction{t. The experi-
* Monatsber. der Konigl. Akademie der Wissenschaften zu Berlin. Trans-
lated from a separate impression communicated by the Author.
+ Hittorf, Poge. Ann. cxxxyl.
{ Herr J. Puluj (Ween. Ber. 1880, [2] p. 886) is the only physicist
who has assumed a limited power of reflection of the kathode-rays,
under the assumption that the kathode-light consists of scattered particles
of the electrode, since “it is not intelligible why these should in general
suffer no reflection at the wall.” The conditions of an experiment made
by Herr Puluj to examine whether reflection takes place were not, in my
opinion, such that any possible reflection would have been recognizable.
That which Herr Puluj considers phosphorescence produced by reflected
rays is partly phosphorescence produced by the positive light of the so-
450 Dr. E. Goldstein on the
ments which have led me to reject this assumption were sug-
gested by an observation made by Prof. E. Wiedemann*.
Prof. Wiedemann, in using a tube of the form of fig. 1
(Plate VII.), where the disk & at right angles to the axis of
the vessel C forms the kathode, not only observed green phos-
phorescence such as produced by the kathode-rays on the
_ sides of the tube up to the point x which could be reached by
straight lines from /, but saw also a feeble illumination of the
tube 7 beyond the bend, and a brighter phosphorescent sur-
face F on the wall C opposite the mouth of the tube 7. The
motions of the small surface F under the influence of the
magnet showed that it was produced directly by electrical
rays, and not simply by optical rays possibly reflected at the
glass.
Prof. Wiedemann is disposed to explain the appearance as
one of the phenomena of deflection discovered by mef, assu-
ming that the glass wall at « becomes charged and acts as a
weak kathode, causing the deviation of the pencil of rays
passing by it out of the direction at right angles to the plane
of k, into the direction «F.
~ This explanation seemed improbable to me for two reasons:—
(1) Because the surface F is always much more feebly
illuminated than would have been the case if the phospho-
rescence had been exerted by the direct kathode-rays pene-
trating to C. In order to make the comparison, the kathode-
rays may be so curved by the influence of a weak magnet as
to pass the bend w. The comparison may be more certainly
made without the use of a magnet in a vessel of the form
shown in fig. 2, where two paths are offered to the kathode-
rays—on the one side the path as in fig. 1 through the bent
tube 77,, and on the other side the path through the equally
long straight tube 7, at right angles to k.
(2) Because the surface F totally disappears if the tube rr,
has a second bend in it, in whatever direction this second
bend is made. This would not happen with the phenomena
of deflection, which I have examined, where a ray may be bent
any number of times.
If now the rays which produce the surface F are not direct
rays from the kathode /, then we may suppose either (a) that
the portions of the tube about x, upon which the rays from the
called reflex currents in the system of tubes, partly phosphorescence pro-
duced by direct kathode-rays, which Herr Puluj unintentionally produced
by touching the glass with the finger in order to concentrate the light.
* E. Wiedemann, Wied. Ann. xi. p. 236; Phil. Mag. [5] x.
+ Goldstein, Monatsber. d. Konigl. Akad. der Wiss. 1876, p. 285; Phil.
Mag. [5] iv. Also ‘A new Form of Electrical Repulsion’ (Berlin, 1880).
of
Pe
—
:
%
Reflection of Electrical Rays. 451
kathode impinge directly, become charged with negative elec-
tricity, which reaches such a tension that they themselves
form a second kathode and radiate electric rays, which then
produce F'; or (6) that the rays which produce F are rays
from the kathode £, which suffer reflection when they fall
upon the solid wall. In this reflection, either the power of
producing phosphorescence of the rays becomes weakened
or their density, thus explaining the small intensity of light
emitted by F.
The hypothesis (a) may be excluded, as shown further on ;
for the phenomenon in question is not altered if the surface
upon which the kathode-rays impinge directly be metallic,
and if this metal surface be made the anode of the discharge.
If in accordance with this assumption we suppose that
reflection takes place, then again reflection according to the
optical law is at once to be excluded, since the position and
form of the surface F remain unchanged even when the angle
of the bend at « varies from 25° to 80°. Consequently the law
of the equality of the angles of incidence and reflection, or the
rule that when the reflecting surface is rotated while the inci-
dent ray preserves the same direction, the reflected ray rotates
through twice the angle, is not obeyed.
We may, however, easily make numerous experiments
which agree in showing the presence of diffused reflection, in
consequence of which each point of the wall on which the rays
impinge directly diffuses rays in all directions.
If diffuse reflection is proved, we have at once the explana-
tion of the small luminosity of F in comparison with portions
of the tube reached by the direct rays in the diminution in
density of the incident pencil of rays.
In the next place, if we employ a vessel such as fig. 3, we
obtain phenomena corresponding to the surface F in the cylin-
ders C, and C, at the same time. The rays which travel as
far as x nearly parallel to each other, therefore, after reflection,
follow at least two directions at right angles to each other.
The following experiment forms an experimentum crucis:—
A chamber B was introduced between the portion of the tube
containing the kathode and the bend at 2, which contained a
paper diaphragm which could be turned round the axis a, and
which had a slit cut in it about 1 millim. broad and parallel
toa. Ifthe plane of the diaphragm falls along the axis rr,
its edge intercepts no perceptible portion of the pencil of rays
_which reaches the tube 7 from the kathode, and which is about
7 millim. across. But if, on the other hand, D is at right
angles to the axis of r, then only the portion of this pencil
which passes through the narrow slit can reach the bend «
452 Dr. E. Goldstein on the
If the reflection were similar to that of a mirror, the form and
magnitude of the surface F would change perceptibly. This
surface, in all the experiments so far described, and in this one
also, resembles an ellipse of small excentricity, where D has
the position first mentioned. Its smaller axis, which falls in ~
the plane of 7 7, is about twice as large as the diameter of 7,
in the vessel C, which is about 3 centim. in diameter. If now
we mark the position, form, and magnitude of F on the out-
side of the tube C when the diaphragm presents its edge only
to the kathode-rays, and then place the diaphragm at right
angles to the rays, we find that the position, form, and magni-
tude of F remain unchanged; only its luminosity is now consi-
derably diminished.
If, instead of the diaphragm with a slit, a plate without
openings is introduced into the chamber B capable of free
motion, so as to cut off at pleasure either the upper or lower
half (and also the right-hand or the left-hand half of the
kathode-pencil) by covering the corresponding portion of the
mouth of 7, then also the position, form, and magnitude of the
surface F remain unchanged; the luminosity only of the whole
surface decreases, but most in the half which is opposite to the
half that has been intercepted. Thus, for example, the surface
is darkest in the upper half when it is the lower half of the
kathode-pencil which is intercepted.
We easily see how these observations, inconsistent with
optical reflection, entirely agree with the assumption of a dif-
fuse reflection of the kathode-rays.
Tubes of the form of fig. 5 are better adapted for the further
study of this diffuse reflection than the vessels employed by
Wiedemann. The rays emitted by the kathode & which pass
through the connecting tube r into the wider cylinder Z fall
then upon the plate P, which is fastened to a wire d insulated
with glass inside Z. The cylinder is closed air-tight by the
caoutchouc stopper £, by removing which the plate P can be
exchanged for another; or other changes in the apparatus can
be made.
If the plate P consists of phosphorescent glass, then the
rays which fall upon it directly produce at the plate s simply
an oval very bright green phosphorescent surface. We see,
however, distinctly how the diffuse reflection from this surface
causes the whole wall of the tube Z lying above the plane of
P up to the stopper & to phosphoresce with subdued green
light, which is weaker the further the portion of the wall is
removed from s.
If the plate P be covered with chalk, its surface at s shines
with orange-red light, but the wall of Z presents a green
Reflection of Electrical Rays. 453
luminosity as before—a proof that this luminosity does not
depend upon optical reflection. So also the phosphorescence
produced by diffuse reflection remains unaffected if P be con-
structed of some material which does not phosphoresce at all.
Ii is further a matter of indifference whether P is metallic or
consists of an insulator. In the former case P may even be
made the anode of the discharge, without the reflection of the
rays appearing in any way weakened.
The kathode-rays are therefore not absorbed by the anode,
even when they play directly upon the surface of the anode.
Further we see, as already mentioned above, that the pheno-
menon in question cannot be explained by supposing that the
surface struck by the direct kathode-rays is itself converted
into a kathode.
If we bring small objects between the plate P and the phos-
phorescent surface of Z, such, for example, as the wire D
(fig. 6), whose distance from P can be varied by rotation
round the axis D, we can very well recognize the character of
the diffuse reflection which the place s causes in the rays
which fall directly upon it. For the shadow of the wire D
only appears narrow and sharp when the wire is brought close
to the wall of the vessel; if D is moved from the wall towards
P, its shadow soon becomes bread and indistinct. If we cut
off a further portion of the kathode-rays, by means of a small
movable plate of mica introduced into Z at the mouth of 7,
the space s, directly impinged upon by the rays, of course
becomes smaller. ‘The further this decrease proceeds the nar-
rower and sharper does the shadow of D become, exactly as
we should expect on the theory of diffuse-reflection.
I will here cite only one other consequence of this theory
which has been experimentally verified. I may take it as
known that a pencil of rays emitted by a plane kathode after
it has passed, as in fig. 7, through the aperture (supposed cir-
cular) of a diaphragm occupying the whole area of the tube,
gives on the flat wall W a well-defined circular luminous
figure on a dark ground.
Upen our assumption of the diffusion of the kathode-rays,
this ought not to happen any more if the rays are made to
pass through a cylindrical tube open at both ends (fig. 8), in
place of the thin diaphragm. For since the different rays of a
plane kathode are not altogether parallel to each other, but also
diverge somewhat around “the central portion of the kathode,
a part of them must play upon the wall of the tube r, and be
then diffusely reflected. The portion of the diffuse rays which
reach C must then form an extended luminous space round
the bright surface resulting from the direct rays. We find
454 On the Reflection of Electrical Rays.
this confirmed by experiment ; and if we bring into C a wire
§ throwing a shadow, we find that its shadow is sharp and nar-
row in the region illuminated by the direct rays, but broader
and ill defined in the surrounding region. This takes place
also when 6 is made the anode. We see from this that the
difference in breadth of shadow does not depend upon a
stronger deflection which-6, apparently neutral but really act-
ing as a weak kathode, causes in the reflected rays*. These
last are indeed themselves capable of deflection, as we see if,
instead of making 6 an anode, we connect it with the earth, or
give to it a small portion of the current from the kathode.
The motions of the shadow of 6 under the influence of a
magnet, and with other arrangements the motions of the sur-
face F under similar influence, show that the reflected rays
are deflected, as far as one can observe, in the same way as
the direct kathode-rays would be if their course were the same
as that of the reflected rays.
If r be placed equatorially above a horseshoe magnet of
suitable strength, the direct kathode-rays before reaching C
are compressed against the upper or under wall of rv, and the
phosphorescent surface (@) produced by the direct rays disap-
pears ; but the feebly illuminated region remains, occupying
now the position of the surface @: this corresponds exactly to
Wiedemann’s surface F; its production here is due to the dif-
fuse rays which issue from the portions of the straight tube r
struck by the magnetized rays. The further the terminal point
of the direct rays is forced towards C by the action of the mag-
net, the less luminous does the surface F become, since then a
continually smaller portion of r is able to reflect rays.
On the whole, the foregoing series of experiments leads to
the following result, which I propose to describe more fully in
a further communication:—A pencil of kathode-rays does not
end (at any rate under the conditions suitable for producing
phosphorescence) where it strikes upon a solid wall, but elee-
tric rays radiate in all directions through the space oceupied
by the gas from each point of the wall struck by the direct
rays. These rays may be called reflected rays. Any solid
wall, no matter what its properties are, may serve as reflecting
surface. It is a matter of indifference whether it is capable
of becoming phosphorescent or not, whether it consists of a
conductor or of an insulator. The reflection is diffuse, equally
whether the reflecting surface is dead or as smoothly polished
as possible. An anode apparently reflects the kathode-rays,
the same as a neutral conducting surface or an insulator. The
reflected rays, like the direct kathode-rays, have the property
_ * ‘A new Form of Electrical Repulsion,’ p. 124.
Influence of the Shape of the Kathode in Geissler’s Tubes. 455 |
of exciting phosphorescence at their ends. They are capable
of being deflected ; and their ends are bent aside by a magnet
in the same direction as the ends of the kathode-rays would
be which radiated from the reflecting surface to the points
reached by the reflected rays.
LI. On the Influence of the Shape of the Kathode on the Dis-
tribution of the Phosphorescent Light in Geissler’s Tubes.
By Dr. Ei. GoupstEIn*.
[Plate VII. figs. 9-35. ]
YLINDRICAL wires cut off at right angles have been
almost exclusively employed as kathodes in systematic
investigations on the discharge of the induction-coil in rarefied
gases, or, in particular cases, spherical electrodes or plane
circular disks. Kathode-surfaces, which can be divided into
two halves of similar shape by an infinite number of cuts, do
not give rise to a class of phenomena which I have observed
with kathodes of regular surface, in which nevertheless there
is no axis of symmetry corresponding to an infinite number
of equivalent sections.
We are concerned with extremely regular figures, in which
the phosphorescent light of the walls illuminated by the
raystrom those kathodes arranges itself, which, however, are for
the most part altogether unlike the shape of the kathode itself.
Reserving a detailed description, | may here give the general
characters of the most important types of these figures +.
Kathodes of concave spherical form were first examined,
constructed of thin soft iron, which was first of all stamped
and then ground into the desired form.
The kathodes were soldered at the middle points of their
convex sides to wires which conveyed the current, and which
were insulated by being covered with glass thermometer-tubing
between their junction to the kathode and the point at which
they entered the vessel.
The discharge-tubes were glass bulbs of 4 to 5 centim.
radius; the axis of the spherical concave mirror which formed
the kathode was placed in a diameter of the bulb. The dis-
tance of the kathode from the wall, measured along this dia-
meter from the centre of the mirror, could be varied ; in the
* Monatsber. der Konigl. Akademie der Wissenschaften zw Berlin, July
1881 Translated from a separate impression communicated by the Author.
t A preliminary notice appeared in the Wien. Akad. Anzeiger of the
13th Jan. 1882. The phenomenon of figures in phosphorescent light dis-
similar from the kathode was described “by me for the case of a kathode
of cylindrical curvature so long ago as 1876 ( Wien. Sttzungsber. xxiv.
[2] p. 465).
456 Dr. E. Goldstein on the Influence of the
experiments next to be mentioned it was made equal to twice
the radius of curvature of the spherical kathode.
If we now assume, as for example Crookes does in his well-
known memoirs, that from each point of a concave kathode
only one rectilinear ray radiates, and that along the normal to
the surface, it would follow that the phosphorescent image of
a concave kathode on a concave spherical wall, at a distance
of twice the radius of curvature of the kathode, would be iden-
tical in form and dimensions with the kathode itself, if the
radius of the vessel were equal to that of the kathode; it would
be coincident in form and nearly in dimensions with the ka-
thode itself if, as in my experiments, the radius of the vessel
were greater than that of the kathode, without the kathode
having any considerable aperture. There will be no essential
change in the character of the phenomena to be expected, if
we also take into account the feebler phosphorescence caused
by the rays* emitted by the elements of the kathode on its
edge in variously oblique directions up to the tangential di-
rection. But experiments show very different phenomena.
1. Fig. 9a represents a square of the actual size, ground into
a spherical surface of 40 millim. diameter; and fig. 9b repre-
sents the phosphorescent image, also of the actual size, formed
by this kathode in a highly exhausted glass vessel of 8 centim.
diameter ; we remarka star of light with four rays, the axes of
the rays being at right angles to the sides of the square ka-
thode. In the figure representing the luminous star, the edge
of the kathode is marked by black dots in order to indicate the
relative positions of kathode and image. At extreme exhaus-
tions there appear, less distinctly marked, four much shorter
rays coming from the centre of the image and corresponding
to the directions of the diagonals of the kathodef.
An equilateral triangle having the same curvature (fig. 10)
produced a star with three rays, whose axes were at right
angles to the sides of the triangle. So also polygons of 5, 6,
7, and 8 sides gave stars, with a corresponding number of
rays, whose axes appeared to bisect the sides of the polygon
at right angles.
The position of these figures with reference to the kathode
* Eine neue Form electrischer Abstossung, i. p. 11.
t In the accompanying figures of portions of the surface of a sphere,
the ares of great circles between the centre of the light-figure and the
separate points forming the bounding surface of the figures are approxi-
mately represented by the chords of these arcs, or in the smaller figures
by the corresponding aliquot parts of these chords. This corresponds
with the method of measurement employed, in which distances on the
spherical surface were determined by the direct distance between the
points of a pair of compasses applied to the surface.
Shape of the Kathode in Geissler’s Tubes. 457
is worthy of remark, as throwing light upon their mode of
production. If we cover up the upper portion of a polygonal
kathode by a screen placed between the kathode and the
centre of curvature, then the wpper arms of the star are want-
ing in theimage. The arms are therefore not produced, as we
might have expected, by the radiation from the portions of
the kathode diametrically opposite.
A four-armed cross, fig. 11 a (actual size), forming a portion
of a sphere of 40 millim. diameter, gives fig. 11 on the wail
of a vessel 8 centim. in diameter, in which again the position
of the kathode is marked by dots. The metallic arms of
the kathode thus correspond to the dark arms of the cross
in the phosphorescent figure, and the light is concentrated
in fields corresponding to the intermediate spaces in the
kathode.
If, again, the kathode has three arms, with angles of 120°
between the arms, we obtain a figure with three dark arms.
These again fall upon the metallic arms, and the bright fields
upon the intermediate spaces between the metal arms *.
The dark arms of the image, however, are much narrower
with the four-rayed figure than with the three-rayed one, if
the arms of the kathode are of equal width and equal length
in the two cases.
We obtain analogous figures when the kathode has five or six
(uniformly distributed) arms, except that as the number of
arms increases the dark fields which correspond to the metallic
arms become narrower, not only absolutely but also relatively
ee is, in proportion to the width of the bright intermediate
fields.
These two typical forms—the polygon, and the star consisting
of rectangles—may suffice as a preliminary indication of the
forms of the images which appear when the exhaustion is
sufficient.
2. The images formed by kathodes of this sort alter very
much when the density of the gas is altered.
The image-forms described above are obtained with den-
sities of gas about 7), millim. mercury. We can, however,
trace the phosphorescence at pressures only slightly less than
1 millim., or even over this pressure, by including in the dis-
charge at the same time sparks in free air. We obtain then,
for example, for the four-armed cross-shaped kathode, fig. 11 a
(radius of curvature 20 millim.), the images 12a to 12e in
* I have made repeated attempts to obtain a result described in Carl’s
Repert. 1880, p. 244, where a sort of three-rayed star gave simply an erect
image of the kathode, but never with success.
Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 2H
ail
458 Dr. E. Goldstein on the Influence of the i
succession, to which succeeds the image represented in fig.
114 when the exhaustion becomes sufficient.
We obtain then at first an image of the kathode itself—a
cross having nearly the dimensions of the cylindrical projec-
tion of the kathode upon the wall. The arms of the cross in
the image grow smaller and become the central lines of a
well-defined square, that appears as a luminous background
round the cross. As the density decreases, the square be-
comes smaller and its luminosity increases. Its sides lengthen
beyond the angular points, and form points resting on the
sides of the square. The central cross disappears ; only the
intersection of its arms remains as the bright centre point of
the whole figure.
The square now becomes smaller; and the points superposed
on the sides become narrower in the same proportion. This
takes place in consequence of the concave sides of the contour-
lines approaching each other, and passing over each other,
12d and 12¢, As this displacement continues in the same
direction while the density of gas decreases, the pair of ares
which previously intersected finally pass apart, and leave a
dark space between their convex sides: thus finally, at
great exhaustion, the dark cross already figured in fig. 115
results,
The series of changes thus described is typical also for the
successive images given by crosses or stars with other numbers
of arms.
We obtain in each case at first an image closely resembling
the kathode, and of nearly the same dimensions. Observation
with three- and four-rayed stars (fig. 13 and fig. 14), shows—
what was not evident with the four-rayed star, nor generally —
with regular figures with an even number of arms—that these
figures are reversed images of the kathode, formed by the rays
from the kathode crossing each other. Next, the background
round these figures becomes brighter, bounded by as many
sides as the kathode-star has rays. The rays of the star-
figure form the smaller radii of the polygon so formed. As
the exhaustion of the gas continues, this polygonal figure
decreases, its surface becoming brighter; and the inserted star
disappears, its bright centre point remaining visible the
longest. On each side of the polygon appears a point similar
to those in fig. 12d. The concave sides of the bounding
arcs approach each other more the further the exhaustion
proceeds ; and at last, as the result of displacements exactly
similar to those of figs. 12 and 12g, there appear dark rays
between bright fields, which again correspond to the metallic
arms of the kathode.
Shape of the Kathode in Geissler’s Tubes. 459
The type of successive changes in decreasing density of gas
with polygonal kathodes may be illustrated by the series of
images given by a concave spherical square (fig. 15). Figs.
cand d, for the sake of greater distinctness, are represented
ona scale somewhat larger. If the kathode-polygon possesses
an odd number of sides, then the luminous polygonal images
corresponding to figures 15 b-d are reversed with reference to
the polygonal kathodes, corresponding with the observation
made with star-shaped kathodes with an odd number of rays.
It is these luminous figures so far described and figured
which first strike the observer, in the phosphorescent images
of the corresponding kathodes ; upon closer observation we see
that the other surfaces of the glass vessel are also not devoid
of luminosity, but show phosphorescent surfaces of feeble
luminosity at different points. The boundaries of these sur-
faces, in the case of star-shaped kathodes, are prolongations of
the luminous curves which bound the chief figures; with
polygonal kathodes they are extensions of the star-rays
observed in the luminous figure. Partly because, from what
has been said, a sufficient preliminary account of the way in
which these less-luminous portions complete the figures already
figured and described is now possible to the reader, and partly
to economize space, I abstain from further description of
these outlying portions until the separate observations have
been completely described. The image obtained in a spherical
vessel of about 9 centim. diameter, employing as kathode the
cross figured in fig. 11 a, may serve as a good example : it is
represented in figs. 16 a and 16¢, in the pointed phase and in
the dark-cross phase.
3. Besides the forms obtained by simple variation of the
number of sides and arms of polygons and stars composed of
rectangles, I have further examined the images given by
numerous other forms of kathode—some simpler, some more
complex—in order to separate as far as possible that which is
general from that which is special. Thus, for example, of
simpler forms were examined :—rectangle, rhombus, rhomboid,
isosceles right-angled triangle, &c. of compound forms; crosses
composed of obliquely compounded rectangles, and crosses
formed of isosceles triangles (the latter either with the
vertices or with the bases outwards); further, figures such as
are obtained by cutting out of squares segments of circles or
smaller squares at the four sides.
So far as the effect of the form of the kathode, and of the
variation in density of gas, manifests itself with these images,
I must defer a description of the phenomena observed until
I give a more complete explanation of the whole. The
2H 2
460 Dr. E. Goldstein on the Influence of the
following general rules (4—7), however, hold good for all the
kathode-forms mentioned.
4, At constant density of gas, the forms of the phospho-
rescent images (not only their absolute dimensions) alter when
the distance of the kathode from the wall of the vessel is
made to change; as the distance of the wall decreases, the same
figures appear, in the same order, as when the distance of the
wall remains constant and the density of gas decreases.
Instead of altering the distance of the wall by displacing
the kathode, we may, as in the vessel represented in fig. 17,
displace the wall which receives the rays with reference to the
kathode.
If we experiment with varying distance of wall, and also
with varying density of gas at the same time, then, in order to
pass from one given figure to another of the same series, the
wall must be displaced through a greater distance the smaller
the density of gas is.
This shows that all the figures which a kathode can call
forth upon a fixed wall as the density of gas decreases, do at
any fixed density of gas already exist in space one behind
the other at the same time, and that the different figures are
produced by the rays intersecting each other in various ways
at different points of space. As the density of gas decreases,
the images move further apart and further away from the
kathode, no doubt because the rays which first converge
become less convergent, and then, when after intersection
they diverge, their divergence is decreased.
The influence of the distance of wall thus described would
lead us to expect that the series of images given in figs. 12 and
15 as examples obtained with a kathode at a distance equal to
twice the radius of curvature, would not include all the forms
which the particular kathode is capable of producing, but that
a diminution of the distance of the wall at the highest obtain-
able exhaustion would in general give other figures besides
these. This conclusion is found to be confirmed by ex-
perience, although the forms thus obtained are not for the
most part so striking as those previously described. It may,
however, be mentioned at this stage as worthy of consideration
further on, that upon diminishing the distance of the wall the
dark arms of ihe cross in fig. 1le increase considerably in
width.
5. If we take similar plane figures, and then bend them into
portions of spheres of different radii, p;, ps2, p3, and place
them as kathodes in similar vessels with equal distance of
wall, then at equal density their images represent different
phases ot the series of figures obtained from a single such
ce tethake se tp en
Shape of the Kathode in Geissler’s Tubes. 461
kathode with varying distance of wall: and the figure pro-
duced by a particular kathode & corresponds to a greater dis-
tance of wall from the kathode used to compare with, the
greater the curvature of the kathode & is.
This result might indeed have been regarded as & priori
probable. We might indeed expect to obtain simultaneously
like figures from different kathodes (similar in their original
plane condition) by making the distance of the wall equal to
Np, NPi, NPs, &e. for different radii of curvature p, pj, ps2, Ke.
—that is, the distance of the wall in each case the same mul-
tiple or submultiple of the radius of curvature—as, for example,
by placing each kathode at a distance from the wall equal to
twice its radius of curvature.
But experiment shows also that in this case the phases are
different; and the increased curvature acts in the same way
as, ceteris paribus, the increase of the distance of the wall or
an increase of the density of gas. This influence goes so far
that, with kathodes which are much curved, it has not been
found possible by exhausting the gas to produce those forms
of the series of figures which, with electrodes of less curvature,
correspond to the lowest degrees of the scale of density. Thus,
for example, with the four-armed cross fig. lla, of a radius
of curvature of 124 millim. instead of 20 millim., and with a
distance of wall 2p, we find it impossible by exhausting to
reach the phase of the dark cross fig. 116. The figure
obtained immediately before the cessation of the current at
the greatest exhaustion is the figure with curved points,
fig. 12¢.
6. If we leave the general form of the kathode and its cur-
vature unaltered, but increase the aperture of the kathode,
this increase acts also as an increase of the distance of the wall
would do.
If, for example, we replace a square of 12 millim. in the
side which has been bent to form a spherical surface or 40 mil-
lim. diameter by a square of similar curvature, but with sides
30 millim. long, then at the extreme exhaustion we do not
advance further than fig. 15d, whilst the small square gives
us figures up to 15g.
We obtain similar results with the more complicated forms
of kathodes—for example, the four-armed cross made up of
rectangles, fig. lla. If the length of the cross be increased
from 20 to 25 millim. without altering the width of the arms,
then at the greatest exhaustion at which the current will pass,
the dark cross is just visible ; but it cannot be obtained with
arms of any considerable breadth.
If the cross is increased to 40 millim. the dark cross is no
462 Dr. E. Goldstein on the Influence of the
longer to be obtained, and fig. 12¢ is the last obtained at
extreme exhaustion.
The results are qualitatively identical if we increase the
breadth of the arms in the same proportion*.
7. The experiments mentioned in No. 5 show thatthe phase
alters when plane kathodes of similar shape are bent into
spherical surfaces of different curvature. Since the same
figure, formed to different spheres, will form a mirror of
greater aperture the smaller the radius of the sphere is, the
result described in No. 5 as to the influence of increased
curvature might possibly seem to be only another state-
ment of the influence mentioned in No. 6 of increased aper-
ture. In that case we should expect that kathodes of like form
and different curvature but like aperture, at distances forming
the same multiples of their radii of curvature, would give like
figures at like densities of gas.
To test this I constructed a series of kathodes (e. g. three
four-armed crosses, I., IJ., I1I.), whose dimensions were as
follows:—
Radius of fone Breadth
curvature (p). ane of arms.
millim. millim. millim.
| Pp 121 124 1
Dy, wisnes adits 20 20 +
Tide ete 263 263 54
The kathodes thus all covered equal aliquot parts of the
spheres from which they were formed. They were placed at
a distance 2p from the spherical wall of the similar containing
vessels—that is, 25 millim., 40 millim., and 534 millim. re-
spectively.
Here also the result was obtained that there is no identity
of phase for equal density, but the figures given by kathodes
IJ. and III. corresponded to the figures which kathode I.
would have given if the distance of the wall had been increased.
This occurred indifferently, whether the two electrodes of each
of the three discharge-vessels were separately connected with
the poles of the induction-coil, or whether, in order to secure
equal intensity of discharge, the current was sent at the same
time through the three vessels, connected together in line.
* The changes in curvature and aperture of kathode described in the
two preceding paragraphs cannot, in one respect, be always compensated
by changes in density of gas or in distance of wall: the last term of the
series of figures (corresponding to fig. 15g) for a polygonal kathode shows
with kathodes of greater curvature or larger aperture richer differentia-
ae ad finer detail. The rougher figure cannot be reproduced with these
athodes.
.
4
Pas
Shape of the Kathode in Geissler’s Tubes. A63
8. The phosphorescent figures which appear when spherical
electrodes are employed, as might have been expected, become
replaced by others when the originally plane kathodes are
formed, not into spherical surfaces, but into cylindrical or
conical surfaces. I will content myself in this cursory report
with mentioning that, with cylindrical kathodes, the phospho-
rescent images are different according to the position which
the axis of the cylinder has with reference to the axis of sym-
metry of the kathodes. Thus, for example, with a square
kathode formed to a cylindrical surface we obtain different
figures according as the axis of the cylinder is parallel to a
side of the square or to one of its diagonals. In the same way
there are marked differences in the images of cross-figures
according as the axis of the cylinder is parallel to one of the
arms of the cross, or bisects the angle between the arms.
9. With reference to the explanation of the phenomena so
far described, it is only wise to maintain a certain reserve
towards a class of phenomena as yet very imperfectly known.
A doubt as to the success of the attempt to bring a large
portion of these phenomena into any simple relationship with
known causes, could only be supported by the observations
described in No. 10, on the images given by plane kathodes.
All that I hope to do is to give some indications, derived from
experiment, on the direction in which the explanation of many
of the phenomena observed with star-shaped kathodes is to be
sought. As to the explanation of most of the phenomena
given by the above-mentioned polygonal kathodes, I do not
here venture upon any hypothesis. ‘The star-shaped kathodes
are of course also polygons with reentrant angles; and their
separation from the polygonal surfaces appears unnatural at
first sight. Nevertheless the phenomena which we have to ex-
plain with star-shaped kathodes are for the most part just those
which are closely connected with the presence of reentrant
angles, and which may be approximately explained by taking
into account only the edges of the kathode. The phenomena
due to the surfaces themselves, in those forms of kathode
where the surface of the kathode is relatively unimportant
as compared with the extent of its bounding edge, are insig-
nificant in comparison with the phenomena due to the curves
of its circumference ; and the former remain unexplained here
just as with the polygons with convex angles, where the phe-
nomena of the surface constitute the chief part of the pheno-
mena observed. Only the surface-phenomena produced at
small exhaustions can be approximately accounted for with
both kinds of polygons That the images of a star-shaped
kathode which appear at relatively small exhaustions result
464 Dr. E. Goldstein on the Influence of the
from the intersection of the rays emitted by one half of the
cross with those from the other half, was shown to be probable
by the experiments already described with stars of an uneven
number of arms. This may, however, be better shown b
experiments with screens arranged to throw shadows, whic
also prove the same thing for kathodes with an even number
of arms. ;
If we arrange (fig. 18 a) ascreen of paper or of mica in front
‘of the kathode, and at a distance from its centre less than the
radius of curvature, so that, for example, the lower half of the
kathode-cross is covered, then in the phosphorescent image it
is the upper half of the cross which is wanting (fig. 18 D).
. Since at a certain density these images formed on the wall
at the distance 2p from the kathode possess nearly the same
dimensions as the kathode itself, it follows that the rays which
produce the images, at least for the most part, are under these
circumstances at right angles to the surface from which they
are emitted, assuming, of course, that their course till they
strike upon the walls of the tube is rectilinear.
(Exactly similar experiments show that the images of ordi- |
nary polygonal kathodes observed at small pressures are
formed by the intersection of the rays which issue from points
situated symmetrically with reference to the centre of the
kathode. )
As with the figure of the kathode-cross, so also in the con-
tour of the square (fig. 12 6) which appears surrounding the
figure of the cross as the density decreases, each side is formed
by rays which come from the opposite side of the kathode.
We may obtain a more satisfactory explanation of the figures
of kathode-crosses which appear at small densities; we only
need to place a screen P(fig. 19 a) between two of the arms
of a cross, so that it projects beyond the kathode on the con-
cave side. The screen may be rectangular, and the edge
which faces towards the image may be called its front edge.
I anticipated, and the anticipation was verified by experiment,
that the figures which correspond to the higher degrees of
exhaustion are formed by the rays emitted by one arm of the
kathode suffering a repulsion by the neighbouring arm, of the
same or a similar kind to that described in my work on ka-
thodic deflection, This deflection cannot take place through a
solid plate.
If now, at high exhaustion, we obtain repeatedly the figure
with the dark cross so often mentioned, then, when the plate
is introduced, we obtain the figure 194; or, if the plate
does not project so far beyond the kathode, we obtain 19 ¢,
We have therefore, in the first case, only the left bounding
Shape of the Kathode in Geissler’s Tubes _ 465
are of the upper arm of the cross, and only the lower bound-
ing arc of the right-hand arm: the two dark arms themselves
cannot be perceived; but the space between the bounding arcs
mentioned is uniformly illuminated.
The two bounding ares, which are now absent, result there-
fore from an action between the upper and right-hand arms,
prevented or hindered by the presence of the screen.
If the plate is withdrawn a little, then, as already men-
tioned, the figure 19 ¢ is seen.
The dark arms which were wanting in the first image are here
seen as very narrow strips, and the corresponding two bound-
ary curves are of feeble luminosity. The more the screen is
withdrawn towards the kathode the broader do the two dark arms
become, and the more closely does the luminosity of the two
‘curves approach to the normal luminosity. The mutual action
between each two neighbouring arms, to which the production
of the dark cross is due, may be supposed to take place in
three different ways :—either (1) as an immediate action of
each of the arms of the kathode upon the other, which thus in-
directly produces an effect upon the course of the electric rays;
or (2) as an action of each arm upon the system of electric
rays emitted by the other; or (3) as a mutual action of the
two systems of rays.
Any further discussion of the utility of the three hypotheses
at present would lead us too far away. I will content myself
with remarking that the assumption (1), so far asI see, is
opposed to the details of the phenomena of kathodic deflection;
but it is not possible to decide certainly between (2) and (8).
Taking account, however, of the fact that the third assump-
tion involves certain accessory assumptions which have not
yet been verified by experiment, I shall employ the language
of the second hypothesis in seeking for further explanation;
which hypothesis, moreover, | have employed throughout in |
my research on kathodic deflection, m describing the phe-
nomena observed.
If now (fig. 20) rays issue from the edge a of the right-
hand arm (1) towards 6, then, according to the laws of ka-
thodic deflection, these rays will be repelled by the edged and
the whole surface of (2). The same holds good for the rays
emitted by the left arm atc. Let fig. 21 be a rough repre-
sentation of the kathode, turned through 90° from its position
in fig. 20, the upper half having moved forwards; and let
/ and r represent the upper edges of the left and right arms
respectively, and o the (fore-shortened) upper arm. The
repulsion which o exerts upon the systems of rays emitted by
y and J will cause the mutual convergence of these two last
466 Dr. E. Goldstein on the Influence of the
to decrease, but so that the two systems of rays still intersect
each other (at wz, in fig. 22).
If now a plate capable of phosphorescing move at right
angles to the plane of the drawing in the space free from rays
between the points of intersection # and o, a dark space will
be seen on it, bounded by its luminous intersection with the
repelled systems of rays; thus the upper arm of the dark cross
is bounded by its two luminous curves. ‘As the density of
the gas decreases, the repulsion increases; the convergence
of the two pencils of rays will therefore be still further di-
minished; the point of intersection, 2, moves further away
from the kathode; and the plate may now be further off from
the kathode and still show the dark cross. As we saw already,
in examining deflection, the rays further off from the repelling
surface are carried with those which are nearer to it, but are
not deflected through so great an angle; the deflected rays are
therefore compressed together on the side turned towards the
repelling surfaces; hence the greater brilliancy of the narrow
contour-line immediately bounding the dark arms.
If the phosphorescent plate moves away from o beyond 2,
the dark cross on it must of course disappear, since the plate
comes into a space occupied by rays. We must therefore
have a bright field on the plate opposite o, the outer contour
of which is again formed by the intersection of the plate with
bounding surface of the deflected system of rays.
If we take account of the fact that, according to the form of
the dark cross, the curved surfaces of these systems of rays
have their convex sides turned towards each other before the
intersection, we see that beyond « they will have their concave
sides towards each other, and will thus form the “ curved
points,”’ which observation shows to exist.
Consequently the upper “ curved point” (fig. 23) is not
formed, as we should have expected at first, by rays from the
upper arm of the kathode, but it is formed by rays from the
two horizontal arms of the kathode—the left-hand half, and in
particular the contour-line /, being formed by rays from the
right-hand arm R, and the right-hand half by rays from the
arm L.
If this is the right way of regarding the curved points,
we ought to find it confirmed by experiments in which
shadows are thrown. This is, in fact, the case.
If we put a plate as a screen close in front of the kathode,
so that, as in fig. 24a, it covers one half of the kathode ob-
liquely, then at the density at which the curved points appear
we observe the phosphorescent figure 246. The bounding
eurves shown in dotted lines are now wanting. The phe-
aE
Shape of the Kathode in Geissler’s Tubes. 467
nomenon thus agrees most exactly with the explanation given
above.
If we exhaust up to the density which corresponds to the
figure with a dark cross for the uncovered kathode, we obtain
the figure 25. By comparison with fig. 246, we see here
also very plainly that the bounding curves of the dark cross,
with their convex sides turned towards each other, are nothing
else than the bounding lines of a “ curved point” with con-
cave sides turned towards each other, which have become
displaced across each other.
10. The most remarkable phenomena of the kind we are
now considering, however, are undoubtedly those produced by
plane kathodes.
That plane kathodes cut into figures would present pheno-
mena similar to those of the dark cross was probable, since
rays emitted by one edge of an arm of the figure would be
repelled by the other edge. Thus, in fact, a four-armed plane
(fig. 26 a) gives a figure resembling fig. 26 b, with a distance
of wall from 3 to 4 centim.
The figures 12 c, 12 d, &e., observed with the curved cross-
shaped kathode, do not appear with the plane kathode, but as
the density decreases the first figure recognizable is the dark
cross; if the density is still further diminished the arms in-
erease in width, and show in the part nearest the centre a
nebulous luminosity, with convex contour line (fig. 27).
Tf the distance of the wall be made less than 3-4 centim., this
nebulous portion increases in brightness, and contracts, be-
coming better defined; and with a distance of wall of about
14 millim. we obtain the figure represented in fig. 28. In each
of the four arms, which would otherwise be dark, there appears
a beautifully forked line of light, the space between the forks
being filled with uniform light with convex contour, while
each fork is connected with the others by a slightly luminous
are of light.
In using a concave spherical cross of the same dimensions
as kathode, the radius of curvature being, however, greater
than 25 millim., we observe in the arms of the dark cross, so
often mentioned, which appears at low pressures, this same
luminous fork. We have therefore, as was to be expected, a
gradual passage from the forms given by the curved kathodes
to those of the plane kathodes, the figures given by the plane
kathodes regulating those of the spherical kathodes. Inas-
much as no explanation of the images produced by the former
is possible, so for the present no explanation is to be given for
a number of phenomena obtained with the curved surfaces.
The dark cross produced by the plane crogs-shaped kathode
468 Dr. E. Goldstein on the Influence of the
we might foresee ; but it is not possible to predict, a priori,
the phenomena produced by plane kathodes, not cut out,
nor having concave edges, and these constitute an pais
new class of phenomena. I make here the general remar.
that, while it is true that the images given by plane kathodes
alter somewhat with decreasing density, they do so much less
than the figures obtained with curved kathodes, and often
the changes consist only in the acquisition of richer detail
and more definite contour, or perhaps somewhat larger dimen-
sions. If these images are produced by kathodes of relatively
small surfaces (1 to 14 square centimetre), the kathodes
must be placed tolerably near to the wall of the vessel. The
larger the surface of the kathode is, the greater the distance
of wall at which it first appears. If with a given kathode we
go further off than a certain distance, we obtain a uniform y
illuminated phosphorescent surface, whose luminosity slowly
and gradually decreases from the centre outwards.
If a plane square be employed as kathode, we obtain fig. 29
on the wall of the spherical discharge-tube of 9 centim. diameter.
The relative size and position of the kathode (2% centim. distant
from the wall) is marked by the dotted lines. We obtain
therefore a star of eight arms, four of whose rays correspond
in direction to the diagonals of the-kathode, and the others to
its central lines. The centre of the figure is formed by a
feebly illuminated square space, upon which the star appears;
a luminous zone surrounds the dark central space, formed of
four arcs, convex outwards,
The four rays corresponding to the central lines of the
kathodes have their maxima of light within this outer zone ;
the four diagonal rays, which are narrower than the others,
are uniformly luminous, except that all eight rays are more
luminous at the centre of the whole figure. The whole figure
is considerably larger than the kathode-square, the darker
central square space being larger than the kathode.
The figure given by a rectangle 2 centim. by 1 centim., with
its longest sides horizontal, on the wall at a distance of 14
centim., is represented in fig. 80. The main figure is thus a
narrow line of light, corresponding to the central line of the
rectangle, which forks at each end, and is surrounded by a
broad band. The lower ground is an oblong, rounded at the
small ends.
A plane circular disk, as mentioned in the introduction, gives
no special figure on the illuminated ground obtained in all the
figures, unless we regard the bright central point of the image
as such a figure. The rays produce a circular disk, which is
not sharply defined, with the feebly illuminated ground, and
Shape of the Kathode in Geissler’s Tubes. 469
brighter zone at the edge ; the centre point is, of course, bright.
An ellipse whose axes measure 10 mm. and 20 mm., on the
other hand, gives a comparatively complicated figure (fig. 31)
at a distance of wall of 1 cm. in a vessel of 94 cm. diameter.
Tn allthese figures the ground expands the more the density
of the gas is reduced.
If we use kathodes made up of several of these simpler
forms joined together, we of course obtain much more com-
plicated images. The images obtained with the comparatively
simple form of kathode fig. 32a may serve as example.
A square out of whose edges smaller squares have been cut
(fig. 326) shows the central portion of the phosphorescent
image completely; but, to save space, the figure gives only
two of the streams of light which project from the four sides.
To enter at present further into detail in describing a large
number of these phenomena, which are often characterized by
surprising beauty, would be without scientific interest, since
the simpler cases already described sufiiciently represent
whatever is new and characteristic amongst phenomena of
the kind, viz. :—
(1) The fact that such figures are produced.
(2) The circumstance that the magnitude of the images
varies with the density of the gas, and exceeds the magnitude
of the kathode itself at high exhaustions.
This latter phenomenon, to which I have devoted a separate
series of experiments, may be supposed to occur in either of
two ways: either the direction of the rays varies with the
change of density, the pencil emitted by a plane becoming
more divergent the smaller the density of the gas becomes ;
or the direction of the rays remains constant, and as the den-
sity of the gas decreases the previously unobserved rays of
those elements of the surface which are situated obliquely to
the outward-directed rays become strengthened.
Hixperimental trial gives as result that the first-named
reason (variation in direction of rays with variation of den-
sity) is to be preferred. Of the different methods of proof
employed I will mention only one here.
If we cut slits in a plane disk, the spaces in the disk show
themselves in the phosphorescent image, for which the disk
acts as a kathode, as narrow dark lines. A number of con-
centric and equidistant semicircular cuts were made in a disk,
so that the outside one lay near the edge of the disk (fig. 33),
In the phosphorescent image there appear, even at the highest
density at which it is visible, the same number of dark semi-
circular lines, showing that even at the highest density the
phosphorescence produced by the elements on the edge of the
470 Dr. HE. Goldstein on the Influence of the
disk is manifest. If the exhaustion be carried further, the
dark semicircular lines move further apart ; and at a constant
density the distance between any two of the dark semicircles is
greater the further the pair in question lies from the centre.
This last behaviour manifests itself also if the phosphorescent
image is received on a plane surface parallel to the kathode
instead of upon a spherical wall.
The phenomena described for plane disks lead to the follow-
ing conclusions :—
(1) The different points of a plane kathode-surface are not
of equal value in the emission of kathode-rays, but the inten-
sity of the rays depends on the position of the elements by
which they are radiated with respect to the contour-line of
the kathode. ,
(2) The rays of a plane kathode-plate do not in general form a
parallel pencil* ; but the inclination of the rays varies from
element to element, in accordance with the distance from the
contour-line of the plate.
(3) The direction of the radiation from each separate ele-
ment varies moreover with the density of the gas. Thesmaller
the density becomes, the more does the direction of radiation
differ from the normal to the element; and the direction of
deviation is always outwards.
Whether any density exists at which there would be devia-
tion from the normal in the opposite direction (7. e. inwards),
at which therefore the rays would be convergent, is a question
to which an answer must for the present be deferred. The
deviations which make their appearance as the density dimi-
nishes are the more considerable the nearer the element in
question lies to the edge of the surface.
11. Convex kathodes of regular outline also produce regular
phosphorescent images.
Convex spherical forms, so far as I have observed, give the
same figures as plane kathodes of the same outline—only of
larger dimensions at an equal distance of wall, in consequence
of the stronger divergence of the rays.
With cylindrical convex surfaces the figures obtained with
plane surfaces of similar outline are deformed, as might have
been expected ; the image is, ceteris paribus, more expanded at
right angles to the axis of the cylinder than parallel to the
* If we assume that each point of a kathode emits, not simply one ray,
but a small conical pencil of rays, then in the above proposition, ins
of “ray” we must read “ axis of conical pencil of rays.” I am still oceu-
pied with experiments to determine the limit of aperture which we can
ascribe to the pencil of rays from a point of a surface.
Shape of the Kathode in Geissler’s Tubes. 471
axis, and that in greater degree the greater the curvature of
the surface.
12. Still another class of simple forms of kathodes which
produce figures are such as may be termed “ interrupted;’’ to
which belong, amongst others, prismatic tubes open at the
ends and cut off at right angles, then (plane) figures formed
by bending wire (¢. g. polygons of wire), and so on.
The images given by such wire kathodes are amongst the
most beautiful which can be obtained. In order to render
intelligible at least the general mode of their formation, the fol-
lowing may be mentioned:—
If a cylindrical or prismatic tube cut off at right angles to
its axis and open at both ends be employed as a kathode, then
as the exhaustion proceeds a conical pencil of rays issues from
each of the open ends of the tube, the axis of which is coin-
cident with the axis of the tube, and which expands more and
more into the gas-space the further the exhaustion is carried.
Assuming rectilinear rays, the pencil is then so directed as if
it issued from a metal plate closing the actual opening of the
tube. When the exhaustion is sufficiently great, this pencil
reaches to the wall of the vessel and excites phosphorescence
there.
The phosphorescent image of this pencil forms the phos-
phorescent figure produced by a tube-shaped kathode.
In general, there are two images produced corresponding
to the two pencils which issue from the two openings of the
tube, and which are congruent if, for example, the discharge-
vessel be spherical and the middle point of axis of the tube
coincide with the centre of the sphere.
We have a similar result to that obtained with a cylindrical
kathode, when the wall of the tube kathode is saddle-shaped,
such for example as is formed by the revolution of an are of
a circle about an axis lying on its convex side.
If we imagine such a tube of very small height, we obtain
a ease which can also be realized by surrounding a space with
a wire of the corresponding form. Just as pencils of rays
issued at right angles to the opening of the tube, so they
issue from the wire kathode at right angles to its plane, to all
appearance as if the empty space surrounded by the wire acted
as a kathode.
The luminous figures obiained from wire kathodes are
larger than the space enclosed by the wire, even at small dis-
tances of the wall from the kathode. The images may show
great changes with change of pressure. I content myself with
472 Notices respecting New Books.
giving as example the image represented in fig. 34 6, given at
high exhaustion on the wall of a spherical vessel by a regular
pentagon of 12 millim. in the side bent out of wire about
1 millim. thick (fig. 34). The normal to the polygon at its
centre point was placed radially.
The waving contour-line which passes through the ends of
the five-rayed star forms a perfectly sharply defined contour-
line.
If we employ a regular wire polygon of some other number
of sides (3-8), we obtain a similar luminous star with the
corresponding number of rays. With polygons with an odd
number of sides, the rays of the star correspond in direction
to the longer radii of the kathode-poly gon.
With polygons of an even number of sides, on the other
hand, the axes of the rays correspond to the shorter radii of
the polygon, and thus appear to intersect the sides of the
polygon at right angles.
With the phenomena which are given by interrupted
kathodes may be connected an observation made with plates
perforated with holes, which is at first sight surprising. If
we make use of a square plate perforated with a number of
holes (fig. 35), we might perhaps expect that the places from
which the metal has been removed would appear dark in the
phosphorescent images, or at least would correspond te
mimima of light. We find, however, that these points are
really maxima of light; thus with the kathode fig. 35 we
obtain 16 very bright points of light. The reason is to be
found in the fact that the walls of each perforation form a
short open tube ; and, according to what we have seen, a bright
pencil of light issues from such a tube, which at suitable
exhaustion extends to the wall and excites phosphorescence
there.
‘Berlin, Physical Institute
of the University.
LII. Notices respecting New Books.
Graphical Determination of Forces in Engineering Structures. By
James B. Coatmers, C.L. London: Macmillan. 1881. 405+
xxvi pages, 6 plates, 267 cuts.
(pais is a large and important work, aiming at being a complete
treatise on use of graphic methods in engineering-designs. It
is a high-class work, requiring a fair knowledge of modern geo-
metry for its comprehension. To facilitate this (to the Engineer)
a special Chapter on ‘* Projective Geometry” (66 pages) is given ;
within this compass a wide range is compressed, e. g. projections,
homology, Carnot’s, Pascal’s, Desargues’s theorems, &e.
Notices respecting New Books. 473
In application to Engineering great superiority is claimed for
graphic methods over computation. The practical applications are
skilfully and neatly worked out; and the study of them is an intellec-
tual treat (not easy reading). The scope of the work is very wide:
Resultants of Forces, Moments, Centre of Gravity, Moments of
Inertia, and Stresses in Structures, ¢.g.in Frames, Beams (supported,
fixed, and continuous), Arches (rigid and elastic), Suspension-
Bridges, Retaining Walls, and Tunnels are all treated by graphic
methods. ‘These processes are only meant to supersede computa-
tion: analysis is often used for their actual elucidation; thus the
explanation of the graphic methods for the Elastic Arch covers
20 pages of a somewhat difficult analysis.
In some cases the graphic methods have decided advantage,
chiefly when the work is simply a repeated application of the
theorem of the “polygon of forces ;” the diagrams of these are
simple and can be quickly drawn. But in cases where sums of pro-
ducts are required (e. g. m moments of forces, moments of inertia,
&c.), the advantage is not so clear: the process increases greatly in
complexity as the number of variable factors in each product in-
creases, the diagrams become intricate, and are finally a network.
of lines (see fig. 65-1, fig. 143 pl. 1, pl. va), requiring great skill
in their original preparation, and-not to be unravelled in after-ex-
amination without careful study. The risk of mistake in construc-
tion, not so much from inaccurate drawing as from mistaking one
point or line for another, in such a network must be considerable,
and quite analogous to that of numerical slips in computing. Even in
the simple case of the sum of the products of two factors, the result
would probably be got more quickly with a slide-rule or Crelle’s
mutiplication-table than by the very neat graphic process given;
but in the more complex cases of several factors computation would
surely be quicker.
The processes given are by no means always the shortest. Thus
the determination of the pressures on the supports due to a single
load placed on a beam requires only the division of the line repre-
sentative of the load into segments inversely proportional to the
segments of the beam on either side of the load. This requires only
three lines for its complete graphic solution; but the process given
(the same as for the general case of many loads) requires seven
lines.
When several processes are available for the same purpose, it
would surely suffice to give the best, unless each has peculiar ad-
vantages in special cases, which should then be stated. Now, for
finding stresses in frameworks three processes are given, covering
66 pages. No. i., by “‘ Method of Sections,” requiring at every
section a preliminary reduction of the frame on one side thereof to
an ideal triangle and evaluation of the Resultant force thereon:
this is a difficult and troublesome process. This troublesome pre-
- liminary is avoided in No. ii., the Method of Sections proper: this
is nearly the same in its application as No. iii., but gives rise to
Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 21
474 Notices respecting New Books.
stress-diagrams sometimes imperfectly “reciprocal” to the original
—a slight disadvantage. No. iii. is Clerk-Maxwell’s beautiful pro-
cess: this is the simplest and easiest of the three; its simplicity
seems to depend on the complete reciprocity of the stress-diagram
with the original figure. Methods i. and ii. might have been omitted
with advantage, and more space given to the last. This Chapter
is illustrated by numerous* well-chosen examples. The three pro-
cesses therein are really a graphic solution of the “conditions of
equilibrium ” among the forces at each section or joint; as there
are thus only two equations for each section or jomt, the magni-
tudes of two stresses can be found for each section or joint. Thus
the problem is indeterminate for a frame at any of whose joints so
many bars meet as to require the determination of more than two
stresses thereat. This is actually the case with two of the frames
(figs. 49 and 51) for which finished stress-diagrams are given with-
out comment. Some explanation is surely wanted in the text as to
how this indeterminateness (which is inherent in both) is to be met.
One of these (No. 51) is solved in Rankine’s ‘ Civil Engineering,’
art. 576, by a method of dissecting the complex Truss into partial
Trusses, which bridges the difficulty by (tacitly) assuming the inter-
action of the partial Trusses.
In Clerk-Maxwell’s process for Frames under dead load the
graphic methods probably appear at their best; but with moving
load the greatest stress in each bar occurs with a different state of
load, thus involving a tolerably complete special diagram for each
bar, greatly increasing the work and the intricacy of the finished
drawing. ;
In investigating the stability of Retaining Walls and Masonry
Arches, again, the graphic methods have decided advantage over
computation: this arises partly from the fact of the cross-sections
being solid, so that the limit within which the centre of pressure at
each joint should fall is easily known to be the middle third. The
tracing of lines of pressure and resistance therein is well ex-
plained and illustrated.
In the case of the Arch, however, one difficulty (indeterminate-
ness) has not been adequately met. In general many lines of
pressure and resistance could perhaps be traced within the “ core”
or admissible limits (the middle third); and the question is, which
is the true line? The author says, “the true line of pressures is
that which is nearest the axial line” (art. 181); this seems
doubtful. Moseley’s Principle of Least Resistance gives a means
of locating it so that the passive resistance required at the spring-
ing shall be the least: this seems sound for rigid material; but its
applicability to non-rigid material is not so clear.
Of all the processes given, the applications to Continuous Beams
and the Elastic Arch are naturally the most intricate. These are
masterly specimens of the power of graphic work in the hands of
* There are several lines wrong in lower part of fig. 57 b.
Notices respecting New Books. 475
one skilled in its use. The amount of drawing required for the
complete investigation of any one arch seems very great. PI. v.a,
the finished (?) result for an arch, is so complex a whole (although
several preliminary drawings are omitted from it) as to require
great care for its comprehension; and even it seems (arts. 214, 219)
to be only a part of what is required.
Among practical details, it is laid down (art. 121) that “an arch
ought to be wholly in compression.” Now this principle is ob-
viously right for masonry ; but there can be no occasion for applying
it to iron or steel arches (as in art. 183): this would surely be a
waste of power.
The theory of earth-pressure given, depending on the “angle of
repose” and frictional stability, is complex and difficult (covering
23 pages before application to retaining walls). The “angle of
repose” is an item which in many cases can hardly be said to be
known at all, so that mathematical refinements are of little use.
Rankine’s theory (which is much simpler) seems good enough for
such imperfect data.
There are numerous references to foreign works on geometry
and graphic statics ; the influence of these is obvious in the diction.
The author is thoroughly at home in the practical application of
graphic methods ; but for a didactic work the mathematical render-
ing might be improved. Thus there is occasional obscurity in the
explanations, e. g. props. xxxix., xlii.,and arts. 80, 161, 223: results
to be derived as the fourth term of a proportion are commonly pre-
sented as(a:b::c: Us mere identity; the insertion of the
a
name or symbol for the required fourth term would be more useful
(e. g. in aiding its discovery in the diagrams). There is also a cer-
tain looseness of exp7ession, e. g. moments termed forces (pp. 113,
139), the use of the term “ centre of gravity” of forces (pp. 268,
274): also of notation, ¢. g. in use of symbols A and d, & and J
(passim), and of — in geometry (pp. 363, 364); also of analysis,
ێ. g. omission, removal, or change of variables under summatory
symbol (pp. 162, 268; 150, 275, 277; 281); these latter mistakes
generally correct themselves in the final results. There are also
two mistakes in the geometric theorems. Thus, Poncelet’s condi-
tion of projectivity (prop. xxxii.) is stated in too general terms
without due limitations, and the example given is non-projective.
Again, in the proof of Pascal’s theorem (prop. xlvi.), the conic and
its inscribed hexagon are projected into a circle and inscribed
hexagon with opposite sides parallel and one pair equal (which is
not generally possible); and it is stated that ‘the points of the
hexagon joined two and two concur in a point P” (and they actu-
ally do in the figure in consequence of its being a regular hexagon),
which is not generally true.
Several minor points might be improved (in a new edition).
Thus there is hardly enough lettering on some of the diagrams for
their easy comprehension ; and in many cases the symbols given are
DEAS ge . 77
476 Votices respecting New Books.
too complex for use on a diagram—e. g. one length in fig. 100 is
marked thus : . ,
2
a om.(2+S ye Bie.
a Z, a
Now in all such cases a single symbol (with reference in the
text) would be better. The numbering of the diagrams also should
be made consecutive; there are at present three numberings inter-
mixed, which renders reference difficult. The number of mis-
prints also is very great, especially among the references. Even with
these faults the work is a valuable one, and no one can read it
without learning much. ALLAN CunnineHaM, Major R.E.
Questions in Pure Mathematics proposed at the B.A. and B.Sc. Pass
and Honours Examinations of the University of London, with
complete Solutions by J. E. A. Straeatt, M.A. Van Voorst,
1882; pp. viii+245.
Tue title sufficiently indicates the nature of the work. The solu-
tions, we think, are in all cases neat, and in many instances they
are elegant. Mr. Steggall does not confine himself to single solu-
tions, but often gives two or more proofs of the same question.
The work is very carefully printed, and there are, we believe, very
few typographical errors. On p. 13 another mode of solution
might have been indicated, depending on the fact that the sinister
side vanishes when vw=y=z. We venture to suggest that on p. 25
reference might have been made to Euc. vi. 3 and A as also readily
furnishing a solution; and the equation on p. 37 might be worked
from the fact that the terms on one side are reciprocals of those
on the other. But these and other instances we could bring for-
ward only illustrate the well-known fact that there are more ways
than one of attacking problems; and the exigencies of space have
no doubt restricted the author in general to the single solution he
adopts. On pp. 21, 45, occur, as we think, two slight maccuracies in
expression. We note the following slips :—p. 120, “Solving for y”
read “w,” and for “cosxv” read “cos*v”; p. 164, for “ —3y”
read “+3y”; p. 224, for “ >1” read “<1.” <A few others are
easily corrected ; but on p. 205 there is a great derangement of
“subscripts,” and this may puzzle some readers. We hope that
Mr. Steggall will receive sufficient encouragement to bring out a
second edition in a few years time, with additional solutions up to
date ; for such works as this are of great service to students.
Geological Chart, arranged by Professor Joun Morris, M_A., 7.G.S.,
gc. New Edition. Large Sheet. Reynolds and Sons, Strand,
London. 1882.
Tuts enlarged and revised edition of a good Geological Table shows
the order of the many stratified formations in their regular succes-
sion, their mineral characters, uses in the arts, principal fossils,
Geological Society. AT7
places of occurrence in the British Isles, and their relative thick-
nesses. Notes also, to similar effect, on the Metamorphic and
Igneous rocks are supplied. The later determinations of geologists
as to the better division and classification of some of the recognized
groups of strata are, in several instances, incorporated where they
are not likely to be otherwise than clear and useful to the student ;
and there are but few points in printing or arrangement which
we would find fault with. We therefore recommend this Chart
as having been carefully revised by its well-known accomplished
author, and as having been brought up to the latest date in useful
information, and forming a complete and ready Geological Synopsis
for the several lines of study indicated above.
LILI. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from p. 151.]
November 1, 1882.—J. W. Hulke, Esq., F.R.S., President,
in the Chair.
ee following communications were read :—
1, “The Hornblendic and other Schists of the Lizard Dis-
trict, with some Additional Notes on the Serpentine.” By Prof.
T. G. Bonney, M.A., F.B.S., Sec. G.S.
The author described the metamorphic series, chiefly characterized
by hornblendic schist, which occupies the southern portion of the
Lizard and an extensive tract to the north of the serpentine region,
besides some more limited areas. He found that this series was
separable into a lower or micaceous group—schists with various
green minerals (often a variety of hornblende), or with brownish
mica; a middle or hornblendic group, characterized by black horn-
blende ; and an upper or granulitic group, characterized by bands
of quartz-felspar rock, often resembling in appearance a vein-granite.
These are all highly metamorphosed ; yet the second and third occa-
sionally retain to a remarkable extent indications of the minuter
bedding structures, such as alternating lamination and current-
bedding of various kinds. They form, in the author’s opinion, one
continuous series, of which the uppermost is the thinnest. The
general strike of the series, though there are many variations, is
- either N.W. or W.N.W.
The junctions of the Paleozoic with the metamorphic series at
Polurrian and at Porthalla were described. ‘These are undoubtedly
faulted; and the two rocks differ greatly, the former being a slate
like any ordinary Paleozoic rock, the other a highly metamorphosed
schist. Moreover fragments of the hornblende schist and a kind of
gneiss occur in a conglomerate in the former, 8. of Nare Point.
The author considers the metamorphic series (the microscopic
478 Intelligence and Miscellaneous Articles.
structure of which was fully described) undoubtedly Archean, and
probably rather early in that division. The rocks of the micaceous
group have considerable resemblance to the greenish and lead-
coloured schists of Holyhead Island and the adjoining mainland of
Anglesey, and of the Menai Strait.
Two outlying areas of serpentine, omitted in his former paper, were
described—one at Polkerris, the other at Porthalla. The latter
shows excellent junctions, and is clearly intrusive in the schist. The
author stated that he had reexamined a large part of the district
described in his former paper, and had obtained additional evidence
of the intrusion of the serpentine into the sedimentary rock with
which it is associated. This evidence is of so strong a nature that
he could not conceive the possibility of any one who would carefully
examine the district for himself entertaining a doubt upon the
matter.
2. “ Notes on some Upper Jurassic Astrorhizide and Lituolide.”
By Dr. Rudolf Hiusler, F.G.S.
LIV. Intelligence and Miscellaneous Articles.
ON MR. C. W. SIEMENS’S NEW THEORY OF THE SUN.
BY M. G. A. HIRN.
T° the grave objection brought forward by M. Faye against
Mr. Siemens’s new theory of the conservation of the solar
energy, another, also a very serious one, may be added. This objec-
tion may be summed up in few words.
Up to the present time there is no general agreement as to the
real value of the Sun’s temperature. Pere Secchi carried it to
millions of degrees. Other physicists, especially in France, lowered
it to about twenty thousand degrees. According to the magnificent
experiments of Mr. Langley (of Alleghany) this latter amount is,
at any rate, a minimum. What is certain then, starting from the
fine memoirs upon dissociation of our lamented colleague Henri
Sainte-Claire Deville, ‘s that none of the chemical compounds that
we know upon our Earth could exist at the surface of the Sun.
All, even those which are most refractory in our laboratories, would
be dissociated and reduced to their constituent elements. And
this is what is admitted in M. Faye’s theory of the Sun.
The natural and direct consequence of the preceding fact is, that
the chemical compounds which Mr. Siemens supposes to be disso-
ciated by degrees in space by the solar radiation, might certainly,
in returning under the action of gravity and in the elementary state
towards the central body, become reformed, and regenerate the
heat expended in their dissociation in space ; but this recombination
could only be effected at an appreciable distance from the solar
photosphere, and the compounds reproduced, on falling into the
bosom of the latter, would be again completely dissociated. This
action, therefore, would cause the expenditure of all the heat
——
Intelligence and Miscellaneous Articles. A79
previously developed by the combination. From this it follows
evidently that this return of the elements towards the centre would
contribute nothing at all towards the conservation, or rather the
continuous reproduction, of the solar temperature.
It seems to me that Mr. Siemens’s theory may be subjected to
another decisive critical test. If the solar radiation, or say the
heat, whether visible or not, emitted or sent off by any celestial
body, during its course effects the chemical dissociation of the
hypothetical compounds disseminated in stellar space, the intensity
of this radiation must necessarily be reduced by the positive work
effected, and all that serves for this work is lost for the visibility
of the star.
From this, then, it follows that the lustre of the sun, of the ~
stars, and of the planets must diminish according to a much more
rapid law than that of the inverse proportion of the square of the
distances. I say much more rapid; but we must say extremely
rapid. In fact, from the moment when the recombination of the
elements at the surface of the Sun would be capable of regenerating
the heat emitted, it is evident that ail this emitted heat would be
employed in its turn in dissociating the chemical compounds in
space. In order that the Sun could be thus continually maintained
in its energy, it would be necessary that the distance at which it
is visible, far from being unlimited as it probably is, should, on the
contrary, be restricted ; for wherever it would be still visible there
would be light not employed in chemical dissociation, and conse-
quently there would still be a definite loss possible. Nothing in
the aspect of our planets and their satellites, it seems to me,
authorizes us to assume that there is any other reduction in the
brilliancy of the light than that resulting from the inverse propor-
tion of the square of their distance from the central body. We
see stars the light of which has taken at least three years, and
others of which the light has perhaps taken thousands of years to
reach us. None of this light, therefore, has been employed in
chemical dissociation; nothing could have been restored to them
by the mode indicated by the ingenious theory of Mr. Siemens.
May I be permitted, in concluding this note, to revert to the
objection formulated by M. Faye, and to render it in some degree
palpable by a numerical example? In an extensive work upon
which I am engaged, upon the constitution of the stellar space, I
naturally examine into the consequences that the resistance of a
gas diffused in space would have upon the movements of the
planets. From this work I extract an example relating to the
application of analysis to the motion of our Earth. According to
Laplace, the diminution or augmentation which one may attribute
to the duration of our sidereal year 3000 years ago, taking into
account the uncertainty of the observations, would be 90 seconds
at the maximum (a modification of which, however, there is nothing
to demonstrate the reality). Accepting a reduction of this amount
as real, I inquire what density a gas would need to have to produce
480 Intelligence and Miscellaneous Articles.
it; and I show that it would suffice if there were 1 kilogr. of matter
in vapour in 700 thousand millions of cubic metres—in other words,
that the density would be 0-000 000 000 001 43 kilogr. It will be
seen that we are far from the reduction to the 5,45, and even
to the millionth assumed by Mr. Siemens. If, instead of taking
account only of the resistance opposed by such a gas to the motion
of our planet, we direct our attention to the consequences which
its existence would have upon that of our atmosphere, we find that,
unless we multiply our 700 thousand millions of cubic metres by
10,000, and reduce the density sought for to 0-000 000 000 000 0001
kilogr., our atmosphere would be in a few moments swept away by
the pressure exerted above by the interstellar gas.
M. Faye is perfectly justified in saying that it is not such or
such a degree of rarefaction, but that it is the vacuum (of matter, of
course) that the astronomer requires to ensure the stability of the
movements that his analysis shows. This vacuum no doubt upsets
the doctrine, supposed to be so undeniable, which ascribes all the
phenomena of the physical world to movements and collisions of
material atoms independent of each other. One day or another,
no doubt, this doctrine will have to give up its existence, and its
defenders will have to resign themselves to admit in the physical
world something more than matter in motion. In a remarkable
letter to Bentley, Newton said that one must be destitute of all
aptitude for a serious philosophical discussion to suppose that
between two bodies which seem to attract each other at an
unlimited distance, there is not something which establishes this
relation; but, he adds immediately, is this intermediary material
or immaterial? This I leave to the reader to decide. With that
great genius undoubtedly there was no uncertainty upon this latter
_ point; but, perhaps justly, he refrained from putting before his
contemporaries a solution which might have seemed incomprehen-
sible to them, as it still is, apparently, to so many minds of the
present day.— Comptes Rendus, November 6, 1882, p. 812.
REPLY TO M. FAYE’S OBJECTIONS TO MR. C. W. SIEMENS’S THEORY
OF THE SUN. BY C. W. SIEMENS.
M. Faye, while approving, generally, of the physical part of my
investigations, questions their application to astronomy, and for
the following reasons :—
1. That the presence of a universal gaseous medium at a pressure
of 55 atmosphere would oppose an excessive resistance to the
movements of the planets; 2. That this vapour, thus distributed,
would be gradually attracted towards the sun and would tend to
augment its mass considerably.
Allow me to point out, as regards, in the first place, the second
of M. Faye’s objections, that the degree of diffusion supposed by
me is such as may ensure the permanence of the statical equilibrium
between the forces of expansion and diffusion on the one hand, and
Intelligence and Miscellaneous Articles. _ 488
the attraction towards the sun and the celestial bodies on the other.
Tf no such equilibrium were established, M. Faye’s objection would
at once upset my theory. I am, moreover, inclined to admit that
if Mariotte’s law with regard to the tension of gases could be applied
indefinitely, the pressure of the interplanetary gaseous medium
would be reduced almost beyond any thing of which we can form
an idea; but it seems to me, from considerations drawn from the
dynamical theory of gases, and from the manner in which, as
demonstrated by Mr. Crookes, gases behave when rarefied to an
extraordinary degree in tubes—it seems to me, I say, that at least
there exists no reason @ priori why this law should be extended
rigorously to vapours beyond the confines of our atmosphere and
of that of the Sun.
As regards M. Faye’s first objection, I admit that a density of
Zo atmosphere would have the consequences which he so correctly
establishes ; and I remember having said (see ‘ Proceedings of the
Royal Society,’ p. 395) that assuming as demonstrated the results
of my experiments on the dissociation of vapours by the solar
energy, and that stellar space is filled with vapour at a pressure
not exceeding the limit of 4,5 atmosphere, which corresponds to
the highest rarefaction that I was able to obtain in my experiments,
a dissociation of this cosmical vapour must ensue by the radiation
of the Sun. It must nevertheless be remarked that this obser-
vation only relates to the physical phenomena submitted to my
experiments, and that it is evident that if, the dissociation of aqueous
vapour and of carbon-compounds is effected by the direct radiation
of the sun at so high a pressure as ;,455 atmosphere, it would with
still more reason be effected in the much more rarefied medium.
In another passage of my memoir (p. 397), when I apply my
hypothesis to comets, I assume that, even at their perihelion, they
represent a vapour-medium with a density of only ;,4;5 atmosphere,
and that this density suffices to give rise to incandescence by com-
pression. This supposition proves, at any rate indirectly, that I
regarded stellar space as filled with vapour at a pressure much
below 3,45 atmosphere, while still speaking of this medium (in the
absence of all data of experiment and observation) as in an extremely
rarefied state, without fixing any linit of this rarefaction.
Since then new facts of observation have tended to confirm my
hypothesis of a stellar space filled with rarefied matter analogous
to that which we can actually produce in our vacuum-tubes. The
equatorial prolongations of the solar atmosphere observed in America
during the eclipse of 1859, seem to demonstrate the existence of
matter extending from the Sun for several millions of leagues, and
rendered visible, no doubt, by solid particles, illuminated partly by
the reflection of the solar light, and partly by discharges of elec-
tricity towards the Sun.
My hypothesis has found a still more direct confirmation in the
remarkable spectroscopic investigations communicated by Capt.
Abney to Section A of the British Association in the month of
August last, which demonstrate that carbon-compounds, probably
Phil. Mag. 8. 5. Vol. 14. No. 90. Dec. 1882. 2K
482 Intelligence and Miscellaneous Articles.
analogous to ethyl, easy to observe distinctly, exist, and at a low
temperature, between the Sun’s atmosphere and our own. The
observations made in America by Prof. Langley with his bolometer,
although made for a totally different purpose, tend to confirm the
results obtained by Capt. Abney upon the Riffel. We may also
add to these proofs the interesting observation of Prof. Schwedoff
(still unpublished, and communicated to me on the same occasion
by Prof. Silvanus Thompson), according to which large hailstones
of cosmical origin have sometimes fallen upon the earth. This
observation, however, needs to be confirmed.
Accepting these observations as founded upon facts, physical
considerations are not wanting for the approximate determination
of the actual density of the stellar vapour, which, in this case, is
only a function of the temperature of space. As Gorschow, on
30th November 1871, observed a temperature of — 63° C. in the
Arctic regions, it follows that the stellar medium (which, if it con-
sists of a vapour, must be able to intercept calorific rays) must be
at a temperature comprised between —63° and the absolute zero
(— 273°); the solar radiation must maintain in it some temperature,
or, at least, such a temperature that the dissociation of this medium
is very active.
It is to Regnault that we owe our most exact knowledge of the
density of vapours at different temperatures ; but his researches did
not extend below —32° C., and his formule cannot be rigorously
applied below that point; nevertheless they enable us to estimate
approximately -what may be the densities of a vapour at lower
temperatures ; and it is thus that we are led to believe that at
—130° the density of aqueous vapour does not exceed 590,000
atmosphere. If we assume, further, that the gaseous mass which
fills space contains only 4 of aqueous vapour, the other four fifths
being composed of hydrocarbons, carbonic acid, and nitrogen, the
total pressure of the vapour would not exceed y-gp4-990 atmosphere.
These vapours would traverse space with a velocity equal, pro-
bably, to half the tangential velocity at the surface of the Sun, or
at about 1 kilometre per second. It would be easily demonstrated
that a column of these dissociated gases travelling with this velocity
towards the polar surfaces of the sun and taken at a distance of
5,500,000 kilom. from the Sun (equal to the mean distance of
Mercury, the nearest of his planets) would present a section of
flow towards the Sun equal to 140,000 milliards of square kilometres,
much more than sufficient to furnish the material necessary to
yield by combustion the heat required to maintain the solar radi-
ation.
Perhaps the eminent Director of the Bureau des Longitudes
may be inclined to think that a gaseous medium of a density equal
at most to -5p0,000 Of that of our atmosphere might still interfere
with planetary movements to a degree incompatible with the facts
ascertained by astronomical observations. If this be the case, it
would suffice to assume a still lower temperature for this medium,
Intelligence and Miscellaneous Articles. 483
and in consequence a more attenuated rarefaction of the interstellar
gaseous matter.— Comptes Rendus de? Académie des Sciences, Oct. 30,
1882, p. 769.
ON A PROPERTY OF THE COEFFICIENT OF ABSORPTION.
BY EILHARD WIEDEMANN.
Bunsen represents the absorption-coefficient a at a temperature
t by the formula
a=a—bi+ct?,
in which a and 6= a constant.
Instead of this, we can write
a=a{ ig ag \
os tats: iil
In the tollowing Table I have set down, together with the values
of a, 6. 10°, and c. 10”, the values of 6/a@ and c/a for a series of
gases and water :—
Nl l
| a. Gos Neel aa: es st
| a a
| ee EEE EEE eee
| Hydrogen ..........20:000 0:0193 Ooh 2 0f HERG 0
PNitropen ......c....c.2---- | 00203 539, 112 0-02648 | 0-000548
et te wate ees | 0-0247 654 135 | 0-026487) 0:000548
Diethyl ..... necteneesen eres | 0:0315 1045 | 251 | 0:033198 0:000796
_| Carbonic oxide ............ | 0:0329 816 | 164 | 0-0243 | 0:000499
OXygeM .....-0---eee eee ee eee 0:0412 1089 | 226 | 002648 | 0000548
Marsh-gas ......------..200+ 0-0545 1180 | 103 | 0-02166 | 0-:000188
| Dimethyl Bree halla at a 0:0871 3324 603 | 0:03816 | 0-:000692
| Hydride of ethyl ......... 0:0946 3582 628 | 003735 | 0:000663
Hthylene .......-.-.-.....- 0:2563 9136 1881 | 0:03564 | 0-000654
piropyleuer...<7-------.--2-- 0-4465 | 22075 5388 | 0:04943 | 0:000206
| Nitrous oxide ............ | 13052 | 45362 | 6483 | 0-03475 | 0-000496
Carbonic acid .....-...... 17967 | 77610 | 16424 | 0-04320 /0-000914
| Sulphuretted hydrogen...|° 43706 | 83687 8213 | 0-01914 | 0-000119
| Sulphurous acid ......... 79-789 {2607700 | 263490 | 0:03268 0:000367
BO@liderme: -.t..2- 2-3... 30361 | 46196 | 1107 |
Tt will be remarked that the values of 6/a in this Table vary only
from 0°02 to 0°05, while a itself ascends from 0°02 to 79-789, 7. e.
up to 4000 times the former value. But the values of 6/a indicate
how large a fraction of the gas absorbed at 0° escapes on the tem-
perature being raised 1°; and from the above it follows that that
fraction varies within very narrow limits for all gases.
In order to further test this proposition, it would be necessary
to institute experiments for larger intervals of temperature.
A comparison of the absorptions in alcohol gave similar results.
—Wiedemann’s Annalen, vol. xvii. p. 349 (1882).
484
INDEX to VOL. XIV.
ABSORPTION, on a property of
the coefficient of, 485.
Accumulators, on the construction
and charging of, 249.
Aerial vibrations, on an instrument
capable of measuring the intensity
of, 186.
Air-thermometer, on an, 253,
Amagat (E. H.) on the elasticity of
rarefied gases, 403.
Anemometer, on an
212.
Aniline, on the melting-points of
some derivatives of, 6.
Atmosphere, on carbon dioxide as a
constituent of the, 587.
Atom, on the motion of a spherical,
in an ideal gas, 157.
Attwood (G.) on the geology of Costa
Rica, 141.
Ayrton (Prof. W. E.) on the Faure
‘accumulator, 41; on a simplified
dispersion-photometer, 45,
Babo (L. vy.) on the connexion be-
tween viscosity and density in
fluids, 51.
Baily (W.) on an integrating anemo-
meter, 212.
Barometric pressure, on the mecha-
nical effects of, on the earth’s sur-
face, 409.
Battery, on the oscillations of the
plane of polarization produced by
the discharge of a, 79
Benzol, on the melting-points of some
derivatives of, 2.
Bevan (E. J.) on the correlation of
the chemistry of the carbon com-
integrating,
pounds with the phenomena of
e, 346.
Bichat (D.) on the oscillations of the
plane of polarization produced by
the discharge of a ha 79.
Blondlot (R.) on the oscillations of
the plane of polarization produced
by the discharge of a battery, 79.
Boltzmann (Prof.) on the average
distribution of energy in a system
of material points, 299,
Bonney (Prof. T. G.) on the Horn-
blendic and other schists of the
Lizard district, 477.
Books, new :—Selwyn’s Geological
and Natural History Survey of
Canada, 70; Geikie’s Geological
Sketches, 71; Clifford’s Mathema-
tical Papers, 135; Muir’s Theory of
Determinants, 140 ; Lunge’s Distil-
lation of Coal-tar, 228; Hulme’s
Examination Questions in Plane
Geometrical Drawing, 230; Lati-
mer Clark’s Treatise on the Transit
Instrument, 319; Geology of Wis-
consin, 319; Stuckenberg’s Life of
Immanuel Kant, 322; Stallo’s
Concepts and Theories of Modern
Physics, 396; Chalmers’s Gra- .
hical Determination of Forces in
ngineering Structures, 472; Steg-
gall’s Questions in Pure Mathema-
tics, 476; Prof. Morris’s Geolo-
gical Chart, 476.
Bosanquet (R. H. M.), notes on prac-
tical electricity by, 241.
Boys (C. V.) on the measurement of
curvature and refractive index, 30,
INDEX.
Brongersma (H.) on double refrac-
' tion produced by electrical influ-
ence in glass and bisulphide of
carbon, 127.
Brown (F. D.) on thermometry, 57.
Carbon, on double refraction pro-
duced by electrical influence in
bisulphide of, 127; on the appear-
ances of the electric arc in the va-
pour of the bisulphide of, 324.
— compounds, on the correlation
_ of the chemistry of the, with the
phenomena of life, 346,
Carbonic acid, on the viscosity of
liquid, 55; on the surface-tension
of some liquids in contact with, 327.
Charpentier (A.) on the duration of
the perception of light in direct
and indirect vision, 230.
Chase (Dr. P. E.) on the conserva-
tion of solar energy, 522.
Chemical affinity, on the determina-
tion of, in terms of electromotive
force, 188.
Chemistry of the carbon compounds,
on the correlation of the, with the
henomena of life, 346.
Clausius (Prof. R.) on the dimensions
of a unit of magnetism in the elec-
trostatic system of measures, 124.
Comets, on the tails of, 292.
Cook (HE. H.) on carbon dioxide as a
constituent of the atmosphere, 387.
Copper pyrites, on twins of, 276.
Crafts (J.-M.) on the depression of
the zero-point in mercurial ther-
mometers, 76.
Cross (C. F.) on the correlation of
the chemistry of the carbon com-
pounds with the phenomena of life,
346.
Crystallographic notes, 119, 276.
Cunningham (Major A.) on Mose-
ley’s theory of steady flow, 110.
Curvature, on the measurement of,
Darwin (G. H.) on variations in the
yertical due to elasticity of the
earth’s surface, 409.
Debray (H.) on some explosive alloys
of zinc and the platinum metals,
152.
Deville (H. Sainte-Claire) on some
explosive alloys of zine and the
platinum metals, 152.
485
Dunstan (W. R.) on science and me-
taphysic, 75..
Earth, on the physics of the crust of
the, 218; on variations in the ver-
tical due to elasticity of the surface
of the, 409,
Earth-moon system, on Darwin’s
theory of the, 427.
Edison’s tasimeter, on the influence
of time on the change in the re-
sistance of the carbon disk of, 115.
Electric and magnetic quantities, on
systems of absolute measures for,
430.
—— are, on the reaction-current of
the, 154; on the appearances of
the, in the vapour of bisulphide of
carbon, 324.
discharge in rarefied gases, on
the, 366.
resistance of glass at low tem-
peratures, on the, 325.
spark, on vision by the light of
the, 313.
Electrical influence, on double refrac-
tion produced by, 127.
rays, on the reflection of, 449.
Electricity of flame, on the, 161; on
the equilibrium of liquid conduct-
ing masses charged with, 184;
notes on practical, 241,
Electromotive force, on the determi-
nation of chemical affinity in terms
of, 188. :
Electrostatic system of units, on the
dimensions of a magnetic pole in
the, 124, 225, 357, 395.
Het (J.) on the electricity of fame,
161.
Energy, on the average distribution
of, in a system of material points,
299.
Faure accumulator, experiments on
the, 41.
Faye (M.) on Dr. Siemens’s new
theory of the sun, 400. i
Fisher (Rey. O.) on the effect upon
the ocean-tides of a liquid sub-
stratum beneath the earth’s crust,
213.
Flame, on the electricity of, 161.
Fletcher (L.), crystallographic notes
by, 276.
Fluids, on the connexion between
viscosity and density in, 51.
486
Forel (F.-A.) on the structure and
movement of glaciers, 258.
Foussereau (G.) on the electric resist-
cae of glass at low temperatures,
5.
Gas, on a property of the isentropic
curve for a perfect, 233.
Gaseous fluids, on the connexion be-
tween viscosity and density in, 51.
Gases, on the electric discharge in
rarefied, 366; on the elasticity of
rarefied, 403.
Geissler tubes, on the connexion be-
tween the gas-density and stratum-
interval in, 402; on the distribu-
tion of phosphorescent light in, 455.
ay (H.) on the electricity of flame,
161.
Geological Society, proceedings of
the 73, 141, 477, : :
time, on the duration of, 427.
Glacial period, on the, 151.
Glaciers, on the structure and move-
ment of, 258.
Glass, on double refraction produced
by electrical influence in, 127; on
the electric resistance of, 325.
Goldstein (Dr. E.) on the electric
discharge in rarefied gases, 366;
on the connexion between the gas-
density and stratum-interval in
Geissler tubes, 402; on the reflec-
tion of electrical rays, 449; on
the influence of the shape of the
kathode on the distribution of
phosphorescent light in Geissler
tubes, 4565.
Haughton (Rev. 8S.) on Darwin’s
theory of the evolution of the
earth-moon system, 427.
Helmholtz (Prof. H.) on systems of
absolute measures for electric and
magnetic quantities, 430.
Hirn (G, A.) on Siemens’s new theory
of the sun, 478.
Holman (S, W.) on a simple method
for calibrating thermometers, 294.
Idocrase, on the crystalline form of,
121,
Isentropic curve, on a property of the,
for a perfect gas, 235.
Jamieson (T. F.) on the cause of the
depression and re-elevation of the
land during the glacial period, 151,
Jamin (M.) on the reaction-current
INDEX.
of the electric arc, 154; on the -
appearances of the electric arc in
the vapour of bisulphide of carbon,
324.
Johnston-Lavis (H. J.) on the com-
parative specific gravities of molten
and solidified Vesuvian lavas, 141.
Judd (Prof. J. W.) on the relations
of the eocene and oligocene strata
in the Hampshire Basin, 73.
Kerr’s phenomena, observations on,
127.
Lapworth (Prof. C.) on the Girvan
succession, 147.
Lava, on the specific Fle ot
molten and solidified Vesuvian,
141, ,
Lewis (W. J.), crystallographic
notes by, 119.
Life, on the correlation of the che-
mistry of the carbon compounds
with the phenomena of, 346.
Light, on the duration of the per-
ception of, 230; on the influence
of the shape of the kathode on
the distribution of phosphorescent,
in Geissler tubes, 455.
Lippmann (G.) on a thermoscopic
method for the determination of
the ohm, 407.
Liquid, on the steady flow of a,
110; on the influence of the quan-
tity of gas dissolved in a, on its
surface-tension, 236; on the sur-
face-tension of a, in contact with
carbonic acid, 327.
Lodge (Dr. O. J.) on the dimensions
of a magnetic pole in the electro-
static system of units, 357.
Ludlamite, on the crystalline form of,
120.
Liibeck (G.) on the motion of a sphe-
rical atom in an ideal gas, 157.
Magnetic and electric quantities, on
systems of absolute measures for,
430.
Magnetism, on the dimensions of a
unit of, in the electrostatic system
of measures, 124, 225, 357, 395,
Magnetometer, on a, 227,
Maneuvrier (G.) on the reaction-cur-
rent of the electric are, 154; on ~
the appearances of the electric are
in the vapour of bisulphide of car-
bon, 324,
INDEX.
_ Melting-point, researches on, 1.
Mendenhall (T. C.) on Edison’s tasi-
meter, 115.
Metalloids, on the influence of tem-
perature upon the spectra of,
406
Michelson (A. A.) an an air-thermo-
meter, 255.
Mills (Dr. E. J.) on melting-point, 1.
Monckhoyen (M. D. van) on the in-
fluence of temperature upon the
spectra of metalloids, 406.
Moseley’s theory of steady flow, ob-
servations on, 110.
Naphthalin, on the melting-point of
derivatives of, 25.
Neale (E. V.) on the tails of comets,
292.
Nipher (F. E.) on a property of the
Beteople curve for a perfect gas,
33.
Ocean-tides, on the effect upon the,
of a liquid substratum beneath the
earth’s crust, 213.
Ohm, on the methods employed for
determining the, 258, 329; on a
thermoscopic method for the deter-
mination of the, 407.
Optics, notes on physiological, 312.
Penrose (C. B.) on the Thomson
Effect, 440,
Perry (Prof. J.) on the Faure accu-
mulator, 41; on a simplified dis-
persion-photometer, 45.
Phenol, on the melting-point of deri-
vatives of, 20.
Photometer, on a simplified disper-
sion, 45.
Physical units, on absolute systems
of, 81.
Platinum metals, on some explosive
alloys of zinc and the, 152.
Polarization, on the oscillations of
the plane of, produced by the dis-
charge of a battery, 79.
Pseudobrookite, on the crystalline
form of, 119.
Quartz, on some peculiar crystalline
forms of, 122.
Rayleigh (Lord) on the equilibrium
of liquid conducting-masses charged
with electricity, 184; on an instru-
ment capable of measuring the in-
tensity of aerial vibrations, 186 ;
on the methods for the determina-
487
tion of resistances in absolute mea-
sure, 529.
Refraction, on double, produced by
electrical influence in glass and bi-
sulphide of carbon, 127.
Refractive index, on the measure-
ment of, 30.
Resistances, on the methods for the
determination of, in absolute mea-
sure, 329.
Sargant (E. B.) on the dimensions of
the magnetic pole in electrostatic
measure, 395.
Schmidt (Dr. F.) on the Silurian and
Cambrian strata of the Baltic pro-
vinces, 150,
Science and metaphysic, 75.
Serpentine, notes on, 477.
Siemens (C. W.) on a new theory of
the sun, 480.
Smith (F. J.) on a new form of mag-
netic torsion-balance and magneto-
meter, 227.
een on the conservation of,
322.
Spectra of metalloids, on the influ-
ence of temperature upon the, 406.
Spectral images, on the binocular
union of, 315.
Stevens (W. Le Conte) on physiolo-
gical optics, 312.
Sun, on Dr. Siemens’s new theory of
the, 400, 478, 480.
Sundell (A. F.) on absolute systems
of physical units, 81.
Tasimeter, on the influence of time
on the change in the resistance of
the carbon disk of Edison’s, 115.
Thermometers, on the depression of
the zero-point in mercurial, 76;
oe a simple method for calibrating,
4,
Thermometry, notes on, 57.
Thomson (J. J.) on the dimensions of
a magnetic pole in the electrostatic
system of units, 225.
Thomson effect, on the, 440.
Tide, on the disturbance of the ver-
tical near the coasts of continents
due to the rise and fall of the,
416.
Toluidine, on the melting-point of
some derivatives of, 19.
Toluol, on the melting-points of some
derivatives of, 11.
488
Torsion-balance, on a new form of
magnetic, 227.
Trowbridge (J.) on the Thomson
effect, 440.
Viscosity and density in fluids, on the
connexion between, 51.
Vision by the light of the electric
spark, on, 315.
Warburg (E.) on the connexion be-
tween viscosity and density in
fluids, 51.
Wiedemann (Prof. E.) on a property
of the coefficient of absorption,
483,
Wiedemann (Prof. G.) on the me-
thods employed for determining the
ohm, 258.
INDEX.
Wilson (E.) on the Rheetics of Not-
tinghamshire, 149.
Wood (S. V.) on the Newer Pliocene
period in England, 142.
Wright (C. R. A.) on the determina-
tion of chemical affinity in terms of
electromotive force, 188.
Wroblewski (S.) on the influence of
the quantity of gas dissolyed in
a liquid upon its surface-tension,
236; on the surface-tension of some
liquids in contact with carbonic
acid, 327.
Zinc, on some explosive alloys of, and
the platinum metals, 152,
Zoisite, on the crystalline form of,
121.
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